diff --git a/lit-marker2/david-rumelhart-james-mcclelland-pdp-research-group-parallel-distributed-process-vol-1/david-rumelhart-james-mcclelland-pdp-research-group-parallel-distributed-process-vol-1.md b/lit-marker2/david-rumelhart-james-mcclelland-pdp-research-group-parallel-distributed-process-vol-1/david-rumelhart-james-mcclelland-pdp-research-group-parallel-distributed-process-vol-1.md new file mode 100644 index 0000000000000000000000000000000000000000..78e14faf87d9852091eebe2ce1ea12b7d653dbbe --- /dev/null +++ b/lit-marker2/david-rumelhart-james-mcclelland-pdp-research-group-parallel-distributed-process-vol-1/david-rumelhart-james-mcclelland-pdp-research-group-parallel-distributed-process-vol-1.md @@ -0,0 +1,10161 @@ +PARALLEL DISTRIBUTED + +PROCESSING + +Computational Models of Cognition and Perception + +Editors + +Jerome A. Feldman Patrick J. Hayes David E. Rumelhart + +Parallel Distributed Processing: Explorations in the Microstructure of Cognition. Volume 1: Foundations, by David E. Rumelhart, James L. McClelland, and the PDP Research Group + +Parallel Distributed Processing: Explorations in the Microstructure 0/ Cognition. Volume 2: Psychological and Biological Models, by + +James L. McClelland, David E. Rumelhart, and the + +PDP Research Group + +Neurophilosophy: Toward a Unified Science o/the Mind-Bra;n, by + +Patricia S. Churchland + +Qualitative Reasoning About Physical Systems, edited by + +Daniel G. Bobrow + +Visual Cognition, edited by Steven Pinker + +PARALLEL DISTRIBUTED + +PROCESSING + +Explorations in the Microstructure + +of Cognition + +Volume 1: Foundations + +David E. Rumelhart James L. McClelland + +and the PDP Research Group + +Chisato Asanuma Francis H. C. Crick Jeffrey L. Elman Geoffrey E. Hinton Michael 1. Jordan + +Alan H. Kawamoto Paul W. Munro Donald A. Norman Daniel E. Rabin Terrence 1. Sejnowski + +Paul Smolensky Gregory O. Stone Ronald 1. Williams David Zipser + +Institute for Cognitive Science University of California, San Diego + +A Bradford Book + +The MIT Press Cambridge, Massachusetts London, England + +Twelfth printing, 1999 + +© 1986 by The Massachusetts Institute of Technology + +All ri ghts reserved. No part of this book may be reproduced in any form by any electronic or mechanical means (including photocopying, recordin g, or information + +storage and retrieval) without permission in writing from the publisher. + +Printed and bound in the United States of America + +Library of Congress Cataloging-in-Publication Data + +Rumelhart, David E. + +Parallel distributed processing. + +(Computational models of cognition and perception) + +Vol. I by David E. Rumelhart. James L. McClelland and the PDP Research Group. + +"A Bradford book.'· + +Includes bibliographies and indexes. + +Contents: v.l. Foundations-v.2. Psychological + +and biological models. + +I. Human information processing. 2. Cognition. I. McClelland, James L. + +II. University of California. San Diego. PDP Research Group. Ill. Title. IV. Series. BF 45 S. R853 1986 153 85-24073 ISBN 0-262-18120-7 (v.1 ) he ISBN 0-262-68053-X (v. I ) pb 0-262-13218-4 (v.2) 0-262-63110-5 (v.2) 0-262-18123-1 (set) 0-262-631 12-1 (set) + +Preface + +Acknowledgments + +VOLUME 1 FOUNDATIONS + +Addresses of the PDP Research Group + +Part I THE PDP PERSPECTIVE + +Contents + +ix + +xv xix + +1 The Appeal of Parallel Distributed Processing 3 + +1. L. MCCLELLAND, D. E. RUMELHART, and G. E. HINTON + +2 A General Framework for Parallel Distributed Processing 45 + +D. E. RUMELHART, G. E. HINTON, and 1. L. MCCLELLAND + +3 Distributed Representations 77 + +G. E. HINTON, 1. L. MCCLELLAND, and D. E. RUMELHART + +4 PDP Models and General Issues in Cognitive Science 110 + +D. E. RUMELHART and 1. L. MCCLELLAND + +Part II BASIC MECHANISMS 147 + +5 Feature Discovery by Competitive Learning 151 + +D. E. RUMELHART and D. Z1PSER + +6 Information Processing in Dynamical Systems: + +Foundations of Harmony Theory 194 + +P. SMOLENSKY + +7 Learning and Relearning in Boltzmann Machines 282 + +G. E. HINTON and T. 1. SEJNOWSKI + +8 Learning Internal Representations by Error Propagation 318 + +D. E. RUMELHART, G. E. HINTON, and R J. WILLIAMS + +Part III FORMAL ANALYSES 363 + +9 An Introduction to Linear Algebra in Parallel Distributed + +Processing 365 + +M. I. JORDAN + +10 The Logic of Activation Functions 423 + +R. J. WILLIAMS + +11 An Analysis of the Delta Rule and the Learning of + +Statistical Associations 444 + +G.O STONE + +12 Resource Requirements of Standard and Programmable + +Nets 460 + +J L. MCCLELLAND + +13 P3: A Parallel Network Simulating System 488 + +D. ZIPSER and D. E. RABIN + +References 507 Index 517 + +VOLUME 2 PSYCHOLOGICAL AND BIOLOGICAL MODELS + +Preface to Volume 2 + +Addresses of the PDP Research Group + +Part IV PSYCHOLOGICAL PROCESSES + +IX xi + +14 Schemata and Sequential Thought Processes in PDP Models 7 D. E. RUMELHART. P. SMOLENSKY, 1. L. MCCLELLAND, and G. E. HINTON + +15 Interactive Processes in Speech Perception: + +The TRACE Model 58 + +J. L. MCCLELLAND and J. L. ELMAN + +16 The Programmable Blackboard Model of Reading 122 + +J L. MCCLELLAND + +17 A Distributed Model of Human Learning and Memory 170 + +J. L. MCCLELLAND and D. E. RUMELHART + +18 On Learning the Past Tenses of English Verbs + +D. E. RUMELHART and J. L. MCCLELLAND + +19 Mechanisms of Sentence Processing: Assigning Roles + +216 + +to Constituents 272 + +J. L. MCCLELLAND and A. H. KAWAMOTO + +Part V BIOLOGICAL MECHANISMS 327 + +20 Certain Aspects of the Anatomy and Physiology of the + +Cerebral Cortex 333 + +F H c. CRICK and C. ASANUMA + +21Open Questions About Computation in Cerebral Cortex 372 + +T. 1. SEJNOWSKI + +22 Neural and Conceptual Interpretation of PDP Models 390 + +23 Biologically Plausible Models of Place Recognition and + +Goal Location 432 + +D. ZIPSER + +24 State-Dependent Factors Influencing Neural Plasticity: + +A Partial Account of the Critical Period 471 + +P. W. MUNRO + +25 Amnesia and Distributed Memory J. L. MCCLELLAND and D. E. RUMELHART + +Part VI CONCLUSION + +26 Reflections on Cognition and Parallel Distributed + +Processing D. A. NORMAN Future Directions + +References + +Index + +503 + +529 + +531 + +547 553 581 + +Preface + +One of the great joys of science lies in the moment of shared discovery. One person's half-baked suggestion resonates in the mind of another and suddenly takes on a definite shape. An insightful critique of one way of thinking about a problem leads to another, better understanding. An incomprehensible simulation result suddenly makes sense + +as two people try to understand it together. + +This book grew out of many such moments. The seeds of the book were sown in our joint work on the interactive activation model of word perception. Since then, each of us has worked with the other and with other collaborators. The results of these collaborations are reported in several of the chapters of this book. The book also contains many chapters by other colleagues whose explorations have become intertwined with ours. Each chapter has its own by-line, but each also reflects the influences of other members of the group. We hope the result reflects some of the benefits of parallel distributed processing! The idea of parallel distributed processing-the notion that intelligence emerges from the interactions of large numbers of simple processing units-has come and gone before. The idea began to seem more and more attractive to us as the contrast between our convictions about basic characteristics of human perception, memory, language, and thought and the accepted formal tools for capturing mental processes became more apparent. Symbol-processing machines, for all their Turing equivalence, had fa�}RdHtlJ}jt ri butor , so he could spend more time working on the implications of the Boltzmann machine. Thus, the primary responsibility for putting the book together fell to the two of us. At first we expected to complete the book within a year after we began our work. Soon, however, it became clear that there was much work to be done and many directions to explore. Thus, our work continued and expanded as we and our colleagues followed the implications of the PDP approach in many dif- + +ferent ways . + +A good deal has happened since we began this project. Though much of the initial groundwork was laid in early 1982, most of the material described in these volumes did not take its present form until much + +later. + +The work has been interdisciplinary and represents what we consider a true cognitive science approach. Although the two of us have been trained as cognitive psychologists, the PDP group as a whole includes people from a wide range of backgrounds. It includes people trained in physics, mathematics, neuroscience, molecular biology, and computer sciences, as well as in psychology. We also envision an interdisciplinary audience for our book. We are cognitive psychologists and we hope, primarily , to present PDP models to the community of cognitive psychologists as alternatives to the models that have dominated cognitive psychology for the past decade or so. We also, however, see ourselves as studying architectures for computation and methods for artificial intelligence. Therefore, we hope that this book will be seen as relevant to researchers in computer science and artificial intelligence. Also, the PDP approach provides a set of tools for developing models of the neurophysiological basis of human information processing, and so we hope portions of these books will seem relevant to neuroscien- + +ORGANIZATION OF THE BOOK + +Our book consists of six parts, three in each of the two volumes. The overall structure is indicated in the accompanying table. Part I provides an overview. Chapter 1 presents the motivation for the approach and describes much of the early work that lead to the developments reported in later sections. Chapter 2 describes the PDP framework in more formal terms. Chapter 3 focuses on the idea of distributed representation, and Chapter 4 provides a detailed discussion of several general issues that the PDP approach has raised and explains how these + +issues are addressed in the various later chapters of the book. + +The remaining parts of the book present different facets of our explorations in parallel distributed processing. The chapters in Part II address central theoretical problems in the development of models of parallel distributed processing, focusing for the most part on fundamental problems in learning. The chapters in Part III describe various mathematical and computational tools that have been important in the development and analysis of PDP models. Part IV considers + +> A CONDENSED TABLE OF CONTENTS VOLUME I + +I. THE PDP PERSPECTIVE II. BASIC MECHANISMS + +1. The Appeal of PDP 5. Competitive Learning 2. A Framework for PDP 6. Harmony Theory 3. Distributed 7. Boltzmann Machines Representations 8. Learning by 4. General Issues Error Propagation + +IV. PSYCHOLOGICAL PROCESSES + +14. Schemata and PDP 15. Speech Perception 16. Model of Reading 17. Learning and Memory 18. Morphology Acquisition 19. Sentence Processing + +VOLUME II + +V. BIOLOGICAL MECHANISMS + +20. Anatomy and Physiology 21. Computation in the Brain 22. Neural and + +Conceptual Levels 23. Place Recognition 24. Neural Plasticity 25. Amnesia + +III. FORMAL ANALYSES + +9. Linear Algebra 10. Activation Functions II. The Delta Rule 12. Resource Requirements 13. Parallel Network Simulator + +VI. CONCLUSION + +26. Renections Future Directions + +applications and implications of PDP models to various aspects of human cognition, including perception, memory, language, and higherlevel thought processes. Part V considers the relation between parallel distributed processing models and the brain, reviews relevant aspects of the anatomy and physiology, and describes several models that apply PDP models to aspects of the neurophysiology and neuropsychology of information processing , learning , and memory. Part VI contains two short pieces: a reflection on PDP models by Don Norman and a brief + +discussion of our thoughts about promising future directions . + +How to read this book? It is too long to read straight through. Nor is it designed to be read this way. Chapter 1 is a good entry point for readers unfamiliar with the PDP approach, but beyond that the various parts of the book may be approached in various orders, as one might explore the different parts of a complex object or machine. The various facets of the PDP approach are interrelated, and each part informs the others; but there are few strict sequential dependencies. Though we have tried to cross - reference ideas that come up in several places, we hope that most chapters can be understood without reference to the rest of the book. Where dependencies exist they are noted in the intro- + +ductory sections at the beginning of each part of the book. + +This book charts the explorations we and our colleagues have made in the microstructure of cognition. There is a lot of terrain left to be explored. We hope this book serves as a guide that helps others join us + +in these ongoing explorations. + +December 1985 James L. McClelland + +PITTSBURGH, PENNSYLVANIA + +David E. Rumelhart LA JOLLA, CALIFORNIA + +Acknowledgments + +As we have already said, nearly all the ideas in this book were born out of interactions, and one of our most important acknowledgments is to the environment that made these interactions possible. The Institute for Cognitive Science at UCSD and the members of the Institute have + +made up the core of this environment. + +Don Norman, our colleague and friend, the Founder and Director of the Institute, deserves special credit for making ICS an exciting and stimulating place, for encouraging our explorations in parallel distributed processing, and for his central role in arranging much of the financial support this book has benefited from {of which more below} . The atmosphere depends as well on the faculty, visiting scholars, and graduate students in and around ICS. The members of the PDP Research Group itself, of course, have played the most central role in helping to shape the ideas found in this book. All those who contributed to the actual contents of the book are listed on the cover page; they have all contributed, as well, in many other ways. Several other participants in the group who do not have actual contributions to the book also deserve mention. Most prominent among these are Mike Mozer and Yves Chauvin, two graduate students in the Cognitive Science Lab, and Gary Cottrell, a recent addition to the groupfrom the University of + +Rochester. + +Several other members of the intellectual community in and around ICS have played very important roles in helping us to shape our thoughts. These include Liz Bates, Michael Cole, Steve Draper, Don Copyrighted Material + +Gentner. Ed Hutchins, Jim Hollan, Jean Mandler, George Mandler, Jeff Miller, Guy van Orden, and many others, including the participants + +in Cognitive Science 200. + +There are also several colleagues at other universities who have helped us in our explorations. Indeed, the annual connectionist workshops (the first of which resulted in the Hinton and Anderson book) have been important opportunities to share our ideas and get feedback on them from others in the field. and to learn from the contributions of others. Jim Anderson, Dana Ballard, Jerry Feldman, Geoff Hinton and Terry Sejnowski all had a hand in organizing different ones of these meetings; and we have learned a great deal from discussions with them and other participants, particularly Andy Barto, Scott Fahlman, Christof von der Malsburg, John Hopfield, Dave Touretzky, and more recently Mark Fanty and Gene Charniak. McClelland's discussions at MIT (particularly with Jerry Fodor and Molly Potter) helped in the clarification of several aspects of our thinking, and various colleagues at and around CMU -particularly John Anderson, Mark Derthick, Dave Klahr, Brian MacWhinney, and Jeff Sokolov-have contributed a great deal through discussions over the last year and a half or so, as we have worked toward the completion of the book. Others one or both of us have interacted with a great deal include Bill Brewer, Neal Cohen, AI Collins, Billy Salter, Ed Smith, and Walter Schneider. All of these people have contributed more or less + +directly to the development of the ideas presented in this book. + +An overlapping group of colleagues deserves credit for helping us improve the book itself. Jim Anderson, Andy Barto, Larry Barsalou, Chris Reisbeck, Walter Schneider, and Mark Seidenberg all read several chapters of the book and sent useful comments and suggestions. Many other people read and commented on individual chapters, and we are sincerely grateful for their careful contributions, which we acknowledge + +in the appropriate chapters. + +This project owes a tremendous amount to the help of the excellent staff of the Institute for Cognitive Science. Kathy Farrelly, in particular, has played an enormous role in all aspects of the production of the book; her cheerful, thoughtful, and very careful assistance made the production of the book run much more smoothly than we have had any right to hope and allowed us to keep working on the content of some of the chapters even as the final production was rolling forward on other sections. Eileen Conway's assistance with graphics and formatting has also been invaluable and we are very grateful to her as well. Mark Wallen kept the computers running, served as chief programming consultant and debugger par excellence, and tamed troff, the phototypesetter. Without him we would never have gotten all the formatting to come out right. Karol Lightner worked very hard toward the end of the Copyrighted Material + +project on final proofing and indexing, and Sondra Buffett, as the Administrative Director of ICS, held everything together and kept everything running throughout the entire four years of the project. + +Our project has been supported by a number of different agencies and foundations. Primary support came from the System Development Foundation and the Office of Naval Research. The System Development Foundation has provided direct support for the PDP research group through a grant to Norman and Rumelhart, and has also supported several of the individual members of the group (Crick, Hinton, Sejnowski, and Zipser). ONR contracts that have contributed support include N00014-79-C-0323, NR 667-437; N00014-85-K-0450, NR 667- + +548; and N00014-82-C-0374, NR 667-483. + +The people behind both SDF and ONR deserve acknowledgment too. The entire PDP enterprise owes a particular debt of gratitude to Charlie Smith, formerly of SDF, who appreciated the appeal of para\1el distributed processing very early on, understood our need for computing resources, and helped provide the entire PDP research group with the funds and encouragement needed to complete such project. Henry Halfr, formerly of ONR, was also an early source of support, encouragement, and direction. Charlie Smith has been succeeded by Carl York, and Henry Halff has been succeeded by Susan Chipman, Michael Shafto, and Harold Hawkins. We are grateful to a\1 of these people for their commitment to the completion of this book and to the + +ongoing development of the ideas. + +Several other sources have contributed to the support of individual members of the group. These include the National Institute of Mental Health, through a Career Development Award-PHS-MH-00385-to McCle\1and and post-doctoral fe\1owships to Paul Smolensky and Paul Munro under Grant PHS-MH-14268 to the Center for Human Information Processing at UCSD. Smolensky received support in the form of a fellowship from the Alfred P. Sloan Foundation, and some of McClelland's work was supported by a grant from the National Science Foundation (BNS-79-24062). These and other sources of support for specific individuals or projects are acknowledged in the appropriate + +chapters. + +Fina\1y, we would like to thank our wives, Heidi and Marilyn. Their understanding, encouragement, and support throughout the four years of this project helped to make the process of bringing this book to life + +much more rewarding than it might have been. + +JLM/DER + +Addresses of the PDP Research Group + +Chisato Asanuma + +Francis H. C. Crick + +Jeffrey L. Elman + +Geoffrey E. Hinton + +Michael I. Jordan + +Alan H. Kawamoto + +Salk Institute P.O. Box 85800 San Diego, C A 92138 + +Salk Institute P.O. Box 85800 San Diego, CA 92138 + +Department of Linguistics + +University of California, San Diego + +La Jolla, CA 92093 + +Department of Computer Science Carnegie-Mellon University Pittsburgh, PA 15213 + +Department of Computer and Information Science University of Massachusetts Amherst, MA 01003 + +Department of Psychology Carnegie-Mellon Uni versity Pittsburgh, PA 15213 + +James L. McClelland + +Paul W. Munro + +Donald A. Norman + +Daniel E. Rabin + +David E. Rumelhart + +Terrence J. Sejnowski + +Paul Smolensky + +Gregory O. Stone + +Ronald 1. Williams + +David Zipser + +Department of Psychology Carnegie-Mellon University Pittsburgh, PA 15213 + +Department of Information Science + +University of Pittsburgh Pittsburgh, PA 15260 + +Institute for Cognitive Science University of California, San Diego + +La Jolla, CA 92093 + +Intellicorp + +1975 EI Camino Real West Mountain View, CA 94040 + +Institute for Cognitive Science University of California, San Diego + +La Jolla, CA 92093 + +Department of Biophysics Johns Hopkins University Baltimore, MD 21218 + +Department of Computer Science + +University of Colorado Boulder, CO 80309 + +Center for Adaptive Systems Department of Mathematics + +Boston University Boston, MA 02215 + +Institute for Cognitive Science Universi�y of California, San Diego + +La Jolla, CA 92093 + +Insitute for Cognitive Science University of California, San Diego + +La Jolla, CA 92093 + +PART I + +THE PDP PERSPECTIVE + +CHAPTER 1 + +The Appeal of + +Parallel Distributed Processing + +J. L. McCLELLAND, D. E. RUMELHART, and G. E. HINTON + +What makes people smarter than machines? They certainly are not quicker or more precise. Yet people are far better at perceiving objects in natural scenes and noting their relations , at understanding language and retrieving contextually appropriate information from memory, at making plans and carrying out contextually appropriate actions, and at a wide range of other natural cogni t i ve tasks. People are also far better at learning to do these things more accurately and nuently through pro- + +cessing experience. + +What is the basis for these differences? One answer, perhaps the classic one we might expect from artificial intel ligence, is " software ." If we only had the right computer program, the argument goes, we might be able to capturethe nuidity and adaptability of human information + +processing. + +Certainly this answer is partially correct . There have been great breakthroughs in our understanding of cognition as a result of the development of expressive high- level computer languages and powerful algorithms. No doubt there will be more such breakthroughs in the future. However, we do not think that software is the whole story. + +In our view, people are smarter than today's computers because the brain employs abasic computational architecture that is more suited to deal with a central aspect of the natural information processing tasks that people are so good at. In this chapter, we will show through examples that these tasks generally requi re the simultaneous consideration of many pieces of information or const raints . Each constraint may be + +decisive role in determining the outcome of processing. After examining these points, we will introduce a computational framework for modeling cognitive processes that seems well suited to exploiting these constaints and that seems closer than other frameworks to the style of computation as it might be done by the brain. We wi ll review several early examples of models developed in this framework, and we will show that the mechanisms these models employ can give rise to powerful emergent properties that begin to suggest attractive alternati ves to traditional accounts of various aspects of cognition. We wi ll also show that models of this class provide a basis for understanding how learning + +can occur spontaneously, as a by-product of processing activity. + +Multiple Simultaneous Constraints + +Reaching and grasping. Hundreds of times each day we r�ach for things. We nearly never think about these acts of reaching. And yet, each time, a large number of different considerations appear to jointly determine exactly how we wi ll reach for the object. The position of the object, our. posture at the time, what else we may also be holding, the size, shape, and antici pated weight of the object, any obstacles that may be in the way-all of these factors jointly determine the exact method + +we wil l use for reaching and grasping. + +Consider the situation shown in Figure 1. Figure 1 A shows Jay McClelland's hand, in typing position at his terminal . Figure 1B indicates the position his hand assumed in reaching for a smal l knob on the desk beside the terminal. We will let him describe what happened in + +the first person: + +On the desk next to my terminal are several objects-a chi pped coffee mug, the end of a computer cable, a knob from a clock radio. I decide to pick the knob up. At first I hesitate, because it doesn't seem possible. Then I just reach for it, and find myself grasping the knob in what would normal ly be considered a very awkward position -but it solves all of the constraints. I'm not sure what all the details of the movement were, so I let myself try it a few times more. I observe that my right hand is carried up off the keyboard, bent at the elbow, until my forearm is at about a 30° angle to the desk top and parallel to the side of the terminal . The palm is facing downward through most of this. Then, my arm extends and lowers down more or less paral lel to the edge of the desk and parallel to the side of the terminal and, as it drops, it turns about 90° so that the + +A + +B + +FIGURE I. A: An everyday situation in which it is necessary to take into account a large number of constraints to grasp a desired object. In this case the target object is the small knob to the left of the cup. B: The posture the arm arrives at in meeting these + +palm is facing the cup and the thumb and index finger are below. The turning motion occurs just in time, as my hand drops, to avoid hitting the coffee cup. My index finger and thumb close in on the knob and grasp it, with my hand com- + +pletely upside down. + +Though the detai ls of what happened here might be quibbled with, the broad outl ines are apparent. The shape of the knob and its position on the table; the starting position of the hand on the keyboard; the positions of the terminal, the cup, and the knob; and the constraints imposed by the structure of the arm and the musculature used to control it -all these things conspired to lead to a solution which exactly suits the problem. If any of these constraints had not been included, the movement would have failed. The hand would have hit the cup or + +the terminal -or it would have missed the knob. + +The mutual itifluence of syntax and semantics. MUltiple constraints operate just as strongly in language processing as they do in reaching and grasping. Rumelhart (977) has documented many of these multiple constraints. Rather than catalog them here, we wi ll use a few examples from language to illustrate the fact that the constraints tend to be reci procal: The example shows that they do not run only from + +syntax to semantics-they also run the other way. + +It is clear, of course, that syntax constrains the assignment of meaning. Without the syntactic rules of English to guide us, we cannot correctly understand who has done what to whom in the fol lowing sen- + +tence: + +The boy the man chased kissed the girl. + +But consider these examples (Rumelhart, 1977; Schank, 1973): + +I saw the grand canyon flying to New York. + +I saw the sheep grazing in the field. + +Our knowledge of syntactic rules alone does not tell us what grammatical role is played by the prepositional phrases in these two cases. In the first, "flying to New York" is taken as descri bi ng the context in which the speaker saw the Grand Canyon-while he was flying to New York. In the second, "grazing in the field" could syntactically descri be an analogous situation, in which the speaker is grazing in the field, but this possi bility does not typical ly become available on first reading. Instead we assign "grazing in the field" as a modifier of the sheep (roughly, .. who were grazing in the field"). The syntactic structure of each of Copyrighted Material + +these sentences, then, is determined in part by the semantic relations that the constituents of the sentence might plausibly bear to one another. Thus, the influences appear to run both ways, from the syn- + +tax to the semantics and from the semantics to the syntax. + +In these examples, we see how syntactic considerations influence semantic ones and how semantic ones influence syntactic ones. We + +cannot say that one kind of constraint is primary. + +Mutual constraints operate, not only between syntactic and semantic processing, but also within each of these domains as wel l. Here we consider an example from syntactic processing, namely, the assignment + +of words to syntactic categories. Consider the sentences: + +I like the joke. I like the drive. I like to joke. I like to drive. + +In this case it looks as though the words the and to serve to determine whether the fol lowing word wi ll be read as a noun or a verb. This, of course, is a very strong constraint in English and can serve to force a + +verb interpretation of a word that is not ordinarily used this way: + +I like to mud. + +On the other hand, if the information specifying whether the function word preceding the final word is to or the is ambiguous, then the typical reading of the word that follows it wil l determine which way the function word is heard. This was shown in an experiment by Isenberg, Walker, Ryder, and Schweikert ( 1 980). They presented sounds halfway between to (actually/0) and the (actual ly / er f) and found that words like joke, which we tend to think of first as nouns, made subjects hear the marginal stimuli as the. while words like drive, which we tend to think of first as verbs, made subjects hear the marginal stimuli as to. General ly, then, it would appear that each word can help constrain the + +syntactic role, and even the identity, of every other word. + +Simultaneous mutual constraints in word recognition. Just as the syntactic role of one word can influence the role assigned to another in analyzing sentences, so the identity of one letter can influence the identity assigned to another in reading. A famous example of this, from Selfridge, is shown in Figure 2 . Along with this is a second example in which none of the letters, considered separately, can be identified unambiguously, but in which the possibil ities that the visual + +TAE CAT + +��8 + +S�OT + +�ISH + +DEQT + +FIGURE 2. Some ambiguous displays. The first one is from Selfridge, 1955. The second line shows that th ree ambiguous characters can each constrain the identity of the others. The third, fourth, and fifth lines show that these characters are indeed ambiguous in that they assume other identities in other contexts. (The ink-blot technique of + +making letters ambiguous is due to Lindsay and Norman, 1972). + +information leaves open for each so constrain the possi ble identities of + +the others that we are capable of identi fying all of them. + +At first glance, the situation here must seem paradoxical: The identity of each letter is constrained by the identities of each of the others. But since in general we cannot know the identities of any of the letters + +until we have established the identities of the others, how can we get + +the process started? + +The resolution of the paradox, of course, is simple. One of the different possible letters in each position fits together with the others. It appears then that our perceptual system is capable of exploring all these possibi lities without committing itself to one unti l all of the constraints + +are taken into account. + +Understanding through the interplay of mUltiple sources of knowledge. It is clear that we know a good deal about a large number of different standard situations. Several theorists have suggested that we store this knowledge in terms of structures called variously: scripts (Schank, 1976), frames (Minsky, 197 5), or schemata (Norman & Bobrow, 1976; Rumelhart, 1975). Such knowledge st ructures are assumed to be the basis of comprehension. A great deal of progress + +has been made within the context of this view. + +However, it is important to bear in mind that most everyday situations cannot be rigidly assigned to just a single script. They general ly involve an interplay between a number of different sources of information. Consider, for example, a chi ld's birthday party at a restaurant. We know things about birthday parties, and we know things about restaurants, but we would not want to assume that we have explicit knowledge (at least, not in advance of our first restaurant bi rthday party) about the conjunction of the two. Yet we can imagine what such a party might be like. The fact that the party was being held in a restaurant would modify certain aspects of our expectations for birthday parties (we would not expect a game of Pin-the-Tail-on-the-Donkey, for example), while the fact that the event was a bi rthday party would inform our expectations for what would be ordered and who would pay + +the bill. + +Representations like scri pts, frames, and schemata are useful structures for encoding knowledge, although we believe they only approximate the underlying structure of knowledge representation that emerges from the class of models we consider in this book, as explained in Chapter 14. Our main point here is that any theory that tries to account for human knowledge using scri pt-like knowledge structures will have to allow them to interact with each other to capture the generati ve capacity of human understanding in novel situations. Achieving such interactions has been one of the greatest difficulties associated with implementing models that real ly think generatively using script- or + +frame-like representations . + +PARALLEL DISTRIBUTED PROCESSING + +In the examples we have considered, a number of different pieces of information must be kept in mind at once. Each plays a part, constraining others and being constrained by them. What kinds of mechanisms seem well suited to these task demands? Intuitively, these tasks seem to require mechanisms in which each aspect of the information in the situation can act on other aspects, simultaneously influencing other aspects and being influenced by them. To articulate these intuitions, we and others have turned to a class of models we call Parallel Distributed Processing (POP) models. These models assume that information processing takes place through the interactions of a large number of simple processing elements called units, each sending excitatory and inhibitory signals to other units. In some cases, the units stand for possible hypotheses about such things as the letters in a particular display or the syntactic roles of the words in a particular sentence. In these cases, the activations stand roughly for the strengths associated with the different possible hypotheses, and the interconnections among the units stand for the constraints the system knows to exist between the hypotheses. In other cases, the units stand for possible goals and actions, such as the goal of typing a particular letter, or the action of moving the left index finger, and the connections relate goals to subgoals, subgoals to actions, and actions to muscle movements. In still other cases, units stand not for particular hypotheses or goals, but for aspects of these things. Thus a hypothesis about the identity of a word, for example, is itself distributed in the activations of + +a large number of units. + +PDP Models: Cognitive Science or Neuroscience? + +One reason for the appeal of POP models is their obvious "physiological" flavor: They seem so much more closely tied to the physiology of the brain than are other kinds of information-processing models. The brain consists of a large number of highly interconnected elements (Figure 3) which apparently send very simple excitatory and inhibitory messages to each other and update their excitations on the basis of these simple messages. The properties of the units in many of the POP models we will be exploring were inspired by basic properties of the neural hardware. In a later section of this book, we will examine in + +FIGURE 3. The arborizations of about I percent of the neurons near a vertica' ,lice th rough the cerebral cortex. The full height of the figure corresponds to the thickness of the cortex, which is in this instance about 2 mm. (From Mechanics of the Mind, p. 84, by C. Blakemore, 1977, Cambridge, England: Cambridge University Press. Copyright 1977 + +by Cambridge University Press. Reprinted by permission.) + +Though the appeal of POP models is definitely enhanced by their physiological plausi bility and neural inspi ration , these are not the primary bases for their appeal to us . We are, after all, cognitive scientists, and POP models appeal to us for psychological and computational reasons. They hold out the hope of offering computational ly sufficient and psychologically accurate mechanistic accounts of the phenomena of human cognition which have eluded successful explication in conventional computational formalisms; and they have radically altered the way we think about the time-course of processing , the nature of + +representation, and the mechanisms of learning. + +The Microstructure of Cognition + +The process of human cognition , examined on a time scale of seconds and minutes, has a distinctly sequential character to it. Ideas come, seem promising, and then are rejected; leads in the solution to a problem are taken up, then abandoned and replaced with new ideas. Though the process may not be discrete, it has a decidedly sequential character, with transitions from state-to-state occurring, say, two or three times a second. Clearly, any useful description of the overall organization of this sequential flow of thought wi ll necessarily describe + +a sequence of states. + +But what is the internal structure of each of the states in the sequence, and how do they come about? Serious attempts to model even the simplest macrosteps of cognition -say, recognition of single words-require vast numbers of microsteps if they are implemented sequentially. As Feldman and Ballard (I982) have pointed out, the biological hardware is just too sluggish for sequential models of the microstructure to provide a plausible account, at least of the microstructure of human thought. And the time limitation only gets worse, not better, when sequential mechanisms try to take large numbers of constraints into account. Each additional constraint requires more time in a sequential machine, and, if the constraints are imprecise, the constraints can lead to a computational explosion. Yet people get faster, not slower, when they are able to exploit additional + +constraints. + +Parallel distri buted processing models offer alternatives to serial models of the microstructure of cognition. They do not deny that there is a macrostructure, just as the study of subatomic particles does not deny the existence of interactions between atoms. What POP models do is describe the internal structure of the larger units, just as subatomic physics describes the internal structure of the atoms that + +form the constituents of larger units of chemical structure. + +We shal l show as we proceed through this book that the analysis of the microstructure of cognition has important implications for most of the central issues in cognitive science. In general , from the POP point of view, the objects referred to in macrostructural models of cognitive processing are seen as approximate descri ptions of emergent properties of the microstructure. Sometimes these approximate descri ptions may be sufficiently accurate to capture a process or mechanism well enough; but many ti mes, we wi ll argue, they fail to provide sufficiently elegant or tractable accounts that capture the very flexibility and openendedness of cognition that their inventors had originally intended to capt ure. We hope that our analysis of POP models wi ll show how an Copyrighted Material + +for the second to inhibit the third and following letters, and so on. As a result of the interplay of activation and inhibition among these units, the unit for the first letter was at first the most strongly active, and the + +units for the other letters were partially activated. + +Each letter unit exerts influences on the hand and finger involved in typing the letter. The v unit, for example, tends to cause the index finger to move down and to cause the whole hand to move down with it. The e unit, on the other hand, tends to cause the middle finger on the left hand to move up and to cause the whole hand to move up also. The r unit also causes the left index finger to move up and the left + +hand to move up with it. + +The extent of the influences of each letter on the hand and finger it directs depends on the extent of the activation of the letter. Therefore , at first, in typing the word very, the v exerts the greatest control. + +Response System + +Keypress Schemata + +Word Schema THUMB + +RESPONSE SYSTEM L1(.I, + 05) LM(+ 1 ·03) LJ(+ 1, ·03) RII+ 1. + 1 3) + +> . target finger POSition current finger POSition + +FIGURE 4. The interaction of activations in typing the word very. The very unit is activated from outside the model. It in turn activates the units for each of the component letters. Each letter unit specifies the target finger positions, specified in a keyboard coordinate system. L and R stand for theleft and right hands. and I and M for the index and middle fingers. The letter units receive information about the current finger position from the response system. Each letterunit inhibits the activation of all letter units that follow it in the word: inhibitory connections are indicated by the lines with solid dots at their terminations. (From "Simulating a Skilled Typist: A Study of Skilled Motor Performance" by D. E. Rumelhart and D. A. Norman. 1982, Cognitive Science. 6, + +balance and bringing the tip closer to the target. After a number of iterations, the stick-person settled on postures that satisfied the goal of reaching the target and the goal of maintaining the center of gravity + +over the" feeL" + +Though the simulation was able to perform the task, eventually satisfying both goals at once, it had a number of inadequacies stemming from the fact that each joint processor attempted to achieve a solution in ignorance of what the other joints were attempting to do. This problem was overcome by using additional processors responsible for setting combinations of joint angles. Thus, a processor for flexion and extension of the leg would adjust the knee, hip, and ankle joints synergistical ly, while a processor for flexion and extension of the arm would adjust the shoulder and elbow together. With the addition of processors of this form, the number of iterations required to reach a sol ution was greatly reduced, and the form of the approach to the solution looked very natural. The sequence of configurations attained in one + +processing run is shown in Figure 5. + +Explicit attempts to program a robot to cope with the problem of maintaining balance as it reaches for a desired target have revealed the difficulty of deriving explicitly the right combinations of actions for each possible starting state and goal state. This simple model illustrates that we may be wrong to seek such an explicit solution. We see here that a solution to the problem can emerge from the action of a number of simple processors each attempting to honor the constraints + +independently. + +FIGURE S. A sequence of configurations assumed by the stick "person" performing the reaching task described in the text, from Hinton (I 984). The small circle represents the center of gravity of th: whole stick-figure, and the cross represents the goal to be + +What kind of a mechanism might we propose to account for these facts? Marr and Poggio (976) began by explicitly represen ting the two views in two arrays, as human observers might in two di fferent reti nal images. They noted that corresponding black dots at different percei ved distances from the observer will be offset from each other by gi fferent amounts i n the two views. The job of the model is to determine which points correspond. This task is, of course, made difficult by the fact that there will be a very large number of spurious correspondences of individual dots. The goal of the mechanism, then, is to find those correspondences that represent real correspondences in depth and suppress those that represent spurious correspondences. + +To carry out this task, Marr and Poggio assigned a processing unit to each possible .conjunction of a point in one image and a poi nt in the other. Since the eyes are offset horizontally, the possible conjunctions occur at various offsets or disparities along the horizontal dimension. Thus, for each point in one eye, there was a set of processing units with one unit assigned to the conjunction of that poi nt and the point at + +each horizontal offset from it in the other eye. + +Each processing unit recei ved activation whenever both of the points the unit stood for contained dots. So far, then, units for both real and spurious correspondences would be equal ly activated. To allow the mechani sm to find the right correspondences, they pointed out two general princi ples about the visual world: (a) Each point in each view generally corresponds to one and only one point in the other view, and Cb) neighbori ng points in space tend to be at nearly the same depth and therefore at about the sam( disparity in the two images. While there are discontinuities at the edges of things, over most of a twodimensional view of the world there will be continuity. These principles are called the uniqueness and continuity constraints , respectively. Marr and Poggio incorporated these princi ples into the interconnections between the processing units. The uniqueness constraint was captured by inhibitory connections among the units that stand for alternative correspondences of the same dot . The continuity principle was captured by excitatory connections among the units that stand for simi- + +lar offsets of adjacent dots. + +These additional connections allow the Marr and Poggio model to "sol ve" stereograms like the one shown in the figure. At first, when a pair of patterns is presented, the units for all possible correspondences of a dot in one eye with a dot in the other will be equally excited. However, the excitatory connections cause the units for the correct conjunctions to receive more excitation than units for spurious conjunctions, and the inhi bitory connections allow the units for the correct conjunctions to turn off the units for the spurious connections. Thus, + +the model tends to settle down into a stable state in which only the + +correct correspondence of each dot remains active. + +There are a number of reasons why Marr and Poggio (I979) modified this model (see Marr, 1982, for a discussion) , but the basic mechanisms of mutual excitation between units that are mutually consistent and mut ual inhibition between units that are mutually incompatible provide a natural mechanism for settli ng on the right conjunctions of points and rejecting spurious ones. The model also il lustrates how general principles or rules such as the uniqueness and continuity principles may be embodied in the connections between processing uni ts, and how behavior in accordance with these princi ples can emerge from the + +interactions determined by the pattern of these interconnections. + +Perceptual completion of familiar patterns. Perception, of course, is influenced by familiarity. It is a well-known fact that we often misperceive unfamiliar objects as more famil iar ones and that we can get by with less time or with lower-quality information in perceiving fami liar items than we need for percei ving unfamil iar items. Not only does familiarity help us determine what the higher-level structures are when the lower-level information is ambiguous; it also allows us to fi ll in missing lower-level information within famil iar higher-order patterns. The well-known phonemic restoration effect is a case in point. [n this phenomenon, perceivers hear sounds that have been cut out of words as if they had actually been present . For example, Warren (I970) presented legi#lature to subjects, with a click in the location marked by the #. Not only did subjects correctly identify the word legislature; they also heard the missing /s/ just as though it had been presented. They had great difficulty localizing the click, which they tended to hear as a disembodied sound. Simi lar phenomena have been observed in + +visual perception of words since the work of Pi lIsbury (897). + +Two of us have proposed a model describing the role of familiarity in perception based on excitatory and inhibitory interactions among units standing for various hypotheses about the input at different levels of abstraction (McClelland & Rumelhart, 1981; Rumelhart & McClelland, 1982). The model has been applied in detail to the role of familiarity in the perception of letters in visually presented words, and has proved to provide a very close account of the results of a large number of + +experiments. + +The model assumes that there are units that act as detectors for the visual features which distinguish letters , with one set of units assigned to detect the features in each of the di fferent letter-positions in the word. For four-letter words, then , there are four such sets of detectors. There are also four sets of detectors for the letters themselves and a set + +FIGURE 7. The unit for the letter T in the fi rst position of a four-letter array and some of its neighbors . Note that the feature and letter units stand only for the fi rst position; in a complete picture of the units needed from processing four-letter displays , there would be four fu ll sets of feature detectors and four full sets of letter detectors. (From " An Interactive Activation Model of Contex t Effects in Letter Perception: Part I. An Account of Basic Findings" by J. L. McClelland and D. E. Rumelhart, 1981, Psychological Review, 88, p. 380. Copyright 1981 by the American Psychological Association. Reprin ted by + +permission .) + +them and to inhibit detectors for words which do not have these letters. A number of words are partial ly consistent with the active letters, and receive some net excitation from the letter level , but only the word WORK matches one of the active letters in all four positions. As a result, WORK becomes more acti ve than any other word and inhibits the other words, thereby successfully dominating the pattern of activation among the word units. As it grows in strength, it sends feedback to the letter level , reinforci ng the activations of the W, 0, R, and K in the corresponding positions. In the fourth position, this feedback gi ves K the upper hand over R, and eventual ly the stronger activation of the Copyrighted Material + +0.8 + +5 0.4 .� .2: o « 0.0 + +0.8 + +c: 0.4 .Q iii .� o « 0.0 Word Level + +\_---- work + +---------------------- + +---------- -- fork + +weak + +Letter Level ",- + +\_ -- - --- - K + +./" ,- // / / ./ + +'-------------------- ---- A + +0 + +8 16 24 Time + +32 40 + +FIGURE 8. A possible display which might be presented to the interactive activation model of word recognition, and the resulting activations of selected letter and word units. The letter units are for theletters indicated in the fou rth position of a four-letter display. + +K detector allows it to dominate the pattern of activation, suppressing + +the R detector completely. + +This example illustrates how PDP models can allow knowledge about what letters go together to form words to work together with natural constraints on the task (i .e., that there should only be one letter in one place at one time) , to produce perceptual completion in a simple and + +direct way. + +perception of letters in unfamili ar letter strings which are word - like but + +not themselves actually familiar . + +One way of accounting for such performances is to imagine that the percei ver possesses, in addition to detectors for famil iar words, sets of detectors for regular subword units such as fami l iar letter cl usters , or that they use abstract rules, specifying which classes of letters can go with which others in different contexts. It turns out, however, that the model we have already described needs no such additional structure to produce perceptual facilitation for word-l ike letter strings� to this extent it acts as if it "knows" the orthographi c struct ure of Engl ish . We illustrate this feature of the model with the example shown in Figure 9, where the nonword YEAD is shown in degraded form so that the second letter is incompletely visi ble. Gi ven the information about this letter, considered alone, either E or F would be possible in the second position . Yet our model wi ll tend to complete this letter as an E. + +The reason for this behavior is that, when YEAD is shown , a number of words are partially acti vated. There is no word consistent with y. E or F. A. and D, but there are words which match YEA (YEAR, for example) and others which match EAD (BEAD. DEAD. HEAD. and + +READ, for example) . These and- other near + +' misses are partial ly + +acti vated as a result of the pattern of activation at the letter level . While they compete with each other, none of these words gets strongly enough acti vated to completely suppress all the others. Instead, these units act as a group to reinforce particularly the letters E and A. There are no close partial matches which incl ude the letter F in the second position, so this letter recei ves no feedback support. As a result , E comes to dominate, and eventual ly suppress, the F in the second + +position . + +The fact that the word perception model exhibits perceptual faci litation to pronounceable non words as wel l as words illustrates once again how behavior in accordance with general princi ples or rules can emerge from the interactions of simple processing elements. Of course, the behavior of the word perception model does not implement exactly any of the systems of orthographic rules that have been proposed by linguists (Chomsky & Hal le , 1968; Venesky, 1970) or psychologists (Spoehr & Smith , 1975) . In this regard , it only approximates such rule-based descriptions of perceptual processing. However, rule systems such as Chomsky and Halle's or Venesky's appear to be only approximately honored in human performance as wel l (Smith & Baker, 1976) . Indeed , some of the discrepancies between human performance data and rule systems occur in exactly the ways that we would predict from the word perception model (Rumelhart & McClelland, 1982) . This ill ustrates the possibil ity that POP models may provide more accurate accounts of the detai ls of human performance than models Copyrighted Material + +can access informat ion in memory based on nearly any attribute of the + +representation we are trying to ret rieve. + +Of course, some cues are much better than others. An attribute which is shared by a very large number of thi ngs we know about is not a very effective ret rieval cue, since it does not accurately pick out a particular memory representation. But, several such cues, in conjunction, can do the job. Th us, if we ask a friend who goes out with several women , "Who was that woman I saw you with?", he may not know which one we mean -but if we specify something else about her-say the color of her hai r, what she was wearing (in so far as he remembers this at all) , whe re we saw him with her-he wi ll likely be able to h i t + +upon the right one . + +It is, of course , possible to implement some kind of content addressabi lity of memory on a standard computer in a variety of different ways . One way is to search sequentially, examining each memory in the system to find the memory or the set of memories which has the particular content specified in the cue. An alternative, somewhat more efficient, scheme involves some form of index ingkeepi ng a list, for every con tent a memory might have, of which + +memories have that content . + +Such an indexing scheme can be made to work with error-free probes , but it wi ll break down if there is an error in the specification of the retrieval cue. There are possible ways of recovering from such errors , but they lead to the kind of combinatorial explosions which + +plague this kind of computer implementation. + +But suppose that we imagi ne that each memory is represented by a unit which has mutually excitatory interactions with units standing for each of its properties. Then , whenever any property of the memory became active, the memory would tend to be acti vated , and whenever the memory was acti vated , all of its contents would tend to become activated . Such a scheme would automatically produce content addressabi lity for us. Though it would not be immune to errors, it would not be devastated by an error in the probe if the remaining + +properties specified the correct memory . + +As descri bed thus far, whenever a property that is a part of a number of di fferent memories is activated, it will tend to acti vate al l of the memories it is in. To keep these other acti vities from swamping the "correct" memory unit, we simply need to add initial inhi bitory connections among the memory units. An additional desi rable feat ure would be mutually inhibi tory interactions among mutually incompatible property uni ts. For example, a person cannot both be single and married at the same time, so the units for di fferent marital states wou ld be + +McClel land (1981) developed a simu lation model that ill ustrates how a system with these properties would act as a content addressable memory. The model i s obviously oversimplified, but it ill ust rates many of the characteristics of the more complex models that wi ll be con- + +sidered in later chapters . + +Consider the information represented in Figure 10, which lists a number of people we might meet if we went to live in an unsavory neighborhood, and some of thei r hypothetical characteristics. A subset + +The Jets and The Sharks + +Name Gang Age Edu Mar Occupation + +Art Jets 40's J.H. Si ng. Pusher AI Jets 30's J.H. Mar. Burglar + +Sam Jets 20's COL. Si + +ng. Bookie + +Clyde Jets 40's J.H. Sing. Bookie Mike Jets 30's J.H. Sing. Bookie Jim Jets 20's J.H. Di y . Burgtar Greg Jets 20's H.S. Mar. Pushe r John Jets 20's J.H. Mar. Burglar Doug Jets 30's H.S. Sing. Bookie Lance Jets 20's J.H. Mar. Burglar George Jets 20's J.H. Di v . Burglar + +Pete Jets 20's H.S. Si + +ng. Bookie + +Fred Jets 20's H.S. Sing. Pusher Gene Jets 20's COL. Sing. Pusher Ralph Jets 30's J.H. Sing. Pusher Phil Sharks 30's COL. Mar . Pusher Ike Sharks 30's J.B. Sing. Bookie Nick Sharks 30's H . S. Si ng. Pusher Don Sharks 30's COL. Mar. Burglar Ned Sharks 30's COL. Mar. Bookie Karl Sharks 40's H. S. Mar . Bookie Ken Sharks 20's H.S. Sing. Burglar Earl Sharks 40's H.S. Mar. Burglar Rick Sharks 30's H.S. Div. Burgl ar 01 Sharks 30's COL. Mar. Pusher Neal Sharks 30's H.S. Sing. Bookie Daye Sharks 30's H.S. Di y. Pusher + +FIGURE 10. Characteristics of a number of individuals belonging to two gangs, the Jets and the Sharks. (From "Retrieving General and Specific Knowledge From Stored Knowledge of Specifics" by 1. L. McClelland, 1981, Proceedings of the Third Annual Conference of the Cognitive Science SOCiety, Berkeley, CA. Copyright 1981 by 1. L. McClel land + +of the units needed to represent this information is shown in Figure 11 . In this network, there is an "instance unit" for each of the characters described in Figure 10, and that unit is linked by mutually excitatory connections to al l of the units for the fellow's properties. Note that we have included property units for the names of the characters, as well as + +units for their other properties. + +Now, suppose we wish to retrieve the properties of a particular individual , say Lance. And suppose that we know Lance's name. Then we can probe the network by activating Lance's name unit, and we can see what pattern of activation arises as a result. Assuming that we know of no one else named Lance, we can expect the Lance name unit to be hooked up only to the instance unit for Lance. This wi ll in turn activate the property units for Lance, thereby creating the pattern of + +FIGURE 11. S o m e o f the units and interconnections needed to represent the indi viduals shown in Figure 10. The units connected with double-headed arrows are mutually excitatory. All the units within the same cloud are mutually inhibitory. (From "Retrieving General and Specific .Knowledge From Stored Knowledge of Specifics" by J. L. McClelland, 198 1, Proceedings of the Third Annual Coriference of the Cognitive Science Society, 8erkeley, CA. Copyright 1981 by J. L. McClelland. Reprinted by permission.) + +activation corresponding to Lance. In effect, we have retrieved a representation of Lance. More wi ll happen than just what we have + +described so far, but for the moment let us stop here. + +Of course, sometimes we may wish to retrieve a name, given other information. In this case, we might start with some of Lance's properties, effectively asking the system, say "Who do you know who is a Shark and in his 20s?" by activating the Shark and 20s units. In this case it turns out that there is a single individual , Ken, who fits the description . So, when we actiyate these two properties, we wi ll acti vate the instance unit for Ken, and this in turn wi ll acti vate his name unit, + +and fill in his other properties as well. + +Graceful degradation. A few o f t h e desirable properties of this kind of model are visible from considering what happens as we vary the set of features we use to probe the memory in an attempt to retrieve a particular indi vidual 's name. Any set of features which is sufficient to uniquely characterize a particular item wi ll acti vate the instance node for that item more strongly than any other instance node. A probe which contains misleading features wi ll most strongly acti vate the node that it matches best. This wi ll clearly be a poorer cue than one which contains no misleading information -but it wi ll still be sufficient to activate the "right answer" more strongly than any other, as long as the introduction of misleading information does not make the probe closer to some other item. In general, though the degree of activation of a particular instance node and of the corresponding name nodes varies in this model as a function of the exact content of the probe, errors in the probe wi ll not be fatal unless they make the probe poi nt to the wrong memory. This kind of model's handl ing of incomplete or partial probes also requires no special error-recovery scheme to work -it is a natural by-product of the nature of the retrieval mechanism that it is capable of + +graceful degradation. + +These aspects of the behavior of the Jets and Sharks model deserve more detai led consideration than the present space allows. One reason we do not go into them is that we view this model as a stepping stone in the development of other models, such as the models using more distributed representations, that occur in other parts of this book. We do, however, have more to say about this simple model , for like some of the other models we have already examined, this model exhibits some useful properties which emerge from the interactions of the pro- + +cessing uni ts. + +Default assignment. It probably wi ll have occurred to the reader that in many of the situations we have been examining, there wi ll be other Copyrighted Material + +activations occurring which may influence the pattern of acti vation which is retrieved. So, in the case where we retrieved the properties of Lance, those properties, once they become active, can begin to activate the units for other indi viduals with those same properties. The memory unit for Lance will be in competition with these units and wi ll tend to keep their activation down, but to the extent that they do become active, they wi ll tend to acti vate their own properties and therefore fill them in. In this way, the model can fi ll in properties of indi viduals based on what it knows about other, simi lar instances. + +To ill ustrate how this might work we have simulated the case in which we do not know that Lance is a Burglar as opposed to a Bookie or a Pusher. It turns out that there are a group of indi viduals in the set who are very similar to Lance in many respects. When Lance's properties become acti vated, these other units become partially activated, and they start activating their properties. Since they all share the same "occupation," they work together to fill in that property for Lance. Of course, there is no reason why this should necessarily be the right answer, but generally speaking, the more simi lar two things are in respects that we know about, the more li kely they are to be similar in respects that we do not, and the model implements this heuristic. + +Spontaneous generalization. The model we have been descri bing has another valuable property as well -it tends to retrieve what is common to those memories which match a retrieval cue which is too general to capture any one memory. Thus, for example, we could probe the system by activating the unit corresponding to membership in the Jets. This unit wi ll partially acti vate all the instances of the Jets, thereby causing each to send activations to its properties. In this way the model can retrieve the typical values that the members of the Jets have on each dimension-even though there is no one Jet that has these typical values. In the example, 9 of 15 Jets are single, 9 of 15 are in their 20s, and 9 of 15 have only a Junior High School education; when we probe by acti vating the Jet unit, all three of these properties dominate. The Jets are evenly divided between the three occupations, so each of these units becomes partially activated. Each has a different name, so that each name unit is very weakly activated, nearly cancel ling + +each other out. + +In the example just given of spontaneous general ization , it would not be unreasonable to suppose that someone might have explicitly stored a generalization about the members of a gang. The account just given would be an alternati ve to ·' explicit storage" of the generalization. It has two advantages, though, over such an account. First, it does not require any special generalization formation mechanism. Second, it can provide us with general izations on unanticipated lines, on demand. + +Thus, if we want to know, for example, what people in their 20s with a junior high school education are l ike, we can probe the model by acti vating these two units. Since all such people are Jets and Burglars, these two units are strongly acti vated by the model in this case; two of them are divorced and two are married, so both of these units are par- + +tially activated. I + +The sort of model we are considering, then , is considerably more than a content addressable memory. In addition, it performs default assignment, and it can spontaneously retrieve a general concept of the individuals that match any specifiable probe. These properties must be explicitly implemented as complicated computational extensions of other models of knowledge retrieval , but in POP models they are + +natural by-products of the retrieval process itself. + +REPRESENTATION AND LEARNING IN PDP MODELS + +In the Jets and Sharks model , we can speak of the model 's active representation at a particular time, and associate this with the pattern of activation over the units in the system. We can also ask: What is the stored knowledge that gi ves rise to that pattern of acti vation? In considering this question , we see immediately an important difference between POP models and other models of cognitive processes. In most models, knowledge is stored as a static copy of a pattern. Retrieval amounts to finding the pattern in long-term memory and copying it into a buffer or working memory. There is no real difference between the stored representation in long-term memory and the active representation in working memory. In PDP models, though , this is not the case. In these models, the patterns themselves are not stored. Rather, what is stored is the connection strengths between units that allow these patterns to be re-created. In the Jets and Sharks model, there is an instance unit assigned to each individual, but that unit does not contain a copy of the representation of that individual . Instead, it is simply the case that the connections between it and the other units in the system are such that activation of the unit wi ll cause the pattern for the + +individual to be reinstated on the property units. + +IIn this and all other cases , there is a tendency for Ihe pattern of activation to be influ· enced by partially activated, near neigh bors, which do not quite match the probe. Thus, in this case, there is a Jet AI, who is a Mar ried Burglar. The unit for AI gets slightly + +activated, giving Married a slight edge over Divorced in the simulation . + +This difference between POP models and conventional models has enormous implications, both for processing and for learning. We have already seen some of the implications for processing. The representation of the knowledge is set up in such a way that the knowledge necessari ly influences the course of processing. Using knowledge in processing is no longer a matter of finding the relevant information in memory and bringing it to bear� it is part and parcel of the processing itself. + +For learning, the implications are equal ly profound. For if the knowledge is the strengths of the connections, learning must be a matter of finding the right connection strengths so that the right patterns of activation wi ll be produced under the right circumstances. This is an extremely important property of this class of models, for it opens up the possibil ity that an information processing mechanism could learn, as a result of tuning its connections, to capture the interdependencies between activations that it is exposed to in the + +course of processing. + +In recent years, there has been quite a lot of interest in learning in cognitive science. Computational approaches to learning fall predominantly into what might be called the " explicit rule formulation " tradition, as represented by the work of Winston (1975) , the suggestions of Chomsky, and the ACT\* model of 1. R. Anderson ( 1983) . All of this work shares the assumption that the goal of learning is to formulate explicit rules (propositions, productions, etc.) which capture powerful generalizations in a succinct way. Fairly powerful mechanisms, usually with considerable innate knowledge about a domain, and/or some starting set of primitive propositional representations, then formulate hypothetical general rules, e.g. , by comparing particular cases and for- + +mulating explicit general izations. + +The approach that we take in developing POP models is completely different. First, we do not assume that the goal of learning is the formulation of explicit rules. Rather, we assume it is the acquisition of connection strengths which allow a network of simple units to act as though it knew the rules. Second, we do not attri bute powerful computational capabi lities to the learning mechanism. Rather, we assume very simple connection strength modulation mechanisms which adjust the strength of connections between units based on information locally + +available at the connection . + +These issues wi ll be addressed at length in later sections of this book. For now, our purpose is to give a simple, ill ustrati ve example of the connection strength modulation process, and how it can produce net- + +works which exhibit some interesting behavior. + +Local vs. distributed representation. Before we turn to an explicit consideration of this issue, we raise a basic question about Copyrighted Material + +representation. Once we have achieved the insight that the knowledge is stored in the strengths of the interconnections between units, a question arises. Is there any reason to assign one unit to each pattern that we wish to learn? Another possi bi l ity-one that we explore extensi vely in this book -is the possi bi l ity that the knowledge about any indi vidual pattern is not stored in the connections of a special unit reserved for that pattern, but is distributed over the connections among a large number of processing units. On this view, the Jets and Sharks model represents a special case in which separate units are reserved for each + +instance. + +Models in which connecion information is explicitly thought of as distributed have been proposed by a number of investigators. The units in these collections may themselves correspond to conceptual primiti ves, or they may have no particular meaning as indi viduals. In either case , the focus shifts to patterns of activation over these units and to mechanisms whose explicit purpose is to learn the right connection st rengths to allow the right patterns of activation to become + +activated under the right circumstances. + +In the rest of this section, we wi ll give a simple example of a POP model in which the knowledge is distributed. We wi ll first explain how the model would work, given pre-existing connections, and we wi l l then describe how it could come to acquire the right connection strengths through a very simple learning mechanism. A number of models which have taken this distributed approach have been discussed in this book's predecessor, Hinton and 1. A. Anderson's (1 98 1) Parallel Models of Associative Memory. We wi ll consider a simple version of a common + +type of distributed model, a pattern associator. + +Pattern associators are models in which a pattern of activation over one set of units can cause a pattern of acti vation over another set of units without any intervening units to stand for either pattern as a whole. Pattern associators WOUld, for example, be capable of associating a pattern of activation on one set of units corresponding to the appearance of an object with a pattern on another set corresponding to the aroma of the object, so that, when an object is presented visually, causing its visual pattern to become active, the model produces the + +pattern corresponding to its aroma. + +How a pattern associator works. For purposes of i llust ration, we present a very simple pattern associator in Figure 12. In this model , there are four units in each of two pools. The first pool , the A units, wi ll be the pool in which patterns corresponding to the sight of various objects might be represented. The second pool, the B units, will be the pool in which the pattern corresponding to the aroma wi ll be represented. We can pr�pyh�alMaflMiHe patterns of activation on + +A Units + +From Vision + +� + +�====�===\*====\*==�-V + +-1 From V Ollaction + +c::::==============:::::==::::::::8 ':;( + +B Units + +FIGURE 12 - A simple pattern associator\_ The example assumes that patterns of activation in the A units can be produced by the visual system and patterns in the B units can be produced by the olfactory system. The synaptic connections allow the outputs of the A units to influence the activations of the B units. The synaptic weights linking the A units to the B units were selected so as to al low t he pal lern of acti vation shown on the A units to reproduce the pallern of activation shown on the B units without the need for + +any olfactory input. + +the A units are produced upon viewing a rose or a grilled steak, and alternative patterns on the B units are produced upon sniffing the same objects . Figure 13 shows two pai rs of patterns, as wel l as sets of interconnections necessary to allow the A member of each pai r to reproduce + +the B member. + +The detai ls of the behavior of the individual units vary among different versions of pattern associators . For present purposes, we'll assume that the units can take on positive or negative activation values, with 0 representing a kind of neutral intermediate value. The strengths of the interconnections between the units can be positive or negative + +real numbers. + +The effect of an A unit on a B unit is determined by multiplying the activation of the A unit times the strength of its synaptic connection with the B unit. For example, if the connection from a particular A unit to a particular B unit has a positive sign , when the A unit is Copyrighted Material + ++1 -1 -1 +1 -1 +1 -1 +1 + +-.25 +.25 +.25 -.25 - + +1 +.25 -.25 +.25 -. 25 - + +1 + +-.25 +.25 +.25 -.25 -1 -.25 +.25 -.25 +.25 +1 + ++.25 -.25 -.25 +.25 +1 -. + +25 +.25 -.25 +.25 +1 + ++.25 -.25 -.25 +25 +1 +.25 -.25 +.25 -.25 -1 + +FIGURE 13. Two simpleassociators represented as matrices. The weights in the first two matrices allow the A pattern shown above the matrix to produce the B pattern shown to the right of it. Note that the weights in the first matrix are the same as those shown in + +the diagram in Figure 12. + +excited (activation greater than 0) , it will excite the B unit. For this example, we'll simply assume that the activation of each unit is set to the sum of the excitatory and inhibitory effects operating on it. This is + +one of the simplest possible cases. + +Suppose, now, that we have created on the A units the pattern corresponding to the first visual pattern shown in Figure 13, the rose. How should we arrange the strengths of the interconnections between the A units and the B units to reproduce the pattern corresponding to the aroma of a rose? We simply need to arrange for each A unit to tend to excite each B unit which has a positive activation in the aroma pattern and to inhibit each B unit which has a negative activation in the aroma pattern. It turns out that this goal is achieved by setting the strength of the connection between a given A unit and a gi ven B unit to a value proportional to the product of the activation of the two units. In Figure 12 , the weights on the connections were chosen to allow the A pattern ill ustrated there to produce the illustrated B pattern according to this principle. The actual strengths of the connections were set to ± .25, rather than ± 1, so that the A pattern will produce the right magnitude, as well as the right sign , for the activations of the units in the B pattern . The same connections are reproduced in matri x form in Fig- + +ure l3A. + +Pattern associators like the one in Figure 12 have a number of nice properties. One is that they do not require a perfect copy of the input to produce the correct output, though its strength wi ll be weaker in this case. For example, suppose that the associator shown in Figure 12 were presented with an A pattern of (1,-1,0,1). This is the A pattern shown in the figure, with the acti vation of one of its elements set to 0. The B pattern produced in response will have the activations of all of the B units in the right direction; however, they wi ll be somewhat weaker than they would be, ha£qp;rightfffMfa�r4alttern been shown . Similar + +effects are produced if an element of the pattern is distorted -or if the model is damaged, either by removing whole units, or random sets of connections, etc. Thus, thei r pattern retrieval performance of the model degrades gracefully both under degraded input and under + +damage. + +How a pattern associator learns. So far, we have seen how we as model builders can construct the right set of weights to allow one pattern to cause another. The interesting thing, though, is that we do not need to build these interconnection strengths in by hand. Instead, the pattern associator can teach itself the right set of interconnections through experience processing the patterns in conjunction with each + +other. + +A number of different rules for adjusting connection strengths have been proposed. One of the first -and definitely the best known -is due to D. O. Hebb (1949). Hebb's actual proposal was not sufficiently quantitative to build into an explicit model . However, a number of different variants can trace their ancestry back to Hebb. Perhaps the sim- + +plest version is: + +When unit A and unit B are simultaneously excited, increase + +the strength of the connection between them. + +A natural extension of this rule to cover the positive and negative + +activation values allowed in our example is: + +Adjust the strength o f t h e connection between units A and B in proportion to the product of their simultaneous activation. + +In this formulation , if the product is positive, the change makes the connection more excitatory, and if the product is negative, the change makes the connection more inhibitory. For simplicity of reference, we will call this the Hebb rule, although it is not exactly Hebb's original + +formulation. + +With this simple learning rule, we could train a "blank copy " of the pattern associator shown in Figure 12 to produce the B pattern for rose when the A pattern is shown, simply by presenting the A and B patterns together and modulating the connection st rengths according to the Hebb rule. The size of the change made on every trial would, of course, be a parameter. We general ly assume that the changes made on each instance are rather smal l, and that connection strengths build up gradual ly. The values shown in Figure l3 A, then , would be acqui red as a result of a number of experiences with the A and B pattern pai r. + +It is very important to note that the information needed to use the Hebb rule to determine the value each connection should have is locally available at the connection. All a given connection needs to consider is the acti vation of the units on both sides of it. Thus, it would be possible toactual ly implement such a connection modulation scheme local ly, in each connection , without requiring any programmer to reach into + +each connection and set it to just the right val ue. + +It turns out that the Hebb rule as stated here has some serious limitations, and, to our knowledge, no theorists continue to use it in this simple form. More sophisticated connection modulation �chemes have been proposed by other workers; most important among these are the delta rule, discussed extensi vely in Chapters 8 and 11 ; the competi tive learning rule, discussed in Chapter 5 ; and the rules for learning in stochastic paral lel models, descri bed in Chapters 6 and 7. All of these learning rules have the property that they adjust the strengths of connections between units on the basis of information that can be assumed to be local ly avail able to the unit. Learning, then, in all of these cases, amounts to a very simpleprocess that can be implemented local ly at each connection without the need for any overall supervision. Thus , models which incorporate these learning rules train themselves to have the right interconnections in the course of processing the members of + +an ensemble of patterns. + +Learning multiple patterns in the same set of interconnections. Up to now, we have considered how we might teach our pattern associator to associate the visual pattern for one object with a pattern for the aroma of the same object . Obviously, different patterns of interconnections between the A and 8 unitsare appropriate for causing the visual pattern for a different object to gi ve rise to the pattern for its aroma. The same principles apply, however, and if we presented our pattem associator with the A and 8 patterns for steak , it would learn the ri&ht set of interconnections for that case instead (these are shown in Figure 138) . In fact, it turns out that we can actually teach the same pattern associator a number of different associations. The matrix representing the set of interconnections that would be learned if we taught the same pattern associator both the rose association and the steak association is shownin Figure 14. The reader can verify this by adding the two matrices for the indi vidual patternstogether. The reader can also verify that this set of connections wi ll allow the rose A pattern to produce the rose 8 pattern , and the steak A pattern to produce the steak 8 pattern: when either input pattern is presented , the correct corresponding output + +The examples used here have the property that the two different visual patterns are ompl�t lyuncorrelated with each other. This being Copyrighted Material + ++ + + + + + + + + ++ + ++ + ++ + ++ + + ++ + ++ + ++ + + +++ -- + +-- ++ + +-- ++ + +++ -- + +FIGURE 14. The weights in the third matrix allow either A pattern shown in Figure \3 to recreate the corresponding B pattern . Each weight in this case is equal to the sum of + +the weight for the A pattern and the weight for the B pattern , as illustrated. + +the case , the rose pattern produces no effect when the interconnections for the steak have been establ ished, and the steak pattern produces no effect when the interconnections for the rose association are in effect. For this reason , it is possible to add together the pattern of interconnections for the rose association and the pattern for the steak association, and still be able to associate the sight of the steak with the smell of a steak and the sight of a rose with the smell of a rose. The two sets + +of interconnections do not interact at al l. + +One of the limitations of the Hebbian learning rule is that it can learn the connection strengths appropriate to an entire ensemble of patterns only when all the patterns are completely uncorrelated. This rest riction does not, however, apply to pattern associators which use + +more sophisticated learning schemes. + +Attractive properties of pattern associator models. Pattern associator models have the property that uncorrelated patterns do not interact with each other, but more similar ones do. Thus, to the extent that a new pattern of acti vation on the A units is similar to one of the old ones, it wi ll tend to have simi lar effects. Furthermore, if we assume that learning the in terconnections occurs in small increments, similar patterns wi ll essentially reinforce the strengths of the links they share in common with other patterns. Thus, if we present the same pai r of patterns over and over, but each time we add a little random noise to each element of each member of the pai r, the system wi ll automatical ly learn to associate the central tendency of the two patterns and wi ll learn to ignore the noise. What wi ll be stored will be an average of the similar patterns with the slight variations removed . On the other hand, when we present the system with completely uncorrelated patterns, they will not interact with each other in this way. Thus , the same pool of units can extract the central tendency of each of a number of pairs of unrelated patterns. This aspect of distributed models is exploited extensi vely + +Extracting the structure of an ensemble of patterns. The fact that similar patterns tend to produce similar effects al lows di stributed models to exhibit a kind of spontaneous general ization , extending behavior appropriate for one pattern to other simi lar patterns. This property is shared by other POP models, such as the word perception model and the Jets and Sharks model described above; the main difference here is in the existence of simple, local , learning mechanisms that can allow the acquisition of the connection strengths needed to produce these general izations through experience with members of the ensemble of patterns . Distributed models have another interesting property as well: If there are regularities in the correspondences between pai rs of patterns , the model will natural ly extract these regularities. This property al lows distri buted models to acquire patterns of interconnections that lead them to behave in ways we ordinari ly take as + +evidence for the use of linguistic rules. + +A detailed example of such a model is described in Chapter 18. Here, we describe the model very briefly. The model is a mechanism that learns how to construct the past tenses of words from thei r root forms through repeated presentations of examples of root forms pai red with the corresponding past-tense form. The model consists of two pools of units. In one pool , patterns of activation representing the phonological structure of the root form of the verb can be represented, and, in the other , patterns representing the phonological structure of the past tense can be represented. The goal of the model is simply to learn the right connection strengths between the root units and the past-tense units, so that whenever the root form of a verb is presented the model wi ll construct the corresponding past· tense form. The model is trained by presenting the root form of the verb as a pattern of activation over the root units, and then using a simple, local , learning rule to adjust the connection strengths so that this root form wi ll tend to produce the correct pattern of activation over the past-tense units. The model is tested by simply presenting the root form as a pattern of activation over the root units and examining the pattern of activation + +produced over the past-tense units. + +The model is trained initially with a small number of verbs children learn early in the acquisition process . At this point in learning, it can only produce appropriate outputs for inputs that it has explicitly been shown. But as it learns more and more verbs, it exhibits two interest· ing behaviors. Fi rst, it produces the standard ed past tense when tested with pseudo-verbs or verbs it has never seen. Second, it "overregularizes " the past tense of irregular words it previously completed correctly. Often, the model wi ll blend the irregular past tense of the word with the regular ed ending, and produce errors like CAMED as the past of + +COME. These phenomena mi rror those observed in the early phases of + +acquisition of control over past tenses in young chi ldren. + +The generativity of the chi ld's responses -the creation of regular past tenses of new verbs and the overregularization of the irregular verbs-has been taken as strong evidence that the child has induced the rule which states that the regular correspondence for the past tense in Engl ish is to add a final ed (Berko, 1958) . On the evidence of its performance, then, the model can be said to have acqui red the rule. However, no special rule-induction mechanism is used, and no special language-acquisition device is required. The model learns to behave in accordance with the rule, not by explicitly noting that most words take ed in the past tense in English and storing this rule away explicitly, but simply by building up a set of connections in a pattern associator through a long series of simple learning experiences . The same mechanisms of paral lel distributed processing and connection modification which are used in a number of domains serve, in this case, to produce implicit knowledge tantamount to a linguistic rule. The model also provides a fai rly detailed account of a number of the specific aspects of the error patterns children make in learning the rule. In this sense, it provides a richer and more detai led description of the acquisition process than any that falls out natural ly from the assumption that the child is building up a repertoi re of expl icit but inaccessible rules. There is a lot more to be said about distributed models of learning, about thei r strengths and thei r weaknesses , than we have space for in this prel iminary consideration. For now we hope mainly to have suggested that they provide dramatically different accounts of learning and acquisition than are offered by traditional models of these processes . We saw in earl ier sections of this chapter that performance in accordance with rules can emerge from the interactions of simple, interconnected units. Now we can see how the aquisition of performance that conforms to linguistic rules can emerge from a simple, local , connec- + +tion strength modulation process. + +We have seen what the properties of PDP models are in informal terms , and we have seen how these properties operate to make the models do many of the kinds of things that they do. The business of the next chapter is to lay out these properties more formal ly, and to introduce some formal tools for their descri ption and analysi s. Before we turn to this, however, we wish to describe some of the major + +sources of inspi ration for the PDP approach . + +ORIGINS OF PARALLEL DISTRIBUTED PROCESSING + +The ideas behi nd the POP approach have a history that st retches back indefinitely. In this section, we mention briefly some of the people who have thought in these terms, particularly those whose work has had an impact on our own thinking. This section should not been seen as an authoritative review of the history, but only as a description of + +our own sources of inspiration. + +Some of the earl iest roots of the POP approach can be found in the work of the unique neurologi sts, Jackson 0869/ 1958) and Luria (1 966) . Jackson was a forceful and persuasive critic of the si mplistic localizationist doctrines of late nineteenth century neurology, and he argued convincingly for distributed, multilevel conceptions of processing systems . Luria, the Russian psychologist and neurologi st, put forward the notion of the dynamic fUnctional system. On this view, every behavioral or cogniti ve process resulted from the coordination of a large number of different components, each roughly local ized in different regions of the brain, but all working together in dynamic interaction. Neither Hughlings-Jackson nor Luria is noted for the clarity of his views , but we have seen in thei r ideas a rough characterization of the + +kind of parallel distributed processing system we envision. + +Two other contributors to the deep background of POP were Hebb (1949) and Lashley (1 950) . We al ready have noted Hebb' s contribution of the Hebb rule of synaptic modification; he also introduced the concept of cell assemblies -a concrete example of a limited form of di stributed processing-and discussed the idea of reverberation of activation within neural networks. Hebb's ideas were cast more in the form of speculations about neural functioning than in the form of concrete processing models, but his thinking captures some of the flavor of parallel distributed processing mechanisms. Lashley 's contribution was to insist upon the idea of distributed representation. Lashley may have been too radical and too vague, and his doct rine of equipotential ity of broad regions of cortex clearly overstated the case. Yet many of his insights into the difficulties of storing the "engram" locally in the brain are telling, and he seemed to capture quite precisely the essence of distributed representation in insisting that "there are no special cells + +reserved for special memories" (Lashley, 1950, p. 500) . + +In the 1950s, there were two major figures whose ideas have contributed to the development of our approach. One was Rosenblatt 0959, 1962) and the other was Selfridge (1955) . In his Principles of Neurodynamics (I 962) , Rosenblatt articulated clearly the promise of a neurally inspi red approach to computation, and he developed the perceptron convergence procedure, aeojJyW�i�I¥��mge over the Hebb rule for + +changing synaptic connections. RosenblaU's work was very controversial at the time, and the specific models he proposed were not up to all the hopes he had for them. But his vision of the human information processing system as a dynamic, interactive, self-organizing system lies at the core of the POP approach. Selfridge's contri bution was his insistence on the importance of interactive processing, and the development of Pandemonium, an explicitly computational example of a dynamic, interactive mechanism appl ied to computational problems in + +perception. + +In the late 60s and early 70s, serial processing and the von Neumann computer dominated both psychology and artificial intel ligence, but there were a number of researchers who proposed neural mechanisms which capture much of the flavor of POP models. Among these figures, the most influential in our work have been J. A. Anderson, Grossberg, and Longuet-Higgins. Grossberg 's mathematical analysis of the properties of neural networks led him to many insights we have only come to appreciate through extensi ve experience with computer simulation, and he deserves credit for seeing the relevance of neural ly inspired mechanisms in many areas of perception and memory well before the field was ready for these kinds of ideas (Grossberg, 1978) . Grossberg (1 976) was also one of the first to analyze some of the properties of the competitive learning mechanism explored in Chapter 5. Anderson's work differs from Grossberg's in insisting upon distributed representation , and in showing the relevance of neural ly inspired models for theories of concept learning (Anderson, 1973, 1977) ; the work in Chapters 17 and 25 on distributed memory and amnesia owes a great deal to Anderson's inspiration. Anderson's work also played a crucial role in the formulation of the cascade model (McClel land, 1979) , a step away from serial processing down the road to POP. Longuet-Higgins and his group at Edinburgh were also pursuing distri buted memory models during the same period, and Oavid Wi llshaw, a member of the Edinburgh group, provided some very elegant mathematical analyses of the properties of various distri buted representation schemes (Wi l lshaw, 1981). His insights provide one of the sources of the idea of coarse coding described at length in Chapter 3. Many of the contri butions of Anderson, Wi llshaw, and others distributed modelers may be found in Hinton and Anderson (981 ) . Others who have made important contributions to learning in POP models incl ude Amari ( 1 977a) , Bienenstock, Cooper, and Munro (I 982) , Fukushima (I 97 5) , Kohonen ( 1 977 , 1984) , and von der + +Malsburg (I 973) . + +Toward the middle of the 1970s, the idea of paral lel processing began to have something of a renaissance in computational circles. We have already mentioned the Marr and Poggio (976) model of stereoscopic Copyrighted Material + +depth perception. Another model from this period , the HEARSA Y model of speech understanding, played a prominent role in the development of our thinking. Unfortunately , HEARSAY's computational architecture was too demandi ng for the avai lable computational resources , and so the model was not a computational success . But its basically parallel , interactive character inspi red the interactive model of reading (Rumelhart, 1977) , and the interactive activation model of word recogni tion (McClel land & Rumelhart, 1981; Rumelhart & + +McClelland, 1982) . + +The ideas represented in the interactive activation model had other precursors as wel l . Morton's logogen model (Morton , 1 969) was one of the first models to capture concretely the pri nciple of interaction of different sources of information, and Marslen-Wi lson (e.g., Marslen-Wi lson & Welsh, 1978) provided important empi rical demonstrations of interaction between different levels of language processing. Levin's (1 976) Proteus model demonst rated the virtues of activationcompetition mechanisms, and Glushko (1 979) hel ped us see how conspi racies of partial activations could account for certain aspects of + +apparently rule-guided behavior. + +Our work also owes a great deal to a number of col leagues who have been working on related ideas in recent years . Many of these col leagues appear as authors or coauthors of chapters in this book . But there are others as well. Several of these people have been very influential in the development of the ideas in this book. Feldman and Ballard (1 982) laid out many of the computational pri nciples of the POP approach (under the name of connectionism), and stressed the biological implausibility of most of the prevai l ing computational models in artificial intelligence. Hofstadter (1979, 1985) deserves credit for st ressing the exi stence of a subcognitive-what we call microstructural -level , and pointing out how important it can be to del ve into the microstructure to gain insight . A sand dune, he has said, is not a grain of sand. Others have contributed crucial technical insights. Sutton and Barto (981) provided an insightful analysis of the connection modification scheme we call the delta rule and i l l ust rated the power of the rule to account for some of the subtler properties of classical conditioning. And Hopfield's (982) contri bution of the idea that network models can be seen as seeking minima in energy landscapes played a prominent role in the development of the Boltzmann machine (Chapter 7) , and in the crystallization of the ideas presented in + +Chapters 7 and 14 on harmony theory and schemata. + +The power of paral lel distributed processing is becoming more and more apparent, and many others have recently joined in the exploration of the capabi lities of these mechanisms. We hope this book represents Copyrighted Material + +the nature of the enterprise we are al l involved in, and that it does jus- + +tice to the potential of the PDP approach. + +ACKNOWLEDGMENTS + +This research was supported by Contract N00014-79-C-03 23, NR 667-437 with the Personnel and Training Research Programs of the Office of Naval Research, by grants from the System Development Foundation, and By a NIMH Career Development Award (MH00385 ) + +to the first author. + +CHAPTER 2 + +A General Framework for + +Parallel Distributed Processing + +D. E. RUMELHART, G. E. HINTON, and 1. L. McCLELLAND + +In Chapter 1 and throughout this book, we describe a large number of models, each different in detail-each a variation on the parallel distributed processing (PDP) idea. These various models, and indeed many in the literature, clearly have many features in common, but they are just as clearly distinct models. How can we characterize the general model of which these specific models are instances? In this chapter we propose a framework sufficiently general so that all of the various models discussed in the book and many models in the literature are special cases. We will proceed by first sketching the general framework and then by showing properties of certain specific realizations of the + +general model. I + +The General Framework + +It is useful to begin with an analysis of the various components of our models and then describe the various specific assumptions we can + +I We are, of course, not the first to attempt a general characterization of this general class of models. Kohonen 0977, 1984), Amari (l977a), and Feldman and Ballard (1982) + +are papers with similarly general aims. + +make about these components. There are eight major aspects of a + +parallel distributed processing model: + +• A set of processing units • A state of activation + +• An output junction for each unit • A pattern of connectivity among units + +• A propagation rule for propagating patterns of activities through + +the network of connectivities + +• An activation rule for combining the inputs impinging on a unit with the current state of that unit to produce a new level of + +activation for the unit. + +• A learning rule whereby patterns of connectivity are modified by + +experience + +• An environment within which the system must operate + +Figure 1 illustrates the basic aspects of these systems. There is a set of processing units generally indicated by circles in our diagrams; at each point in time, each unit Uj has an activation value, denoted in the diagram as aj (t); this activation value is passed through a function fj to produce an output value OJ (t). This output value can be seen as passing through a set of unidirectional connections (indicated by lines or arrows in our diagrams) to other units in the system. There is associated with each connection a real number, usually called the weight or strength of the connection designated wi) which determines the amount of effect that the first unit has on the second. All of the inputs must then be combined by some operator (usually addition) -and the combined inputs to a unit, along with its current activation value, determine, via a function F, its new activation value. The figure shows illustrative examples of the function f and F. Finally, these systems are viewed as being plastic in the sense that the pattern of interconnections is not fixed for all time; rather, the weights can undergo modification as a function of experience. In this way the system can evolve. What a unit represents can change with experience, and the system can come to perform in substantially different ways. In the fol lowing sections we develop an explicit notation for each of these components and describe some of the alternate assumptions that have been made concerning + +each such component. + +A set of processing units. Any parallel activation model begins with a set of processing units. Specifying the set of processing units and what they represent is typically the first stage of specifying a PDP model. In some models these units may represent particular conceptual objects such as features, letters, words, or concepts; in others they are Copyrighted Material + +Threshold OU'pu' Function + +o + +·lZJ ·m 0 + +nor, = �"'JOJ(I) Sigmoid ActiValion Function + +FIGURE 1. The basic components of a parallel distributed processing system. + +simply abstract elements over which meaningful patterns can be defined. When we speak of a distributed representation, we mean one in which the units represent small, feature-like entities. In this case it is the pattern as a whole that is the meaningful level of analysis. This should be contrasted to a one-unit-one-concept representational system in which single units represent entire concepts or other large meaning- + +ful entities. + +We let N be the number of units. We can order the units arbitrarily and designate the ith unit Ui' All of the processing of a PDP model is carried out by these units. There is no executive or other overseer. There are only relatively simple units, each doing it own relatively simple job. A unit's job is simply to receive input from its neighbors and, as a function of the inputs it receives, to compute an output value which it sends to its neighbors. The system is inherently parallel in that + +Within any system we are modeling, it is useful to characterize three types of units: input, output, and hidden. Input units receive inputs from sources external to the system under study. These inputs may be either sensory input or inputs from other parts of the processing system in which the model is embedded. The output units send signals out of the system. They may either directly affect motoric systems or simply influence other systems external to the ones we are modeling. The hidden units are those whose only inputs and outputs are within the system we are modeling. They are not "visible" to outside systems. + +The state of activation. In addition, to the set of units, we need a representation of the state of the system at time t. This is primarily specified by a vector of N real numbers, a (t), representing the pattern of activation over the set of processing units. Each element of the vector stands for the activation of one of the units at time t. The activation of unit Ui at time t is designated 0i (t ). It is the pattern of activation over the set of units that captures what the system is representing at any time. It is useful to see processing in the system as the evolu- + +tion, through time, of a pattern of activity over the set of units. + +Different models make different assumptions about the activation values a unit is allowed to take on. Activation values may be continuous or discrete. If they are continuous, they may be unbounded or bounded. If they are discrete, they may take binary values or any of a small set of values. Thus in some models, units are continuous and may take on any real number as an activation value. In other cases, they may take on any real value between some minimum and maximum such as, for example, the interval [0,11. When activation values are restricted to discrete values they most often are binary. Sometimes they are restricted to the values 0 and I where I is usually taken to mean that the unit is active and 0 is taken to mean that it is inactive. In other models, activation values are restricted to the values {- I,+ I} (often denoted simply (-,+}). Other times nonbinary discrete values are involved. Thus, for example, they may be restricted to the set {- I,O,+I}, or to a small finite set of values such as {I,2,3,4,5,6,7,8,9}. As we shall see, each of these assumptions leads to a model with slightly different characteristics. It is part of the program of research represented in this book to determine the implications of these various + +assumptions. + +Output of the units. Units interact. They do so by transmitting signals to their neighbors. The strength of their signals, and therefore the degree to which they affect their neighbors, is determined by their degree of activation. Associated with each unit, Ui, there is an output function, Ii (0, (1», which maps the current state of activation 0i (I) to Copyrighted Material + +CD � Q. CD ::::r- c5' � � + +Network Representation + +Input + +u6 Us u4 u3 u2 U, + +Output + +u, Us + +Matrix Representation + +U, Uz u3 u4 U + +s Us u7 uB + ++3 + +-4 + +0 0 +1 + ++4 + +0 0 + ++4 + +0 0 +6 + +-1 + +0 -2 + +0 +4 + +§: + +FIGURE + +2. + +The connectivity of a network represented by a network + +drawing + +and in a matrix. The figure shows an + +eight-unit + +network with + +units umbered + +from 1 to 8. Units 1 to 4 + +are input units. They receive + +inputs + +from + +he outside world and feedback + +from the output units- + +units 5 through + +8. + +The connections among the units are indicated + +by the ope + +n and + +filled + +disks. The size of + +the + +disk indicates the strength of + +connection. Thus, + +the + +large black disk on the line connecting unit + +1 to unit 8 + +indicates a strong + +inhibitory connection + +from 1 o 8. Simirythe + +lar + +ge open disk on the + +output line + +from uit 8 + +to unit 2 idicas + +that unit + +8 strongly + +excites unit 2. The + +same connections + +are shown in the + +matrix representation on + +the left. + +The +6 in he + +column + +for Us + +and the r + +w for u2 indices that unit 8 + +strongly ex + +cits unit 2. It + +should be + +noted that + +whenever there is a disk + +on a lin + +e connecting t + +he output of + +one unit + +to the input of another + +in the netwr + +k diagram there is a + +corresponding nonzero + +entry + +in the matrix. If + +the + +disk is filled, the + +entry in + +he matrix is + +negative. If the + +disk is + +open, the + +entry + +is positive. + +The + +arger l the + +disk the greater the magnitude of + +he entry + +in the matrix. + +It + +might also be noted + +hat the conectins in the + +network have been + +laid out to correspond to the + +entries of + +the matrix. The black disk in + +he upper + +left corner of the + +network corresponds + +to the -6 in + +the upper + +left corner of the + +matrix. + +Each + +disk in the network is in the corresponding position of its location in the matrix. The network would not + +have + +to be drawn + +in this way, + +of course, and the matrix would s + +ill + +capture all + +of + +the connectivity + +information in + +the + +network. In general, + +because + +network drawings are + +difficult + +to work with we wi + +ll + +often simply + +use the matri + +x representation + +(0 + +specify (he + +pattern of c + +nnectiviy + +inhibitory connection and an excitatory connection. When the models assume simple addition of inhibition and excitation they do not constitute different types of connections in our present sense. They only constitute distinct types when they combine through some more complex + +rules. + +The pattern of connectivity is very important. It is this pattern which determines what each unit represents. As we shall see below, many of the issues concerning whether top-down or bottom-up processing systems are correct descriptions or whether a system is hierarchical and if so how many levels it has, etc., are all issues of the nature of the connectivity matrix. One important issue that may determine both how much information can be stored and how much serial processing the network must perform is the fan-in and fan-out of a unit. The fan-in is the number of elements that either excite or inhibit a given unit. The fanout of a unit is the number of units affected directly by a unit. Note, in some cases we need more general patterns of connectivity. Specifying such a pattern in the general case is complex and will be addressed + +in a later section of this chapter. + +The rule of propagation. We also need a rule which takes the output vector, 0 (t), representing the output values of the units and combines it with the connectivity matrices to produce a net input for each type of input into the unit. We let netij be the net input of type i to unit u). Whenever only one type of connectivity is involved we suppress the first subscript and use net) to mean the net input into unit u). In vector notation we can write net; (I) to represent the net input vector for inputs of type i. The propagation rule is generally straightforward. For example, if we have two types of connections, inhibitory and excitatory, the net excitatory input is usually the weighted sum of the excitatory inputs to the unit. This is given by the vector product nete = Weo (I). Similarly, the net inhibitory effect can be written as net j=W jO(t). When more complex patterns of connectivity are involved, more complex rules of propagation are required. We treat this in the final section + +of the chapter. + +Activation rule. We also need a rule whereby the net inputs of each type impinging on a particular unit are combined with one another and with the current state of the unit to produce a new state of activation. We need a function, F, which takes a (t) and the vectors net) for each different type of connection and produces a new state of activation. In the simplest cases, when F is the identity function and when all connections are of the same type, we can write a (t+ 1) = Wo (t } = net (t}. Sometimes F is a threshold function so that the net input must exceed + +Virtually all learning rules for models of this type can be considered a variant of the Hebbian learning rule suggested by Hebb in his classic book Organization of Behavior (949) . Hebb's basic idea is this: If a unit, U;, receives a input from another unit, Uj; then, if both are highly active, the weight, wij, from Uj to U; should be strengthened. This idea has been extended and modified so that it can be more generally stated + +as + +aW;j = g (a; (t) ,1; (I» h(Oj (t), w;), + +where t; (t) is a kind of leaching input to U;. Simply stated, this equation says that the change in the connection from Uj to U; is given by the product of a function, gO, of the activation of U; and its teaching input I; and another function, hO, of the output value of Uj and the connection strength wij. In the simplest versions of Hebbian learning there is no teacher and the functions g and h are simply proportional to their + +first arguments. Thus we have + +where TJ is the constant of proportionality representing the learning rate. Another common variation is a rule in which h (OJ (t), wij) = OJ (I) and g(a; (I) ,1; (I» = TJ (I; (t )-a; (I». This is often called the Widrow-Hoff rule (Sutton & Barto, 1981). However, we call it the delta rule because the amount of learning is proportional to the difference (or delta) between the actual activation achieved and the target activation provided by a teacher. (The delta rule is discussed at length in + +Chapters 8 and 11.) In this case we have + +aWij = TJ (tj (I)-Oj (t ))OJ (t). + +This is a generalization of the perceptron learning rule for which the famous perception convergence theorem has been proved. Still another + +variation has + +aWij = TJOi (t) (OJ (t )- Wi) ). + +This is a rule employed by Grossberg (1976) and a simple variant of which has been employed in Chapter 5. There are many variations on this generalized rule, and we will describe some of them in more detail + +when we discuss various specific models below. + +Representation of the environment. It is crucial in the development of any model to have a clear model of the environment in which this model is to exist. In PDP models, we represent the environment as a time-varying stochastic function over the space of input patterns. That Copyrighted Material + +is, we imagine that at any point in time, there is some probability that any of the possible set of input patterns is impinging on the input units. This probability function may in general depend on the history of inputs to the system as well as outputs of the system. In practice, most PDP models involve a much simpler characterization of the environment. Typically, the environment is characterized by a stable probability distribution over the set of possible input patterns independent of past inputs and past responses of the system. In this case, we can imagine listing the set of possible inputs to the system and numbering them from 1 to M. The environment is then characterized by a set of probabilities, Pi for i = 1, ... , M. Since each input pattern can be considered a vector, it is sometimes useful to characterize those patterns with nonzero probabi lities as constituting orthogonal or linearly independent sets of vectors. 2 Certain PDP models are restricted in the kinds of patterns they are able to learn: some being able to learn to respond correctly only if the input vectors form an orthogonal set; others if they form a linearly independent set of vectors; and still others are able to + +learn to respond to essentially arbitrary patterns of inputs. + +CLASSES OF PDP MODELS + +There are many paradigms and classes of PDP models that have been developed. In this section we describe some general classes of assumptions and paradigms. In the following section we describe some specific PDP models and show their relationships to the general framework out- + +lined here. + +Paradigms of Learning + +Although most learning rules have roughly the form indicated above, we can categorize the learning situation into two distinct sorts. These + +are: + +• Associative learning, in which we learn to produce a partIcular pattern of activation on one set of units whenever another particular pattern occurs on another set of units. In general , such a learning scheme must allow an arbitrary pattern on one set of + +units to produce another arbitrary pattern on another set of + +units. + +• Regularity discovery, in which units learn to respond to "interesting" patterns in their input. In general, such a scheme should be able to form the basis for the development of feature detectors and therefore the basis for knowledge representation in a + +PDP system. + +In certain cases these two modes of learning blend into one another, but it is valuable to see the different goals of the two kinds of learning. Associative learning is employed whenever we are concerned with storing patterns so that they can be re-evoked in the future. These rules are primarily concerned with storing the relationships among subpatterns. Regularity detectors are concerned with the meaning of a single units response. These kinds of rules are used when feature discovery is + +the essential task at hand. + +The associative learning case generally can be broken down into two subcases-pattern association and auto-association. A pattern association paradigm is one in which the goal is to build up an association between patterns defined over one subset of the units and other patterns defined over a second subset of units. The goal is to find a set of connections so that whenever a particular pattern reappears on the first set of units, the associated pattern will appear on the second set. In this case, there is usually a teaching input to the second set of units during training indicating the desired pattern association. An auto-association paradigm is one in which an input pattern is associated with itself. The goal here is pattern completion. Whenever a portion of the input pattern is presented , the remainder of the pattern is to be filled in or completed. This is similar to simple pattern association, except that the input pattern plays both the role of the teaching input and of the pattern to be associated. It can be seen that simple pattern association is a special case of auto-association. Figure 3 illustrates the two kinds of learning paradigms. Figure 3A shows the basic structure of the pattern association situation. There are two distinct groups of units-a set of input units and a set of output units. Each input unit connects with each output unit and each output unit receives an input from each input unit. During training, patterns are presented to both the input and output units. The weights connecting the input to the output units are modified during this period. During a test, patterns are presented to the input units and the response on the output units is measured. Figure 3B shows the connectivity matrix for the pattern associator. The only modifiable connections are from the input units to the output units. All other connectionsate fixed tal, zero .. Fl igure 3C shows the hasic (;opyngTi au Matena + +A B Matrix at Cannectivities OJ + +> Inpul UnllS + +OUlpul Unll. + +SeIDl Inpul Unils Sel 01 Oulpul Unils + +c 0 + +Inpul & Oulput Units + +Inputs + +Inpul Unlls Oulpul Unll. + +Modlflable Welghls + +> Connacllvlly Malrl. lor Pall.rn Assoclalor + +> > All weights .r. Modifi abl. + +Connecllvlly IIIllrl. lor AulO Auoetslor + +FIGURE 3. A: The basic structure of the pattern association situation. There are two distinct groups of units-a set of input units and a set of output units. Each input unit connects with each output unit and each output unit receives an input from each input unit. During training, patterns are presented to both the input and output units. The weights connecting the input to the output units are modified during this period. During a test, patterns are presented to the input units and the response on the output units is measured. (After Anderson, 1977.) B: The connectivity matrix for the pattern associ ator. The only modifiable connections are from the input units to the output units. All other connections are fixed at zero. C: The basic structure of the auto-association situation. All units are both input and output units. The figure shows a group of 6 units feeding back on itself through modifiable connections. Note that each unit feeds back on itself as well as on each of its neighbors. (After Anderson, Silverstein , Ritz , & Jones, 1977.) D: The connectivity matrix for the auto-associator. All units connect to all other + +units with modifiable weights. + +structure of the auto-association situation. All units are both input and output units. The figure shows a group of 6 units feeding back on itself through modifiable connections. Note that each unit feeds back on itself as well as on each of its neighbors . Figure 3D shows the connectivity matrix for the auto-associator. All units connect to all other units with modifiable weights. In the case of auto-association, there is + +potentially a modifiable connection from every unit to every other unit. In the case of pattern association, however, the units are broken into two subpatterns, one representing the input pattern and another representing the teaching input. The only modifiable connections are those from the input units to the output units receiving the teaching input. In other cases of associative learning the teaching input may be more or less indirect. The problem of dealing with indirect feedback is difficult, but central to the development of more sophisticated models of learning. Barto and Sutton (I 981) have begun a nice analysis of + +such learning situations. + +In the case of regularity detectors, a teaching input is not expl icitly provided; instead, the teaching function is determined by the unit itself. The form of the internal teaching function and the nature of its input patterns determine what features the unit will learn to respond to. This is sometimes called unsupervised learning. Each different kind of unsupervi sed learning procedure has its own evaluation function . The particular evaluation procedures are mentioned when we treat these models. The three unsupervi sed learning models discussed in this book + +are addressed in Chapters 5, 6, and 7. + +Hierarchical Organizations of PDP Networks + +It has become commonplace in cognitive science to describe such processes as top-down , bottom-up, and interactive to consist of many stages of processing, etc. It is useful to see how these concepts can be represented in terms of the patterns of connectivity in the PDP framework. It is also useful to get some feel ing for the processing conse- + +quences of these various assumptions. + +Bottom-Up Processing + +The fundamental characteristic of a bottom-up system is that units at level i may not affect the activity of units at levels lower than i. To see how this maps onto the current formulation, it is useful to partition the coal itions of units into a set of discrete categories corresponding to the levels their inputs come from. There are assumed to be no coal itions with inputs from more than one level . Assume that there are L; units at level i in the system. We then order the units such that those + +in level L 1 are numbered u 1, ••. , UL + +' those in level L 2 are numbered + +bottom-up system is equivalent to the constraint that the connectivity matrix, W, has zero entries for wi} in which Uj is the member of a level no higher than Uj. This amounts to the requirement that the upper right-hand region of W contains zero entries. Table 1 shows this constraint graphical ly. The table shows an example of a three-level system with four units at each level. 3 This leads to a 12 x 12 connectivity matrix and an a vector of length 12. The matrix can be divided up into 9 regions. The upper-left region represents interactions among Level 1 units. The entries in the left-middle region of the matrix represents the effects of Level 1 units on Level 2 units. The lower-left region represents the effects of Level 1 units on Level 3 units. Often bottom-up models do not allow units at level i effect units at level i+ 2. Thus, in the diagram we have left that region empty representing no effect of Level 1 on Level 3. It is typical in a bottom-up system to assume as well that the lowest level units (Level 1) are input units and that the highest level units (Level 3) are output units. That is, the lowest level of the system is the only one to receive direct inputs from outside of this module and only the highest level units affect other + +units outside of this module. + +TABLE I + +Levell Level 2 Level 3 Input Units HiddenUnitsOutput Units ul u2 u3 u4 uS u6 u7 u8 u9 ulO ull u12 + +ul within + +Levell u2 Level I Units u3 effects u4 + +uS Levell within + +Level 2 u6 affecting Level 2 Units u7 Level 2 effects + +u8 + +u9 Level 2 within + +Level 3 ulO affecting Level 3 Units ull Level 3 effects + +ul2 + +Top-Down Processing + +The generalization to a hierarchical top-down system should be clear enough. Let us order the units into levels just as before. A top-down model then requires that the lower-left regions of the weight matrix be empty-that is, no lower level unit affects a higher level unit. Table 2 illustrates a simple example of a top-down processing system. Note, in this case, we have to assume a top-down input or "message" that is propagated down the system from higher to lower levels as well as any + +data input that might be coming directly into Levell units. + +Interactive Models + +Interactive models are simply models in which there can be both top-down and bottom-up connections. Again the generalization is straightforward. In the general interactive model, any of the cells of the weight matrix could be nonzero. The more restricted models in which information flows both ways, but in which information only flows between adjacent levels, assume only that the regions of the matrix more than one region away from the main diagonal are zero. Table 3 illustrates a simple three-level interactive model with both topdown and bottom-up input. Most of the models that actually have been + +suggested count as interactive models in this sense. + +TABLE 2 + +Levell Level 2 Level 3 Input Units Hidden Units Output Units ul u2 u3 u4 u5 u6 u7 u8 u9 ulO u11 ul2 + +ul within Level 2 + +Level I u2 Level I affecting Units u3 effects Levell + +u4 + +u5 within Level 3 + +Level 2 u6 Level 2 affecting Units u7 effects Level 2 + +u8 + +u9 within + +Level 3ulO Level 3 Units u11 effects + +ul2 G6-{JYfighied MtJf� jar + +ul + +Level I u2 Units u3 + +> u4 uS + +Level 2 u6 Units u7 + +> uS u9 + +Level 3 ulO Units ull + +ul2 + +TABLE 3 + +Level I Level 2 Level 3 Input Units Hidden Units Output Units ul u2 u3 u4 uS u6 u7 uS u9 ulO ull u12 + +within Level 2 Level I affecting effects Level I + +Levell within Level 3 affecting Level 2 affecting Level 2 effects Level 2 + +> Level 2 within affecting Level 3 Level 3 effects + +It is sometimes supposed that a "single level" system with no hierarchical structure in which any unit can communicate with any other unit is somehow less powerful than these multi level hierarchical systems. The present analysis shows that , on the contrary, the existence of levels amounts to a restriction, in general , of free communication among all units. Such nonhierarchical systems actually form a superset of the kinds of layered systems discussed above. There is, however, something Ito the view that having multi ple levels can increase the power of certain systems. In particular, a "one-step" system consisting of only input and output units and no communication between them in which there is no opportunity for feedback or for hidden units is less powerful than systems with hidden units and with feedback. Since, in general , hierarchical systems involve many hidden units, some intralevel communication, and some feedback among levels, they are more powerful than systems not involving such hidden units. However, a system with an equal number of hidden units, but one not characterizable as hierarchical by the communication patterns is, in general , of more potential computational power. We address the issue of hidden units and "single-step" versus "multiple-step" systems in our discussion of + +speci fic models below. + +Synchronous Versus Asynchronous Update + +Even given all of the components of the PDP models we have described so far, there is still another important issue to be resolved in the development of specific models; that is the timing of the application of the activation rule. In some models, there is a kind of central timing pulse and after each such clock tick a new value is determined simultaneously for all units. This is a synchronous update procedure. It is usually viewed as a discrete, difference approximation to an underlying continuous, differential equation in which al l units are continuously updated. In some models, however, units are updated asynchronously and at random. The usual assumption is that at each point in time each unit has a fixed probability of evaluating and applying its activation rule and updating its activation value. This later method has certain theoretical advantages and was developed by Hopfield (1982) and has been employed in Chapters 6, 7, and 14. The major advantage is that since the units are independently being updated, if we look at a short enough time interval, only one unit is updating at a time. Among other things, this system can help the stability of the network by keeping it out of oscil lations that are more readily entered into with + +synchronous update procedures . + +SPECIFIC VERSIONS OF THE GENERAL PARALLEL + +ACTIV ATION MODEL + +In the following sections we will show how specification of the particular functions involved produces various kinds of these models. There have been many authors who have contributed to the field and whose work might as well have been discussed. We discuss only a representa- + +tive sample of this work. + +Simple Linear Models + +Perhaps the simplest model of this class is the simple linear model. In the simple linear model, activation values are real numbers without restriction. They can be either positive or negative and are not bounded. The output function, f (a/), in the linear model is just equal to the activation level ai' Typically, linear models consist of two sets of + +below, there is no need for hidden units since all computation possible with a multiple-step linear system can be done with a single-step linear system.) In general , any unit in the input layer may connect to any unit in the output layer. All connections in a linear model are of the same type. Thus, only a single connectivity matrix is required. The matrix consists of a set of positive, negative, and zero values, for excitatory values, inhibitory values, and zero connections, respectively. The new value of activation of each unit is simply given by the weighted sums of the inputs. For the simple linear model with connectivity matrix W we + +have + +a(t+1) = Wa(t). + +In general , it can be shown that a linear model such as this has a number of limitations. In particular, it can be shown that nothing can be computed from two or more steps that cannot be computed by a + +single step. This follows because the above equation implies + +a (t) = W' a (0). + +We can see this by proceeding step by step. Clearly, + +a(2) = Wa (1) = W (Wa (0» = W2a (0) . + +It should be clear that similar arguments lead to a (t) = W' a (0). From this, it follows that for every linear model with connectivity matrix W that can attain a particular state in t steps, there is another linear model with connectivity matrix W ( that can reach the same state in one step. This means, among other things, that there can never be any computational advantage in a linear model of multi ple-step systems, nor can there ever be any advantage for allowing feedback. + +The pattern association paradigm is the typical learning situation for a linear model. There is a set of input units and a set of output units. In general , each input unit may be connected to any output unit. Since this is a linear network, there is no feedback in the system nor are there hidden units between the inputs and outputs. There are two sources of input in the system. There are the input patterns that establish a pattern of activation on the input units, and there are the teaching units that establish a pattern of activation on the output units. Any of several learning rules could be employed with a linear network such as this, but the most common are the simple Hebbian rule and the delta rule. The linear model with the simple Hebbian rule is called the simple linear associator (cf. Anderson, 1970; Kohonen, 1977, 1984). In this case, the increment in weight wI} is given by A wi} = TJaj t;. In matrix notation, this means that A W = TJT aT. The system is then tested by presenting an input pattern without a teaching input and Copyrighted Material + +seeing how close the pattern generated on the output layer matches the original teaching input. It can be shown that if the input patterns are orthogonal,4 there will be no interference and the system will perfectly produce the relevant associated patterns exactly on the output layer. If they are not orthogonal , however, there wi ll be interference among the input patterns. It is possible to make a modification in the learning rule and allow a much larger set of possible associations. In particular, it is possible to build up correct associations among patterns whenever the set of input patterns are linearly independent. To achieve this, an error correcting rule must be employed. The delta rule is most commonly + +employed. In this case, the rule becomes !:1wij = ",(tj-aj)aj + +' What is + +learned is essentially the difference between the desired response and that actually attained at unit Uj due to the input. Although it may take many presentations of the input pattern set, if the patterns are linearly independent the system wi ll eventually be able to produce the desired outputs . Kohonen 0977, 1984) has provided an importantanalysis of + +this and related learning rules. + +The examples described above were for the case of the pattern associator. Essentially the same results hold for the auto-associator version of the linear model . In this case, the input patterns and the teaching patterns are the same, and the input layer and the output layer are also the same. The tests of the system involve presenting a portion of the input pattern and having the system attempt to reconstruct the missing + +parts. + +Linear Threshold Units + +The weaknesses of purely linear systems can be overcome through the additionof nonlinearities . Perhaps the simplest of the nonlinear system consists of a network of linear threshold units. The linear threshold unit is a binary unit whose activation takes on the values {O, I} . The activation value of unit Uj is I if the weighted sum of its inputs is greater than some threshold 9 jand is 0 otherwise. The connectivity matri x for a network of such units, as in the linear system, is a matrix consisting of positive and negative numbers. The output function, /, is the identity function so that the output of a unit is equal to + +its activation value. + +It is useful to see some of the kinds of functions that can be computed with linear threshold units that cannot be computed with simple linear models. The classic such function is the exclusive or (XOR) illustrated in Figure 4. The idea is to have a system which responds (I} if it receives a ( 0, l) or a (1 ,OJ and responds (O} otherwise. The figure shows a network capable of this pattern. In this case we require two + +Output Unit + +Internal Units + +> Input Units + +XOR Netwo rk + ++1 +1 + +Thresholds = .01 + +Input Output + +1 1 J 0 00 + +10] 1 01 + +layers of units. Each unit has a zero threshold and responds just in case its input is greater than zero. The weights are ± 1. Since the set of stimulus patterns is not linearly independent, this is a discrimination that can never be made by a simple linear model and cannot be done in + +a single step by any network of linear threshold units. + +Although multi layered systems of linear threshold units are very powerful and, in fact, are capable of computing any boolean function, there is no generally known learning algorithm for this general case (see Chapter 8) . There is, however, a wel l-understood learning algorithm for the special case of the perceplron. A perceptron is essentially a single-layer network of linear threshold units without feedback. The learning situation here is exactly the same as that for the linear model . An input pattern is presented along with a teaching input. The perceptron learning rule is precisely of the same form as the delta rule for error correcting in the linear model, namely, �wij = 'Y/(/;-a; )aj . Since the teaching input and the activation values are only 0 or 1, the rule + +reduces to the statements that: + +1. Weights are only changed on a given input line when that line + +is turned on (Le., aj = O. + +2. If the system is correct on unit i (i .e., I; = a; ), make no change + +on any of the input weights. + +3. If the unit j responds 0 when it should be I, increase weights + +on all active lines by amount 'Y/. + +4. If the unit j responds 1 when it should be 0, decrease weights + +on all active lines by amount 'Y/. + +There is a theorem, the perceptron convergence theorem, that guarantees that if the set of patterns are learnable by a perceptron, this learning procedure wi ll find a set of weights which allow it to respond correctly to all input patterns. Unfortunately, even though multilayer linear threshold networks are potentially much more powerful than the linear associator, the percept ron for which a learning result exi sts can learn no patterns not learnable by the linear associator. It was the limitations on what perceptrons could possibly learn that led to Minsky and Papert's (969) pessimistic evaluation of the perceptron. Unfortunately that evaluation has incorrectly tainted more interesting and powerful networks of linear threshold and other nonlinear units. We have now developed a version of the delta rule -the generalized delta rule-which is capable of learning arbitrary mappings. It does not work for linear threshold units but does wor foL the class of semilinear activation , (.;opyng teu Matenal + +functions (i.e. , differentiable activation functions) . See Chapter 8 for a full discussion. As we shall see in the course of this book, the limitations of the one-step perceptron in no way apply to the more complex + +networks. + +Brain State in a Box + +The brain state in a box model was developed by J. A. Anderson (I 977) . This model too is a close relative of the simple linear associator. There is, however, a maximum and minimum activation value associated with each unit. Typically, units take on activation values in the interval [- I, lL The brain state in a box (BSB) models are organized so that any unit can, in general , be connected to any other unit. The auto-associator illustrated in Figure 3 is the typical learning paradigm for BSB. Note that with this pattern of interconnections the system feeds back on itself and thus the activation can recycle through the system in a positive feedback loop. The positive feedback is especially evident in J. A. Anderson and Mozer's (1980 version. Their acti vation + +rule is gi ven by + +aj (t+ I) = aj (1 )+ L wij a; (I ) + +if aj is less than I and greater than -I. Otherwise, if the quantity is greater than I, aj = I and if it is less than -I , aj = -1. That is, the activation state at time t+ 1 is given by the sum of the state at time t and the activation propagated through the connectivity matrix provided that total is in the interval [- I,ll. Otherwise it simply takes on the maximum or minimum value. This formulation wi ll lead the system to a state in which all of the units are at either a maximum or minimum value. It is possible to understand why this is cal led a brain state in a box model by considering a geometric representation of the system. Figure 5 illustrates the "activation space " of a simple BSB system consisting of three units. Each point in the box corresponds to a particular value of activation on each of the three units. In this case we have a three-dimensional space in which the first coordinate corresponds to the activation value of the first unit, the second coordinate corresponds to the activation val ue of the second unit, and the third coordinate corresponds to the activation value of the third unit. Thus, each point in the space corresponds to a possi ble state of the system. The feature that each unit is limited to the region (- I,l lmeans that all points must lie somewhere within the box whose vertices are given by the points (- 1,-1,- 0, (- 1,-1,+ I), (-1,+ 1,-0 , (- 1,+1,+ 0, (+ 1 ,- 1,-0, (+ 1,-1,+0 , (+ 1,+1,-0 , and (+ 1,+1,+0 . Moreover, since the Copyrighted Material + +(-,+,+) + +( -, -,+) I-----'"�-----..{ + +Activation ! of Unit 2 + +(-, -,-) ----------.1 + +Activation of Unit 1 + +(+ .+.-) + +FIGURE 5. The state space for a three-unit version of a BSB model . Each dimension of the box represents the activation value of one unit. Each unit is bounded in activation between [- I,ll. The curving arrow in the box represents the sequence of states the system moved through. It began at the black spot near the middle of the box and, as processing proceeded, moved to the (- ,+ ,+ ) corner of the box. BSB systems always end up in one or another of the corners. The particular corner depends on the start state of the network, the input to the system, and the pattern of connections among the units. + +system involves positive feedback, it is eventually forced to occupy one of these vertices . Thus , the state of the system is constrained to lie within the box and eventually , as processing continues, is pushed to one of the vertices. Of course, the same geometric analogy carries over to higher dimensional systems. If there are N units, the state of the system can be characterized as a point within this N-dimensional hyper- + +cube and eventually the system ends up in one of the 2 + +N corners of the + +hypercube. + +Learning in the BSB system involves auto-association. In different applications two different learning rules have been applied. J. A. Anderson and Mozer (1 98 1) appl ied the simplest rule. They simply allowed the system to settle down and then employed the simple Hebbian learning rule. That is, � wI} = 'Y/a/aj' The error correction rule has also been applied to the BSB model . In this case we use the input as the teaching input as well as the source of activation to the system. The learning rule thus becomes � wI} = 'Y/ (t,-a, )aj where t, is the input to .unit i and where a, and aj are the activation values of the system + +after it has stabi lized in one of the corners of the hypercube. + +Thermodynamic Models + +Other more recent developments are the thermodynamic models. Two examples of such models are presented in the book. One, harmony theory, was developed by Paul Smolensky and is described in detai l in Chapter 6. The other, the Boltzmann machine, was developed by Hinton and Sejnowski and is described in Chapter 7. Here we describe the basic .idea behind these models and show how they relate to the general class of models under discussion. To begin, the thermodynamic models employ binary units which take on the values {O, 1) . The units are divided into two categories: the visible units corresponding to our input and output units and the hidden units. In general , any unit may connect to any other unit. However, there is a constraint that the connections must be symmetric. That is, the wi} = wji ' In these models, there is no distinction between the output of the unit and its activation value. The activation values are, however, a stochastic func- + +tion of the inputs. That is, + +where 'Y/, is the input from outside of system into unit i, 0, is the threshold for the unit, and T is a parameter, called temperature, which determines the slope of the probability function. Figure 6 shows how the probabilities vary with various values of T. It should be noted that as T approaches zero, the individual units become more and more like linear threshold units. In general , if the unit exceeds threshold by a great enough margin it wi ll always attain value 1. If it is far enough below threshold, it always takes on value O. Whenever the unit is above threshold, the probabi lity that it wi ll turn on is greater than 112. + +apply so that Il Wjj = .,.,ajaj + +. Note, since activations take on values of 0 + +and 1 this says that the weight is incremented by an amount .,., whenever unit ; and j are on, otherwise no change occurs. During the second phase of learning, the system is al lowed to respond for an equal period of time in a so-cal led free-running state in which no inputs are presented. Since the system is stochastic, it wi ll continue to respond even though no actual stimuli are presented. During this phase, a sim- + +ple anti-Hebbian rule is employed, Il wi} = -.,.,ajQj + +' The intuition is + +roughly that the performance during the environmentally driven phase is determined by both the pattern of interconnections and by the environment. The performance during the free-running phase is determined only by the internal set of connections. To correctly reflect the environment, we should look at its performance due to the environment plus internal structure and then subtract out its performance due to internal structure alone. This is actually quite a powerful learning scheme. It can be shown that if a portion of the input units are turned on after the system has learned, it wi ll complete the remaining portion of the visible units with the probability that those units had been present in the stimulus patterns given the subpattern that had been + +turned on. These issues are again addressed in Chapter 7. + +Grossberg + +Stephen Grossberg has been one of the major contributors to models of this class over the years. His work is complex and contains many important details which we cannot review here. We will instead describe some of the central aspects of his work and show how it relates to the general framework. Perhaps the clearest summary of Grossberg's work appears in Grossberg (1980) . Grossberg's units are allowed to take on any real activation value between a minimum and a maximum value. The output function is, in many of Grossberg's applications , a threshold function so that a given unit wi ll affect another unit only if its activation level is above its threshold. Moreover, Grossberg argues that the output function must be a sigmoid or S-shaped function of the activation value of the unit. Grossberg's activation rule is rather more complex than the others we have discussed thus far in that excitatory and inhibitory inputs don't simply sum, but appear separately in the activation rule. Grossberg has presented a number of possible + +activation rules, but they typically have the form + +aj (1+ 1) = aj (r ) O-A ) + (B-aj (r ) netej (t) - (aj (t }+C)neti) (t ) + +where A is the decay rate, B represents the maximal degree of excitation of the unit, and C is much smaller in magnitude than B and represents the maximal amount the unit can be inhibited below the resting value of O. Grossberg generally assumes that the inhibitory inputs come from a kind of recurrent inhibitory field in which the unit is embedded and the excitatory inputs come from the unit itself and + +from another level of the system. + +Grossberg has studied learning in these networks over a number of years and has studied several different learning schemes. The learning rule he has studied most, however, is similar to the one analyzed in + +Chapter 5 and is given by + +A wi) = "f)a; (OJ- wi) . + +Grossberg has applied this and similar learning rules in a number of cases, but a review of these appl ications is beyond the scope of the + +present discussion. + +Interactive Activation Model + +The interactive activation model of McClelland and Rumelhart (98 1) and Rumelhart and McClelland (982) had units which represented visual features, letters and words. Units could take on any value in the range [min,max] . The output function was a threshold function such that the output was 0 if the activation was below threshold and was equal to the difference of the activation value and the threshold if the activation was above threshold. The interactive activation model involves a connectivity pattern in which units are organized in layers , such that an element in a layer connects with excitatory connections with all elements in the layers above and below that are consistent with that unit, and connects negatively to all units in the layers above and below that are inconsistent with that unit. In addition, each unit inhibits all units in its own layer that are inconsistent with the unit in question. Thus, the interactive activation model is a kind of positive feedback systerr.. with maximum and minimum values for each unit, like the BSB model. The information coming into each unit is weighted (by the interconnection strengths) and summed algebraically to yield a "net input" to the unit. Let net) = r. Wi) a; be the net input to unit j. This net input is then combined with the previous activation Copyrighted Material + +value to produce the new activation value according to the fol lowing + +activation rule: + +where e is the decay rate of the activation given no input. In other words, the new activation value is given by the old activation value properly decayed, plus (or minus) a factor that pushes toward the minimum or maximum value depending on the magnitude of the net input into the unit. This activation rule is similar to that employed by Grossberg, except in this formulation the excitation and inhibition are + +algebraically combined. + +The interactive activation model was designed as a model for a processing system and our goals were to show how we could account for specific aspects of word perception. Thus, there was no specific model of learning proposed to explain where the particular network we assumed came from. As we shall see, much of the work on learning reported in this book has been aimed at giving plausible accounts of how such a network might have been learned. (See especial ly Chapters + +5 and 6.) + +Feldman and Ballard + +Feldman and Bal lard (982) have proposed a framework they cal l connectionist modeling. The units have continuous activation values, which they cal l potential which can take on any value in the range [- 10,10] . Their output function is a kind of threshold functIOn which is allowed to take on a smal l number of discrete integer values (O� OJ � 9) . They have proposed a number of other unit types each with a somewhat different activation rule. Their simplest unit type is what they call the P-unit . In this case the activation rule is given by + +aj (t+ 1) = aj (t ) + (3 netj (r ). + +Once the activation reaches its maximum or minimum value i t i s simply pinned to that value. Decay is implemented by self inhibition. Feldman and Bal lard also have a cOrUunctive unit similar to our sigma-pi units described below. Feldman 098I) has also considered learning. In general , the approach to learning offers more machinery than is avai lable within our current framework. In practice, however, the learning rules actually examined are of the same class we have already + +SIGMA-PI UNITS + +Before completing our section on a general framework , it should be mentioned that we have sometimes found it useful to postulate units that are more complex than those described up to this point in this chapter. In our descriptions thus far, we have assumed a simple additive unit in which the net input to the unit is given by L wij a/ . This is certainly the most common form in most of our models. Sometimes, however, we want multiplicative connections in which the output val ues of two (or possibly more) units are mUltiplied before entering into the sum. Such a multiplicative connection allows one unit to gate another. Thus, if one unit of a multipl icative pair is zero, the other member of the pair can have no effect, no matter how strong its output. On the other hand, if one unit of a pair has value 1, the output of the other is passed unchanged to the receiving unit. Figure 7 illustrates several such connections. In this case, the input to unit A is the weighted sum of the products of units B and C and units D and E. The pairs, BC and DE are called co,yuncts. In this case we have conjuncts of size 2. In general , of course , the conjuncts could be of any size. We have no appl ications, however, which have required conjuncts larger than size 2. In general , then, we assume that the net input to a unit is given by the weighted sum of the products of a set of individual inputs. That is, the + +net input to a unit is given by L wijIIai + +\ + +ai2 •.. aik where i indexes the + +conjuncts impinging on unit j and Ui \ + +' Ui2 ••••• Uik are the k units in + +the conjunct. We call units such as these sigma-pi units. + +In addition to their use as gates, sigma-pi units can be used to convert the output level of a unit into a signal that acts like a weight connecting two units. Thus, assume we have the pattern of connections illustrated in the figure. Assume further that the weights on those connections are all 1. In this case, we can use the output levels of units B and D to, in effect, set the weights from C to A and E to A respectively. Since, in general , it is the weights among the units that determine the behavior of the network, sigma-pi units allow for a dynamically programmable network in which the activation value of some units + +determine what another network can do. + +In addition to its general usefulness in these cases, one might ask whether we might not sometime need still more complex patterns of interconnections. Interestingly, as described in Chapter 10, we wi ll never be forced to develop any more complex interconnection type, since sigma-pi units are sufficient to mimic any function monotonic of + +Sigma Pi Units + +Con ) - QB . QC Con 2- aD ' aE + +FIGURE 7. Two conjunctive inputs to unit A from the conjunct Band C and D and E. The input to unit A is the sum of the product of the outputs of units BC and DE. + +CONCLUSION + +We have provided a very general mathematical and conceptual framework within which we develop our models. This framework provides a language for expressing PDP models, and, though there is a lot of freedom within it, it is at least as constrained as most computational formalisms , such as production systems or high-level languages such as + +Lisp. + +We must take note of the fact, however, that the framework does not specify a/l of the constraints we have imposed on ourselves in our model building efforts. For example, virtually any computing device, serial or parallel, can be described in the framework we have described + +There is a further set of considerations which has guided our particular formulations. These further considerations arise from two sources: our beliefs about the nature of the hardware avai lable for carrying out mental processes in the brain and our beliefs about the essential character of these mental processes themselves. We discuss below the additional constraints on our model bui lding which arise from these two + +beliefs . + +. + +First, the operations in our models can be characterized as .. neurally inspired." We wish to replace the " computer metaphor" as a model of mind with the "brain metaphor" as model of mind. This leads us to a number of considerations which further inform and constrain our model building efforts. Perhaps the most crucial of these is time. Neurons are remarkably slow relative to components in modern computers. Neurons operate in the time scale of mi l l iseconds whereas computer components operate in the time scale of nanoseconds-a factor of 106 faster. This means that human processes that take on the order of a second or less can involve only a hundred or so time steps. Since most of the processes we have studied- perception, memory retrieval , speech processing , sentence comprehension, and the l ike - take about a second or so, it makes sense to impose what Feldman ( 985) cal ls the " 1 00 step program " constraint. That is, we seek explanations for these mental phenomena which do not require more than about a hundred elementary sequential operations. Given that the processes we seek to characterize are often quite complex and may involve consideration of large numbers of simultaneous constraints, our algorithms must involve considerable paral lelism. Thus, although a serial computer could be created out of the kinds of components represented by our units, such an implementation would surely violate the 100-step program constraint + +for any but the simplest processes . + +A second consideration differentiates our models from those inspired by the computer metaphor: that is, the constraint that all the knowledge is in the connections. From conventional programmable computers we are used to thinking of knowledge as being stored in the state of certain units in the system. In our systems we assume that only very short term storage can occur in the states of units; long term storage takes place in the connections among units. Indeed, it is the connections -or perhaps the rules for forming them through experience-which primari ly differentiate one model from another. This is a profound difference between our approach and other more conventional approaches, for it means that almost al l knowledge is implicit in the structure of the device that carries out the task rather than explicit in the states of units themselves. Knowledge is not directly accessible to interpretation by some separate processor, but it is bui lt into the processor itself and d rectly determines the course of Copyrighted Material + +processing. It is acquired through tuning of connections as these are used in processing, rather than formulated and stored as declarative + +facts. + +In addition to these two neurally inspired working assumptions, there are a number of other constraints that derive rather directly from our understanding of the nature of neural information processing. These + +assumptions are discussed more fully in Chapter 4. + +The second class of constraints arises from our beliefs about the nature of human information processing considered at a more abstract, computational level of analysis. We see the kinds of phenomena we have been studying as products of a kind of constraint satisfaction procedure in which a very large number of constraints act simultaneously to produce the behavior. Thus , we see most behavior not as the product of a single, separate component of the cognitive system, but as the product of large set of interacting components, each mutually constraining the others and contributing in its own way to the global ly observable behavior of the system. It is very difficult to use serial algorithms to implement such a conception, but very natural to use highly paral lel ones . These problems can often be characterized as best match or optimization problems. As Minsky and Papert (I969) have pointed out, it is very difficult to solve best match problems serially. However, this is precisely the kind of problem that is readily implemented using highly parallel algorithms of the kind we consider in this book. See Kanerva (I 984) for a discussion of the best match problem and its + +solution with parallel processing systems. + +To summarize, the PDP framework consists not only of a formal language, but a perspective on our models. Other qual itative and quantitative considerations arising from our understanding of brain processing and of human behavior combine with the formal system to form what might be viewed as an aesthetic for our model building enterprises. The remainder of our book is largely a study of this aesthetic in + +practice. + +ACKNOWLEDGMENTS + +This research was supported by Contract N0001 4-79-C-03 23 , NR 667-437 with the Personnel and Training Research Programs of the Office of Naval Research, by grants from the System Development Foundation, and by a NIMH Career Development Award (MHOO385) + +to the second author. + +CHAPTER 3 + +Distributed Representations + +G. E. HINTON, 1. L. McCLELLAND, and D. E. RUMELHART + +Given a network of simple computing elements and some entities to be represented, the most straightforward scheme is to use one computing element for each entity. This is cal led a local representation. It is easy to understand and easy to implement because the structure of the physical network mirrors the structure of the knowledge it contains. The naturalness and simplicity of this relationship between the knowledge and the hardware that implements it have led many people to simply assume that local representations are the best way to use parallel hardware. There are, of course, a wide variety of more compl icated implementations in which there is no one-to-one correspondence between concepts and hardware units, but these implementations are only worth considering if they lead to increased efficiency or to interesting emergent properties that cannot be conveniently achieved + +using local representations. + +This chapter describes one type of representation that is less familiar and harder to think about than local representations. Each entity is represented by a pattern of activity distributed over many computing elements, and each computing element is involved in representing many different entities. The strength of this more complicated kind of representation does not lie in its notational convenience or its ease of implementation in a conventional computer, but rather in the efficiency with which it makes use of the processing abi lities of networks of sim- + +Every representational scheme has its good and bad points. Distributed representations are no exception. Some desirable properties arise very naturally from the use of patterns of activity as representations. Other properties, like the ability to temporarily store a large set of arbitrary associations, are much harder to achieve. As we shall see, the best psychological evidence for distributed representations is the degree to which their strengths and weaknesses match those of the human + +mind. + +The first section of this chapter stresses some of the virtues of distributed representations. The second section considers the efficiency of distributed representations, and shows clearly why distributed representations can be better than local ones for certain classes of problems. A final section discusses some difficult issues which are often avoided by advocates of distributed representations, such as the representation of constituent structure and the sequential focusing of + +processing effort on different aspects of a structured object. + +Disclaimers. Before examining the detailed arguments in favor of distributed representations, it is important to be clear about their status within an overall theory of human information processing. It would be wrong to view distributed representations as an alternative to representational schemes like semantic networks or production systems that have been found useful in cognitive psychology and artificial intelligence. It is more fruitful to view them as one way of implementing these more abstract schemes in parallel networks, but with one proviso: Distributed representations give rise to some powerful and unexpected emergent properties. These properties can therefore be taken as primitives when working in a more abstract formalism. For example, distributed representations are good for content-addressable memory, automatic generalization, and the selection of the rule that best fits the current situation. So if one assumes that more abstract models are implemented in the brain using distributed representations, it is not unreasonable to treat abilities like content-addressable memory, automatic generalization, or the selection of an appropriate rule as primitive operations, even though there is no easy way to implement these operations in conventional computers. Some of the emergent properties of distributed representations are not easily captured in higher-level formalisms. For example, distributed representations are consistent with the simultaneous application of a large number of partially fitting rules to the current situation, each rule being applied to the degree that it is relevant. We shall examine these properties of distributed representations in the chapter on schemata (Chapter 14). There we will see clearly that schemata and other higher-level constructs provide only approximate characterizations of mechanisms which rely on dist ributed Copyrighted Material + +representations. Thus, the contribution that an analysis of distributed representations can make to these nigher-level formalisms is to legitimize certain powerful, primitive operations which would otherwise appear to be an appeal to magic; to enrich our repertoire of primitive operations beyond those which can conveniently be captured in many higher-level formalisms; and to suggest that these higher-level formalisms may only capture the coarse features of the computational capabi l i- + +ties of the underlying processing mechanisms. + +Another common source of confusion is the idea that distributed representations are somehow in conflict with the extensive evidence for localization of function in the brain (Luria, 1973). A system that uses distributed representations still requires many different modul('s for representing completely different kinds of thing at the same time. The distributed representations occur within these localized modules. For example, different modules would be devoted to things as different as mental images and sentence structures, but two different mental images would correspond to alternative patterns of activity in the same module. The representations advocated here are local at a global scale but global + +at a local scale. + +VIRTUES OF DISTRIBUTED REPRESENTATIONS + +This section considers three important features of distributed representations: (a) their essentially constructive character; (b) their ability to generalize automatically to novel situations; and (c) their tunability to changing environments. Several of these virtues are shared by certain local models, such as the interactive activation model of word perception, or McClelland's (1980 model of generalization and + +retrieval described in Chapter 1. + +Memory as Inference + +People have a very flexible way of accessing their memories: They can recall items from partial descriptions of their contents (Norman & Bobrow, 1979). Moreover, they can do this even if some parts of the partial description are wrong. Many people, for example, can rapidly retrieve the item that satisfies the following partial description: It is an actor, it is intelligent, it is a politician. This kind of content-addressable memory is very useful and it .is very hard. to implement on a conven- + +tional computer becaus'i + +°eKf\$!!£efSM�o�J each item at a particular + +address, and to retrieve an item they must know its address. If all the combinations of descriptors that will be used for access are free of errors and are known in advance, it is possible to use a method called hash coding that quickly yields the address of an item when given part of its content. In general , however, content-addressable memory requires a massive search for the item that best fits the partial description. The central computational problem in memory is how to make this search efficient. When the cues can contain errors, this is very difficult because the failure to fit one of the cues cannot be used as a fi lter + +for quickly eliminating inappropriate answers. + +Distributed representations provide an efficient way of using parallel hardware to implement best-fit searches. The basic idea is fairly simple, though it is quite unlike a conventional computer memory. Different items correspond to different patterns of activity over the very same group of hardware units. A partial description is presented in the form of a partial activity pattern, activating some of the hardware units. 1 Interactions between the units then al low the set of active units to influence others of the units, thereby completing the patteft1, and generating the item that best fits the description. A new item is "stored" by modifying the interactions between the hardware units so as to create a new stable pattern of activity. The main difference from a conventional computer memory is that patterns which are not active do not exist anywhere. They can be re-created because the connection strengths between units have been changed appropriately, but each connection strength is involved in storing many patterns, so it is impossible to point to a particular place where the memory for a particular item is + +stored. + +Many people are surprised when they understand that the connections between a set of simple processing units are capable of supporting a large number of different patterns. Illustrations of this aspect of distributed models are provided in a number of papers in the literature (e.g., Anderson, 1977; Hinton, 1981a) ; this property is illustrated in the model of memory and amnesia described in Chapters 17 and 25. One way of thinking about distributed memories is in terms of a very large set of plausible inference rules. Each active unit represents a "microfeature" of an item, and the connection strengths stand for plausible "microinferences" between microfeatures. Any particular pattern + +IThis is easy if the partial description is simply a set of features, but it is much more difficult if the partial description mentions relationships to other objects. If, for example, the system is asked to retrieve John's father, it must represent John, but if John and his father are represented by mutually exclusive patterns of activity in the very same group of units , it is hard to see how this can be done without preventing the representation of + +John's father. A distributed solution to this problem is described in the text. + +of activity of the units will satisfy some of the microinferences and violate others. A stable pattern of activity is one that violates the plausible microinferences less than any of the neighboring patterns. A new stable pattern can be created by changing the inference rules so that the new pattern violates them less thanits neighbors. This view of memory makes it clear that there is no sharp distinction between genuine memory and plausible reconstruction. A genuine memory is a pattern that is stable because the inference rules were modified when it occurred before. A "confabulation" is a pattern that is stable because of the way the inference rules have been modified to store several different previous patterns. So far as the subject is concerned, this may + +be indistinguishable from the real thing. + +The blurring of the distinction between veridical recall and confabulation or plausible reconstruction seems to be characteristic of human memory (Bartlett, 1932� Neisser, 1981). The reconstructive nature of human memory is surprising only because it conflicts with the standard metaphors we use. We tend to think that a memory system should work by storing literal copies of items and then retrieving the stored copy, as in a filing cabinet or a typical computer database. Such sys- + +tems are not naturally reconstructive. + +If we view memory as a process that constructs a pattern of activity which represents the most plausible item that is consistent with the given cues, we need some guarantee that it will converge on the representation of the item that best fits the description, though it might be tolerable to sometimes get a good but not optimal fit. It is easy to imagine this happening, but it is harder to make it actually work. One recent approach to this problem is to use statistical mechanics to analyze the behavior of groups of interacting stochastic units. The analysis guarantees that the better an item fits the description, the more likely it is to be produced as the solution. This approach is described in Chapter 7, and a related approach is described in Chapter 6. An alternative approach, using units with continuous activations (Hopfield, + +1984) is described in Chapter 14. + +Similarity and Generalization + +When a new item is stored, the modifications in the connection strengths must not wipe out existing items. This can be achieved by modifying a very large number of weights very slightly. If the modifications are all in the directionthat helps the pattern that is being stored, there will be a conspiracy effect: The total help for the intended pattern will be��t@f1�aNJ;;§Jl1all separate modifications. + +For unrelated patterns, however, there will be very little transfer of effect because some of the modifications will help and some will hinder. Instead of all the small modifications conspiring together, they will mainly cancel out. This kind of statistical reasoning underpins most distributed memory models, but there are many variations of the basic idea (See Hinton & Anderson, 1981, for several examples). + +It is possible to prevent interference altogether by using orthogonal patterns of activity for the various items to be stored (a rudimentary example of such a case is given in Chapter O. However, this eliminates one of the most interesting properties of distributed representations: They automatically give rise to generalizations. If the task is simply to remember accurately a set of unrelated items, the generalization effects are harmful and are called interference. But generalization is normally a helpful phenomenon. It allows us to deal effectively with situations that are similar but not identical to previously experienced + +situations. + +People are good at generalizing newly acquired knowledge. If you learn a new fact about an object, your expectations about other similar objects tend to change. If, for example, you learn that chimpanzees like onions you will probably raise your estimate of the probability that gorillas like onions. In a network that uses distributed representations, this kind of generalization is automatic. The new knowledge about chimpanzees is incorporated by modifying some of the connection strengths so as to alter the causal effects of the distributed pattern of activity that represents chimpanzees. 2 The modifications automatically change the causal effects of all similar activity patterns. So if the representation of gorillas is a similar activity pattern over the same set + +of units, its causal effects will be changed in a similar way. + +The very simplest distributed scheme would represent the concept of onion and the concept of chimpanzee by alternative activity patterns over the very same set of units. It would then be hard to represent chimps and onions at the same time. This problem can be solved by using separate modules for each possible role of an item within a larger structure. Chimps, for example, are the" agent" of the liking and so a pattern representing chimps occupies the" agent" module and the pattern representing onions occupies the "patient" module (see Figure I). + +2The internal structure of this pattern may also change. There is always a choice between changing the weights on the outgoing connections and changing the pattern itself so that different outgoing connections become relevant. Changes in the pattern itself alter its similarity to other patterns and thereby alter how generalization will occur in the future. It is generally much harder to figure out how to change the pattern that represents an item than it is to figure out how to change the outgoing connections so that a particu- + +Each module can have alternative patterns for all the various items, so this scheme does not involve local representations of items. What is + +localized is the role. + +If you subsequently learn that gibbons and orangutans do not like onions your estimate of the probability that gorillas like onions will fall, though it may still remain higher than it was initially. Obviously, the combination of facts suggests that liking onions is a peculiar quirk of chimpanzees. A system that uses distributed representations will automatically arrive at this conclusion, provided that the alternative patterns that represent the various apes are related to one another in a particular way that is somewhat more specific than just being similar to one another: There needs to be a part of each complete pattern that is identical for all the various apes. In other words, the group of units used for the distributed representations must be divided into two + +RELATIONSHIP + +AGENT PATIENT + +FIGURE I. In this Simplified scheme there are two different modules, one of which represents the agent and the other the patient. To incorporate the fact that chimpanzees like onions, the pattern for chimpanzees in one module must be associated with the pattern for onions in the other module. Relationships other than "liking" can be implemented by having a third group of units whose pattern of activity represents the relationship. This pattern must then "gate" the interactions between the agent and patient groups. Hinton (1981a) describes one way of doing this gating by using a fourth group of + +subgroups, and all the various apes must be represented by the same pattern in the first subgroup, but by different patterns in the second subgroup. The pattern of activity over the first subgroup represents the type of the item, and the pattern over the second subgroup represents additional microfeatures that discriminate each instance of the type from the other instances. Note that any subset of the microfeatures can be considered to define a type. One subset might be common to all apes, and a different (but overlapping) subset might be common to all pets. This allows an item to be an instance of many different types + +simultaneously. + +When the system learns a new fact about chimpanzees, it usually has no way of knowing whether the fact is true of all apes or is just a property of chimpanzees. The obvious strategy is therefore to modify the strengths of the connections emanating from all the active units, so that the new knowledge will be partly a property of apes in general and partly a property of whatever features distinguish chimps from other apes. If it is subsequently learned that other apes do not like onions, correcting modifications will be made so that the information about onions is no longer associated with the subpattern that is common to all apes. The knowledge about onions will then be restricted to the subpattern that distinguishes chimps from other apes. If it had turned out that gibbons and orangutans also liked onions, the modifications in the weights emanating from the subpattern representing apes would have reinforced one another, and the knowledge would have become associated with the subpattern shared by all apes rather than with the patterns + +that distinguish one ape from another. + +A very simple version of this theory of generalization has been implemented in a computer simulation (Hinton, 1981a). Several applications that make use of this property can be found in Part IV of this + +book. + +There is an obvious generalization of the idea that the representation of an item is composed of two parts, one that represents the type and another that represents the way in which this particular instance differs from others of the same type. Almost all types are themselves instances of more general types, and this can be implemented by dividing the pattern that represents the type into two subpatterns, one for the more general type of which this type is an instance, and the other for the features that discriminate this particular type from others instances of the same general type. Thus the relation between a type and an instance can be implemented by the relationship between a set of units and a larger set that includes ·it. Notice that the more general the type, the smaller the set of units used to encode it. As the number of terms in an intensional description gets smaller, the corresponding + +In traditional semantic networks that use local representations, generalization is not a direct consequence of the representation. Given that chimpanzees like onions, the obvious way of incorporating the new knowledge is by changing the strengths of connections belonging to the chimpanzee unit. But this does not automatically change connections that belong to the gorilla unit. So extra processes must be invoked to implement generalization in a localist scheme. One commonly used method is to allow activation to spread from a local unit to other units that represent similar concepts (Collins & Loftus, 1975; Quillian, 1968). Then when one concept unit is activated, it will partially activate its neighbors and so any knowledge stored in the connections emanating from these neighbors will be partially effective. There are many variations of this basic idea (Fahlman, 1979; Levin, 1976; + +McClelland, 1981). + +It is hard to make a clean distinction between systems that use local representations plus spreading activation and systems that use distributed representations. In both cases the result of activating a concept is that many different hardware units are active. The distinction almost completely disappears in some models such as McClelland's (981) generalization model, where the properties of a concept are represented by a pattern of activation over feature units and where this pattern of activation is determined by the interactions of a potentially very large number of units for instances of the concept. The main difference is that in one case there is a particular individual hardware unit that acts as a "handle" which makes it easy to attach purely conventional properties like the name of the concept and easier for the theorist who constructed the network to know what the individual parts of the network + +stand for. + +If we construct our networks by hand-specifying the connections between the units in the network, a local representation scheme has some apparent advantages. First, it is easier to think one understands the behavior of a network if one has put in all the "knowledge" -all the connections-oneself. But if it is the entire, distributed pattern of interacting influences among the units in the network that is doing the work, this understanding can often be illusory. Second, it seems intuitively obvious that it is harder to attach an arbitrary name to a distributed pattern than it is to attach it to a single unit. What is intuitively harder, however, may not be more efficient. We will see that one can actually implement aribitrary associations with fewer units using distributed representations. Before we turn to such considerations, however, we examine a different advantage of distributed representations: They make it possible to create new concepts without allocating new + +Creating New Concepts + +Any plausible scheme for representing knowledge must be capable of learning novel concepts that could not be anticipated at the time the network was initially wired up. A scheme that uses local representations must first make a discrete decision about when to form a new concept, and then it must find a spare hardware unit that has suitable connections for implementing the concept involved. Finding such a unit may be difficult if we assume that, after a period of early development, new knowledge is incorporated by changing the strengths of the existing connections rather than by growing new ones. If each unit only has connections to a small fraction of the others, there will probably not be any units that are connected to just the right other ones to implement a new concept. For example, in a collection of a million units each connected at random to ten thousand others, the chance of there being any unit that is connected to a particular set of 6 others is only one in a + +million. + +In an attempt to rescue local representations from this problem, several clever schemes have been proposed that use two classes of units. The units that correspond to concepts are not directly connected to one another. Instead, the connections are implemented by indirect pathways through several layers of intermediate units (Fahlman, 1980; Feldman, 1982). This scheme works because the number of potential pathways through the intermediate layers far exceeds the total number of physical connections. If there are k layers of units, each of which has a fan-out of n connections to randomly selected units in the follow- + +ing layer, there are n + +k potential pathways. There is almost certain to be + +a pathway connecting any two concept-units, and so the intermediate units along this pathway can be dedicated to connecting those two concept-units. However, these schemes end up having to dedicate several intermediate units to each effective connection, and once the dedication has occurred, all but one of the actual connections emanating from each intermediate unit are wasted. The use of several intermediate units to create a single effective connection may be appropriate in switching networks containing elements that have units with relatively small fan-out, but it seems to be an inefficient way of using the + +hardware of the brain. + +The problems of finding a unit to stand for a new concept and wiring it up appropriately do not arise if we use distributed representations. All we need to do is modify the interactions between units so as to create a new stable pattern of activity. If this is done by modifying a large number of connections very slightly, the creation of a new pattern need not disrupt the existing representations. The difficult problem is Copyrighted Material + +to choose an appropriate pattern for the new concept. The effects of the new representation on representations in other parts of the system wi ll be determined by the units that are active, and so it is important to use a collection of active units that have roughly the correct effects. Fine-tuning of the effects of the new pattern can be achieved by slightly altering the effects of the active units it contains, but it would be unwise to choose a random pattern for a new concept because major changes would then be needed in the weights, and this would disrupt other knowledge. Ideally, the distributed representation that is chosen for a new concept should be the one that requires the least modification of weights to make the new pattern stable and to make it have the + +required effects on other representations. + +Naturally, it is not necessary to create a new stable pattern all in one step. It is possible for the pattern to emerge as a result of modifications on many separate occasions. This alleviates an awkward problem that arises with local representations: The system must make a discrete allor-none decision about when to create a new concept. If we view concepts as stable patterns, they are much less discrete in character. It is possible, for example, to differentiate one stable pattern into two closely related but different variants by modifying some of the weights slightly. Unless we are allowed to clone the hardware units (and all their connections) , this kind of gradual, conceptual differentiation is + +much harder to achieve with local representations. + +One of the central problems in the development of the theory of distributed representation is the problem of specifying the exact procedures by which distributed representations are to be learned. All such procedures involve connection strength modulation, following "learning rules" of the type outlined in Chapter 2. Not all the problems have been solved, but significant progress is being made on these prob- + +lems. (See the chapters in Part II.) + +DISTRIBUTED REPRESENTATIONS THAT + +WORK EFFICIENTLY + +In this section, we consider some of the technical details about the implementation of distributed representations. First, we point out that certain distributed representation schemes can fail to provide a sufficient basis for differentiating different concepts, and we point out what is required to avoid this limitation. Then, we describe a way of using distributed representations to get the most information possible out of a simple network of connected units. The central result is a surprising one' If you want to eru:.ode features\_ a�curately using as few units as . (;opyngntea Matenal + +possible, it pays to use units that are very coarsely tuned, so that each feature activates many different units and each unit is activated by many different features. A specific feature is then encoded by a pattern of activity in many units rather than by a single active unit, so coarse + +coding is a form of distributed representation. + +To keep the analysis simple, we shall assume that the units have only two values, on and off.3 We shall also ignore the dynamics of the system because the question of interest, for the time being, is how many units it takes to encode features with a given accuracy. We start by considering the kind of feature that can be completely specified by giving a type (e.g. , line-segment, corner, dot) and the values of some continuous parameters that distinguish it from other features of the same type (e. g., position, orientation, size.) For each type of feature there is a space of possible instances. Each continuous parameter defines a dimension of the feature space, and each particular feature corresponds to a point in the space. For features like dots in a plane, the space of possible features is two-dimensional . For features like stopped, oriented edge-segments in three-dimensional space, the feature space is si x-dimensional . We shall start by considering twodimensional feature spaces and then generalize to higher dimensionali- + +ties. + +Suppose that we wish to represent the position of a single dot in a plane, and we wish to achieve high accuracy without using too many units. We define the accuracy of an encoding scheme to be the number of different encodings that are generated as the dot is moved a standard distance through the space. One encoding scheme would be to divide the units into an X group and a Y group, and dedicate each unit to encoding a particular X or Y interval as shown in Figure 2. A given dot would then be encoded by activity in two units, one from each group, and the accuracy would be proportional to the number of units used. Unfortunately , there are two problems with this. First, if two dots have to be encoded at the same time, the method breaks down. The two dots will activate two units in each group, and there will be no way of telling, from the active units, whether the dots were at (x 1, y 1) and + +(x 2, y 2) or at (x 1, Y 2) and (x 2 + +, y 1). This is called the binding prob- + +lem. It arises because the representation does not specify what goes + +with what . + +3Similar arguments apply with multi valued activity levels, but it is important not to allow activity levels to have arbitrary precision because this makes it possible to represent an infinite amount of information in a single activity level. Units that transmit a discrete impulse with a probability that varies as a function of their activation seem to approximate the kind of precision that is possible in neural circuitry (see Chapters 20 and 21). Copyrighted Material + +Y group + +Y group + +o o + +o + +• + +o + +1 • + +X group + +X group + +FIGURE 2. A: A simple way of using two groups of binary units to encode the position of a point in a two-dimensional space. The active units in the X and Y groups represent the x- and y-coordinates. B: When two points must be encoded at the same time, it is + +impossible to tell which x-coordinate goes with which y-coordinate. + +The second problem arises even if we allow only one point to be represented at a time. Suppose we want certain representations to be associated with an overt response, but not others: We want (x I, y 1) and (x 2, y 2) to be associated with a response, but not (x I, y 2) or (x 2, y 1). We cannot implement this association using standard weighted connections to response units from units standing for the values on the two dimensions separately. For the unit for x 1 and the + +unit for x 2 would both have o activ.a.te + +y 1 and the unit for y 2 would both have to activate the response. There would be no way of preventing the response from being activated when the unit for x 1 and the unit for y 2 were both activated. This is another aspect of the binding problem since, again, the representation fails to + +specify what must go with what. + +In a conventional computer it is easy to solve the binding problem. We simply create two records in the computer memory. Each record contains a pair of coordinates that go together as coordinates of one dot, and the binding information is encoded by the fact that the two coordinate values are sitting in the same record (which usually means they are sitting in neighboring memory locations). In parallel networks + +it is much harder to solve the binding problem. + +Conjunctive Encoding + +One approach is to set aside, in advance, one unit for each possible combination of X and Y values. This amounts to covering the plane with a large number of small, nonoverlapping zones and dedicating a unit to each zone. A dot is then represented by activity in a single unit so this is a local representation. The use of one unit for each discriminable feature solves the binding problem by having units which stand for the conjunction of values on each of two dimensions. In general, to permit an arbitrary association between particular combinations of features and some output or other pattern of activation, some conjunc- + +tive representation may be required. + +However, this kind of local encoding is very expensive. It is much less efficient than the previous scheme because the accuracy of pinpointing a point in the plane is only proportional to the square root of the number of units. In general, for a k -dimensional feature space, the local encoding yields an accuracy proportional to the kth root of the number of units. Achieving high accuracy without running into the + +binding problem is thus very expensive. + +The use of one unit for each discriminable feature may be a reasonable encoding if a very large number of features are presented on each occasion, so that a large fraction of the units are active. However, it is a very inefficient encoding if only a very small fraction of the possible features are presented at once. The average amount of information conveyed by the state of a binary unit is 1 bit if the unit is active half the time, and it is much less if the unit is only rarely active.4 It would + +therefore be more efficient to use an encoding in which a larger fraction of the units were active at any moment. This can be done if we abandon the idea that each discriminable feature is represented by + +activity in a single unit. + +Coarse Coding + +Suppose we divide the space into larger, overlapping zones and assign a unit to each zone. For simplicity, we will assume that the zones are circular, that their centers have a uniform random distribution throughout the space, and that all the zones used by a given encoding scheme have the same radius. The question of interest is how accurately a feature is encoded as a function of the radius of the zones. If we have a given number of units at our disposal is it better to use large zones so that each feature point falls in many zones, or is it better to use small zones so that each feature is represented by activity in + +fewer but more finely tuned units? + +The accuracy is proportional to the number of different encodings that are generated as we move a feature point along a straight line from one side of the space to the other. Every time the line crosses the boundary of a zone, the encoding of the feature point changes because the activity of the unit corresponding to that zone changes. So the number of discriminable features along the line is just twice the number of zones that the line penetrates. 5 The line penetrates every zone whose center lies within one radius of the line (see Figure 3). This number is proportional to the radius of the zones, r, and it is also proportional to their number, n. Hence the accuracy, a, is related to + +the number of zones and to their radius as follows: + +aa: nr. + +In general, for a k-dimensional space, the number of zones whose centers lie within one radius of a line through the space is proportional to the volume of a k-dimensional hypercylinder of radius r. This volume is equal to the length of the cylinder (which is fixed) times its (k - 1) -dimensional cross-sectional area which is proportional to r + +k - I. + +5Problems arise if you enter and leave a zone without crossing other zone borders in between because you revert to the same encoding as before, but this effect is negligible if the zones are dense enough for there to be many zones containing each point in the + +space. + +FIGURE 3. The number of zone boundaries that are cut by the line is proportional to + +the number of zone centers within one-zone radius of the line. + +Hence, the accuracy is given by + +So, for example, doubling the radius of the zones increases by a factor of 32, the linear accuracy with which a six-dimensional feature like a stopped oriented three-dimensional edge is represented. The intuitive idea that larger zones lead to sloppier representations is entirely wrong because distributed representations hold information much more efficiently than local ones. Even though each active unit is less specific in its meaning, the combination of active units is far more specific. Notice also that with coarse coding the accuracy is proportional to the number of units, which is much better than being proportional to the + +kth root of the number. + +Units that respond to complex features in retinotopic maps in visual cortex often have fairly large receptive fields. This is often interpreted as the first step on the way to a translation invariant representation. However, it may be that the function of the large fields is not to achieve translation invariance but to pinpoint accurately where the + +feature is! + +Limitations on coarse coding. So far, only the advantages of coarse coding have been mentioned, and its problematic aspects have been ignored. There are a number of limitations that cause the coarse coding strategy to break de'tYIJyrYf}Hl�dt�iew5FPtive fields" become too + +large. One obvious limitation occurs when the fields become comparable in size to the whole space. This limitation is generally of little interest because other, more severe, problems arise before the recep- + +tive fields become this large. + +Coarse coding is only effective when the features that must be represented are relatively sparse. If many feature points are crowded together, each receptive field will contain many features and the activity pattern in the coarse-coded units will not discriminate between many alternative combinations of feature points. (If the units are allowed to have integer activity levels that reflect the number of feature points faIling within their fields, a few nearby points can be tolerated, but not many.) Thus there is a resolution/accuracy trade-off. Coarse coding can give high accuracy for the parameters of features provided that features are widely spaced so that high resolution is not also required. As a rough rule of thumb, the diameter of the receptive fields should be of the same order as the spacing between simultaneously present + +feature points.6 + +The fact that coarse coding only works if the features are sparse should be unsurprising given that its advantage over a local encoding is that it uses the information capacity of the units more efficiently by making each unit active more often. If the features are so dense that the units would be active for about half the time using a local encoding, + +coarse coding can only make things worse. + +A second major limitation on the use of coarse coding stems from the fact that the representation of a feature must be used to affect other representations. There is no point using coarse coding if the features have to be recoded as activity in finely tuned units before they can have the appropriate effects on other representations. If we assume that the effect of a distributed representation is the sum of the effects of the individual active units that constitute the representation, there is a strong limitation on the circumstances under which coarse coding can be used effectively. Nearby features will be encoded by similar sets of active units, and so they will inevitably tend to have similar effects. Broadly speaking, coarse coding is only useful if the required effect of a feature is the average of the required effects of its neighbors. At a fine enough scale this is nearly always true for spatial tasks. The scale at which it breaks down determines an upper limit on the size of the + +receptive fields. + +6 It is interesting that many of the geometric visual illusions illustrate interactions between features at a distance much greater than the uncertainty in the subjects' knowledge of the position of a feature. This is just what would be expected if coarse cod- + +Another limitation is that whenever coarse-coded representations interact, there is a tendency for the coarseness to increase. To counteract this tendency, it is probably necessary to have lateral inhibition operating within each representation. This issue requires further + +research. + +Extension to noncontinuous spaces. The principle underlying coarse coding can be generalized to noncontinuous spaces by thinking of a set of items as the equivalent of a receptive field. A local representation uses one unit for each possible item. A distributed representation uses a unit for a set of items, and it implicitly encodes a particular item as + +the intersection of the sets that correspond to the active units. + +In the domain of spatial features there is generally a very strong regularity: Sets of features with similar parameter values need to have similar effects on other representations. Coarse coding is efficient because it allows this regularity to be expressed in the connection strengths. In other domains, the regularities are different, but the efficiency arguments are the same: It is better to devote a unit to a set of items than to a single item, provided that the set is chosen in such a way that membership in the set implies something about membership in other sets. This implication can then be captured as a connection strength. Ideally, a set should be chosen so that membership of this set has strong implications for memberships of other sets that are also + +encoded by individual units. + +We illustrate these points with a very simple example. Consider a microlanguage consisting of the three-letter words of English made up of w or I, followed by i or e, followed by g or r. The strings wig and leg are words, but weg, fig, and all strings ending in r are not. Suppose we wanted to use a distributed representation scheme as a basis for representing the words, and we wanted to be able to use the distributed pattern as a basis for deciding whether the string is a word or a nonword. For simplicity we wi ll have a single " decision " unit. The problem is to find connections from the units representing the word to the decision unit such that it fires whenever a word is present but does not + +fire when no word is present. 7 + +7 Note that the problem remains the same if the decision unit is replaced by a set of units and the task of the network is to produce a different pattern for the word and nonword decisions. For when we examine each unit, it either takes the same or a different value in the two patterns; in the cases where the value is the same, there is no problem, but neither do such units differentiate the two patterns. When the values are different, + +the unit behaves just like the single decision unit discussed in the text. + +Figure 4 shows three representation schemes: a distributed scheme that does not work, a distributed scheme that does work, and a local scheme. In the first scheme, each letter/positi on combination is represented by a di fferent uni t. Since there are only five letter/ position possibilities, only five units have connections to the output unit. Each word and nonword produces a different and unique pattern over these five units, but the connections from the five units to the decision unit cannot be set in such a way as to make the decision uni t fire whenever one of the words is present and fail to fire whenever one of the non- + +words is present. + +The reason for the problem is simply that the connections between the letter/ position units and the decision units can only capture the degree to which each letter indicates whether the string is a word or not. The g tends to indicate that a word is present, whereas the r indicates that the item is not a word; but each of the other letters , taken + +individually, has absolutely no predictive ability in this case. + +Whether a letter string is a word or not cannot be determined conclusively from the individual letters it contains; it is necessary to consider also what combinations of letters it contains. Thus, we need a representation that captures what combinations of letters are present in a way that is sufficient for the purposes of the network. One could capture this by using local representations and assigning one node to each word, as in the third panel of Figure 4. However, it is important to see that one need not go all the way to local representations to solve the + +FIGURE 4. Three networks applied to the problem of determining which of the strings that can be made from w or I, followed by i or e, followed by g or r form words. Numbers on the connections represent connection strengths; numbers on the units represent the units' thresholds. A unit will take on an activation equal to I if its input + +exceeds it threshold; otherwise, its activation is O. + +problem facing our network . Conjunctive distributed representations + +will suffice. + +The scheme illustrated in the second panel of the figure provides a conjunctive distributed representation. In this scheme, there are units for pairs of letters which, in this limited vocabulary, happen to capture the combinations that are essential for determining whether a string of letters is a word or not. These are, of course, the pairs wi and Ie. These conjunctive units, together with direct input to the decision unit from the g uni t, are sufficient to construct a network which cOlTectly classifies all strings consisting of a w or an I, followed by an i or an e, + +followed by a g or r. + +This example illustrates that conjunctive coding is often necessary if distributed representations are to be used to solve problems that might easily be posed to networks. This same point could be illustrated with many other examples-the exclusive or problem is the classic example (Minsky & Papert, 1969) . Other examples of problems requiring some sort of conjunctive encoding can be found in Hinton (1981 a) and in Chapters 7 and 8. An application of conjunctive coding to a psychologi- + +cal model is found in Chapter 18. + +Some problems (mostly very simple ones) can be solved without any conjunctive encoding at all, and others will require conjuncts of more than two units at a time. In general, it is hard to specify in advance just what "order" of conjunctions will be required. Instead, it is better to search for a learning scheme that can find representations that are adequate. The mechanisms proposed in Chapters 7 and 8 represent two + +steps toward this goal . + +Implementing an Arbitrary Mapping Between Two Domains + +The attentive reader will have noticed that a local representation can always be made to work in the example we have just considered. However , we have already discussed several reasons why distributed representations are preferable. One reason is that they can make more + +efficient use of parallel hardware than local representations. + +This section shows how a distributed representation in one group of units can cause an appropriate distributed representation in another group of units. We consider the problem of implementing an arbitrary pairing between representations in the two groups, and we take as an example an extension of the previous one: the association between the visual form of a word and its meaning. The reason for considering an arbitrary mapping is that this is the case in which local representations seem most helpful. If distributed representations are better in this Copyrighted Material + +case, then they are certainly better in cases where there are underlying regularities that can be captured by regularities in the patterns of activation on the units in one group and the units in another. A discussion of the benefit distributed representations can provide in such cases can + +be found in Chapter 18. + +If we restrict ourselves to monomorphemic words, the mapping from strings of graphemes onto meanings appears to be arbitrary in the sense that knowing what some strings of graphemes mean does not help one predict what a new string means. 8 This arbitrariness in the mapping from graphemes to meanings is what gives plausibility to models that have explicit word units. It is obvious that arbitrary mappings can be implemented if there are such units. A grapheme string activates exactly one word unit, and this activates whatever meaning we wish to associate with it (see Figure SA) . The semantics of simi lar grapheme strings can then be completely independent because they are mediated by separate word units. There is none of the automatic general ization + +that is characteristic of distributed representations. + +Intuitively, it is not at all obvious that arbitrary mappings can be implemented in a system where the intermediate layer of units encodes the word as a distributed pattern of activity instead of as activity in a single local unit. The distri buted alternative appears to have a serious drawback. The effect of a pattern of activity on other representations is the combined result of the individual effects of the active units in the pattern. So similar patterns tend to have similar effects. It appears that we are not free to make a given pattern have whatever effect we wish on the meaning representations without thereby altering the effects that other patterns have. This kind of interaction appears to make it difficult to implement arbitrary mappings from distributed representations of words onto meaning representations. We shall now show that these intuitions are wrong and that distributed representations of words can work perfectly well and may even be more efficient than single word + +units. + +Figure SB shows a three-layered system in which grapheme/ position units feed into word-set units which, in turn, feed into semantic or sememe units. Models of this type, and closely related variants, have been analyzed by Willshaw (1 98 0 , V. Dobson (personal communication, 1984) , and by David Zipser (personal communication, 1981) ; some further relevant analyses are discussed in Chapter 12. For simpli- + +8 Even for monomorphemic words there may be particular fragments that have associated meaning. For example, words starting with sn usually mean something unpleasant to do with the lips or nose (sneer, snarl, snigger) , and words with long vowels are more likely to stand for large, slow things than words with short vowels (George Lakoff, per- + +sonal communication) . Much of Lewis Carroll's poetry relies on such effects. Copyrighted Material + +FIGURE S. A: A three-layer network. The bOllom layer contains units that represent particular graphemes in particular positions within the word. The middle layer contains units that recognize complete words, and the top layer contains units that represent semantic features of the meaning of the word. This network uses local representations of words in the middle layer. B: The top and bollom layers are the same as in (A), but the middle layer uses a more distributed representation. Each unit in this layer can be activated by the graphemic representation of any one of a whole set of words. The unit then provides input to every semantic feature that occurs in the meaning of any of the words that activate it. Only those word sets containing the word cat are shown in this example. Notice that the only semantic features which receive input from all these word + +sets are the semantic features of cat. + +city, we shall assume that each unit is either active or inactive and that there is no feedback or cross-connections. These assumptions can be relaxed without substantially affecting the argument. A word-set unit is activated whenever the pattern of the grapheme/ position units codes a word in a particular set. The set could be all the four-letter words starting with HE, for example, or all the words containing at least two T's. All that is required is that it is possible to decide whether a word is in Copyrighted Material + +the set by applying a simple test to the acti vated grapheme/ position units. So, for example, the set of all words meaning "nice" is not al lowed as a word set. There is an implicit assumption that word meanings can be represented as sets of sememes. This is a contentious issue. There appears to be a gulf between the componential view in which a meaning is a set of features and the structural ist view in which the meaning of a word can only be defined in terms of its relationships to other meanings. Later in this chapter we consider one way of integrating these two views by allowing articulated representations to be + +built out of a number of different sets of active features. + +Returning to Figure 5B, the question is whether it is possible to implement an arbitrary set of associations between grapheme/ position vectors and sememe vectors when the word-set units are each activated by more than one word. It wi ll be sufficient to consider just one of the many possible specific models. Let us assume that an active word-set unit provides positive input to all the sememe units that occur in the meaning of any word in the word set. Let us also assume that each sememe unit has a variable threshold that is dynamically adjusted to be just slightly less than the number of active word-set units. Only sememe units that are receiving input from every active word-set unit + +will then become active. + +All the sememes of the correct word wi ll be activated because each of these sememes will occur in the meaning of one of the words in the active word sets. However, additional sememes may also be activated because, just by chance, they may receive input from every active word-set unit. For a sememe to receive less input than its threshold, there must be at least one active word set that does not contain any word which has the sememe as part of its meaning. For each active + +word set the probabi lity, i, of this happening is + +i= (l \_ p)(w- O + +where p is the proportion of words that contain the sememe and wis the number of words in the word set of the word-set unit. The reason for the term w- 1 is that the sememe is already assumed not to be part of the meaning of the correct word, so there are only w- 1 + +remaining words that could have it in their meaning. + +Assume that when a word is coded at the graphemic level it activates uunits at the word-set level . Each sememe that is not part of the word's meaning has a probabi lity i of failing to receive input from each word-set unit. The probabi lity, f, that al l of these word-set units wi ll + +provide input to it is therefore + +f= (I - j)u + +== [I - (I - p ) + +(w - I)]u + +. + +By inspection, this probability of a "false-positive" sememe reduces to zero when w is 1. Table 1 shows the value of f for various combinations of values of p, u, and w. Notice that if p is very small, f can remain negligible even if w is quite large. This means that distributed representations in which each word-set unit partici pates in the representation of many words do not lead to errors if the semantic features are relatively sparse in the sense that each word meaning contains only a small fraction of the total set of sememes. So the word-set units can be fairly nonspecific provided the sememe units are fairly specific (not shared by too many different word meanings) . Some of the entries in the table make it clear that for some values of p, there can be a negl igible chance of error even though the number of word-set units is considerably less than the number of words (the ratio of words to word-set + +units is w/ u ). + +The example described above makes many simpl ifying assumptions. For example, each word-set unit is assumed to be connected to every relevant sememe unit. If any of these connections were missing, we could not afford to give the sememe units a threshold equal to the number of active word-set units. To allow for missing connections we could lower the threshold. This would increase the false-positive error rate, but the effect may be quite small and can be compensated by adding word-set units to increase the specificity of the word-level representations (Willshaw, 1981) . Alternati vely, we could make each word-set unit veto the sememes that do not occur in any of its words. This scheme is robust against missing connections because the absence of one veto can be tolerated if there are other vetos (V. Dobson, per- + +sonal communication, 1984) . + +There are two more simplifying assumptions both of which lead to an underestimate of the effectiveness of distributed representations for the arbitrary mapping task. First, the calculations assume that there is no fine-tuning procedure for incrementing some weights and decrementing others to improve performance in the cases where the most frequent errors occur. Second, the calculations ignore cross-connections among the sememes. If each word meaning is a familiar stable pattern of sememes, there will be a strong "clean-up" effect which tends to suppress erroneous sememes as soon as the pattern of activation at the sememe level is sufficiently close to the famil iar pattern for a particular word meaning. Interactions among the sememes also provide an explanation for the abi lity of a single grapheme string (e.g. , bank) to elicit two quite different meanings. The bottom-up effect of the activated Copyrighted Material + +w p 5 .2 10 .2 20 .2 40 2 80 .2 + +0.07 1 0.49 0.93 1.0 1.0 + +10 10 .2 0.24 10 20 .2 0.86 10 40 .2 1.0 10 80 .2 1.0 10 160 .2 1.0 + +40 40 .2 0.99 40 80 .2 1.0 40160.2 1.0 40 320 .2 1.0 40 640 .2 1.0 + +100 100 .2 1.0 100200.2 1.0 100 400 .2 1.0 100 800 .2 1.0 + +w + +10 100 10 200 100 400 100 800 + +TABLE 1 + +p .1 .1 . 1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .I .1 .1 .1 .1 + +f + +0.0048 0.086 0.48 0.92 1.0 + +0.0074 0.23 0.85 1.0 1.0 0.52 0.99 1.0 1.0 1.0 + +0.99 1.0 1.0 1.0 + +u + +p + +.0 1 .01 .0 1 .01 .0 1 + +9.5x 10-8 4.8x 10-6 0.00016 0.0036 0.049 .01 2.3x 10-11 .01 2.5x 10-8 .01 I. 3x Hr5 .01 0.0024 .01 0. 10 + +.01 2.7x 10-20 .01 3 . + +5x 10-11 + +.01 0.00012 .01 0. 1 9 .01 0.94 .01 9.0x 10-21 .01 4.8x 10-7 .0 1 0.16 .01 0.97 + +The probability,!, of a false-positive sememe as a function of the number of active wordset units per word, U, the number of words in each word-set, w, and the probability, p, of + +a sememe being part of a word meaning. + +word-set units helps both sets of sememes, but as soon as top-down factors give an advantage to one meaning, the sememes in the other meaning wi ll be suppressed by competitive interactions at the sememe + +level (Kawamoto & Anderson, 1984) . + +A simulation. As soon as there are cross-connections among the sememe units and tine-tuning of individual weights to avoid frequent errors, the relatively straightforward probabilistic analysis given above breaks down. To give the cross-connections time to clean up the output, it is necessary to use an iterative procedure instead of the simple "straight-through " processing in which each layer completely determines the states of all the units in the subsequent layer in a single, synchronous step. Systems containing cross-connections, feedback, and asynchronous processing elements are probably more realistic, but they are generally very hard to analyze. However, we are now beginning to discover that there are subclasses of these more complex systems that behave in tractable wayf00Vi4§"d�fttaJj'falhis subclass is described in + +more detai l in Chapter 7. It uses processing elements that are inherently stochastic. Surprisingly , the use of stochastic elements makes these networks better at performing searches, better at learning, + +and easier to analyze. + +A simple network of this kind can be used to illustrate some of the claims about the ability to " clean Uph the output by using interactions among sememe units and the ability to avoid errors by fine - tuning the appropriate weights. The network contains 30 grapheme units, 20 word - set units, and 30 sememe units. There are no direct connections between grapheme and sememe units, but each word-set unit is connected to all the grapheme and sememe units. The grapheme units are divided into three sets of ten, and each three-letter word has one active unit in each group of ten (units can only have activity levels of 1 or 0) . The "meaning" of a word is chosen at random by selecting each sememe unit to be active with a probability of 0.2. The network shown in Figure 6 has learned to associated 20 different grapheme strings with their chosen meanings. Each word-set unit is involved in the representation of many words, and each word involves many word-set units. The detai ls of the learning procedure used to create this network and the search procedure which is used to settle on a set of active sememes when given the graphemic input are described in Chapter 7. Here we + +simply summarize the main results of the simulation . + +After a long period of learning, the network was able to produce the correct pattern of sememes 99.9% of the time when given a graphemic input. Removal of any one of the word-set units after the learning typical ly caused a slight rise in the error rate for several different words rather than the complete loss of one word. Similar effects have been observed in other distributed models (Wood, 1 978) . In our simulations, some of the erroneous responses were quite interesting. In 10,000 tests with a missing word-set unit there were 140 cases in which the model failed to recover the right sememe pattern. Some of these consisted of one or two missing or extra sememes, but 83 of the errors were exactly the pattern of sememes of some other word. This is a result of the cooperative interactions among the sememe units. If the input coming from the word-set units is noisy or underspecified as it may be when units are knocked out, the clean-up effect may settle on a + +similar but incorrect meaning. + +This effect is reminiscent of a phenomenon called deep dyslexia which occurs with certain kinds of brain damage in adults. When shown a word and asked to read it, the subject wil l sometimes say a different word with a very similar meaning. The incorrect word sometimes has a very different sound and spelling. For example, when shown the word PEACH, the subject might say APRICOT. (See Coltheart , Patterson, & Marshall , 1980, for more information about acquired dyslexia.) Copyrighted Material + +FIGURE 6. A compact display that shows all the connection strengthsof the 20 units in the middle layer of a three-layer network. The network can map from a pattern of acti vity over the 30 units in the bottom layer (representing graphemes) to an associated pal\ern of acti vity over the 30 u nits of the lop layer (representing sememes) . Wi thi n each of the large rectangles that are used to depict middle-layer units, I he 30 black and white rectangles at the top depict the weights of the connections to the top layer, and the 30 rectangles at the bottom depict the weightsfrom the bottom layer. White rectangles are positiveweights, black are negative, and the area of a rectan gle depicts the magn itude of the weight . The singleweight that occurs somewhere in the middle of a unit is its + +th + +reshold (black means a positive threshold). The weights between the 30 units in the + +top layer are not shownin this display . + +Semantic errors of this kind seem bizarre because it seems as if the subject must have accessed the lexical item PEACH in order to make the semantically related error, and if he can get to the lexical item why can't he say it ? (These subjects may know and be able to say the words that they misread.) Distributed representations allow us to dispense wi th the rigid distinction between accessing a word and not accessing it . In a network that has learned the word PEACH, the graphemic representation of PEACH wi ll cause approximately the right input to the sememe units, and interactions at the sememe level can then cause exactly the pattern of sememesfor APRICOT. Another psychologically interesti��ftf&l1fIB�WBJl the network relearns after + +it has been damaged. The network was damaged by adding noise to every connection that involved a word-set unit. This reduced the performance from 99. 3% correct to 64.3%. 9 The network was then retrained and it exhibited very rapid relearning, much faster than its original rate of learning when its performance was 64. 3% correct. This rapid recovery was predicted by a geometrical argument which shows that there is something special about a set of connection strengths that is generated by adding noise to a near-perfect set. The resulting set is very different from other sets of connection strengths that exhibit the + +same performance. (See Chapter 7 for further discussion.) + +An even more surprising effect occurs if a few of the words are omitted from the retraining. The error rate for these words is substantially reduced as the retraining proceeds, even though the other graphemesememe pairings have no intrinsic relation to them because all the pairings were selected randomly. The "spontaneous" recovery of words that the network is not shown again is a result of the use of distributed representations. All the weights are involved in encoding the subset of the words that are shown during retraining, and so the added noise tends to be removed from every weight. A scheme that used a separate unit for each word would not behave in this way, so one can view spontaneous recovery of unrehearsed items as a qualitative signature of dis- + +tributed representations. + +STRUCTURED REPRESENTATIONS AND PROCESSES + +In this section we consider two extensions of distributed representations. These extensions illustrate that the idea of distributed representations is consistent with some of the major insights from the field of artificial intelligence concerning the importance of structure in representations and processes. Perhaps because some proponents of distributed· representations have not been particularly attuned to these issues, it is often unclear how structure is to be captured in a distributed representational scheme. The two parts of this section give some indication of the directions that can be taken in extending distributed + +representations to deal with these important considerations. + +9The error rate was 99.3% rather than 99.9% in this example because the network was forced to respond faster, so the cooperative effects had less time to settle on the optimal + +Representing Constituent Structure + +Any system that attempts to implement the kinds of conceptual structures that people use has to be capable of representing two rather different kinds of hierarchy. The first is the "IS-A" hierarchy that relates types to instances of those types. The second is the part/whole hierarchy that relates items to the constituent items that they are composed of. The most important characteristics of the IS-A hierarchy are that known properties of the types must be "inherited " by the instances, and properties that are found to apply to all instances of a type must normally be attributed to the type. Earlier in this chapter we saw how the IS-A hierarchy can be implemented by making the distributed representation of an instance include, as a subpart, the distributed representation for the type. This representational trick automatically yields the most important characteristics of the IS-A hierarchy, but the trick can only be used for one kind of hierarchy. If we use the part/whole relationship between patterns of activity to represent the type/instance relationship between items, it appears that we cannot also use it to represent the part/whole relationship between items. We cannot make the representation of the whole be the sum of the representa- + +tions of its parts. + +The question of how to represent the relationship between an item and the constituent items of which it is composed has been a major stumbling block for theories that postulate distributed representations. In the ri val , local ist scheme , awhole is a node that is linked by labeled arcs to the nodes for its parts. But the central tenet of the distributed scheme is that different items correspond to alternative patterns of activity in the same set of units, so it seems as if a whole and its parts + +cannot both be represented at the same time. + +Hinton 098 1a) descri bed one way out of this dilemma. It relies on the fact that wholes are not simply the sums of their parts. They are composed of parts that play particular roles within the whole structure. A shape, for example, is composed of smaller shapes that have a particular size, orientation, and position relative to the whole. Each constituent shape has its own spatial role, and the whole shape is composed + +of a set of shape/ role pairs. + +1O Similarly , aproposition is composed of + +objects that occupy particular semantic roles in the whole propositional + +10Relationships between parts are important as well. One advantage of explicitly representing shape/ role pairs is that it allows different pairs to support each other. One can view the various different locations within an object as slots and the shapes of parts of an object as the fillers of these slots. Knowledge of a whole shape can then be imple- + +structure. This suggests a way of implementing the relationship between wholes and parts: The identity of each part should first be combined with its role to produce a single pattern that represents the combination of the identity and the role, and then the distributed representation for the whole should consist of the sum of the distributed representations for these identity/ role combinations (plus some additional "emergent" features) . This proposal differs from the simple idea that the representation of the whole is the sum of the representations of its parts because the subpatterns used to represent identity/ role combinations are quite different from the patterns used to represent the identities + +alone. They do not , for example, contain these patterns as parts. + +Naturally, there must be an access path between the representation of an item as a whole in its own right and the representation of that same item playing a particular role within a larger structure. It must be possible, for example, to generate the identity/ role representation from two separate, expl icit, distributed patterns one of which represents the identity and the other of which represents the role. It must also be possible to go the other way and generate the explicit representations of the identity and role from the single combined representation of the + +identity / role combination (see Figure 7). + +The use of patterns that represent identity/ role combinations al lows the part/ whole hierarchy to be represented in the same way as the type/ instance hierarchy. We may view the whole as simply a particular instance of a number of more general types, each of which can be defined as the type that has a particular kind of part playing a particular + +role (e.g. , men with wooden legs) . + +Sequential Symbol Processing + +If constituent structure is implemented in the way described above, there is a serious issue about how many structures can be active at any one time. The obvious way to al locate the hardware is to use a group of units for each possible role within a structure and to make the pattern of activity in this group represent the identity of the constituent that is currently playing that role. This implies that only one structure can be represented at a time, unless we are wi lling to postulate multiple copies of the entire arrangement. One way of doing this, using units with programmable rather than fixed connections, is described in Chapter 16. However, even this technique runs into difficulties if more than a few modules must be "programmed " at once. However, people do seem to suffer from strong constraints on the number of structures of the same general type that they can process at once. The Copyrighted Material + +AG EN T + +IDENTITY + +PATIENT LOCATION + +FIGURE 7. A sketch of the apparatus that might be necessary for combining separate representations of an identity and a role into a single pattern. Only one identity and only one role can be explicitly represented at a time because the identity and role groups can each have only one pattern of activity at a time. However, the various role groups allow many identity/role combinations to be encoded simultaneously. The small triangular symbols represent the ability of the pattern of activity in the group that expl ictly represents a role to determine which one of the many role groups is currently interacting with the identity group. This allows the identity occupying a particular role to be "read out " as well as allowing the reverse operation of combining an identity and a role. + +sequentiality that they exhibit at this high level of descri ption is initially surprising given the massively parallel architecture of the brain, but it becomes much easier to understand if we abandon our localist predelictions in favor of the distributed alternative which uses the parallelism to give each active representation a very rich internal structure that allows the right kinds of generalization and content-addressability. There may be some truth to the notion that people are sequential symbol processors if each "symbolic representation " is identified with a Copyrighted Material + +successive state of a large interactive network. See Chapter 14 for + +further discussion of these issues. + +One central tenet of the sequential symbol processing approach (Newell, 1980) is the ability to focus on any part of a structure and to expand that into a whole that is just as rich in content as the original whole of which it was a part. The recursive abi lity to expand parts of a structure for indefinitely many levels and the inverse ability to package up whole structures into a reduced form that allows them to be used as constituents of larger structures is the essence of symbol processing. It allows a system to build structures out of things that refer to other whole structures without requiring that these other structures be + +represented in all their cumbersome detail. + +In conventional computer implementations, this ability is achieved by using pointers. These are very convenient, but they depend on the use of addresses. In a parallel network, we need something that is functional ly equivalent to arbitrary pointers in order to implement symbol processing. This is exactly what is provided by subpatterns that stand for identity/ role combinations. They allow the full identity of the part to be accessed from a representation of the whole and a representation of the role that the system wishes to focus on, and they also allow explicit representations of an identity and a role to be combined into a less cumbersome representation , so that several identity/role combinations can be represented simultaneously in order to form the represen- + +tation of a larger structure. + +SUMMARY + +Given a parallel network, items can be represented by activity in a single, local unit or by a pattern of activity in a large set of units with each unit encoding a microfeature of the item. Distributed representations are efficient whenever there are underlying regularities which can be captured by interactions among microfeatures. By encoding each piece of knowledge as a large set of interactions, it is possible to achieve useful properties like content-addressable memory and automatic generalization, and new items can be created without having to create new connections at the hardware level . In the domain of continuously varying spatial features it is relatively easy to provide a mathematical analysis of the advantages and drawbacks of using distri- + +buted representions. + +Distributed representations seem to be unsuitable for implementing purely arbitrary mappings because there is no underlying structure and so general ization only causes unwanted interference. However, even Copyrighted Material + +for this task, distributed representations can be made fairly efficient and they exhibit some psychologically interesting effects when damaged. There are several difficult problems that must be solved before distributed representations can be used effectively. One is to decide on the pattern of activity that is to be used for representing an item. The similarities between the chosen pattern and other existing patterns wi ll determine the kinds of general ization and interference that occur. The search for good patterns to use is equivalent to the search for the underlying regularites of the domain. This learning problem is + +addressed in the chapters of Part II. + +Another hard problem is to clarify the relationship between distributed representations and techniques used in artificial intelligence like schemas, or hierarchical structural descriptions. Existing artificial intelligence programs have great difficulty in rapidly finding the schema that best fits the current situation. Parallel networks offer the potential of rapidly applying a lot of knowledge to this best-fit search, but this potential wi ll only be realized when there is a good way of implementing schemas in parallel networks. A discussion of how this might be + +done can be found in Chapter 14. + +ACKNOWLEDGMENTS + +This chapter is based on a technical report by the first author, whose work is supported by a grant from the System Development Foundation . We thank Jim Anderson, Dave Ackley, Dana Bal lard, Francis Crick, Scott Fahlman, Jerry Feldman , Chri stopher Longuet-Higgins, Don Norman, Terry Sejnowski , and Tim Shallice for helpful + +discussions. + +FIGURE I. The one-layer perceptron analyzed by Minsky and Papert. (From Perceprrons by M. L. Minsky and S. Papert, 1969, Cambridge, MA: MIT Press. Copyright 1969 by + +MIT Press. Reprinted by permission.) + +Minsky and Papert's analysis of the li mitations of the one-layer perceptron, coupled with some of the early successes of the symbolic processing approach in artificial intell igence, was enough to suggest to a large number of workers in the field that there was no future in perceptron-l ike computational devices for artificial intell igence and cognitive psychology. The problem is that although Minsky and Papert were perfectly correct in their analysis, the results apply only to these simple one-layer perceptrons and not to the larger class of perceptronlike models. In particular (as Minsky and Papert actually conceded) , it can be shown that a multi layered percept ron system, including several layers of predicates between the retina and the decision stage, can compute functions such as parity, using reasonable numbers of units each computing a very local predicate. (See Chapters 5 and 8 for examples of multilayer networks that compute parity). Similarly, it is not difficult to develop networks capable of solving the connectedness or inside/outside problem. Hinton and Sejnowski have analyzed a version + +of such a network (see Chapter 7) . + +Essentially, then, although Minsky and Papert were exactly correct in thei r analysis of the one-layer perceptron, the theorems don't apply to systems which are even a little more complex. In particular, it doesn't apply to multilayer systems nor to systems that allow feedback loops . Minsky and Papert argued that there would not be much value to multilayer perceptrons. First, they argued that these systems are sufficiently unrestricted as to be vacuous. They pointed out, for example, that a universal computer could be built out of linear threshold units. Copyrighted Material + +Therefore, restricting consideration of machines made out of linear + +threshold units is no restriction at all on what can be computed. + +We don't, of course, believe that the class of models sketched in Chapter 2 is a smal l or restrictive class. (Nor, for that matter, are the languages of symbol processing systems especially restrictive.> The real issue, we bel ieve, is that different algorithms are appropriate to different architectural designs. We are investigating an architecture in which cooperative computation and paral lelism is natural. Serial symbolic systems such as those favored by Minsky and Papert have a natural domain of algorithms that di ffers from those in PDP models. Not everything can be done in O:1e step without feedback or layering (both of which suggest a kind of "seriality"). We have been led to consider models that have both of these features. The real point is that we seek algorithms that are as parallel as possible. We bel ieve that such algorithms are going to be closer in form to the algorithms which could be employed by the hardware of the brain and that the kind of parallelism we employ allows the exploitation of multiple information sources + +and cooperative computation in a natural way . + +A further argument advanced by Minsky and Papert against perceptron-l ike models with hidden units is that there was no indication how such multilayer networks were to be trained. One of the appealing features of the one-layer perceptron is the existence of a powerful learning procedure, the perceptron convergence procedure of Rosenblatt. In Minsky and Papert's day, there was no such powerful learning procedure for the more complex multilayer systems. This is no longer true. Chapters 5, 6, 7, and 8 all provide schemes for learning in systems with hidden units. Indeed, Chapter 8 provides a direct generalization of the perceptron learning procedure which can be applied to arbitrary networks with multiple layers and feedback among layers. This procedure can , in principle, learn arbitrary functions including, of + +course, parity and connectedness . + +The problem of stimulus equivalence. A second problem with early PDP models-and one that is not necessari ly completely overcome by multi layer systems-is the problem of invariance or stimulus equivalence. An A is an A is an A, no matter where on the retina it appears or how large it is or how it is oriented; and people can, in general, recognize patterns rather well despite various transformations. It has always seemed elegant and natural to imagine that an A, no matter where it is presented, is normalized and then processed for recognition using stored knowledge of the appearance of the letter (Marr, 1982; Neisser, + +1967). + +Letter Units [ + +Canonical Feature Units + +Retinocentric Feature + +Units 8 + +Mapping Units + +FIGURE 2. Hinton's (I981b) scheme for mapping patterns in one coordinate system into patterns in another coordinate system. At the top are two letter-detector units, with mutual excitatory connections to the six canonical feature units (the position and orientation of the line segment each of these detectors represents is indicated by the line segment in the "body" of each unit). At the bottom are six retinocentric feature units, and al the right are units corresponding to each of three different mappings from retinocentric to canonical features. (The arrows on the units indicate which direction in the retinocentric frame corresponds to upright in the canonical frame, and the arrow outside the unit indicates the nature of the transformation imposed on the retinocentric pattern). Each canonical unit receives three pairs of inputs, with each pair arriving at a multiplicative + +connection. These inputs are illustrated for one canonical unit only. + +recetvmg unit. In this case, if a particular retinocentric feature is on and the 90° clockwise mapping unit is on, then the canonical feature corresponding to the active retinal feature will receive an excitatory input. If just one of the two inputs to the connection is on , no activation wi ll flow to the central unit. In this way, when a mapping unit is active, it effectively programs the multipl icati ve connections needed to implement the corresponding mapping by activating one of the two + +inputs to each of the programmable connections. + +Using this mechanism, it is possible to map from retinal to central coordinates if the mapping is known in advance. Object recognition can now proceed as follows: A mapping is chosen (perhaps on the basis of processing the preceding stimulus> , and this is used to map a retinal input onto the canonCCopyMl)iUbd \_tetia�ystem involving variable + +Recursion. There are many other specific points that have been raised with respect to existing PDP models. Perhaps the most common one has to do with recursion. The ability to perform recursive function calls is a major feature of certain computational frameworks, such as augmented transition network (ATN) parsers (Woods, 1973; Woods & Kaplan, 1971), and is a property of such frameworks that gives them the capability of processing recursively defined struct ures such as sentences, in which embedding may produce dependencies between elements of a surface string that are indefinitely far removed from each other (Chomsky , 1957). It has often been suggested that PDP mechanisms lack the capacity to perform recursi ve computations and so are simply incapable of providing mechanisms for processing sentences + +and other recursively defined structures. + +As before, these suggestions are simply wrong. As we have already seen, one can make an arbitrary computational machine out of linear threshold units, including, for example, a machine that can carry out all the operations necessary for implementing a Turing machine; the one limitation is that real biological systems cannot be Turing machines because they have finite hardware. In Chapter 14, however, we point out that with external memory aids (such as paper and pencil and a + +notational system) such limitations can be overcome as well. + +We have not dwelt on PDP implementations of Turing machines and recursive processing engines because we do nut agree with those who would argue that such capabilities are of the essence uf human computation. As anyone who has ever attempted to process sentences like "The man the boy the girl hit kissed moved" can attest, our ability to process even moderate degrees of center-embedded structure is grossly impaired relative to that of an ATN parser. And yet, the human ability to use semantic and pragmatic contextual information to facilitate comprehension far exceeds that of any existing sentence processing + +machine we know of. + +What is needed, then, is not a mechanism for flawless and effortless processing of center-embedded constructions. Compilers of computer languages generally provide such facilities, and they are powerful tools, but they have not demonstrated themselves sufficient for processing natural language. What is needed instead is a parser built from the kind of mechanism which faci litates the simultaneous consideration of large numbers of mutual and interdependent constraints. The challenge is to show how those processes that others have chosen to explain in terms of recursive mechanisms can be better explained by the kinds of + +processes natural for PDP networks. + +This challenge is one that has not yet been fully met. However, some initial steps toward a PDP model of language processing are + +described in Chapter �pyriJfh�d ��Hr)ia/ + +whose implementation is + +A related claim that some people have made is that our models appear to share much in common with behaviorist accounts of behavior. While they do involve simple mechanisms of learning, there is acrucial difference between our models and the radical behaviorism of Skinner and his followers. In our models, we are expl icitly concerned with the problem of internal representation and mental processing, whereas the radical behaviorist explicitly denies the scientific utility and even the validity of the consideration of these constructs. The training of hidden units is , as is argued in Chapters 5 to 8, the construction of internal representations. The models described throughout the book all concern internal mechanisms for activating and acquiring the ability to activate appropriate internal representations. In this sense, our models must be seen as completely antithetical to the radical behaviorist program and strongly committed to the study of representa- + +tion and process. + +PDP Models Are the Wrong Level of Analysis + +It is sometimes said that although PDP models are perfectly correct, they are at the wrong level of analysis and therefore not relevant to psychological data. 2 For example, Broadbent (1985) has argued that psychological evidence is irrelevant to our argument about distributed memory because the distribution assumption is only meaningful at what Marr (I982) has called the implementational (physiological) level and that the proper psychological level of description is the computational + +level . + +The issues of levels of analysis and of theorizing is difficult and requires a good deal of careful thought. It is, we bel ieve, largely an issue of scientific judgement as to what features of a lower level of analysis are relevant to a higher one. We are quite sure that it is not a matter for prescri ption. We begin our response to this objection with a review of Marr's analysis and his three levels of description. We then suggest that indeed our models are stated at the same level (in Marr's sense) as most traditional models from cognitive science. We then describe other senses of levels, including one in which higher level accounts can be said to be convenient approximations to lower level accounts. This sense comes closest to capturing our view of the + +2 The following discussion is based on a paper (Rumelhart & McClelland, 1985) written in response to a critique by Donald Broadbent (1985) on our work on distributed + +relation between our PDP models and other traditional information + +processing models. + +Marr's Notion of Levels + +David Marr (1982) has provided an influential analysis of the issue of levels in cognitive science. Although we are not sure that we agree entirely with Marr's analysis, it is thoughtful and can serve as a starting point. Whereas Broadbent acknowledges only two levels of theory, the computational and the implementational, Marr actual ly proposes three, the computational, the algorithmic, and the implementational levels. Table 1 gives a description of Marr's three levels. We believe that PDP models are generally stated at the algorithmic level and are primarily aimed at specifying the representation of information and the processes or procedures involved in cognition. Furthermore, we agree with Marr's assertions that "each of these levels of descri ption will have their place" and that they are "logically and causal ly related." Thus, no particular level of descri ption is independent of the others. There is an impl icit computational theory in PDP models as wel l as an appeal to certain implementational (physiological) considerations. We believe this to be appropriate. It is clear that different algorithms are more naturally implemented on different types of hardware and, therefore, information about the implementation can inform our hypotheses at the + +algorithmic level. + +TABLE 1 THE THREE LEVELS AT WHICH ANY MACHINE CARRYING OUT INFORMA TION PROCESSING TASKS MUST DE UNDERSTOOD + +Computational Theory What is the goal of the computation, why is it appropriate, and what is the logic of the strategy by which it can be carried + +out? + +Representation and Algorithm How can this computational theory be implemented? In particular, what is the representation for the input and output, and what is the algorithm for the transformation? + +Hardware Implementation How can the representation and algorithm be realized physically? + +Computational models, according to Marr, are focused on a formal analysis of the problem the system is solving-not the methods by which it is solved. Thus, in linguistics, Marr suggests that Chomsky's (1965) view of a competence model for syntax maps most closely onto a compulationa/level theory, whereas a psycholinguistic theory is more of aperformance theory concerned with how grammatical structure might actually be computed. Such a theory is concerned with the algorithmic level of description. It is the algorithmic level at which we are concerned with such issues as efficiency, degradation of performance under noise or other adverse conditions, whether a particular problem is easy or difficult, which problems are solved quickly and which take a long time to solve, how information is represented, etc. These are all questions to which psychological inquiry is directed and to which psychological data is relevant. Indeed, it would appear that this is the level to which psychological data speaks most strongly. At the computational level, it does not matter whether the theory is stated as a program for a Turing machine, as a set of axioms, or as a set of rewrite rules. It does not matter how long the computation takes or how performance of the computation is affected by "performance" factors such as memory load, problem complexity, etc. It doesn't matter how the information is represented, as long as the representation is rich enough, in princi ple, to support computation of the required function. The question is simply what junction is being computed, not how is it being computed. + +Marr recommends that a good strategy in the development of theory is to begin with a careful analysis of the goal of a particular computation and a formal analysis of the problem that the system is trying to solve. He believes that this top-down approach will suggest plausible algorithms more effectively than a more bottom-up approach. Thus, the computational level is given some priority. However, Marr certainly does not propose that a theory at the computational level of description + +is an adequate psychological theory, + +As psychologists, we are committed to an elucidation of the algorithmic level. We have no quarrel with Marr's top-down approach as a strategy leading to the discovery of cognitive algorithms, though we have proceeded in a different way. We emphasize the view that the various levels of description are interrelated. Clearly, the algorithms must, at least roughly, compute the function specified at the computational level . Equally clearly, the algorithms must be computable in amounts of time commensurate with human performance, using the kind and amount of hardware that humans may reasonably be assumed to possess . For example, any algorithm that would require more specific events to be stored separately than there are synapses in the brain should be given a lower plausibility rating than those that require + +4. GENERAL ISSUES 127 + +such primitives wi ll change the shape of higher level theory + +considerably. + +PDP mechanisms may also place some constraints on what we might realistically ask for in the way of computational primiti ves because of the costs of implementing certain kinds of computations in parallel hardware in a single relaxation search. The paral lel matching of variablized productions is one case in point. Theories such as ACT\* (J. R. Anderson, 1983) assume that this can be done without worrying about the implementation and, therefore, provide no principled accounts of the kinds of crosstalk exhibited in human behavior when processing multiple patterns simultaneously . However, it appears to be a quite general property of PDP mechanisms that they wi ll exhibit crosstal k when processing multiple patterns in parallel (Hinton & Lang, 1985; + +Mozer, 1984; see Chapters 12 and 16) . + +High-level languages often preserve some of the character of the lower level mechanisms that implement them, and the resource and time requirements of algorithms drastically depends on the nature of the underlying hardware. Higher level languages that preserve the character of PDP mechanisms and exploit the algorithms that are effective descriptions of parallel networks are not here yet, but we expect such things to be coming along in the future. This wi ll be a welcome development, in our view, since certain aspects of cognitive theory have been too strongly influenced by the discrete, sequential algorithms + +available for expression in most current high-level languages. + +As we look closely, both at the hardware in which cognitive algorithms are implemented and at the fine structure of the behavior that these algorithms are designed to capture, we begin to see why it may be appropriate to formulate models which come closer to describing the microstructure of cognition. The fact that our microstructural models can account for many of the facts about the representation of general and specific information, for example, as discussed in Chapter 18, makes us ask why we should view constructs like logogens, prototypes, and schemata as anything other than convenient approximate descri p- + +tions of the underlying structure of memory and thought. + +Reductionism and Emergent Properties + +A slightly different, though related, argument is that the PDP enterprise is an exercise in reductionism-an exercise in which all of psychology is reduced to neurophysiology and ultimately to physics. It is argued that coherent phenomena which emerge at any level (psychol- + +ogy or physics or sociolW'Jyh���� �9g + +grn language of descri ption + +it has to do with the fact that we can't know everything and find out everything at once. The approach we have been arguing for suggests that to understand something thoroughly at some level requires knowledge at that level , plus knowledge of the lower levels. Obviously, this is impractical . In practice, even though there might be effects of lower levels on higher levels, one cannot always know them. Thus, attempting to formulate a description at this higher level as a first order of approximation is an important research strategy. We are forced into it if we are to learn anything at all . It is possible to learn a good deal about psychology without any reference whatsoever to any lower levels. This practical strategy is not, however, an excuse for ignoring what is known about the lower levels in the formulation of our higher level theories . Thus, the economist is wrong to ignore what we might know about individuals when formulating his theories. The chemist would be wrong to ignore what is known about the structure of the carbon atom in explaining the hardness of diamonds. We argued above that the view that the computational level is correct derives from experience with a very special kind of device in which the higher level was designed to give the right answers-exactly. In describing natural intelligence that can't, we suspect, be right-exactly. It can be a first order of approximation. As we learn more about a topic and as we look at it in more and more detai l we are going to be forced to consider more and more how it might emerge (in the above sense) from the interactions among its constituents. Interaction is the key word here. Emergent properties occur whenever we have nonli near interactions. In these cases the princi ples of interaction themselves must be formulated and the real theory at the higher level is, like chemistry, a theory of interac- + +tions of elements from a theory one level lower. + +Not Enough Is Known From Neuroscience to Seriously + +Constrain Cognitive Theories + +Many cognitive scientists believe that there will eventually be an understanding of the relationships between cognitive phenomena and brain functioning. Many of these same people feel, however, that the brain is such an exceptionally powerful computational device that it is capable of performing just about any computation. They suppose that facts now known from neuroscience place little or no restriction on what theories are possible at a cognitive level . In the meantime, they suppose, a top-down analysis of possible mechanisms of cognition can lead to an understanding of cognition that will stand independently of whatever might be discqsf)pyJ-;�m# �;fHnctioning. Moreover, they + +constraint. Moreover, note that individual neurons probably don ' t compute very complicated functions. It seems unlikely that a single neuron computes a function much more complex than a single instruction in a digital computer. Imagine, again, writing an interesting program in even 1000 operations of this limited complexity of a serial computer. Evidently, the brain succeeds through massive parallelism. Thus, we conclude , the mechanisms of mind are most likely best understood as resulting from the cooperative acti vity of very many relatively simple + +processing units operating in paral lel . + +There is a very large number of neurons. Another self-evident, but important, aspect of brain - style processing is the very large number of processing units involved. Conventional estimates hold that there are on the order of 1010 to 1011 neurons in the brain. Moreover, each neuron is an active processing unit. This suggests parallelism on avery large scale indeed. An understanding of parallel computation involving a few hundred reasonably complex processors provides the wrong model . It may well be that it is the massive scale of the parallel ism of + +the brain that gives it its amazing power. + +Although the human brain is large, the number of neurons is not unl imited. It happens that our models sometimes push the limits of plausibility because of the large number of units they require. This is a real constraint , one that we and others have begun to take into account in evaluating our models (see Chapter 12 for a discussion of this issue). + +Neurons receive inputs from a large number of other neurons. Another important feature of brain processing is the large fan-in and fan - out to and from each unit. Estimates vary, but single cortical neurons can have from 1,000 to 100,000 synapses on their dendrites and, likewise, can make from 1,000 to 100,000 synapses on the dendrites of other neurons. Generally, one or a small number of action potentials received are not enough to generate an action potential (see, for example, Chapter 20) . This suggests that human computation does not involve the kind of logic circuits out of which we make our digital computers, but that it involves a kind of statistical process in which the single units do not make decisions, but in which decisions are the product of the cooperative action of many somewhat independent processing units. Reliability derives from the stabi lity of the statistical behavior of large numbers of units . Again, this degree of connectivity should be contrasted with the number of immediate neighbors of processors in current parallel computers . Usually these numbers are measured in the tens (or less) rather than in the thousands . Moreover, this large degree of connectivity suggests that no neuron is very many synapses away + +modalities. But higher level functions seem very much to be character- + +ized by distributed, rather than central control . + +This point has been made most clearly by the Russian neuropsychologist Luria (I 966; 1973) . Luria's investigations show that for every integrated behavioral function (e.g., visual perception, language comprehension or production, problem solving, reading) , many different parts of the cortex play a role so that damage to any part influences performance but is not absolutely crucial to it. Even the frontal lobes , most frequently associated with executive functions , are not absolutely necessary in Luria's view, in that some residual function is generally observed even after massive frontal damage (and mild frontal damage may result in no detectable symptomatology at al l) . The frontal lobes have a characteristic role to play, facilitating strategy shifts and inhibiting impulsive responding, but the overall control of processing can be as severely impaired by damage to parietal lobe structures that appear to be responsible for maintaining organized representations that + +support coordinated and goal-directed activity. + +Our view of the overall organization of processing is similar to Luria's. We have come to believe that the notion of subroutines with one system "cal ling" another is probably not a good way to view the operation of the brain. Rather, we believe that subsystems may modulate the behavior of other subsystems , that they may provide constraints to be factored into the relaxation computation . An elaboration of some + +aspects of these ideas may be found in Chapter 14. + +Relaxation is the dominant mode oj computation. Although there is no specific piece of neuroscience which compels the view that brainstyle computation involves relaxation, all of the features we have just discussed have led us to bel ieve that the primary mode of computation in the brain is best understood as a kind of relaxation system (cf. Chapters 6, 7, 14, 15, and 21) in which the computation proceeds by iteratively seeking to satisfy a large number of weak constraints. Thus, rather than playing the role of wires in an electric circuit, we see the connections as representing constraints on the co-occurrence of pairs of units. The system should be thought of more as settling into a solution than calculating a solution. Again, this is an important perspective change which comes out of an interaction of our understanding of how the brain must work and what kinds of processes seem to be required + +to account for desired behavior. + +As can be seen, this list does not depend on specific discoveries from neuroscience. Rather, it depends on rather global considerations. Although none of these general properties of the brain tell us in any detai l how the brain functions to support cognitive phenomena, together they lead to aoo��fIAA9�Rhl how the brain works that + +the fact that we normally assume that units communicate via numbers. These are sometimes associated with mean firing rates. In fact, of course, neurons produce spi kes and this spiking itself may have some computational significance (see Chapters 7 and 21 for discussions of the possible computational significance of neural spiking) . Another example of possibly important facts of neuroscience which have not played a role in our models is the diffuse pattern of communication which occurs by means of the dispersal of chemicals into various regions of the brain through the blood stream or otherwise . We generally assume that communication is point-to-point from one unit to another. However. we understand that diffuse communication can occur through chemical means and such communication may play an important role i n setting parameters and modulating the networks so that they can perform rather di fferent tasks in different situations. We have employed the idea of diffuse distribution of chemicals in our account of amnesia (Chapter 25) , but, in general , we have not otherwise integrated such assumptions into our models. Roughly, we imagine that we are studying networks in which there is a fixed setting of such parameters, but the situation may well be much more complex than that. (See Chapter 24 for some discussion of the role of norepinephrine and other neuro- + +modulators.) + +Most of our models are homogeneous with respect to the functioning of our units. Some of them may be designated as inhibitory and others as excitatory, but beyond that, they are rarely differentiated. We understand that there are perhaps hundreds of kinds of neurons (see Chapter 20) . No doubt each of these kinds play a slightly different role in the information processing system. Our assumptions in this regard are obviously only approximate. Simi larly, we understand that there are many different kinds of neurotransmitters and that there are different systems in which different of these neurotransmitters are dominant. Again, we have ignored this difference (except for excitatory and inhibitory connections) and presume that as more is understood about the information processing impl ications of such facts we will be + +able to determine how they fit into our class of models. + +It is also true that we have assumed a number of mechanisms that are not known to exist in the brain (see Chapter 20) . In general , we have postulated mechanisms which seemed to be required to achieve certain important functional goals, such as, for example, the development of internal representations in multilayer networks (see Chapter 8) . It is possible that these hypothesized mechanisms do exist in the brain but have not yet been recognized. In that sense our work could be considered as asource of hypotheses for neuroscience. It is also possible that we are correct about the computations that are performed, but that they are perfo�&JKf6MfM1 kind of neural mechanism + +certain patterns of behavior which, in evolutionary time, have proven to be useful (such as sucking, reaching, or whatever) we can bui ld them in, but we leave the organism free to modify or completely reverse any of these behavioral predispositions.7 At the same time, we have the best of the empiricist view- namely, we place no a priori limitations on how the organism may adapt to its environment. We do, however, throw out the weakest aspect of the empiricist dogmanamely, the idea of the tabula rasa (or totally random net) as a starting point. The organism could start at whatever initial state its evolutionary + +history prepared it for. + +Perhaps, at this stage, all of this seems painfully obvious. It seems obvious to us too, and nevertheless, it gives us a new perspective on the nativism /empiricism issue. The issue is not what is the set of predetermined modules as some would suggest (cf. Fodor, 1983) . On this view it seems quite reasonable, we submit, that to the degree that there are modules, they are co-determined by the start state of the system (the genetic predisposition) and by the environment. (We take a module to be roughly a set of units whi ch are powerfully interconnected among themselves and relatively weakly connected to units outside of the set; of course, this concept admits all gradations of modularity, just as our view of schemata allows al l degrees of schematization of knowledge.) There is, on this view, no such thing as "hardwiring." Neither is there any such thing as "software." There are only connections. All connections are in some sense hardwired (in as much as they are physical entities) and all are software (in as much as they can be changed.) Thus, it may very well be that there is a part of the network prewired to deal with this or that processing task. If that task is not relevant in the organism's environment, that part of the network can be used for something else. If that part of the network is damaged, another part can come to play the role "normally" carried out by the damaged portion. These very properties have been noted characteristics of the brain since Hughlings-Jackson 's work in the late 19th century (e.g. , Jackson, 1869/1958) ; Jackson pointed them out as difficulties for the strict local izationist views then popular among students of the brain. Note too that our scheme allows for the organism to be especial ly sensitive to certain relationships (such as the relationship between nausea and eating, for which there might be stronger or more direct prewired + +7Here agai n. our organ ism oversimplifies a bit. It appears that some parts of the nervous system -particularly lower level. reOexive. or regulatory mechanisms -seem to be prewired and subject only to control by trainable modulatory connectionsto higher level. more adaptive mechanisms. rather than to be directly modifiable themselves: for discus- + +connections) while at the same time allowing quite arbitrary associa- + +tions to be learned. + +Finally, it should be mentioned that all of the learning schemes that have been proposed for networks of the sort we have studied are incremental (cf. Chapters 7, 8, 11 , 18, 19, and 25) , and therefore as an organism moves from its primarily genetically predetermined start state to its primarily environmentally determined final state, it will pass through a sequence of more or less intermediate states. There will be a kind of trajectory through the space of possible networks. This trajectory will constitute the developmental sequence for the organism. To the degree that different individuals share the same genetics (start state) and to the degree that their environments are similar, they will pass through similar trajectories. It should also be said that since, in PDP systems, what is learned is a product of both the current state of the organism and the current pattern of inputs, the start state will have an important effect on what is learned and the shape of the network following any given set of experiences. However, the greater the amount of experience, the more independent the system should be from its start state and the more dependent it should be on the struc- + +ture of its environment. + +Of course, not all connections may be plastic-certainly, many subcortical mechanisms are considerably less plastic than cortical ones. Also, plasticity may not continue throughout life (see Chapter 24) . It would, of course, be a simple matter to suppose that certain connections are not modifiable. This is an issue about which our framework provides no answer. The major point is that there is no inconsistency between prewired, innate knowledge, and mutability and adaptability. We cannot resist making one more point about the nativism/empiricism issue. This is that our PDP account of innate knowledge seems to provide a rather plausible account of how we can come to have innate "knowledge." To the extent that stored knowledge is assumed to be in the form of explicit, inaccessible rules of the kind often postulated by linguists as the basis for linguistic competence (see Chapter 18), it is hard to see how it could "get into the head" of the newborn. It seems to us implausible that the newborn possesses elaborate symbol systems and the systems for interpreting them required to put these explicit, inaccessible rules to use in guiding behavior. On our account, we do not need to attribute such complex machinery. If the innate knowledge is simply the prewired connections, it is encoded from the start in just the right way to be of use by the processing + +mechanisms. + +Why Are People Smarter Than Rats? + +Some have argued that since we claim that human cognition can be explained in terms of PDP networks and that the behavior of lower animals such as rats can also be described in terms of such networks we have no princi pled way of explaining why rats are not as smart as people. Given all of the above, the Question does seem a bit puzzl ing. We are not claiming, in any way, that people and rats and all other organisms start out with the same prewired hardware. People have much more cortex than rats do or even than other primates do; in particular they have very much more prefrontal and parietal cortex-more brain structure not dedicated to input /output -and presumably, this extra cortex is strategically placed in the brain to subserve just those functions that differentiate people from rats or even apes. A case in point is the part of the brain known as the angular gyrus. This part of the brain does not exist even in chimpanzees. It sits at the intersection between the language areas of the temporal lobe and the visual areas of the parietal lobe, and damage to this area produces serious deficits in language and in the mapping of words onto meanings. While it is possible that structures like the angular gyrus possess some special internal wiring that makes them fundamental ly different, somehow, in the kinds of cognitive operations they perform , their cytoarchitecture is not markedly different from that of other parts of the brain (see Chapters 20 and 21). Thus it seems to us quite plausible that some of the differences between rats and people lie in the potentiality for forming connections that can subserve the vital functions of language and thought + +that humans exhibit and other animals do not. + +But there must be another aspect to the difference between rats and people as wel l. This is that the human environment includes other people and the cultural devices that they have developed to organize their thinking processes. Some thoughts on how we imagine these cultural devices are exploited in higher forms of intelligent behavior are + +presented in Chapter 14. + +Conscious Knowledge and Explicit Reasoning + +There may be cognitive scientists who accept some or al l of what we have said up to this point, but still feel that something is missing, namely, an account of how we guide behavior using explicit, conscious knowledge, how we reason from what we know to new conclusions based on that knowled�'O�9r1gRRW1 'NIBtQR9t a path through a problem + +PART II + +BASIC MECHANISMS + +The chapters of Part II represent explorations into specific architectures and learning mechanisms for PDP models. These explorations proceed through mathematical analysis coupled with results from simulations. The major theme which runs through all of these explorations is a focus on the learning problem. How can PDP networks evolve to perform the kinds of tasks we require of them? Since one of the primary features of PDP models in general is their ability to self-modify, these studies form an important base for the application of these + +models to specific psychological and biological phenomena. + +In Chapter 5, Rumelhart and Zipser begin with a summary of the history of early work on learning in parallel distributed processing systems. They then study an unsupervised learning procedure called competitive learning. This is a procedure whereby feature detectors capable of discriminating among the members of a set of stimulus input patterns evolve without a specific teacher guiding the learning. The basic idea is to let pool s of potential feature detector units compete among themselves to respond to each stimulus pattern. The winner within each pool-the one whose connections make it respond most strongly to the pattern-then adjusts its connections slightly toward the pattern that it won. Several earlier invest igators have considered variants of the competitive learning idea (e.g., Grossberg, 1976; von der Malsberg, 1973). Rumelhart and Zipser show that when a competitive network is trained through repeated presentations of members of a set of patterns, each unit in a pool CO�}P;d"RPic?�at���P patterns with a particular + +attribute or property are presented. If there are two units in a pool, each comes to respond to opposite values of a binary feature which is useful in describing the stimulus set. If there are three units in the pool, each unit comes to respond to a value of a trinary feature, etc. It is shown through simulations and mathematical analysis that the competitive learning system can serve as a basis for the development of + +useful pattern descriptions. + +Chapters 6 and 7 describe Smolensky's harmony theory and Hinton and Sejnowski's Boltzmann machine, respectively. These approaches were developed at the same time, and they have much in common. Both harmony theory and Boltzmann machines employ binary units whose values are determined probabilistically according to the Boltzmann equation. Each employs simulated annealing in which the temperature of the Boltzmann equation is moved slowly to zero as the system relaxes into its solution state where it finally freezes. Both systems apply mathematical formulations borrowed from physics to their + +systems to describe and analyze their behavior. + +In spite of these similarities, the two systems were developed from very different perspectives. The similarities arose largely because both systems tapped mathematical physics as a tool for formalizing their ideas. Smolensky's harmony theory grew from an attempt to formalize the notion of schema and the ideas of schema theory. Hinton and Sejnowski's Boltzmann machine is based on the idea that stochastic units can be used as a mechanism of search-for finding globally good states of networks through simulated annealing. It combines insights on simulated annealing from Kirkpatrick, Gelatt, and Vecchi (1983) with the proof by Hopfield (982) that there is a global energy function that can be locally minimized through a process of asynchronously + +updating individual units. + +Chapter 6 provides a mathematical development of harmony theory and shows how a symbolic level of description can be seen as emerging from interactions among the individual processing units in harmony theory. It shows how harmony theory can be applied to a variety of phenomena, including intuitive problem solving and aspects of perception. It also provides a useful description of the mathematical relationships among harmony theory, Boltzmann machines, and the related + +mechanisms studied by S. Geman and D. Geman (1984). + +Chapter 7 focuses on the issue of learning in Boltzmann machines. One of the most important contributions of the work on Boltzmann machines is the development of the two phase (wake/sleep) learning procedure. Hinton and Sejnowski show that if a Boltzmann machine runs under the influence of environmental inputs for a while and then runs "freely" -without inputs from the environment-there is a very simple learning rule which will allow the Boltzmann machine to pick up Copyrighted Material + +environmental regularities and develop its own internal representations for describing those regularities. The major part of Chapter 7 is an + +analysis of this learning procedure. + +Chapter 8 is the study of still another learning procedure. In this chapter, Rumelhart, Hinton, and Williams show that it is possible to develop a generalization of the delta rule described in Chapter 2 so that arbitrary multilayered networks of units can be can be trained to do interesting tasks . Using this learning rule, the system can learn to associate arbitrary input/ output pairs and in this way can learn to compute arbitrary input/output functions . The generalized delta rule is shown to provide a method of modifying any weight in any network, based on locally available information, so as to implement a gradient descent process that searches for those weights that minimize the error at the output units. Further, simulation work presented in the chapter shows that the problems of local minima often associated with gradient des- + +cent and other hill- climbing methods are suprisingly rare. + +In general , the chapters in this section demonstrate that the barriers to progress in understanding learning in networks of simple neuron-like units have begun to crumble. There are still deep problems that remain unsolved, but the learning mechanisms described in these chapters make several inroads into some of the most challenging aspects of the + +theory of parallel distributed processing. + +CHAPTER S + +Feature Discovery by Competitive Learning + +D. E. RUMELHART and D. ZIPSER + +This chapter reports the results of our studies with an unsupervised learning paradigm that we call competitive learning. We have examined competitive learning using both computer simulation and formal analysis and have found that when it is applied to parallel networks of neuron-like elements, many potentially useful learning tasks can be accomplished. We were attracted to competitive learning because it seems to provide a way to discover the salient, general features which can be used to classify a set of patterns. The basic components of the + +competitive learning scheme are: + +• Start with a set of units that are all the same except for some randomly distributed parameter which makes each of them + +respond slightly differently to a set of input patterns. + +• Limit the "strength" of each unit. + +• Allow the units to compete in some way for the right to + +respond to a given subset of inputs. + +The net result of correctly applying these three components to a learning paradigm is that individual units learn to specialize on sets of + +similar patterns and thus become "feature detectors" or "pattern classifiers." In addition to Frank Rosenblatt, whose work will be discussed below, several others have exploited competitive learning in one form or another over the years. These include von der Malsburg (973), Grossberg (976), Fukushima (975), and Kohonen (982). Our analyses differ from many of these in that we focus on the development of feature detectors rather than pattern classification. We address + +these issues further below. + +One of the central issues in the study of the processing capacities of neuron-like elements concerns the limitations inherent in a one-level system and the difficulty of developing learning schemes for multilayered systems. Competitive learning is a scheme in which important features can be discovered at one level that a multilayer system can use to classify pattern sets which cannot be classified with a single level + +system. + +Thirty-five years of experience have shown that getting neuron-li ke elements to learn some easy things is often quite straightforward, but designing systems with powerful general learning properties is a difficult problem, and the competitive learning paradigm does not change this fact. What we hope to show is that competitive learning is a powerful strategy which, when used in a variety of situations, greatly expedites some difficult tasks. Since the competitive learning paradigm has roots which go back to the very beginnings of the study of artificial learning devices, it seems reasonable to put the whole issue into historical perspective. This is even more to the point, since one of the first simple learning devices, the perceptron, caused great furor and debate, the + +reverberations of which are still with us. + +In the beginning, thirty-five or forty years ago, it was very hard to see how anything resembling a neural network could learn at all, so any example of learning was immensely interesting. Learning was elevated to a status of great importance in those days because it was somehow uniquely associated with the properties of animal brains. After McCulloch and Pitts (943) showed how neural-like networks could compute, the main problem then facing workers in this area was to + +understand how such networks could learn. + +The first set of ideas that really got the enterprise going were contained in Donald Hebb's Organization oj Behavior (I 949). Before Hebb's work, it was believed that some physical change must occur in a network to support learning, but it was not clear what this change could be. Hebb proposed that a reasonable and biologically plausible change would be to strengthen the connections between elements of the network only when both the presynaptic and postsynaptic units were active simultaneously. The essence of Hebb's ideas still persists today in many learning paradigms. The details of the rules for changing weight Copyrighted Material + +may be different, but the essential notion that the strength of connections between the units must change in response to some function of the correlated activity of the connected units still dominates learning + +models. + +Hebb's ideas remained untested speculations about the nervous system until it became possible to build some form of simulated network to test learning theories. Probably the first such attempt occurred in 1951 when Dean Edmonds and Marvin Minsky built their learning machine. The flavor of this machine and the milieu in which it operated is captured in Minsky's own words which appeared in a wonderful New Yorker profile of him by Jeremy Bernstein (1981): + +> In the summer of 1951 Dean Edmonds and I went up to Harvard and bui lt our machine. It had three hundred tubes and a lot of motors. It needed some automaticelectric clutches, which we machined ourselves. The memory of the machine was stored in the positions of its control knobs, 40 of them, and when the machine was learning, it used the clutches to adjust its own knobs. We used a surplus gyropilot from a B24 + +bomber to move the clutches. (p. 69) + +This machine actually worked and was so fascinating to watch that + +Minsky remembers: + +We sort of quit science for awhil eto watch the machine. We were amazed that it could have several activities going on at once in this little nervous system. Because of the random wiring it had a sort of fail safe characteristic. If one of the neurons wasn't working, it wouldn't make much difference and with nearly three hundred tubes, and the thousands of connections we had soldered there would usual ly be something wrong somewhere. . I don't think we ever debugged our machine completely, but that didn't matter. By having this crazy random design it was almost sure to work no matter how + +you built it. (p. 69) + +In fact , the functioning of this machine apparently stimulated Minsky sufficiently to write his PhD thesis on a problemrelated to learning (Minsky, 1954). The whole idea must have generated rather wide interest; von Neumann, for example, was on Minsky's PhD committee and gave him encouragement. Although Minsky was perhaps the first on the scene with a learning machine, the real beginnings of meaningful neuron-li ke network learning can probably be traced to the work of Frank Rosenblatt, a BE?� �g�1 of Science classmate of + +Minsky's. Rosenblatt invented a class of simple neuron-l ike learning networks which he called perceptrons. In his book, Principles of Neurodynamics (1962), Rosenblatt brought together all of his results on perceptrons. In that book he gives a particularly clear description of what + +he thought he was doing: + +Perceptrons are not intended to serve as detai led copies of any actual nervous system. They're simplified networks, designed to permit the study of lawful relationships between the organization of a nerve net, the organization of its environment, and the "psychological" performances of which it is capable. Perceptrons might actually correspond to parts of more extended networks and biological systems� in this case, the results obtained will be directly appl icable. More li kely they represent extreme simplifications of the central nervous system, in which some properties are exaggerated and others suppressed. In this case, successive perturbations and refinements of the system + +may yield a closer approximation. + +The main strength of this approach is that it permits meaningful questions to be asked and answered about particular types of organizations, hypothetical memory mechanisms, and neural models. When exact analytical answers are unobtainable, experimental methods, either with digital simulation or hardware models, are employed. The model is not the terminal result, but a starting point for exploratory analysis of its + +behavior. (p. 28) + +Rosenblatt pioneered two techniques of fundamental importance to the study of learning in neural-like networks: digital computer simulation and formal mathematical analysis, although he was not the first to simulate neural networks that could learn on digital computers (cf. + +Farley & Clark, 1954). + +Since the paradigm of competitive learning uses concepts that appear in the work of Rosenblatt, it is worthwhile reviewing some of his ideas in this area. His most influential result was the "perceptron learning + +theorem" which boldly asserts: + +Gi ven an elementary IX -percept ron , a stimulus world W, and any classification C (W) for which a solution exists� let all stimuli in W occur in any sequence, provided that each stimulus must reoccur in finite time� then beginning from an arbitrary initial state, an error correction procedure wi ll always + +yield a solution to C (W) in finite time, . " (p. 596) + +As it turned out, the real problems arose out of the phrase "for which a + +solution exists" -more about this later. + +Less widely known is Rosenblatt's work on what he called " spontaneous learning." All network learning models require rules which tell how to present the stimuli and change the values of the weights in accordance with the responseof the model. These rules can be characterized as forming a spectrum, at one end of which is learning with an errorcorrecting teacher, and at the other is completely spontaneous, unsupervised discovery . In between is a continuum of rules that depend on manipulating the content of the input stimulus stream to bring about learning. These intermediate rules are often referred to as "forced learning." Here we are concerned primari ly with attempts to design a perceptron that would discover something interesting without a teacher because this is similar to what happens in the competitive learning case. In fact, Rosenblatt was able to build a perceptron that was able to spontaneously dichotomize a random sequence of input patterns into classes such that the members of a single class were similar to each other, and different from the members of the other class. Rosenblatt realized that any randomly initialized perceptron would have to dichotomize an arbitrary input pattern stream into a "I-set," consisting of those patterns that happened to produce a response of I, and a "O-set," consisting of those that produced a response of O. Of course one of these sets could be empty by chance and neither would be of much interest in general. He reasoned that if a perceptron could reinforce these sets by an appropriate rule based only on the perceptron's spontaneous response and not on a teacher's error correction, it might eventually end up with a dichotomization in which the members of each set were more like each other than like the members of the opposite set. What was the appropriate rule to use to achieve the desired dicotomization? The first rule he tried for these perceptrons, which he called C -type, was to increment weights on l ines active with patterns in the I-set, and decrement weights on lines active with patterns in the O-set. The idea was to force a dichotomization into sets whose members were similar in the sense that they activated overlapping subsets of lines. The· results were disastrous . Sooner or later all the input patterns were classified in one set. There was no di chotomy but there was stability. Once one of the + +sets won, it remained the victor forever. + +Not to be daunted, he examined why this undesirable result occurred and realized that the problem lay in the fact that since the weights could grow without limit, the set that initially had a majority of the patterns would receive the majority of the reinforcement. This meant that weights on lines which could be activated by patterns in both sets would grow to infinite magnitudes in favor of the majority set, which in turn would lead to the captuBbPYr1BiHBaw!81�»Sfns by the majority set and + +ultimate total victory for the maJorIty. Even where there was initial equality between the sets, inevitable fluctuations in the random presentation of patterns would create a majority set that would then go on to win. Rosenblatt overcame this problem by introducing mechani sms to limit weight growth in such a way that the set that was to be positively reinforced at active lines would compensate the other set by giving up some weight from all its lines. He called the modi fied perceptrons C. An example of a C rule is to lower the magnitude of all weights by a fixed fraction of their current value before specifically incrementing the magni tude of some of the weights on the basis of the response to an input pattern. This type of rule had the desired result of making an equal dichotomy of patterns a stable rather than an unstable state. Patterns in each of the sets were similar to each other in the sense that they depended on simi lar sets of input lines to produce a response. In Rosenblatt's initial experiment, the main feature of similarity was not so much the shape of the patterns involved, but their location on the retina. That is , his system was able to spontaneously learn something about the geometry of its input line arrangement. Later, we will examine this important property of spontaneous geometry learning in considerable detail. Depending on the desired learning task, it can be either a + +boon or a nuisance. + +Rosenblatt was extremely enthusiastic about his spontaneous learning results. In fact, his response can be described as sheer ecstasy. To see what he thought about his achievements, consider his claim + +(Rosenblatt, 1959): + +It seems clear that the class C perceptron introduces a new kind of information processing automaton: For the first time, we have a machine which is capable of having original ideas . As an analogue of the biological brain, the perceptron, more precisely, the theory of statistical separabi lity, seems to come closer to meeting the requirements of a functional explanation of the nervous system than any system previously proposed. + +(p. 449) + +Although Rosenblatt's results were both interesting and significant, the claims implied in the above quote struck his contemporaries as unfounded. What was also significant was that Rosenblatt appeared to be saying that the type of spontaneous learning he had demonstrated was a property of perceptrons, which could not be repl icated by ordinary computers. Consider the fol lowing quote from the same source: + +> As a concept, it would seem that the perceptron has established, beyond doubt, the feasibi lity and principle of + +non-human systems which may embody human cognitive functions at a level far beyond that which can be achieved through present day automatons. The future of information processing devices which operate on statistical, rather then logical princi- + +ples seems to be clearly indicated. (p. 449) + +It is this notion of Rosenblatt's-that perceptrons are in some way superior to computers-that ignited a debate in artificial intel ligence that had significant effects on the development of neural-like network models for both learning and other cognitive processes. Elements of the debate are sti ll wi th us today in arguments about what the brain can do that computers can't do. There is no doubt that this was an important issue in Rosenblatt's mind, and almost certai nly contri buted to the acrimonious debate at that time. Consider the following statement by Rosenblatt made at the important conference on Mechanization of + +Thought Processes back in 1959: + +Computers seem to share two main functions with the brain: (a) Decision making, based on logical rule, and (b) control, again based on logical rules. The human brain performs these functions, together with a third: interpretation of the environment. Why do we hold interpretation of the environment to be so important? The answer, I think, is to be found in the laws of thermodynamics. A system with a completely self contained logic can never spontaneously improve its abi lity to organize, and to draw valid conclusions from information. (Rosenblatt, + +1959, p. 423) + +Clearly in some sense, Rosenblatt was saying that there were things that the brain and perceptrons, because of their statistical properties, could do which computers could not do. Now this may seem strange since Rosenblatt knew that a computer program could be written that would simulate the behavior of statistical perceptrons to any arbitrary degree of accuracy. Indeed, he was one of the pioneers in the application of digital simulation to this type of problem. What he was actual ly referring to is made clear when we examine the comments of other partici pants at the conference, such as Minsky (I959) and McCarthy (I 959), who were using the symbol manipulating capabilities of the computer to directly simulate the logical processes involved in decision making, theorem proving, and other intellectual activities of this sort. Rosenblatt believed the computer used in this way would be inadequate to mimic the brain's true intellectual powers. This task, he thought, could only be accompl ished if the computer or other electronic devices were used to simulate perceptrons. We can summarize these di vergent Copyrighted Material + +points of view by saying that Rosenblatt was concerned not only with what the brain did, but with how it did it, whereas others, such as Minsky and McCarthy, were concerned with simulating what the brain did, and didn't real ly care how it was done. The subsequent history of AI has shown both the successes and failures of the standard AI approach. We sti ll have the problems today, and it's still not clear to what degree computational strategies similar to the ones used by the brain must be + +employed in order to simulate its performance. + +In addition to producing fertilizer, as all debates do, this one also stimulated the growth of some new results on perceptrons, some of which came from Minsky. Rosenblatt had shown that a two layer perceptron could carry out any of the 22N possible classifications of N binary inputs; that is, a solution to the classification problem had always existed in principle. This result was of no practical value however, because 2N units were required to accomplish the task in the completely general case. Rosenblatt's approach to this problem was to use a much smaller number of units in the first layer with each unit connected to a small subset of the N inputs at random. His hope was that this would give the percept ron a high probability of learning to carry out classifications of interest. Experiments and formal analysis showed that these random devices could learn to recognize patterns to a significant degree but that they had severe limitations. Rosenblatt (I 962) + +characterized his random perceptron as follows: + +It does not generalize well to similar forms occurring in new positions in the retinal field, and its performance in detection experiments, where a familiar figure appears against an unfamiliar background, is apt to be weak. More sophisticated psychological capabilities, which depend on the recognition of topological properties of the stimulus field, or on abstract relations between the components of a complex image, are lacking. + +(pp. 191-192) + +Minsky and Papert worked through most of the sixties on a mathematical analysis of the computing powers of perceptrons with the goal of understanding these limitations. The results of their work are available in a book cal led Perceptrons (Minsky & Papert, 1969). The central theme of this work is that parallel recognizing elements, such as perceptrons, are beset by the same problems of scale as serial pattern recognizers. Combinatorial explosion catches you sooner or later, although sometimes in di fferent ways in parallel than in serial. Minsky and Papert's book had a very dampening effect on the study of neuron-l ike networks as computational devices. Minsky has recently + +I now bel ieve the book was overkill. . So after being irritated with Rosenblatt for overclaiming and diverting all those people along a false path, I started to real ize that for what you get out of it - the kind of recognition it can do-it is such a simple machine that it would be astonishi ng if nature did not make use + +of it somewhere. (Bernstein, 1981, p. 103) + +Perhaps the real lesson from all this is that it real ly is worthwhile trying + +to put things in perspective. + +Once the problem of scale has been understood, networks of neuron-like elements are often very useful in practical problems of recognition and classification. These networks are somewhat analogous to computers, in that they won't do much unless programmed by a clever person; networks, of course, are not so much programmed as designed. The problem of finding networks of practical size to solve a particular problem is challenging because relatively small changes in network design can have very large effects on the scale of a problem. Consider networks of neuron-like units that determine the parity of their N bi nary inputs (see Figure 1). In the simple perceptrons studied by Minsky and Papert, units in the first layer output 1 only if all their inputs are 1 and output 0 otherwise. This takes 2N units in the first layer, and a single linear threshold unit with a fan-in of 2N in the second layer, to determine parity. If the units in the first layer are changed to linear threshold elements, then only N of them are required, but all must have a fan-in of N. If we allow a multilayer network to do the job, then about 3N units are needed, but none needs a fan-in of more than 2. The number of layers is of order log2N. The importance of all this to the competitive learning paradigm, or any other for that matter, is that no network can learn what it is not capable of doing in principle. What any particular network can do is dependent on its structure and the computational properties of its component elements. Unfortunately, there is no canonical way to find the best network or to determine what it will learn, so the whole enterprise still has + +much of the flavor of an experimental science. + +THE COMPETITIVE LEARNING MECHANISM + +Paradigms of Learning + +It is possible to classify learning mechanisms in several ways. One useful classification is in. terms of e learning paradigm in which the Gopynghted Malenal + +A B + +1 -1 cp + +c o + +=� + +FIGURE I. A: Parity network from Minsky and Papert (1969). Each.p unit has an output of I only if all of its inputs are I. 1: is a linear threshold unit with threshold of 0, i.e., like all the other linear threshold units in the figure, it fires only when the sum of its weighted inputs is greater than the threshold. This and all the other networks signal odd parity with a I in the rightmost unit of the network. B: Parity network made from two layers of linear threshold units. C: Three-unit network for determining the parity of a pair of inputs. D: Two-layer network using the subnetwork described in (C). In general, the number of P-units is of order N and the number of layers is of order log2N. + +model is supposed to work. There are at least four common learning + +paradigms in neural-li ke processing systems: + +• Auto Associator. In this paradigm a set of patterns are repeatedly presented and the system is supposed to "store" the patterns. Then, later, parts of one of the original patterns or possibly a pattern similar to one of the original patterns is presented, and the task is to "retrieve" the original pattern through a kind of pattern completion procedure. This is an auto-association process in which a pattern is associated with itself so that a degraded version of the original pattern can act + +as a retrieval cue. + +• Pattern Associator. This paradigm is really a variant on the auto-association paradigm. A set of pairs of patterns are repeatedly presented. The system is to learn that when one member of the pair is presented it is supposed to produce the other. In this paradigm one seeks a mechanism in which an essentially arbitrary set of input patterns can be paired with an arbitrary set + +of output patterns. + +• Classification Paradigm. The classification paradigm also can be considered as a variant on the previous learning paradigms, although the goals are sufficiently different and it is sufficiently common that it deserves separate mention. In this case, there is a fixed set of categories into which the stimulus patterns are to be classified. There is a training session in which the system is presented with the stimulus patterns along with the categories to which each stimulus belongs. The goal is to learn to correctly classify the stimuli so that in the future when a particular stimulus or a slightly distorted version of one of the stimuli is presented, the system will classify it properly. This is the typical paradigm in which the perceptron is designed to operate and in which the perceptron convergence theorem is + +proved. + +• Regularity Detector. In this paradigm there is a population of stimulus patterns and each stimulus pattern, Sk' is presented with some probability Pk. The system is supposed to discover statistically salient features of the input population. Unlike the classification paradigm, there is no a priori set of categories into which the patterns are to be classified; rather, the system must develop its own featural representation of the input stimuli which captures the most salient features of the population of + +input patterns. + +Layer 3 Inhibitory Clusters + +Layer 2 Inhibitory Clusters + +> Layer 1 Input Units + +INPUT PATTERN + +Excitatory Connections + +Excitatory Connections + +FIGURE 2. The architecture of the competitive learning mechanism. Competitive learning takes place in a context of sets of hierarchically layered units. Units are represented in the diagram as dots. Units may be active or inactive. Active units are represented by filled dots, inactive ones by open dots. In general, a unit in a given layer can receive inputs from aJl of the units in the next lower layer and can project outputs 10 all of the units in the next higher layer. Connections between layers are excitatory and connections within layers are inhibitory. Each layer consists of a set of clustersof mutually inhibitory units. The units within a cluster inhibit one another in such a way that only one unit per cluster may be active. We think of the configuration of active units on any given layer as representing the input pattern for the next higher level. There can be an arbitrary number of such layers. A given cluster contains a fixed number of units, but different + +• Every element in every cluster receives inputs from the same + +lines. + +• A unit learns if and only if it wins the competition with other + +units in its cluster. + +• A stimulus pattern S. consists of a binary pattern in which each element of the patteln is either active or inactive. An active element is assigned the value I and an inactive element is + +assigned the value O. + +• Each unit has a fixed amount of weight (all weights are positi ve) which is distributed among its input lines. The weight on the line connecting unit i on the lower (or input) layer to unitj on the upper layer, is designated wi}. The fixed total amount of weight for unit j is designated I, wi} = 1. A unit learns by i shifting weight from its inactive to its active input lines. If a unit does not respond to a particular pattern, no learning takes place in that unit. If a unit wins the competition, then each of its input lines give up some proportion g of its weight and that weight is then distributed equal ly among the active input lines. 2 + +More formally, the learning rule we have studied is: + +if unit j loses on stimulus k + +if unit j wins on stimulus k + +where Cik is equal to 1 if in stimulus pattern Sk, unit i in the lower layer is active and zero otherwise, and nk is the number + +of acti ve units in pattern Sk (thus nk = I,Cik). + +Figure 3 illustrates a useful geometric analogy to this system. We can consider each stimulus pattern as a vector. If all patterns contain the same number of active lines, then all vectors are the same length and each can be viewed as a point on an N-dimensional hypersphere, + +2This learning rule was proposed by von der Malsburg (1973). As Grossberg (1976) points out, renormalization of the weights is not necessary. The same result can be obtained by normalizing the input patterns and then assuming that the weights approach the values on the input lines. Normalizing weights is simpler to implement than normalizing pallerns, so we chose that option. For most of our experiments, however, it does not mailer which of these two rules we chose since all pallerns were of the same + +Each x in Figure 3A represents a particular pattern. Those patterns that are very simi lar are near one another on the sphere; those that are very different wi ll be far from one another on the sphere. Now note that since there are N input lines to each unit in the upper layer, its weights can also be considered a vector in N-dimensional space. Since all ul'lits have the same total quantity of weight, we have N-dimensional vectors of approximately fi xed length for each unit in the cluster. 3 Thus, properly scaled, the weights themselves form a set of vectors which (approximately) fall on the surface of the same hypersphere. In Figure 38, the o's represent the weights of two units superimposed on the same sphere with the stimulus patterns. Now, whenever a stimulus pattern is presented, the unit which responds most strongly is simply the one whose weight vector is nearest that for the stimulus. The learning rule specifies that whenever a unit wins a competition for a stimulus pattern, it moves a percentage g of the way from its current location toward the location of the stimulus pattern on the hypersphere. Now, suppose that the input patterns fell into some number, M, "natural" groupings. Further, suppose that an inhibitory cluster receiving inputs from these stimuli contained exactly M units (as in Figure 3C). After sufficient training, and assuming that the stimulus groupings are sufficiently distinct, we expect to find one of the vectors for the M units placed roughly in the center of each of the stimulus groupings. In this case, the units have come to detect the grouping to which the input patterns belong. In this sense, they have "discovered" the + +structure of the input pattern sets. + +Some Features of Competitive Learning + +There are several characteristics of a competitive learning mechanism that make it an interesting candidate for further study, for example: + +• Each cluster classifies the stimulus set into M groups, one for each unit in the cluster. Each of the units captures roughly an equal number of stimulus patterns. It is possible to consider a cluster as forming an M-ary feature in which every stimulus pattern is classified as having exactly one of the M possible + +3 It should be noted that this geometric interpretation is only approximate. We have used the constraint that 1: Wu = 1 rather than the constraint that 1: wJ = 1. This latter I I constraint would ensure that all vectors are in fact the same length. Our assumption only + +assures that they will be approximately the same length. + +values of this feature. Thus, a cluster containing 2 units acts as a binary feature detector. One element of the cluster responds when a particular feature is present in the stimulus pattern , oth- + +erwise the other element responds. + +• If there is structure in the stimulus patterns, the units will break up the patterns along structurally relevant lines. Roughly speaking, this means that the system will find clusters if they are there. (A key problem, which we address below, is specifying the nature of the structure that this system discovers.) + +• If the stimuli are highly structured, the classi fications are highly stable. If the stimuli are less well-structured, the classifications are more variable, and a given stimulus pattern will be responded to first by one and then by another member of the cluster. In our experiments, we started the weight vectors in random directions and presented the stimuli randomly. In this case, there is rapid movement as the system reaches a relatively stable configuration (such as one with a unit roughly in the center of each cluster of stimulus patterns). These configurations can be more or less stable. For example , if the stimulus points don't actually fall into nice clusters , then the configurations will be relatively unstable, and the presentation of each stimulus will modi fy the pattern of responding so that the system will undergo continual evolution. On the other hand, if the stimulus patterns fall rather nicely into clusters, then the system will become very stable in the sense that the same units + +will always respond to the same stimuli.4 + +• The particular grouping done by a particular cluster depends on the starting value of the weights and the sequence of stimulus patterns actually presented. A large number of clusters , each receiving inputs from the same input lines can, in general, classify the inputs into a large number of different groupings , or alternatively, discover a variety of independent features present in the stimulus population. This can provide a kind of coarse + +coding of the stimulus patterns. 5 + +4Grossberg(976) has addressed this problem in hisvery similar system. He has proved that if the patterns are sufficiently sparse, and/ or when there are enough units in the cluster, then a system such as this will find a perfectly stable classification. He also points out that when these conditions don't hold, the classification can be unstable. Most of our work is with cases in which there is no perfectly stable classification and the number of patterns is much larg.er than the number of units in the inhibitory clusters. (;opyrighted Material + +wins, P (li nei = 11 unitj wins) . Thus, if all patterns are of the same size , i.e., nk = n for all k, then the weight wi} becomes proportional to + +the probability that line i is active given unit j wins. That is, + +wi} - ! P ( Iinei = 11 unitj wins ). + +We are now in a position to speci fy the response, at equilibri um, of unit j when stimulus S, is presented. Let Ol jI be the input to unit j in the face of stimulus S, . This is simply the sum of weights on the acti ve + +input lines. This can be written + +1: Pk Cik VJk k nk LPk vjk k + +which implies that at equi librium + +Oljl = + +where 'Ii represents the overlap between stimulus I and stimulus i, + +',,' \_\_ � Cki Ck' L. + +Thus, at equi librium a unit responds most strongly to + +k ni + +patterns that overlap other patterns to which the unit responds and responds most weakly to patterns that are far from patterns to which it responds. Finally, it should be noted that there is another set of + +restrictions on the value of Vj + +k - the probabi lity that unit j responds to + +stimulus Sk + +' In fact , the competitive learning rule we have studied has + +the further restriction that + +\_1 1 Oljk > Olik for all i,cj + +Vjk - 0 otherwise. + +Thus, in general , there are many solutions to the equilibrium equations described above. The competitive learning mechanisms can only reach those equi librium states in which the above-stated relationships + +between the Vjk and the Ol jk also hold. + +Whenever the system is in a state in which, on average , the weights are not changing, we say that the system has reached an equilib,ium state. In such a state the values of Ol Jk become relati vely stable, and therefore, the values of Vik become stable. When this happens, the system always responds the same way to a particular stimulus pattern. However, it is possible that the weights will be pushed out of Copyrighted Material + +equilibrium by an unfortunate sequence of stimuli. In this case, the system can move toward a new equilibrium state (or possibly back to a previous one) . Some equi librium states are more stable than others in the sense that the "ik become very unlikely to change values for long periods of time. In particular, this wi ll happen whenever the largest otjk is much larger than any other otik for all stimulus patterns Sk ' In this case, small movements in the weight vector of one of the units is very unli kely to change which unit responds to which stimulus pattern. Such equilibrium states are said to be highly stable. We should expect, then, that after it has been learning for a period of time, the system wi ll spend most of its time in the most highly stable of the equilibrium states. One good measure of the stability of an equil ibrium state is given by the average amount by which the input to the winning units is greater than the response of all of the other units averaged over all patterns and all units in a cluster. This measure is given by T below: + +T = LPkl>jk (otjk - otik ) ' + +k j ,i + +The larger the value of T, the more stable the system can be expected to be and the more time we can expect the system �o spend in that state. Roughly, if we assume that the system moves into states which maximize T, we can show that this amounts to maximizing the overlap among patterns within a group while minimizing the overlap among patterns between groups. In the geometric analogy above, this will occur when the weight vectors point toward maximally compact stimulus regions that are as distant as possible from other such regions. + +SOME EXPERIMENTAL RESULTS + +Dipole Experiments + +The essential structure that a competiti ve learning mechanism can discover is represented in the overlap of stimulus patterns. The simplest stimulus population in which stimulus patterns can overlap with one another is one constructed out of dipoles-stimulus patterns consisting of exactly two active elements and the rest inactive. If we have a total of N input units there are N(N-J)/2 possible dipole stimuli. Of course, if the actual stimulus population consists of al lN(N-J) / 2 possibi lities, there is no structure to be discovered. There are no clusters for our units to point at (unless we have one unit for each of the possible stimUl i, in which case we can point a weight vector at each of the Copyrighted Material + +FIGURE 5. The architecture of a competitive learning system with 16 input units and + +one cluster of size two in the second layer. + +that Unit 1 was the winner, the narrow line indicates that Unit 2 was the winner. It should be noted, therefore, that two unfilled circles must always be joi ned by a narrow line and two fi lled circles must always be joined by a wide line. The reason for this is that if a particular unit has more weight on both of the active lines then that unit must win the competition. The results clearly show that the weights move from a rather chaotic initial arrangement to an arrangement in which essentially al l of those on one side of the grid are fi lled and all on the other side are unfil led. The border separating the two halves of the grid may be at any orientation , but most often it is oriented vertical ly and hori zontal ly, as shown in the upper two examples. Only rarely is the orientation diagonal, as in the example in the lower right-hand grid. Thus, we have a case in which each unit has chosen a coherent half of the grid to which they respond. It is important to real ize that as far as the competitive learn ing mechanism is concerned the si xteen input Copyrighted Material + +A + +J + +o 400 + +B + +o 400 + +c + +50 400 + +FIGURE 6. Relative weight values for the two members of the inhibitory cluster. A: The results for one run with the dipole stimuli defined over a two-dimensional grid. The left-hand grid shows the relative values of the weights initially and the right-hand grid shows the relative values of the weights after 400 trials. A filled circle means that Unit1 had the larger weight on the corresponding input . An unfilled circle means that Unit 2 had the larger weight. A heavy line connecting two circles means that Unit 1 responded to the stimulus pattern consisting of the activation of the two circles, and a light line means that Unit 2 won the corresponding pattern. In this case the system has divided the grid horizontally. B: The results for a second run under the same conditions. In this case the system has divided the grid horizontally. C: The results for a third run. In this case the left-hand grid represents the state of the system after 50 trials. Here the grid + +lines are unordered. The two-dimensional grid-like arrangement exists only in the statistics of the population of stimulus patterns. Thus, the system has discovered the dimensional structure inherent in the stimulus population and has devised binary feature detectors that tell which half of the grid contains the stimulus pattern. Note, each unit responds to roughly half of the stimulus patterns. Note also that while some units break the grid vertically, some break the grid horizontally, and some break it diagonally; a combination of several clusters offers a rather + +more precise classification of a stimulus pattern. + +In other experiments, we tried clusters of other sizes. For example, Figure 7 shows the results for a cluster of size four. It shows the initial configuration and its sequence of evolution after 100, 200, 400, 800, and after 4000 training trials. Again, initially the regions are chaotic. After training, however, the system settles into a state in which stimuli in compact regions of the grid are responded to by the same units. It can be seen, in this case, that the trend is toward a given unit responding to a maximally compact group of stimuli. In this experiment, three of the units settled on compact square regions while the remaining one settled on two unconnected stimulus regions. It can be shown that the state into which the system settled does not quite maximize the value + +T, but does represent a relatively stable equilibrium state. + +In the examples discussed thus far, the system, to a first approximation, settled on a highly compact representation of the input patterns in which all patterns in a region are captured by one of the units. The grids discussed above have all been two-dimensional . There is no need to restrict the analysis to a two-dimensional grid. In fact, a two-unit cluster will, essentially, pass a plane through a space of any dimensionality. There is a preference for planes perpendicular to the axes of the spaces. Figure 8 shows a typical result for the system learning a three-dimensional space. In the case of three dimensions , there are three equally good planes which can be passed through the space and, depending on the starting directions of the weight vectors and on the sequence of stimuli, different clusters wi ll choose different ones of these planes. Thus, a system which receives input from a set of such clusters wi ll be gi ven information as to which quadrant of the space in which the pattern appears . It is important to emphasize that the coherence of the space is entirely in the choice of input stimul i, not in the architecture of the competitive learning mechanism. The system discov- + +ers the spatial structure in the input lines. + +Formal analysis. For the dipole examples described above, it is possible to develop a rather precise characterization of the behavior of the competitive learning system. Recal l our argument that the most stable equi librium state (and therefore the one the system is most likely to Copyrighted Material + +o 100 + +200 400 + +800 4000 + +FIGURE 7. The relative weights of each of the four elements of the cluster after 0, 100, + +200, 400, 800, and 4000 stimulus presentations. + +end up in) is the one that maximizes the function + +T = LPk L Vjk (CXjk - CXik )' + +k j,i + +Now, in the dipole examples, all stimulus patterns of the stimulus population are equally likely (i.e. , Pk = 1/ N) , all stimulus patterns involve two active lines, and for every stimulus pattern in the population of patterns there are a fixed number of other stimulus patterns in Copyrighted Material + +FIGURE 8. The relative weights ror a system in which the stimulus patterns were + +chosen rrom a three-dimensional grid after 4000 presen tations. + +the population which overlap it. 6 This implies that f/kj = R for all j. + +k + +With these assumptions, it is possible to show that maximizing T is + +equivalent to minimizing the function + +fli I N; + +(see appendix for deri vation) , where N; is the number of patterns on which unit i wins, M is the number of units in the cluster, and B; is the number of cases in which unit i responds to a particular pattern and does not respond to a pattern which overlaps it. This is the number of + +border patterns to which unit i responds. Formal ly, we have + +B; = tt vi} (I-v;k ) for rjk &gt;O. + +i k + +From this analysis , it is clear that the most stable states are ones in which the size of the border is minimized . Since total border region is minimized when regions are spherical , we can conclude that in a situation in which stimulus pairs are drawn from adjacent points in a + +6 Note that this latter condition does not Quite hold ror the examples presented above due to edge effects. It is possible to eliminate edge effects by the use or a torus. We have carried out experiments on tori as well, and the results are essentially the same. Copyrighted Material + +high -dimensional hyperspace, our competitive learning mechanism wi ll form essentially spherical regions that partition the space into one such + +spherical region for each element of the cluster. + +Another result of our simulations which can be explained by these equations is the tendency for each element of the cluster to capture roughly equally sized regions. This results from the interconnectedness of the stimulus population . The result is easiest in the case in which M= 2. In this case, the function we want to minimize is given by + +> B IB2 NI + N2 ' + +Now, in the case of M= 2, we have B 1=B2, since the two regions must border on one another. Moreover, we have N 1+N 2 = N, since every pattern is either responded to by Unit 1 or Unit 2. Thus, we + +want to minimize the function + +This function is minimized when NI = N1 2. Thus, there are two pressures which determine the performance of the system in these cases: + +• There is a pressure to reduce the number of border stimuli to a + +minimum. + +• There is a pressure to divide the sti mul uspatterns among the units in a way that depends on the total amount of weight that unit has. If two unitshave the same amount of weight , they wi ll capture roughly equal numbers of equally l ikely stimulus + +patterns . + +Learning Words and Letters + +It is common practice to handcraft networks to carry out particular tasks. Whenever one creates such a network that performs a task rather successfully, the question arises as to how such a network might have evolved. The word perception model developed in McClel land + +and Rumelhart ( + +l98l) and Rumelhart and McClelland (I982) is one + +such case - in - point . That model offers rather detailed accounts of a variety of word perceptionexperiments, but it was crafted to do its job. Copyrighted Material + +possible that one of the units will never win, and therefore never learn . This, of course, takes the competition out of competiti ve learning. This situation is analogous to the situation in the geometric analogy in which all of the stimulus points are relatively close together on the hypersphere, and one of the weight vectors, by chance, points near the cluster while the other one points far from the stimuli. (See Figure 1 0) . It is clear that the more distant vector is not closest to any stimulus and thus can never move toward the collection . We have investigated two modifications to the system which deal with the problem. One, which we call the leaky learning model, modifies the learning rule to state that both the winning and the losing units move toward the presented stimulus: the close vector simply moves much further. + +In symbols this suggests that + +Cik g,- - g,w· nk IJ + +Cik gw -;;; - gw wij if unit j loses on stimulus k + +if unit j wins on stimulus k + +where g, is the learning rate for the losing units, gw is the learning rate for the winning unit, and where g,« gw . In our experiments we made + +FIGURE 10. A geometric interpretation of changes in stimulus sensitivity. The larger the circle around the head of the weight vector the more sensitive the unit. The decision as to which unit wins is made on the basis of the distance from the circle rather than from the head of the weight vector. In the example, the stimulus pattern indicated by the y is actually closer to the head of one vector 0, but since it is closer to the circle sur- + +rounding vector p, unit p wO�jhWftJ?8W�al + +g, an order of magnitude smaller than gw . This change has the property that it slowly moves the losing units into the region where the actual stimuli lie, at which point they begin to capture some units and the + +ordinary dynamics of competitive learning take over. + +The second method is simi lar to that employed by Bienenstock, + +Cooper, and Munro (1982) + +, in which a unit modulates its own sensi- + +tivity so that when it is not receiving enough inputs, it becomes increasingly sensitive. When it is receiving too many inputs , it decreases its sensitivity. This mechanism can be implemented in the present context by assuming that there is a threshold and that the relevant activation is the degree to which the unit exceeds its threshold. If, whenever a unit fails to win it decreases its threshold and whenever it does win it increases its threshold, then this method wi ll also make all of the units eventually respond, thereby engaging the mechanism of competitive learning. This second method can be understood in terms of the geometric analogy that the weight vectors have a circle surrounding the end of the vector. The relevant measure is not the distance to the vector itself but the distance to the circle surrounding the vector. Every time a unit loses , it increases the radius of the circle; every time it wins, it decreases the radius of the circle. Eventually, the circle on the losing unit wi ll be large enough to be closer to some stimulus pat- + +tern than the other units. + +We have used both of these mechanisms in our experiments and they appear to result in essentially similar behavior. The former, the leaky learning method, does not alter the formal analysis as long as the ratio gd gw is sufficiently small. The varying threshold method is more difficult to analyze and may, under some circumstances, distort the competitive learning process somewhat. After this diversion, we can now return to our experiments on the development of word/ position- + +specific letter detectors and other feature detectors. + +Position-specific letter detectors. In our first experiment, we presented letter pairs drawn from the set: AA, AB, BA, and BB. We began with clusters of size two. The results were unequivocal . The system developed position-specific letter detectors. In some experimental runs, one of the units responded whenever AA or AB was presented, and the other responded whenever BA or BB was presented. In this case, Unit 1 represents an A detector in position 1 and Unit 2 represents a B detector for position 1. Moreover, as in the word perception model , the letter detectors are, of course, in a mutually inhibitory pool . On other experimental runs , the pattern was reversed. One of the units responded whenever there was an A in the second position and the other unit responded whenever there was a B in the second position. Figure 11 shows the final configuration of weights for one of Copyrighted Material + +• • • • • ••••• • • • • • • + +•••• • • • • ••• • • • • ••• • + +.. ... ,. • . . • · ... . • • · ....... + +.. ..... • . . • .. .... • • + +· ........ Unit 1 + +Unit 2 + +FIGURE 11. The final configuration of weights for a system trained on the stimulus + +patterns A, B, C, D. + +our experimental runs. Note that although the units illustrated here respond only to the letter in the first position, there is sti ll weight on the active' lines in the second position. It is just that the weights on the first position differentiate between A and 8, whereas those on the second position respond equal ly to the two letters. In particular, as suggested by our formal analysis, asymptotical ly the weights on a given lineare proportionj'! to the probabi lity that that line is active when the unit wins. That i�, wij - p(unit; = 11 unitjwins) . Since the lower level units unique to A occur equally as often as those unique to 8, the weights on those lines are roughly equal . The input lines common to the two letters are on twice as often as those unique to either letter, and hence, they have twice as much weight. Those lines that never + +come on reach zero weight. + +Word detection units. In another experiment, we presented the same stimulus patterns , but increased the elements in thecluster from two to four. In this case, each of the four level-two units came to respond to one of the four input patterns -in short, the system developed word detectors. Thus, if layer two were to consist of a number of clusters of various sizes, large clusters with approximately one unit per word pattern wi II develop into word detectors, while smal ler clusters with approximately the number of letters per spatial position wi II develop into position-specific letter detectors. As we shal l see below, i f the number of elements of a cluster is substantially less than the number of letters per position , then the cluster wi ll come to + +detect position-specific letter features . + +Effects of number of elements per serial position. In another experiment, we varied the number of elements in a cluster and the number of letters per serial P�gW�JMl stimulus patterns drawn + +from the set: AA. AB. AC. AD. BA. BB. BC. BD. In this case, we found that with clusters of size two, one unit responded to the patterns beginning with A and the other responded to those beginning with B. In our previous experiment, when we had the same number of letters in each position, we found that the clusters were indifferent as to which serial position they responded. Some responded to position 1 and others to position 2. In this experiment, we found that a two-element cluster always becomes a letter detector specific to serial position in which two letters vary. Similarly, in the case of clusters of size four we found that they always became letter detectors for the position in which four letters varied. Thus, in this case one responded to an A in the second position, one responded to a B in the second position , one responded to a C in the second position, and one responded to a D in the second position. Clearly, there are two natural ways to cluster the stimulus patterns-two levels of structure. If the patterns are to be put in two categories , then the binary feature A or B in the first position is the relevant distinction. On the other hand, if the stimuli are to be grouped into four groups , the four value feature determining the second letter is the relevant distinction. The competitive learning algorithm can discover either of the levels of structure-depending on the + +number of elements in a cluster . + +Letter similarity effects. In another experiment, we studied the effects of letter similarity to look for units that detect letter features. We presented letter patterns consisting of a letter in the fi rst position only. We chose the patterns so they formed two natural clusters based on the similarity of the letters to one another. We presented the letters A. B. S. and E. The letters were chosen so that they fell natural ly into two classes. In our font, the letters A and E are quite simi lar and the letters B and S are very similar. We used a cluster of size two. Naturally, one of the units responded to the A or the E while the other unit responded to the B or the S. The weights were largest on those features of the stimulus pai rs which were common among each of these similar pai rs. Thus, the system developed subletter-size feature detec- + +tors for the features relevant to the discrimination. + +Correlated teaching inputs. We carried out one other set of experiments with the word/letter patterns. In this case, we used clusters of size two and presented stimuli drawn from the set: AA. BA. SB. EB. Note that on the left-hand side, we have the same four letters as we had in the previous experiment, but on the right-hand side we have only two patterns; these two patterns are correlated with the letter in the first position. An A in the second position means that the first position contains either an A or a B, whereas a B in the second position Copyrighted Material + +means that the first position contains either an S or an E. Note further that those correlations between the first and second positions are in opposition to the "natural" similarity of the letters in the first serial position. In this experiment, we first trained the system on the four stimuli described above. Si nce the second serial position had only two letters in it, the size-two cluster became a position-specific letter detector for the second serial position. One unit responded to the A and one to the B in the second position. Notice that the units are also responding to the letters in the fi rst serial position as wel l. One unit is responding to an A or a B in the first position while the other responds to an E or an S. Figure 12 shows the patterns of weights developed by the two units. After training, the system was then presented patterns containing only the first letter of the pai r and, as expected, the system had learned the "unnatural " classification of the letters in the fi rst position. Here the strong correlation between the fi rst and second position led the competitive learning mechanism to override the strong correlation between the highly similar stimulus patterns in the first serial position. This suggests that even though the competitive learning system is an "unsupervised " learning mechanism, one can control what it learns by controlling the statistical structure of the stimulus patterns being presented to it. In this sense, we can think of the right-hand letter in this experiment as being a kind of teaching stimulus aimed at determining the classification learned for other aspects of the stimulus. It should also be noted that this teaching mechani sm is essentially the same as the so-called errorless learning procedure used by Terrace (963) in training pigeons to peck a certain color key by associating that color with a response situation where their pecking is determined by other factors. As we shall see below, this correlational teaching mechanism is useful in allowing the competitive learning mechanism to + +discover features which it otherwise would be unable to discover . + +. . . • .. • · .... + +· . + +• • . . + +· ... • • · .. . • .. .. . + +• • • + +• • Unit 1 ••• •• + +• • • • • + +• ••• • • • • + +••• Unit 2 + +• • • • • • •• + +FIGURE 12. The pattern of weights developed in the correlated learning experiment. Copyrighted Material + +Horizontal and Vertical Lines + +One of the classical ly difficult problems for a linear threshold device like a perceptron is to distinguish between horizontal and vertical lines. In general , horizontal and vertical lines are not linearly separable and requi re a multi layer perceptron system to distinguish them. One of the goals of the competitive learning device is for it to discover features that, at a higher level of analysis, might be useful for discriminating patterns which might not otherwise be discriminable with a linear threshold-type device. It is therefore of some interest to see what kinds of features the competitive learning mechanism discovers when presented with a set of vertical and horizontal lines. In the following discussion, we chronicle a series of experiments on this problem. Several of the experiments ended in fai lure, but we were able to discover a way i n which competitive learning systems can be put together to build a hierarchical feature detection system capable of discriminating vertical and horizontal lines. We proceed by sketching several of our fai lures as well as our successes because the way in which the system fails is elucidating. It should be noted at the outset that our goal is not so much to present a model of how the human learns to distinguish between vertical and horizontal lines (indeed, such a distinction is probably prewired in the human system) , but rather to show how competitive learning can discover features which allow for the system to learn distinctions with multi ple layers of units that cannot be learned by single-layered systems. Learning to distinguish vertical and horizontal + +lines is simply a paradigm case. + +In this set of experiments, we represented the lower level of units as if they were on a 6x6 grid. We then had a total of 12 stimulus patterns, each consisting of turning on six Level 1 units in a row on the grid. Figure 13 illust rates the grid and several of the stimulus patterns. Ideally, one might hope that one of the units would respond whenever a vertical line is presented� the other would respond whenever a horizontal line is presented. Unfortunately, a little thought indicates that this is impossible. Since every input unit partici pates in exactly one vertical and one horizontal line, there is no configuration of weights which wi ll distinguish vertical from horizontal. This is exactly why no linear threshold device can distinguish between vertical and horizontal lines in one level. Since that must fai l, we might hope that some clusters in the competitive learning device wi ll respond to vertical lines by assigning weights as illustrated in Figure 14. In this case, one unit of the pai r would respond whenever the first, second, or fourth vertical line was presented, and another would respond whenever the third, fifth, or sixth vertical line was presented� since both units would Copyrighted Material + +· ... . .. .. · .. .. .. + +· . . . . . Unit 1 Cluster 1 + +· .. .. . .. · . .. . .. · ...... . + +.. . .. .. .. · .. . .. + +.. . . .. .. Unit 2 Cluster 1 + +· . . . . . · . .. .. . . .. . . .. .. + +•••••• • •••• • + +Unit 1 Cluster 2 + +• •• ••• + +• ••••• Unit 2 Cluster 2 + +• •• ••• • •• • • • + +FIGURE 14. A possible weight configuration which could distinguish vertical rrom + +horizontal. + +· ...... • • • • • · ..... + +• ••• • + +• ••• • • ••• • Unit 1 + +Unit 2 + +FIGURE 15. Atypical configuration or weights for the vertical/horizontal discrimina- + +tion. + +ones. It is this simi larity that the competitive learning mechanism has + +discovered. + +Now, suppose that we change the system somewhat. Suppose that we "teach" the system the difference between vertical and horizontal (as we did in the previous experiments with letter strings) . In this experiment we used a 12 x 6 grid. On the right-hand side of the grid we presented either a vertiebtPyri3hPJ>hiijlOfI);Jjne, as we did before. On + +the right-hand grid are identical for the two cluster members. Thus, when the "teacher" is turned off, and only the right-hand figure is presented, the two units respond randomly and show no evidence of + +having learned the horizontal I vertical distinction. + +Suppose, however, that we have four, rather than two, units in the level-two clusters. We ran this experiment and found that of the four units, two of them divided up the vertical patterns and two of them di vided up the horizontal patterns . Figure 1 7 ill ustrates the weight values for one of our runs. One of the units took three of the vertical line patterns; another unit took three other vertical patterns. A third unit responded to three of the horizontal line patterns , and the last unit responded to the remaining three horizontal lines. Moreover, after we took away the "teaching" pattern, the system continued to classify the vertical and horizontal lines just as it did when the left-hand "teaching" + +pattern was present. + +• • • • • • Unit 1 + +Unit 3 + +Cluster 1 + +• • • • • • Unit 2 + +Unit 4 + +.... .. . . . . . . •••••• + +• • • • Unit 1 + +Unit 3 + +• ••••• + +Cluster 2 + +Unit 2 ...... . . .... + +• • • • • • Unit 4 + +FIGURE 17. The weight values for the two clusters of size four for the vertical/ horizontal discrimination experiment wi th a correlated "teaching" stimulus. Copyrighted Material + +In one final experiment with vertical and horizontal lines, we developed a three-level system in which we used the same stimulus patterns as in the previous experiment; the only difference was that we had two clusters of four units at the second level and one cluster of two units at the third level . Figure 18 shows the architecture employed. In this case, the two four-element clusters each learned to respond to subsets of the vertical and horizontal lines as in the previous experiment. The two clusters generally responded to different subsets , however. Thus, when the upper horizontal line was presented, Unit 1 of the first cluster responded and Unit 3 of the second cluster responded. When the bottom horizontal line was presented, Unit 1 of the first cl uster responded again, but Unit 4 of the second cluster also responded. Thus, the cluster of size two at the highest level was recei ving a kind of dipole stimulus. It has four inputs and on any trial , two of them are act i ve . As with our analysis of di pole stimuli, we know that stimul i that overlap are always put in the same category. Note that when a vertical line is presented, one of the two units in each of the middle layers of clusters that responds to vertical lines wi ll become active, and that none of the units that respond to horizontal lines will ever be active; thus, this means that there are two units in each middle layer cluster that respond to vertical lines . Whenever a vertical line is presented, one of the units in each cluster wi ll become active. None of the horizontal units will ever be active in the face of a vertical stimulus. Thus, one of the units at the highest level learns to respond whenever a vertical line is presented , and the other unit responds whenever a horizontal line is + +Layer 1 + +Layer 2 + +•••• • Input Units + +presented. Once the system has been trained, this occurs despite the absence of the "teachingh stimulus. Thus , what we have shown is that the competitive learning mechanism can, under certain conditions, develop feature detectors which allow the system to distinguish among patterns that are not differentiable by a simple linear unit in one level. + +CONCLUSION + +We have shown how a very simple competitive mechanism can discover a set of feature detectors that capture important aspects of the set of stimulus input patterns. We have also shown how these feature detectors can form the basis of a multilayer system that can serve to learn categorizations of stimulus sets that are not linearly separable. We have shown how the use of correlated stimuli can serve as a kind of ''teachingh input to the system to allow the development of feature detectors which would not develop otherwise. Although we find the competitive learning mechanism a very interesting and powerful learning principle, we do not, of course, imagine that it is the only learning principle. Competitive learning is an essentially nonassociative, statistical learning scheme. We certainly imagine that other kinds of learning mechanisms will be involved in the building of associations among patterns of activation in a more complete neural network. We offer this analysis of these competitive learning mechanisms to further our understanding of how simple adaptive networks can discover features important in the description of the stimulus environment in which the + +system finds itself. + +ACKNOWLEDGMENTS + +This research was supported by grants from the System Development Foundation and by Contract NOOOI4-79-C-0323, NR 667-437 with the Personnel and Training Research Programs of the Office of Naval + +Research. + +APPENDIX + +For the case of homogeneous dipole stimulus patterns, it is possible to derive an expression for the most stable equilibrium state of the system. We say that a set of dipole stimulus patterns is homogeneous if (a) they are equally likely and (b) for every input pattern in the set there are a fixed number of other input patterns that overlap them. These conditions were met in our simulations. Our measure of stability + +is given by + +T = LPkLL Vjk (£rjk - £rik)' + +k j i + +S + +. 1 . + +mce Pk =N + +' we can WrIte + +Summing the first portion of the equation over i and the second over j + +we have + +T = M + +N LL Vjk£rjk - N + +1LL£rikLVjk ' + +j k i k j + +Now note that when Pk = 1/ N, we have £r ik = L 'kj vijl L Vkl' Further- + +j , + +more, L V,k =1 and L V'k = N" where N, is the number of patterns + +I k captured by unit I. Thus, we have + +Now, since all stimuli are the same size, we have 'ij = 'j + +i' Moreover, + +since all stimuli have the same number of neighbors , we have L'/j = L'i} = R, where R is a constant determined by the dimenslonalit/of the stimulus space from which the dipole stimuli are drawn. + +Thus, we have LVii + +M R"" I T =-N LL Vjk£rjk - N �-N.. ' j k I I + +procedure, including languages for precisely expressing them and theoretical machines for realizing them. This body of theory grew out of mathematical logic, and in tum contributed to computer science, physical computing systems, and the theoretical paradigm in cognitive + +science often called the (von Neumann) computer metaphor.l + +In his paper "Physical Symbol Systems," Allen Newell (1 980) articulated the role of the mathematical theory of symbolic computation in cognitive science and furnished a manifesto for what I will call the symbolic paradigm. The present book offers an alternative paradigm for cognitive science, the subsymbolic paradigm, in which the most powerful level of description of cognitive systems is hypothesized to be lower than the level that is naturally described by symbol manipulation. + +The fundamental insights into cognition explored by the subsymbolic paradigm do not involve effective procedures and symbol manipulation. Instead they involve the "spread of activation," relaxation, and statistical correlation. The mathematical language in which these concepts are naturally expressed are probability theory and the theory of dynamical systems. By dynamical systems theory I mean the study of sets of numerical variables (e.g., activation levels) that evolve in time in parallel and interact through differential equations. The classical theory of dynamical systems includes the study of natural physical systems (e.g., mathematical physics) and artificially designed systems (e.g., control theory). Mathematical characterizations of dynamical systems that formalize the insights of the subsymbolic paradigm would be most helpful + +in developing the paradigm. + +This chapter introduces harmony theory, a mathematical framework for studying a class of dynamical systems that . perform cognitive tasks according to the account of the subsymbolic paradigm. These dynamical systems can serve as models of human cognition or as designs for artificial cognitive systems. The ultimate goal of the enterprise is to develop a body of mathematical results for the theory of information processing that complements the results of the classical theory of (symbolic) computation. These results would serve as the basis for a manifesto for the subsymbolic paradigm comparable to Newell's manifesto for the symbolic paradigm. The promise offered by this goal will, I hope, be suggested by the results of this chapter, despite their very lim- + +ited scope. + +1 Mathematical logic has recently given rise to another approach to formalizing information: situation semantics (Barwise & Perry, 1983). This is related to Shannon's (1948/1963) measure of information through the work of Dretske (1981). The approach of this chapter is more faithful to the probabilistic formulation of Shannon than is the symbolic approach of situation semantics. (This results from Dretske's move of identify- + +It should be noted that harmony theory is a "theoryh in the mathematical sense, not the scientific sense. By a "mathematical theory" -e.g., number theory, group theory, probability theory, the theory of computation-I mean a body of knowledge about a part of the ideal mathematical world� a set of definitions, axioms, theorems, and analytic techniques that are tightly interrelated. Such mathematical theories are distinct from scientific theories, which are of course bodies of knowledge about a part of the "real" world. Mathematical theories provide a language for expressing scientific theories� a given mathematical theory can be used to express a large class of scientific theories. Group theory, for example, provides a language for expressing many competing theories of elementary particles. Similarly, harmony theory can be used to express many alternative theories about various cognitive phenomena. The point is that without the concepts and techniques of the mathematical language of group theory, the formulation of any of the current scientific theories of elementary particles would be essen- + +tially impossible. + +The goal of harmony theory is to provide a powerful language for expressing cognitive theories in the subsymbolic paradigm, a language that complements the existing languages for symbol manipulation. Since harmony theory is conceived as a language for using the subsymbolic paradigm to describe cognition, it embodies the fundamental scientific claims of that paradigm. But on many important issues, such as how knowledge is represented in detail for particular cases, harmony theory does not itself make commitments. Rather, it provides a language for stating alternative hypotheses and techniques for studying + +their consequences. + +A Top-Down Theoretical Strategy + +How can mathematical analysis be used to study the processing + +mechanisms underlying the performance of some cognitive task? + +One strategy, often associated with David Marr (I 982), is to characterize the task in a way that allows mathematical derivation of mechanisms that perform it. This top-down theoretical strategy is pursued in harmony theory. My claim is not that the strategy leads to descriptions that are necessarily applicable to all cognitive systems, but rather that the strategy leads to new insights, mathematical results, computer architectures, and computer models that fill in the relatively unexplored conceptual world of parallel, massively distributed systems that perform cognitive tasks. Filling in this conceptual world is a necessary subtask, I believe, for understanding how brains and minds are capable of intelligence and for assessing whether computers with novel architectures + +might share this capabili�opyrighted Material + +introduced by thisexpository organization will be repaid by greater + +accessibility. + +Section 1 is a top-down presentation of how the perceptual perspective on cognition leads to the basic featuresof harmony theory. This presentation starts with a particular perceptual model, the letterperception model of McClelland and Rumelhart (I 98 1), and abstracts from it general features that can apply to modeling of higher cognitive processes. Crucial to the development is a particular formulation of + +aspectsof schema theory, along the lines of Rumelhart (I 980) . + +Section 2, the majority of the chapter, is a bottom-up presentation of harmony theory that starts with the primitives of the knowledge representation. Theorems are informally described that provide a competence theory for a cognitive system that performs thecompletion task, a machine that realizes this theory, and a learning procedure through which the machine can absorb the necessary information from its environment. Then an appl ication of the general theory is described: a model of intuitive, qualitative problem-solving in elementary electric circuits. This model illustrates several points about the relation between symbolic and subsymbolic descriptions of cognitive phenomena; for example, it furnishes a sharp contrast between the description at these two levels of the nature and acquisition of + +expertise. + +The final part of the chapter is an Appendix containing a concise but + +self-contained formal presentation of the definitions and theorems. + +SECTION 1: SCHEMA THEORY AND SELF -CONSISTENCY + +THE LOGICAL STRUCTURE OF HARMONY THEORY + +The logical structure of harmony theory is shown schematically in Figure 1. The box labeled Mathematical Theory represents the use of mathematical analysis and computer simulation for drawing out the implications of the fundamental principles. These principles comprise a mathematical characterization of computational requirements of a cognitive system that perforCJljip}lnyRftJlJJM8mffctask. From these principles + +schemata Inference + +� harmony probabIlity CONCEPTUAL FOUNDATIONS + +descriptive characterization of computational requirements + +- mathematical + +�- characterization + +Of computation raqulrements + +\� + +machine implementation " (simulation): PROCESS + +,, ' + +MATHEMATICAL THEORY + +------, 7) + +• + +formalization derivation + +FIGURE \. The logical structure of harmony theory. + +characterization of performance + +, " , + +> --- � Simulation + +it is possible to mathematically analyze aspects of the resulting performance as well as rigorously derive the rules for a machine implementing the computational requirements. The rules defining this machine have a different status from those defining most other computer models of cognition: They are not ad hoc, or post hoc; rather they are logically derived from a set of computational requirements. This is one sense in + +which harmony theory has a top-down theoretical development. + +Where do the " mathematically characterized computational requirements" of Figure I come from? They are a formalization of a descriptive characterization of cognitive processing, a simple form of schema theory. In Section 1 of this chapter, I will give a description of this form of schema theory and show how to transform the descriptive characterization into a mathematical one-how to get from the conceptual box of Figure 1 into the mathematical box. Once we are in the formal world, mathematical analysis and computer simulation can be put to + +work. + +Throughout Section 1, the main points of the development will be + +explicitly enumerated. + +Point I. The mathematics of harmony theory is founded on familiar concepts Q{ cognitive science: inference through activation q{ schemata. Copyrighted Material + +DYNAMIC CONSTRUCTION OF SCHEMATA + +The basic problem can be posed a la Schank (980), While eating at a fancy restaurant, you get a headache. Without effort, you ask the waitress if she could possibly get you an aspirin. How is this plan created? You have never had a headache in a restaurant before. Ordinarily, when you get a headache your plan is to go to your medicine cabinet and get yourself some aspirin. In the current situation, this plan must be modified by the knowledge that in good restaurants, the management is wi lling to expend effort to please its customers, and that + +the waitress is a liaison to that management. + +The cognitive demands of this situation are schematically illustrated in Figure 2. Ordinari ly, the restaurant context calls for a "restaurant script" which supports the planning and inferencing required to reach the usual goal of getting a meal. Ordinarily, the headache context calls for a "headache script" which supports the planning required to get aspirin in the usual context of home. The completely novel context of a headache in a restaurant calls for a special-purpose script integrating the + +knowledge that ordinarily manifests itself in two separate scripts. + +What kind of cognitive system is capable of this degree of flexi bility? Suppose that the knowledge base of the system does not consist of a set of scripts like the restaurant script and the headache script. Suppose + +restaurant context + +headache contexl + +restaurant ---"'... & headache --v-"'" + +context + +Headache in a Restaurant + +restaurant script + +headache script + +specialpurpose script + +... Inferences, goals + +... inferences, goals + +... 'ask waitress for aspirin' + +However, the model also accounts for the observed facilitation of letter perception within orthographically regular nonwords or pseudowords like MAVE. When the model processes this stimulus, several word units become and stay quite acti ve, including MAKE, WA VE, HA VE, and other words orthographically similar to MA VE. In this case, the perception of a letter in the stimulus is the result of an inference process that is supported by the collection of acti vated units. This + +collection is a dynamically created pseudo word schema. + +When an orthographically irregular non word is processed by the model, letter perception is slowest. As in the case of pseudowords, many word units become active. However, none become very active, and very many are equally active, and these words have very little similarity to each other, so they do not support inference about the letters effectively. Thus the knowledge base is incapable of creating schemata + +for irregular nonwords. + +Point 3. Schemata are coherent assemblies of knowledge atoms; only + +these can support inference. + +Note that schemata are created simply by activating the appropriate atoms. This brings us to what was labeled in Figure 1 the "descriptively + +characterized computational requirements" for harmony theory: + +Point 4: The harmony principle. The cognitive system is an engine for activating coherent assemblies of atoms and drawing inferences that are + +consistent with the knowled,?e represented by the activated atoms. + +Subassemblies of activated atums that tend to recur exactly or approxi- + +mately are the schemata. + +This principle focuses attention on the notion of coherency or consistency. This concept will be formalized under the name of harmony, + +and its centrality is acknowledged by the name of the theory. + +MICRO· AND MACROLEVELS + +It is important to realize that harmony theory, like al l subsymbolic accounts of cognition, exists on two distinctlevels of description: a microlevel involving knowledge atoms and a macrolevel involving schemata (see Chapter 14). These levels of description are completely analogous to other micro- and macrotheories, for example, in physics. The microtheory, quantum physics, is assumed to be universally valid. Part of its job as a theory is to explain why the approximate macrotheory classical phvsics..2 works when it does and why it breaks , COPYflghted Matenal + +TABLE I A PROCEDURE FOR PERFORMING THE COMPLETION TASK + +Input: Activat ion: Inference: + +Assign values to some features in the representation Activate atoms that are consistent with the representation Assign values to unknown features of representation that + +are consistent with the active knowledge + +fil led in, and how the representation is fi lled in affects which atoms are activated. The acti vation and inference processes mutually constrain each other; these processes must run in paral lel . Note also that all the + +decisions come out of a stri ving for consistency. + +Point 6. Assembly of schemata (activation of atoms) and iriference (completing missing parts of the representation) are both achieved by finding maximally self-consistent states Qf the system that are also con- + +sistent with the input. + +The completion of the stimulus shown in Figure 5 is shown in Figure 6. The consistency is high because wherever an active atom is + +o \_ active; + +on + +inactive; off + +above, and reports the results of some particular studies. The most for- + +mal matters are treated in the Appendix. + +SECTION 2: HARMONY THEORY + +. .. the privileged unconscious phenomena, those susceptible of becoming conscious, are those which . . . affect most profoundly our emotional sensibility . .. Now, what are the mathematic entities to which we attribute this character of beauty and elegance . .. ? They are those whose elements are harmoniously disposed so that the mind without effort can embrace their totality while realizing the details. This harmony is at once a satisfaction of our esthetic needs and an aid to the mind, sustaining and guiding. . .. Figure the future elements of our combinations as something like the unhooked atoms of Epicurus. . .. They flash in every direction through the space . .. like the molecules of a gas in the kinematic theory of gases. Then their mutual impacts may produce new combinations. + +> Henri Poincare (1913) Mathematical Creation \0 + +In Section 1, a top-down analysis led from the demands of the completion task and a probabilistic formulation of schema theory to perceptual features, knowledge atoms, the central notion of harmony, and the role of harmony in estimating probabi lities of environmental states. In Section 2, the presentation will be bottom-up, starting from the + +primitives . + +KNOWLEDGE REPRESENTATION + +Representation Vector + +At the center of any harmony theoretic model of a particular cogni- + +tive process is a set of representational features rj, r2, .. + +. These + +Knowledge Atoms + +Representational Features + +> k W,A2 kM A = , 2 kA K = 2 3 + +(- (- (0 + ++ + 0 + + 0 0 0 + + + +FIGURE 8. The graphical representation of a particular harmony model . + +0) 0) -) + +would them be indicated above the atom in the drawing. (For the com- + +pletely general case, see Figure 13.) + +Hierarchies and the Architecture of Harmony Networks + +One of the characteristics that distinguishes harmony models from other paral lel network models is that the graph always contains two layers of nodes, with rather different semantics. As in many networks, the nodes in the upper layer correspond to patterns of values in the lower layer. In the letter-perception model of McClelland and Rumelhart, for example, the word nodes correspond to patterns over the letter nodes, and the letter nodes in turn correspond to patterns over the line-segment nodes. The letter-perception model is typical in its hierarchical structure: The nodes are stratified into a sequence of several layers, with nodes in one layer being connected only to nodes in + +adjacent layers. Harmony models use only two layers. + +The formal ism could be extended to many layers, but the use of two layers has a principled foundation in the semantics of these layers. The nodes in the representation layer support representations of the environment at all levels of abstractness. In the case of written words, this layer could support representation at the levels of line segments, letters, and words, as shown schematically in Figure 9. The upper, knowledge, layer encodes the patterns among these representations. If information is gi ven about line sef!l1p9}fgh;&Y?AcNUfI5l of the knowledge atoms + +The harmony function has as parameters the set of knowledge vectors and their strengths: {(ka,fT a)} ; I wi ll cal l this the knowledge base K. The basic requirement on the harmony function H is that it be additive under decompositions of the system. IJ This means that if a network can be partitioned into two unconnected networks. as in Figure 12. the harmony of the whole network is the sum of the harmonies of the + +parts: + +H(r, a ) = H (r h a l ) + H(r2, a 2) . + +In this case, the knowledge and representational feature nodes can each be broken into two subsets so that the knowledge atoms in subset 1 all have 0 connections with the representational features in subset 2, and vice versa. Corresponding to this partition of nodes there is a decom- + +position of the vectors r and a into the pieces rh r2 and aJ ,a2' The harmony function I have studied (recall Figure 7) is + +(1) + +a + +Here, hI( ( r, ka) is the harmony contributed by acti vating atom a, + +given the current representation r. I have taken this to be + +r"k + +hl« r. ka) =Ikai -I( . + +1--10---------- r ------------1 .. 1 + +FIGURE 12. A decomposable harmony network. + +val + +ues of the unknown rj and those values of the Q + +athat together max- + +imize the harmony H ( r, a) and thereby maximize the estimated proba- + +bi lity p(r ,a). + +This discussion is summarized in the fol lowing theorem: + +Theorem 1: Competence. Suppose a cognitive system can observe + +the frequency of the patterns Ika + +l in its environment. The probabi l- + +ity distribution with the most Shannon missing information that is + +consistent with the observations is + +7T ( r) ex: eV ( + +x) + +with U defined as above. The maximum-likelihood completions of + +this distribution are the same as those of + +p (r ,8) ex: e H(r ,a ) + +with the harmony function defined above. + +This theorem describes how a cognitive system should perform completions, according to some mathematical principles for statistical extrapolation and inference, In this sense, it is a competence theorem. The obvious next question is: Can we design a system that wi ll really compute completions according to the specifications of the competence + +theorem? + +The " Physics Analogy" + +It turns out that designing a machine to do the required computations is a relatively straightforward appl ication of a computational technique from statistical physics. It is therefore an appropriate time to discuss the "analogy" to physics that is exploited in harmony theory. + +Why is the relation between probabi lity and harmony expressed in the competence theorem the same as the relation between probabi lity and energy in statistical physics? The mapping between statistical physics and inference that is being exploited is one that has been known + +for a long time. + +The second law of thermodynamics states that as physical systems evolve in time , they wi ll approach conditions that maximize randomness or entropy, subject to the constraint that a few conserved quantities like the systems' energy must always remain unchanged. One of the triumphs of statistical mechanics was the understanding that this law is the macroscopic manifesfJU(K{i�t�I\1ft(ftff4Ying microscopic descri ption + +functions. Physicists at IBM independently applied the technique, under the name simulated annealing, to both practical computer design problems and classical maximization problems (Kirkpatrick, Gelatt, & Vecchi , 1983) . Benchmarks of simulated anneal ing against other search procedures have produced mi xed results (Aragon, Johnson, & + +McGeoch , 1985) . + +The contribution of harmony theory is not so much the search procedure for finding maxima of H, but rather the function H itself. Theorem 2 is important: It describes a statistical dynamical system that performs completions; it gives an implementation-level descri ption of a kind of completion machine. But Theorem 1 is more central : It gi ves a high , functional-level characterization of the performance of the system-says what the machine does-and introduces the concept of harmony. More central to the theory also is Theorem 3 , which says + +how the harmony function can be tuned with experience. + +The Learnability Theorem + +Performing the completion task in different environments cal ls for different knowledge. In the formal ism of Theorem 1, a gi ven cognitive system is assumed to be capable of observing the frequency in its environment of a predetermi ned set of feature patterns. What varies for a given cognitive system across environments is the frequencies of the patterns; this manifests itself in the variation across environments of the strengths of the knowledge atoms representing those patterns. + +Theorem 3: Learnability. Suppose states of the environment are selected according to the probabi lity distri bution defining that environment, and each state is presented to a cogn itive system. Then there is a procedure for gradual ly modifying the strengths of the knowledge atoms that will converge to the val ues requi red by + +Theorem 1. + +The basic idea of the learning procedure is simple. Whenever one of the patterns the cognitive system can observe is present in a stimulus from the environment, the parameter associated with that pattern is incremented. In harmonium, this means that whenever a knowledge atom matches a stimulus, its strength increases by a smal l amount D.rr . In the simulation machine, this means that the A parameter on al l the connections corresponding to that atom must be incremented by D.A =D.rr (1 - K). In t8b�1nBNiedW/a?�Wl}1 corresponds to a memory + +Instruction, and Ginsburg, 1983.) Even such simple problems as that of Figure 16 have important instructional implications (Riley, 1984) . + +The model I wi ll describe was studied in col laboration with Mary S. Riley (Riley & Smolensky, 1984) and Peter DeMarzo (1984) . This model provides answers, without any symbolic mani pulation of rules, to qual itative questions about the particular circuit of Figure 16. It should not be assumed that we imagine that a different harmony network like the one I wi ll describe is created for every different circuit that is analyzed. Rather we assume that experts contain a small number of fixed networks like the one we propose, that these networks represent the effects of much cumulated experience with many different circuits, that they form the "chunks" with which the expert's intuition represents the circuit domain, and that complex problem sol ving somehow employs these networks to direct the problem solving as a whole through intuitions about chunks of the problem. At this early stage we cannot say much about the coordination of activity in complex problem solving. But we do claim that by gi ving an explicit example of a nonsymbol ic account of problem solving, our model offers insights into expertise that complement nicely those of traditional production-system models. The model also serves to render concrete many of the general + +features of harmony theory that have been described above. + +Representational features. The first step in developing a harmony model is to select features for representing the environment. Here the environment is the set of qualitative changes in the electric circuit of Figure 16 that obey the laws of physics. What must obviously be represented are the changes in the physical components: whether R 1 goes up, goes down , or stays the same, and simi larly for R 2 and the battery's voltage Vrola/' We also hypothesize that experts represent deeper features of this environment, like the current I, the voltage drops VI and V2 across the two resistors, and the effective resistance Rlola/ of the circuit. We claim that experts "see " these deeper features; that perceiving the problem of Figure 16 for experts invol ves fil l ing in the deeper features just as for all sighted people-experts in vision perceiving a scene involves fill ing in the features describing objects in three-dimensional space. Many studies of expertise in the psychological literature show that experts percei ve their domain differently from novices: Their representations are much richer; they possess additional representational features that are specially developed for capt uring the structure of the particular environment. (See, for example, Chase & + +Simon, 1973; Larkin, 1983.) + +So the representational features in our model encode the qual itative changes in the seven circuit variables: R It R 2 , R'o(ail V It V 2, Vrola/' and + +although there seems to be no natural formal definition for the concept. To study the properties of macrodecisions, it is appropriate to look at how the average values of the stochastic node variables change during the computation. For each of the unknown variables, the node val ues were averaged over 30 runs of the completion problem of Figure 16, separately for each time during the computation . The resulting graphs are shown in Figure 20. The plots hover around 0 initially, indicating that values + and - are equal ly likely at high temperatures-lots of + +fl + + ickering. As the system cools, the average values of the representation variables drift toward the values they have in the correct sol ution + +to the problem (RlolaJ = up, I = down, VI = down, V2 = up) . + +Emergent seriality. To better see the macrodecisions, in Figure 21 the graphs have been superimposed and the " indecisive" band around 0 has been removed. The stri king result is that out of the statistical din + +of paral lel microdecisions emerges a sequence of macrodecisions. + +Propagation of givens. The result is even more interesting when it is observed that in symbolic forward-chaining reasoning about this problem, the decisions are made in the order R, I, VI, V2. Thus not on ly ic; the ('(JmnPlpncp of the mnrlel neHt ly clec;cri hahl e <;ym hol ical ly. hut even the performance, when descri bed at Ihe macrolevel , cou ld be modeled by the sequen tial fi ri ng of prod uct ions that chai nIh rough the inferences. Of course, macrodecisions emerge first about those variables that are most directly constrained by the given inputs, but not because rules are being used that have conditions that only al low them to apply when all but one of the variables is known. Rather it is because the variables given in the input are fIXed and do not fluctuate: They provide the information that is the most consistent over time, and therefore the knowledge consistent with the input is most consistently acti vated, allowing those variables involved in this knowledge to be more consistently completed than other variables. As the temperature is lowered, those variables "near" the input (with respect to the connections provided by the knowledge) stop fluctuating first, and their relative constancy of value over time makes them function somewhat like the original input to support the next wave of completion. In this sense, the stability of variables "spreads out " through the network, starting at the inputs and propagating with the help of cool ing. Unlike the simple feedforward "spread of activation " through a standard activation network, this process is a spread of feedback-mediated coherency through a decision-making network. Like the growth of droplets or crystals, this amounts to the expansion of pockets of order into a sea of + +20 + +15 + +u + +10 + +5 + +o \_\_ � \_\_\_\_ � \_\_\_\_ � \_\_ �L-\_\_ � \_\_\_\_ � \_\_\_\_ � \_\_ � + +o 100 200 + +Time + +300 400 + +FIGURE 22. The specific heat of the circuit analysis model th rough the course of t he + +computation. + +/ / / + +/ / \_ / + +o 100 + +/ I -I I / / + +// R + +200 Time 300 400 + +FIGURE 23. There is a peak in the specific heat at the time when the R and I decisions + +are being made. + +The analysis of decision making in this model considered the limit as the number of features and atoms goes to infinity-for only in this "thermodynamic limit" can we see real phase transitions. In this limit, the set of possible values for the averages that define the aggregate variables comes closer and closer to a continuum. The central l imit theorem constrains these averages to deviate less and less from their means; statistical fluctuations become less and less significant; the + +model 's behavior becomes more and more deterministic. + +Thus, just as the statistical behavior of matter disappears into the deterministic laws of thermodynamics as systems become macroscopic in size, so the statistical behavior of individual features and atoms in harmony models becomes more and more closely approximated by the higher level descri ption in terms of schemata as the number of constituents aggregated into the schemata increases. However there are two important differences between harmony theory and statistical physics relevant here. First, the number of constituents aggregated into schemata is nowhere near the number- I023 -of particles aggregated into bulk matter. Schemata provide a useful but significantly limited description of real cognitive processing. And second, the process of aggregation in harmony theory is much more complex than in physics. This point can be brought out by passing from the grossly oversimplified two-choice decision model just considered to a more realistic cogni- + +tive domain. + +Schemata for rooms. In a real istical ly complicated and large network, the schema approximation would go something like this. The knowledge atoms encode clusters of values for features that occur in the environment . Commonly recurring clusters would show up in many atoms that differ slightly from each other. (In a different language, the many exemplars of a schema would correspond to knowledge atoms that differ slightly but share many common features.) These atoms can be aggregated into a schema , and their average activation at any moment defines the activation of the schema. Now among the atoms in the cluster corresponding to a schema for a living-room, for example, might be a subcluster corresponding to the schema for sofa/ coffee-table. These atoms comprise a subschema and the average of their activations would be the activation variable for this subschema. The many atoms comprising the schema for kitchen share a set of connections to representational features relating to cooking devices. It is convenient to group together these connections into a cooking-device slot, Smoking ' Different atoms for different instances of kitchen encode various patterns of values over these representational features, corresponding to instances of stove, con ventional oven, microwave oven , + +Development Foundation, the Alfred P. Sloan Foundation, National Institute of Mental Health Grant PHS MH 14268 to the Center for Human Information Processing, and Personnel and Training Research Programs of the Office of Naval Research Contract N00014-79-C-0323, + +NR 667-437. + +Transducer + +Mental Space: M knowledge A + +FIGURE 26. A schematic representation of the theoretical framework . + +representation are taken to be binary. The prediction problem is to take some features of an environmental state as input and make best guesses about the unknown features. This amounts to extrapolating from some observed statistics of the environment to an entire probability distribution over all possible feature combinations. This extrapolation proceeds by constructing the distribution that adds minimal infor- + +mation (in Shannon's sense) to what is observed. + +Notation. B = (- 1, + I) , the default binary values. R =the real + +numbers. x + +n + +=XxXx ... xX (n times) , where x is the cartesian + +product. If X, y E Xn + +, then x·y = r.�\_lxmYm and Ix i = L�=llxml . + +2x is the set of all subsets of X. IXI is the number of elements of X. Bn is called a binary hypercube. The i th coordinate junction of Bn (; = 1, . . . ,n ) gives for any point (i.e., vector) in Bn its ith B-valued + +coordinate (i.e. , component) . + +De/. A distal environment Edistol = (E, P) is a set E of environmental + +events and a probability distribution P on E. + +De/. A representational space R is a cartesian product Rex x Ren of two binary hypercubes. Each of the N (Nex ; Nen ) binary-valued coordinate functions ri of R (Rex ; Ren ) is cal led an (exogenous; endogenous) + +feature. + +De/. A transduction map T from an environment Edistol to a representational space R = RexxRen is a map T: E --+ Rex. T induces a proba- + +De! Let R be a representational space. Associated with this space + +is the input space I = {- I, 0, + II Na. + +De! A point r in R is called a completion of a point t in I if every nonzero feature of , agrees with the corresponding feature of r. This relationship will be designated r ::> t. A completion junction c is a map from I to 2R (the subsets of R) for which r E dd implies r ::> to The features of L with val ue 0 are the "unknowns" that must be filled in by + +the completion function. + +De! Let p be a probabi lity distribution on a space X = Rex xA . The maximum-likelihood completion junction determined by p, + +c p : I -2R , is defined by + +dd = { r E R I for some a E A, and all (a' ,r') E R x A + +such that r' ::> , : p (r , a ) � p (r + +, a') I + +(A wi ll be either empty or the set of possi ble knowledge atom activa- + +tion vectors.) + +De! A basic event (X has the form + +a : [r· = bl] & [r· = b 2] & ... & [r. = b,,] '1 '2 '{J ,.. + +where {ril' ri 2 • ... . ri + +B + +I is a collection of exogenous features and + +(b I> b 2 ••••• b�) E B� . a can be characterized by the function + +Xor : R -( 0, 1) defined by + +Xa( r) =Ii: 'h I r; (r)+bJ 1' = 1 I' + +which is I if the features al l have the correct values, and 0 otherwise. + +A convenient specification of a is as the knowledge vector + +ka = (0, O •...• 0, bi + +l + +, O •...• 0, b'2 + +' O •...• 0, b;{J ' O•... • 0) + +E {- I, O,+ II N + +in which the i + +l' + +th element is bl' and the remaining elements are all + +zero. + +De! A set 0 of observables is a col lection of basic events. + +De! Let p be an environment and 0 be a set of observables. The observable statistics of p is the set of probabi lities of all the events in 0: + +{p (a )}a E o· + +some arbitrary initial distribution, pr(x (O) = x). Given the initial state x, the new state at Time 1, x(1), is constructed as follows. One of the ncoordinates of M is selected (with uniform distribution) for updating. All the other n- lcoordinates of x (1) will be the same as those of x (0) = x. The updated coordinate can retain its previous value, leading to x (1) = x, or it can flip to the other binary value, leading to a new state that wi ll be denoted x' . The selection of the value of the updated coordinate for x (1) is stochastically chosen according to the + +likelihood ratio: + +pr(x (1) = x' ) + += + +Po(x' ) + +pr(x (1) = x) Po(x ) + +(where Po is the probabil ity distribution for t = 0 in the given sequence (p, } ;",\_ 0) . This process-randomly select a coordinate to update and stochastically select a binary value for that coordinate-is iterated indefinitely, producing states x (t) for all times t= 1, 2, . . . . At each time t, the likelihood ratio of values for the + +stochastic choice is determined by the distribution p, . + +De/. Let P be a probability distribution. Define the one-parameter + +family of distributions Pr by Pr = Ni l p + +v r + +where the normalization constants are + +Nr = I. P (x) v r . x E x + +Tis cal led the temperature parameter. An annealing schedule T is a sequence of positive values (T,},':o that converge to zero. The annealing process determined by P and T is the heat bath stochastic process + +determined by the sequence of distributions, Pr + +. If P is the Gibbs dis- + +I + +tribution determined by V, then + +where + +Pr (x ) = Zi l eV(x )/r + +Zr = I. eV ( x )/T. xEX + +This is the same (except for the sign of the exponent) as the relationship that holds in classical statistical mechanics between the probabi lity P ( x) of a microscopic state x, its energy V (x) , and the temperature T. This is the basis for the name� "temperature" and "anneal ing schedule." In the anneal ing processCfefJ(fli'iJ18tM�ution PH of Theorem 1 on + +which states that in an ensemble of systems with states distributed according to p, the number of transitions from x' to x is equal to the + +number from x to x + +. Detai led balance holds because, for the non- + +trivial case in which x' and x differ in the single coordinate v, the tran- + +sition matrix W determined by the distribution p is + +w. = p p (x ) x I v + +p (x ) + p (x' ) + +where Pv is the probabi lity of selecting for update the coordinate v. + +Now we have + +pr(x (t+l) = x ) = L p ( x') WX' I = L p (x ) WI I· + +x' E X. x' E X. + += p ( x ) LWxx' = p(x ). y' E X. + +The last equal ity follows from + +LWxx' = 1 + +x' E X. + +which simply states that the probability of a transition from x to some state x· is 1. The conclusion is that the probabi l ity distribution at time + +t+ 1 remains p , which is therefore a stationary distribution. + +Part B: Part A assures us that with infinite patience we can arbitrarily well approximate the distribution Pr at any finite temperature T. It seems intuitively clear that with still further patience we could sequential ly approximate in one long stochastic process a series of distributions Pr with temperatures T, monotonical ly decreasing to zero. This pro- + +I + +cess would presumably converge to the zero-temperature distribution that corresponds to the maximum-likel ihood completion function. A + +proof that this is true, provided + +T,>C/lnt + +for suitable C, can be found in S. Geman and D. Geman (1 984) . + +Theorem 3. We now pick up the analysis from the end of the proof + +of Theorem 1. + +Lemma. (S. Geman, personal communication , 1 984 ,) The values of the Lagrange multipliers A. = !A-ala E 0 defining the function U of + +Theorem 2 are those that minimize the convex function: Copyrighted Material + +I rA.a [)Ca (r ) - Pa 1/ + +F(A) = In Zv (A ) = In L e + +aE 0 + +r E R + +Proof of Lemma: Note that + +pu (r) = pv(r) = ZV (}.. )- l e V( r + +) + +where + +V(r) =L A"lx,,( r)- p,,] = U( r)- LA-" p". " E O "E O + +From this it follows that the gradient of F is + +of + +(lA-a =&lt;x'" > Pu - p", + +The constraint that A enforces is precisely that this vanish for all a; then Pu = 1f'. Thus the correct A is a critical point of F. To see that in fact the correct A is a minimum of F, we show that F has a positive-definite matrix of second-partial deri vatives and is therefore + +convex. It is straightforward to verify that the quadratic form + +a 2F L q q,,' + +",,,,' EO + +" OA-" (lA-,,' + +is the variance + +< (Q - &lt; Q>p) + +2 >Pu + +of the random variable Q defined by Q ( r) = L q" x'" ( r). This + +"E O + +variance is clearly nonnegative definite. That Q cannot vanish is assured by the assumption that the Xa are linearly independent. Since a Gibbs distribution Pu is nowhere zero, this means that the variance of + +Q is positive, so the Lemma is proved. + +Proof of Theorem 3: Since F is convex, we can find its minimum, A- , by gradient descent from any starting point. The process of learning the correct A, then, can proceed in time according to the gradient des- + +cent equation + +dA" � ex: + +of - aA" + += - « X,,>pu - p", + +) = P - pu + +where it is understood that the function U changes as A. changes. The two phases of the trace learning procedure generate the two terms in this equation. In the e�tttalA6IImJjallttion phase, the increment + + p is estimated� in the environmental simulation phase, the decrement pu is estimated (following Theorem 2) . By hypothesis, these estimates are accurate. (That is, this theorem treats the ideal case of perfect samples, with sample means equal to the true population means.) Thus A wi ll converge to the correct val ue. The proportional relation between CT and A was derived in the proof of Theorem 1 . + +Theorem 4. The proof of Theorem 3 shows that the trace learning procedure does gradient descent in the function F. The Boltzmann + +learning procedure does gradient descent in the function G: Pu + +(r) G(A) =-L + +r + +P(r) In--P (r) + +where, as always, the function U impl icitly depends on A. Theorem 4 wi ll be proved by showing that in fact F and G differ by a constant independent of A, and therefore they define the same gradient descent + +trajectories. From the above definition of V, we have + +V( r) = U(r) - L Aa = U (r) - + +aEO + +where, here and henceforth, < > denotes expectation values with + +respect to the environmental distribution p. This implies + +i.e. , + +Zv =Zu e-. + +By the definition of F, + +F= In Zv = InZu - < U> = < In Zu - U > . + +To evaluate the last quantity in angle brackets, note that + +pu (r) = ZiJ l eU (r) + +implies + +In p u + +(r) = -ln Zu + U (r) + +so that the preceding equation for F becomes + +F= < InZu - U> = - &lt;Inpu > = - LP(r) InPu(r). + +Now, + +G =- LP (r) In pu(r) + !:p (r) Inp(r), + +so we have + +G (). ) = F (). ) - S (P). + +Thus, as claimed, G is just F minus a constant that is independent of + +).: the entropy of the environment. + +constraints of this kind as well as possible, and the human visual system stores enough plausible constraints and is good enough at applying them that it can arrive at the correct interpretation of most normal + +images. + +The computation may be performed by an iterative search which starts with a poor interpretation and progressively improves it by reducing a cost function that measures the extent to which the current interpretation violates the plausible constraints. Suppose, for example, that each unit stands for a small three-dimensional surface fragment, and the state of the unit indicates the current bet about whether that surface fragment is part of the best three-dimensional interpretation. Plausible constraints about the nature of surfaces can then be encoded by the pairwise interactions between processing elements. For example, two units that stand for neighboring surface fragments of similar depth and surface orientation can be mutually excitatory to encode the constraints that each of these hypotheses tends to support + +the other (because objects tend to have continuous surfaces). + +RELAXATION SEARCHES + +The general idea of using parallel networks to perform relaxation searches that simultaneously satisfy mUltiple constraints is appealing. It might even provide a successor to telephone exchanges, holograms, or communities of agents as a metaphor for the style of computation in cerebral cortex. But some tough technical questions have to be answered before this style of computation can be accepted as either + +efficient or plausible: + +• Wi1\ the network settle down or will it osci1\ate or wander aim- + +lessly? + +• What does the network compute by settling down? We need some characterization of the computation that the network performs other than the network itself. Ideally we would like to be able to say what ought to be computed (Marr, 1982) and + +then to show that a network can be made to compute it. + +• How long does the network take to settle on a solution? If thousands of iterations are required the method becomes implausible as a model of how the cortex solves constraint- + +This means that it is bound to give a significant number of errors in modeling environments where very similar vectors have very different probabilities. Better performance can be achieved by annealing the network to a lower final temperature (which is equivalent to making all the weights larger) , but this will make the learning worse for two separate reasons. First, with less errors there is less to drive the learning because it relies on the difference between the phase+ and phasestatistics. Second, it will be harder to reach thermal equil ibrium at this lower temperature and so the co-occurrence statistics will be unreliable. One way of getting good statistics to drive the learning and also getting very few overt errors is to measure the co-occurrence statistics at a + +temperature higher than the final one. + +Another way of ensuring that the network approaches equilibrium is to el iminate deep, narrow minima that are often not found by the annealing process. Derthick (1984) has shown that this can be done using a longer gentler anneal ing schedule in phase-. This means that the network is more likely to occupy the hard-to-find minima in phasethan in phase+ , and so these minima will get filled in because the learning rule raises the energies of states that are occupied more in phase- + +than in phase+ . + +AN EXAMPLE OF HARD LEARNING + +A simple example which can only be solved by capturing the higher order statistical structure in the ensemble of input vectors is the "shifter" problem. The visible units are divided into three groups. Group VI is a one-di mensional array of 8 units, each of which is clamped on or off at random with a probability of 0. 3 of being on. Group V2 also contains 8 units and their states are determined by shifting and copying the states of the units in group VI' The only shifts allowed are one to the left, one to the right, or no shift. Wrap-around is used so that when there is a right shift, the state of the right-most unit in VI determines the state of the left-most unit in V2• The three possible shifts are chosen at random with equal probabi liti es. Group V3 contains three units to represent the three possible shifts, so at any one + +time one of them is clamped on and the others are clamped off. + +The problem is to learn the structure that relates the states of the three groups. One facet of this problem is to "recognize" the shifti.e., to complete a partial input vector in which the states of VI and V2 are clamped but the units in V3 are left free. It is fairly easy to see why this problem cannot possibly be solved by just adding together a lot of pairwise interactions between units in Vb V2, and V3• If you know Copyrighted Material + +FIGURE 3. Theweights of the 24 hidden units in the shifter network . Each large region corresponds to a unit. Within this region the black rectangles represent negati ve weights and the white rectangles represent positive ones. The size of a rectangle represents t he magnitude of the weight. Thetwo rows of weights at the bottom of each uni t are its connections to the two groups of input units, VI and V2 . These weights the refore represent the"receptive field" of the hiddenunit. The three weights in the middle of the top row of each unit are its connections to the threeoutput units that represent shift - le ft , noshift, and shift-right. The solitary weight at the top left of each unit is its threshold . Each hidden unit is directly connected to all 16 input units and all 3 output units. In this example, the hidden units are not connected to each other. The top-left unit has weights that are easy to understand: Its optimal stimulusis act ivity in thefourth unit of VI and the fifth unit of V2 , and it votes for shift-right. It has negative wei ghts to make it less likely to come on when there is an alternati ve explanation for why its two favoriteinput + +units are act ive. + +different clamped vectors and the co-occurrence statistics were averaged over all 20 runs to yield an estimate, for each connection , of Pi) in Equation 7. In phase- , none of the units were clamped and the network was annealed in the same way. The network was then run for a further 10 iterations and the co-occurrence statistics were collected for all connected pairs of units. This was repeated 20 times and the co- + +The entire set of 40 annealings that were used to estimate Pit and Pi} was called a sweep. After each sweep, every weight was incremented by 5 (Pit - Pin . In addition, every weight had its absolute magnitude decreased by 0.0005 times its absolute magnitude. This weight decay prevented the weights from becoming too large and it also helped to resuscitate hidden units which had predominantly negative or predominantly positive weights. Such units spend all their time in the same state and therefore convey no information. The phase+ and phasestatistics are identical for these units, and so the weight decay gradually erodes their weights until they come back to life (units with all zero + +weights come on half the time) . + +The Annealing Schedule + +The annealing schedule spent the following number of iterations at the following temperatures : 2 at 40, 2 at 35, 2 at 30, 2 at 25, 2 at 20, 2 at 15, 2 at 1 2 , 2 at 10. One iteration is defined as the number of random probes required so that each unit is probed one time on average. When it is probed, a unit uses its energy gap to decide which of its two states to adopt using the stochastic decision rule in Equation 3. Since each unit gets to see the most recent states of all the other units, an iteration cannot be regarded as a single parallel step. An truly parallel asynchronous system must tolerate time delays. Units must decide on their new states without being aware of very recent changes in the states of other units. It can be shown (Sejnowski , Hinton , Kienker, & Schumacher, 1985) that first-order time delays act like added tempera- + +ture and can therefore be tolerated by networks of this kind. + +The Performance of the Shifter Network + +The shifter network is encouraging because it is a clear example of the kind of learning of higher order structure that was beyond the capability of perceptrons, but it also il lustrates several weaknesses in the + +current approach. + +• The learning was very slow. It required 9000 learning sweeps, each of which invol ved reaching equili brium 20 times in phase+ with vectors clamped on VI> V2, and V3, and 20 times in phase- with no units clamped. Even for low-level perceptual + +magnitude decreased by 1. For each weight, the probability of this hap- + +pening was 0.0005 times the absolute magnitude of the weight. + +We found that the network performed better if there was a preliminary learning stage which just involved the sememe units. In this stage, the intermediate units were not yet connected. During phase+ the required patterns were clamped on the sememe units andPit wasmeasured (annealing was not required because al l the units involved were clamped) . During phase- no units were clamped and the network was allowed to reach equi librium 20 times using the annealing schedule given above. After anneal ing , pi; was estimated from the cooccurrences as before, except that only 20 phase- anneal ings were used instead of 40. There were 300 sweeps of this learning stage and they resulted in weights between pairs of sememe units that were sufficient to give the sememe group an energy landscape with 20 strong minima corresponding to the 20 possible "word meanings." This hel ped subsequent learning considerably, because it reduced the tendency for the intermediate units to be recruited for the job of modeling the structure among the sememe units. They were therefore free to model the structure between the grapheme units and the sememe units.9 The results described here were obtained using the preliminary learning stage and so they correspond to learning to associate grapheme strings with + +"meanings" that are already fami liar. + +The Performance of the Network + +Using the same annealing schedule as was used during learning, the network can be tested by clamping a grapheme string and looking at the resulting activities of the sememe units. After 5000 learning sweeps, it gets the semantic features exactly correct 99.3% of the time. A performance level of 99.9% can be achieved by using a "careful" annealing schedule that spends twice as long at each temperature and + +goes down to half the final temperature. + +The Effect of Local Damage + +The learning procedure generates weights which cause each of the units in the intermediate layer to be used for many different words. + +9 There was no need to have a similar stage for learning the structure among the grapheme units because in the main stage of learning the grapheme units are always clamped and so there is no tendency fr(;ttp�StJtMlltf!HitIfOdel the structure among them. + +yv B + +V\J A B + +increase weights that help B ... + +FIGURE 5. One cross-section of a ravine in weight-space. Each point in weight space corresponds to a whole energy landscape. To indicate this, we show how a very simple landscape changes as the weights are changed. Movement to the right along the K-aKis corresponds to increasing the weights between pairs of units that are both on in state B and not both on in state A. This increases the depth of A. If the task requires that A and B have about the same depth, an imbalance between them will lower the + +performance and thus raise G. + +between the various minima without significantly affecting the gross topography of the energy landscape. Relearning can then restore most of the performance by restoring the balance between the existing + +minima. + +The simulation behaved as predicted. The mean absolute value of the weights connecting the intermediate units to the other two groups was 21. 5. These weights were first perturbed by adding uniform random noise in the range - 2to + 2. This had surprisingly little effect, reducing the performance using the normal annealing schedule from 99.3% to 98.0%. This shows that the network is robust against slight noise in the weights. To cause significant deterioration, uniform random noise between - 22and + 22was added. On average, this perturbs each weight by about half its magnitude which was enough to reduce normal performance to 64.3% correct. Figure 6 shows the course of the relearning and compares it with the speed of the original learning when performance was at this level. It also shows that other kinds of damage + +learning in which the network constructs efficient internal codes for communicating information across narrow bandwidth channels. At present, the learning algorithm is too slow to be tested properly on large networks and future progress hinges on being able to speed it up. + +ACKNOWLEDGMENTS + +This research was supported by grants from the System Development Foundation. We thank David Ackley, Peter Brown, Francis Crick, Mark Derthick, Scott Fahlman, Stuart Geman, John Hopfield, Paul Kienker , Jay McClelland, Barak Pearlmutter, David Rumelhart, Tim + +Shallice, and Paul Smolensky for helpful discussions. + +APPENDIX: + +DERIV ATION OF THE LEARNING ALGORITHM + +When a network is free-running at equilibrium the probability distrib- + +ution over the visible units is given by + +P-( Va) == LP-( VaA Hp) p + +(8) + +where Va is a vector of the states of the visible units, HI3 is a vector of states of the hidden units , and Eal3 is the energy of the system in state + +Va AHp + +Hence, + +Ea/3 - L wij sri3 st13 , i e\_ + +1 aQ al3 -EafJ + +l T + +- -so "'s · enUw-IJ . T I } + +Differentiating (8) then yields + +This derivative is used to compute the gradient of the G -measure + +where P + (Va) is the clamped probability distribution over the visible + +units and is independent of Wij ' So + +8G = \_ L P:(Va) ap -(va) aWl} aP ( Va) aWij + +Now, + +and + +P+(Va AHf,i ) =P+(Hf,i1 Va )P + ( Va), + +P-( Va AHp ) =P-(Hp IVa)P-( Va ) , + +(9) + +Equation 9 holds because the probability of a hidden state given some visible state must be the same in equilibrium whether the visible units were clamped in that state or arrived there by free-running. Hence, + +Also, + +where + +and + +\_ P+ (Va) + P ( Va AHp ) P- (Va ) = P ( VaA Hp ) . + +a + +Pij= !.P+ (VaA Hp )srP slP + +ap + +Pij=!.P - (V>, A HjJ)S/ILS/IL. + +>'IL + +The Boltzmann machine learning algorithm can also be formulated as an input-output model. The visible units are divided into an input set f and an output set 0, and an environment specifies a set of conditional probabi lities of the form P + (Op Ifa)' During phase+ the environment Copyrighted Material + +clamps both the input and output units, and the Pit sare estimated. During phase- the input units are clamped and the output units and hidden units free-run , and the PijS are estimated. The appropriate G + +measure in this case is + +G=l:P + ( + +Ja A O/3 ) lnP+ (O/3l /a ) + +. + +a/3 p- (O/3 l/a ) + +Similar mathematics apply in this formulation and aG/a wij is the same + +as before. + +CHAPTER S + +Learning Internal Representations + +by Error Propagation + +D. E. RUMELHART, G. E. HINTON, and R. 1. WILLIAMS + +THE PROBLEM + +We now have a rather good understanding of simple two-layer associative networks in which a set of input patterns arriving at an input layer are mapped directly to a set of output patterns at an output layer. Such networks have no hidden units. They involve only input and output units. In these cases there is no internal representation. The coding provided by the external world must suffice. These networks have proved useful in a wide variety of appl ications (cf. Chapters 2, 17, and 18). Perhaps the essential character of such networks is that they map similar input patterns to similar output patterns. This is what al lows these networks to make reasonable generalizations and perform reasonably on patterns that have never before been presented. The similarity of patterns in a PDP system is determi ned by their overlap. The overlap in such networks is determined outside the learning system itself-by + +whatever produces the patterns. + +The constraint that similar input patterns lead to similar outputs can lead to an inability of the system to learn certain mappings from input to output. Whenever the representation provided by the outside world is such that the similarity structure of the input and output patterns are very different, a net\\C),\*Jy�ijfltetttMatt8i8h1 representations (Le. , a + +network without hidden units) will be unable to perform the necessary mappings. A classic example of this case is the exclusive-or (XOR) problem illustrated in Table 1. Here we see that those patterns which overlap least are supposed to generate identical output values. This problem and many others like it cannot be performed by networks without hidden units with which to create their own internal representations of the input patterns. It is interesting to note that had the input patterns contained a third input taking the value 1 whenever the first two have value 1 as shown in Table 2 , a two-layer system would be able + +to solve the problem. + +Minsky and Papert (I969) have provided a very careful analysis of conditions under which such systems are capable of carrying out the required mappings . They show that in a large number of interesting cases , networks of this kind are incapable of solving the problems. On the other hand, as Minsky and Papert also pointed out, if there is a layer of simple perceptron-like hidden units, as shown in Figure 1, with which the original input pattern can be augmented, there is always a recoding (i.e., an internal representation) of the input patterns in the hidden units in which the similarity of the patterns among the hidden units can support any required mapping from the input to the output units. Thus, if we have the right connections from the input units to a large enough set of hidden units, we can always find a representation that wi ll perform any mapping from input to output through these hidden units. In the case of the XOR problem, the addition of a feature that detects the conjunction of the input units changes the similarity + +> Input Patterns + +TABLE 1 + +Output Patterns + +TABLE 2 + +o 1 I o + +Output Patterns + +000 0 0101 100 1 + +111 + +0 + +Output Patterns + +Input Patterns + +Internal + +Representation + +Units + +FIGURE I. A multilayer network. In this case the information coming to the input units is reroded into an internal representation and the outputs are generated by the inter· nal representation rather than by the original pattern. Input patterns can always be encoded, if there are enough hidden units, in a form so thatthe appropriate output pat· + +tern can be generated from any input pattern. + +structure of the patterns sufficiently to al low the solution to be learned. As illustrated in Figure 2, this can be done with a single hidden unit. The numbers on the arrows represent the strengths of the connections among the units. The numbers written in the circles represent the thresholds of the units. The value of + 1. 5 for the threshold of the hidden unit insures that it wi ll be turned on only when both input units are on. The value 0.5 for the output unit insures that it will tu rn on only when it receives a net positive input greater than 0.5. The weight of - 2 from the hidden unit to the output unit insures that the output unit wi ll not come on when both input units are on. Note that from the point of view of the output unit, the hidden unit is treated as simply another input unit. It is as jf the jOP'ut . p'atterns consi sted of three + +Copynghted Matenal + +& Anandan, 1985). In this chapter we present another alternative that works with deterministic units, that involves only local computations, and that is a clear generalization of the delta rule. We call this the generalized delta rule. From other considerations, Parker (1985) has independently derived a simi lar generalization, which he calls learninglogic. Le Cun (1985) has also studied a roughly similar learning scheme. In the remainder of this chapter we first derive the generalized delta rule, then we il lustrate its use by providing some results of our simulations , and finally we indicate some further generalizations of + +the basic idea. + +THE GENERALIZED DELTA RULE + +The learning procedure we propose involves the presentation of a set of pairs of input and output patterns. The system first uses the input vector to produce its own output vector and then compares this with the desired output, or target vector. If there is no difference, no learning takes place. Otherwise the weights are changed to reduce the difference. In this case, with no hidden units, this generates the standard delta rule as described in Chapters 2 and 11. The rule for changing + +weights following presentation of input/ output pair p is given by + +(1) + +where tpj is the target input for jth component of the output pattern for pattern p, Opj is the jth element of the actual output pattern produced by the presentation of input pattern p, ip; is the value of the ith element of the input pattern, 8pi = tpi - 0pi' and flp wi} is the change to be made to the weight from the ith to the jth unit following presentation + +of pattern p . + +The delta rule and gradient descent. There are many ways of deriving this rule. For present purposes, it is useful to see that for linear units it minimizes the squares of the differences between the actual and the desired output values summed over the output units and all pairs of input/ output vectors. One way to show this is to show that the derivative of the error measure with respect to each weight is proportional to the weight change dictated by the delta rule, with negative constant of proportionality. This corresponds to performing steepest descent on a surface in weight space whose height at any point in weight space is equal to the error measure. (Note that some of the following sections Copyrighted Material + +are written in italics. These sections constitute informal derivations of the claims made in the surrounding text and can be omitted by the + +reader who finds such derivations tedious') + +To be more specific, then, let + +1Ep =2'1;: «(pj - Opj)2 + +I + +be our measure of the error on input/output pattern p and let E = LEp be our overall measure of the error. We wish to show that the delta rule implements a gradient descent in E when the units are linear. We will proceed by simply showing + +that + +which is proportional to Lip Wj; as prescribed by the delta rule. When there are no hidden units it is straightforward to compute the relevant derivative. For this purpose we use the chain rule to write the derivative as the product of two parts: the derivative of the error with respect to the output of the unit times the derivative of the out- + +put with respect to the weight. + +aEp aEp aOpj aWj; = aOpj aWj; • (]) + +The first part tells how the error changes with the output of the j th unit and the second part tells how much changing Wj; changes that output. Now, the derivatives + +are easy to compute. First, from Equation 2 + +aEp !l + += - (tpj - op) = - apj' + +uOpj + +(4) + +Not surprisingly, the contribution of unit Uj to the error is simply proportional to a pj . + +Moreover, since we have linear units, + +Opj = LWjlip;. i + +from which we conclude that aOpj . !l = ' + +p i' u Wj; + +Thus, substituting back into Equation 3, we see that + +aEp . - -!l- =apj/PI UWji + +as desired. Now, combining this with the observation that + +aE = 1: aEp aWj; p aWj; + +should lead us to conclude that the net change in Wj; after one complete cycle of pattern presentations is proportional to this derivative and hence that the delta rule implements a gradient descent in E. In fact, this is strictly true only if the values of the weights are not changed during this cycle. By changing the weights after each pattern is presented we depart to some extent from a true gradient descent in E. Nevertheless, provided the learning rate (i.e., the constant of proportionality) is sufficiently small, this departure will be negligible and the delta rule will implement a very close approximation to gradient descent in sum-squared error. In particular, with small enough learning rate, the delta rule will find a set of weights minimizing this + +error function. + +The delta rule for semilinear activation functions in feedforward networks. We have shown how the standard delta rule essentially implements gradient descent in sum-squared error for linear activation functions. In this case, without hidden units, the error surface is shaped like a bowl with only one minimum, so gradient descent is guaranteed to find the best set of weights . With hidden units, however, it is not so obvious how to compute the derivatives , and the error surface is not concave upwards , so there is the danger of getting stuck in local minima. The main theoretical contribution of this chapter is to show that there is an efficient way of computing the deri vatives. The main empirical contribution is to show that the apparently fatal problem of + +local minima is irrelevant in a wide variety of learning tasks. + +At the end of the chapter we show how the general ized delta rule can be appl ied to arbitrary networks , but, to begin With , we confine ourselves to layered feedforward networks . In these networks , the input units are the bottom layer and the output units are the top layer. There can be many layers of hidden units in between , but every unit must send its output to higher layers than its own and must receive its input from lower layers than its own. Given an input vector, the output vector is computed by a forward pass which computes the activity levels of each layer in turn using the already computed activity levels in the ear- + +lier layers. + +Since we are primari ly interested in extending this result to the case with hidden units and since, for reasons outlined in Chapter 2, hidden units with linear activation functions provide no advantage, we begin by general izing our analysis to the set of nonlinear activation functions which we cal lsemilinear (see Chapter 2). A semilinear activation function is one in which the output of a unit is a nondecreasi ng and dif- + +ferentiable function of t�d>MfJl8tjal + +where 0; = i; if unit i is an input unit. Thus, a semilinear acti vation + +function is one in which + +(8) + +and f is differentiable and nondecreasi ng. The gene ral i zed delta rule works if the network consists of units having semilinear activation functions. Notice that li near threshold units do not sati sfy the requirement because their derivative is infinite at the threshold and zero elsewhere. + +To get the correct generalization of the delta rule. we must set + +aEp + +ap wji ex: - -!\-, + +V wji + +where E is the same sum-squared error function defined earlier. As in the standard delta rule it is again useful to see thiS derivative as resulting from the product of two parts: one part reflecting the change in error as a function of the change in the net input to the unit and one part representing the effect of changing a particular weight + +on the net input. Thus we can write + +aEp aEp anetpj aWji = ane/pj aWji . + +By Equation 7 we see that the second factor is + +Now let us define + +aEp + +0· + +PJ = ---anel .. PJ + +(9) + +(JO) + +(By comparing this to Equation 4. note that this is consistent with the definition of o pj used in the original delta rule jor linear units since Opj = netpj when unit Uj is + +linear. ) Equation 9 thus has the equi valent form + +aEp --!\- =OpjOp;. VWji + +This says that to implement gradient descent in E we should make our weight + +changes according to + +just as in the standard delta rule. The trick is to figure out what 8p + +j should be for + +each unit U) in the network. The interesting result, which we now derive, is that there is a simple recursive computation 0/ these 8 's which can be implemented by + +propagating error signals backward through the network. aE + +To compute 8 p) = - �, we apply the chain rule to write this partial deriva- + +onetp) + +tive as the product 0/ two factors, one factor reflecting the change in error as a /unction 0/ the output 0/ the unit and one reflecting the change in the output as a /unc- + +tion 0/ changes in the input. Thus, we have + +aEp aEp aop) 8p) = --- = ------, anetpj aOpj anetpj + +Let us compute the second factor. By Equation 8 we see that + +aOpj \_ I �-- - I ; (netpj), + +onetpj + +(1) + +which is simply the derivative 0/ the squashing /unction Ij for the j th unit, evaluated at the net input netp) to that unit. To compute the first factor, we consider two cases. First, assume that unit Uj is an output unit 0/ the network. In this + +case, it /ollows /rom the definition 0/ Ep that + +aEp + +� = - (tpj - Opj), + +Op) + +which is the same result as we obtained with the standard delta rule. Substituting + +for the two factors in Equation 11, we get + +(J3) + +for any output unit U). /fUj is not an output unit we use the chain rule to write + +12 flEp anetplc = 12 aEp a-Lwk;op + +;= 12 aE + +p Wkj=-L8p1cWkj' + +k anetpk aOpj k anetpk aOpj ; k anetpk k + +In this case, substituting /or the two factors in Equation 12 yields + +8 pj = I 'j (netpj ) 128 pic Wkj + +(J4) + +k + +whenever u) is not an output unit. Equations J3 and 14 give a recursive procedure for computing the 8 's for all units in the network, which are then used to compute the weight changes in the network according to Equation 11. This procedure constitutes the generalized delta rule for a /eed/orward network 0/ semilinear units. + +These results can be summarized in three equations. First, the generalized delta rule has exactly the same form as the standard delta rule of Equation 1. The weight on each line should be changed by an amount proportional to ctbp� MfJitftialrror signal, 8, available to + +the unit receiving input along that line and the output of the unit send- + +ing activation along that line. In symbols, + +The other two equations specify the error signal. Essentially, the determination of the error signal is a recursive process which starts with the output units. If a unit is an output unit, its error signal is very simi lar + +to the standard delta rule. It is given by + +S pj = (tp + +j - Opj)/ j (netp + +j) + +where / j (netpj) is the derivative of the semi linear activation function which maps the total input to the unit to an output value. Finally, the error signal for hidden units for which there is no specified target is determined recursively in terms of the error signals of the units to which it directly connects and the weights of those connections. That is, + +S pj = / j (netp + +j ) I,s pk Wkj k + +whenever the unit is not an output unit. + +The application of the general ized delta rule, thus, involves two phases: During the first phase the input is presented and propagated forward through the network to compute the output value Opj for each unit. This output is then compared with the targets, resulting in an + +error signal Sp + +j for each output unit. The second phase involves a + +backward pass through the network (analogous to the initial forward pass) during which the error signal is passed to each unit in the network and the appropriate weight changes are made. This second, backward pass allows the recursive computation of 8 as indicated above. The first step is to compute S for each of the output units. This is simply the difference between the actual and desired output values times the derivative of the squashing function. We can then compute weight changes for all connections that feed into the final layer. After this is done, then compute 8 's for all units in the penultimate layer. This propagates the errors back one layer, and the same process can be repeated for every layer. The backward pass has the same computational complexity as the forward pass , and so it is not unduly expensive. We have now generated a gradient descent method for finding weights in any feedforward network with semi linear units. Before reporting our results with these networks , it is useful to note some further observations. It is interesting that not all weights need be variable. Any number of weights in the network can be fixed. In this case, error is still propag��.YIfghrJW'M�"GOxed weights are simply not + +modified. It should also be noted that there is no reason why some output units might not recei ve inputs from other output units in earl ier layers. In this case, those units receive two di fferent ki nds of error: that from the direct comparison with the target and that passed through the other output units whose acti vation it affects. In this case , the correct procedure is to simply add the weight changes dictated by the direct comparison to that propagated back from the other output units. + +SIMULATION RESULTS + +We now have a learning procedure which could, in principle, evolve a set of weights to produce an arbitrary mapping from input to output. However, the procedure we have produced is a gradient descent procedure and, as such, is bound by all of the problems of any hill climbing procedure-namely, the problem of local maxima or (in our case) minima. Moreover, there is a question of how long it might take a system to learn. Even if we could guarantee that it would eventually find a solution , there is the question of whether our procedure could learn in a reasonable period of time. It is interesting to ask what hidden units the system actually develops in the solution of particular problems. This is the question of what kinds of internal representations the system actually creates. We do not yet have definitive answers to these questions. However, we have carried out many simulations which lead us to be optimistic about the local minima and time questions and to be surprised by the kinds of representations our learning mechanism discovers. Before proceeding with our results, we must describe our simulation system in more detail. In particular, we must specify an activation function and show how the system can compute the derivative of + +this function. + +A useful activation function. In our above deri vations the derivative of the acti vation function of unit u), r j (net), always played a role. This implies that we need an acti vation function for which a deri vative exists. It is in teresting to note that the linear threshold function, on which the percept ron is based, is discontinuous and hence will not suffice for the generalized delta rule. Simi larly, since a linear system achieves no advantage from hidden uni ts, a linear activation function will not suffice either. Thus, we need a contin uous, nonlinear activation function. In most of our experi ments we have used the logistic + +acti vation function in w��Jyrighted Material + +(15) + +where () j is a bias similar in function to a threshold. 1 In order to apply our learning rule, we need to know the derivative of this function with + +respect to its total input, netpj, where netpj =L, wJ + +; op; + () J + +. It is easy to + +show that this derivative is given by + +aOpj + +-!l-- = Opj 0- op). + +unetpj + +Thus, for the logistic acti vation function, the error signal, Bpj, for an + +output unit is given by + +Bpj = (tP) - Opj )op} (1 - op}), + +and the error for an arbitrary hidden Uj is given by + +Spj = op}O - op})L,SpkWk}' + +k + +It should be noted that the derivative, Opj (1 - op), reaches its maximum for Opj = 0.5 and, since 0::::; Opj::::; 1, approaches its minimum as Opj approaches zero or one. Since the amount of change in a given weight is proportional to this deri vati ve, weights will be changed most for those units that are near their midrange and, in some sense, not yel committed to being either on or off. This feature, we believe, contri- + +butes to the stability of the learning of the system. + +One other feature of this activation function should be noted. The system can not actual ly reach its extreme values of 1 or 0 without infinitely large weights. Therefore, in a practical learni ng situation in which the desired outputs are binary (O, 1), the system can never actually achieve these values. Therefore, we typical ly use the val ues of 0.1 and 0.9 as the targets, even though we wi ll talk as if values of (0, I} are + +sought. + +The learning rate. Our learning procedure requires only that the change in weight be proportional to aEp/aw. True gradient descent requires that infinitesimal steps be taken. The constant of proportionality is the learning rate in our procedure . The larger this constant, the larger the changes in the weights. For practical purposes we choose a + +learning rate that is as large as possi ble without leading to osci llation. This offers the most rapid learning. One way to increase the learning rate without leading to oscillation is to modify the generalized delta rule to include a momentum term. This can be accomplished by the follow- + +ing rule: + +(16) + +where the subscript n indexes the presentation number, 'T/ is the learning rate, and a is a constant which determines the effect of past weight changes on the current direction of movement in weight space. This provides a kind of momentum in weight space that effectively filters out high-frequency variations of the error-surface in the weight space. This is useful in spaces containing long ravines that are characterized by sharp curvature across the ravine and a gently sloping floor. The sharp curvature tends to cause divergent osci llations across the ravine. To prevent these it is necessary to take very small steps, but this causes very slow progress along the ravine. The momentum fi lters out the high curvature and thus allows the effective weight steps to be bigger. In most of our simulations a was about 0.9. Our experience has been that we get the same solutions by setting a = 0 and reducing the size of 'T/, but the system learns much faster overall with larger values of a + +and TJ. + +Symmetry breaking. Our learning procedure has one more problem that can be readily overcome and this is the problem of symmetry breaking. If all weights start out with equal values and if the solution requires that unequal weights be developed, the system can never learn. This is because error is propagated back through the weights in proportion to the values of the weights. This means that all hidden units connected directly to the output inputs will get identical error signals, and, since the weight changes depend on the error signals , the weights from those units to the output units must always be the same. The system is starting out at a kind of local maximum. which keeps the weights equal , but it is a maximum of the error function, so once it escapes it will never return. We counteract this problem by starting the system with small random weights. Under these conditions symmetry problems of + +this kind do not arise. + +The XOR Problem + +It is useful to begin with the exclusive-or problem since it is the classic problem requiring hidden units and since many other difficult Copyrighted Material + +problems involve an XOR as a subproblem. We have run the XOR problem many times and with a couple of exceptions discussed below, the system has always solved the problem. Figure 3 shows one of the solutions to the problem. This solution was reached after 558 sweeps through the four stimulus patterns with a learning rate of." = 0.5. In this case, both the hidden unit and the output unit have positive biases so they are on unless turned off. The hidden unit turns on if neither input unit is on. When it is on, it turns off the output unit. The connections from input to output units arranged themselves so that they turn off the output unit whenever both inputs are on. In this case, the network has settled to a solution which is a sort of mirror image of the + +one illustrated in Figure 2. + +We have taught the system to solve the XOR problem hundreds of times. Sometimes we have used a single hidden unit and direct connections to the output unit as il lustrated here, and other times we have allowed two hidden units and set the connections from the input units to the outputs to be zero, as shown in Figure 4. In only two cases has the system encountered a local minimum and thus been unable to solve the problem. Both cases involved the two hidden units version of the + +Output Unit + +-4.2 I 1 I + +\-42 \ + +I \ -9. 41 + +I + +I � I\_\_ X \ Hidden Unit + +\ \ + +---6.4 + +Input Units + +FIGURE 4. A simple architecture for solving XOR with two hidden units and no direct + +connections from input to output. + +problem and both ended up in the same local mInimum. Figure 5 shows the weights for the local minimum. In this case, the system correctly responds to two of the patterns-namely, the patterns 00 and 10. In the cases of the other two patterns 11 and 01, the output unit gets a net input of zero. This leads to an output value of 0.5 for both of these patterns. This state was reached after 6,587 presentations of each pattern with 'T/=O.25. 2 Although many problems require more presentations for learning to occur, further trials on this problem merely increase the magnitude of the weights but do not lead to any improvement in performance. We do not know the frequency of such local minima, but our experience with this and other problems is that they are quite rare. We have found only one other situation in which a local minimum has occurred in many hundreds of problems of various + +sorts. We wi ll discuss this case below. + +The XOR problem has proved a useful test case for a number of other studies. Using the architecture illustrated in Figure 4, a student in our laboratory, Yves Chauvin, has studied the effect of varying the + +FIGURE 5. A network at a local minimum for the exclusive-or problem. The dotted lines indicate negative weights. Note that whenever the right most input unit is on it turns on both hidden units. The weights connecting the hidden units to the output are arranged so that when both hidden units are on, the output unit gets a net input of zero. This leads to an output value of 0.5. In the other cases the network provides the correct + +answer. + +number of hidden units and varying the learning rate on time to solve the problem. Using as a learning criterion an error of 0.01 per pattern, Yves found that the average number of presentations to solve the problem with '1/ = 0.25 varied from about 245 for the case with two hidden units to about 120 presentations for 32 hidden units. The results can be summarized by P = 280 - 3310g2H, where P is the required number of presentations and H is the number of hidden units employed. Thus, the time to solve XOR is reduced linearly with the logarithm of the number of hidden units. This result holds for values of H up to about 40 in the case of XOR. The general result that the time to solution is reduced by increasing the number of hidden units has been observed in virtually all of our simulations. Yves also studied the time to solution as a function of learning rate for the case of eight hid· den units. He found an average of about 450 presentations with '1/ = 0.1 to about 68 presentations with '1/ = 0.75. He also found that Copyrighted Material + +themselves so that they count the number of inputs. In the diagram, the one at the far left comes on if one or more input units are on , the next comes on if two or more are on, etc. All of the hidden units come on if all of the input lines are on. The first m hidden units come on whenever m bits are on in the input pattern. The hidden units then connect with alternately positive and negative weights . In this way the net input from the hidden units is zero for even numbers and + 1 for odd numbers. Table 3 shows the actual �ol ution attained for one of our simulations with four input lines and four hidden units. This solution was reached after 2,825 presentations of each of the si xteen patterns with "fI = 0.5. Note that the solution is roughly a mirror image of that shown in Figure 6 in that the number of hidden units turned on is equal to the number of zero input values rather than the number of ones. Beyond that the princi ple is that shown above. It should be noted that the internal representation created by the learning rule is to arrange that the number of hidden units that come on is equal to the number of zeros in the input and that the particular hidden units that come on depend only on the number, not on which input units are on. This is exactly the sort of recoding required by parity. It is not the kind of representation readily discovered by unsupervi sed learning schemes + +such as competitive learning. + +The Encoding Problem + +Ackley, Hinton, and Sejnowski (1 985) have posed a problem in which a set of orthogonal input patterns are mapped to a set of orthogonal output patterns through a small set of hidden units. In such cases the internal representations of the patterns on the hidden units must be rather efficient. Suppose that we attempt to map N input patterns onto N output patterns. Suppose further that log2N hidden units are provided. In this case, we expect that the system will learn to use the + +> Number of On Input Units + +TABLE 3 + +Hidden Unit Patterns + +o 1111 1 1011 2 1010 3 0010 4 Copynghted lIfINerial Output Value o 1 o 1 o + +output as in the input. Table 5 shows the mapping generated by our learning system on this example. It is of some interest that the system employed its ability to use intermediate values in solving this problem. It could, of course, have found a solution in which the hidden units took on only the values of zero and one. Often it does just that, but in this instance, and many others, there are solutions that use the intermediate values, and the learning system finds them even though it has a bias toward extreme values . It is possible to set up problems that require the system to make use of intermediate values in order to solve + +a problem. We now turn to such a case. + +Table 6 shows a very simple problem in which we have to convert from a distributed representation over two units into a local representation over four units. The similarity structure of the distributed input pat- + +terns is simply not preserved in the local output representation. + +We presented this problem to our learning system with a number of constraints which made it especially difficult. The two input units were only allowed to connect to a single hidden unit which, in turn, was allowed to connect to four more hidden units. Only these four hidden units were allowed to connect to the four output units. To solve this problem, then, the system must first convert the distributed + +TABLE 5 + +Input Hidden Unit Output Patterns Patterns Patterns 10000000.5 0 0 10000000 01000000 0 1 0 01000000 00100000 1 1 0 00100000 000100001 1 1 00010000 00001 000 0 1 1 00001000 00000100.5 0 1 00000100 000000101 0 .5 00000010 00000001 0 0 .5 00000001 + +TABLE 6 + +Input Patterns Output Patterns + +representation of the input patterns into various intermediate values of the singleton hidden unit in which different activation values correspond to the different input patterns. These continuous values must then be converted back through the next layer of hidden unitsfirst to another distributed representation and then, finally, to a local representation. This problem was presented to the system and it reached a solution after 5,226 presentations with", = 0.05.3 Table 7 shows the sequence of representations the system actually developed in order to transform the patterns and solve the problem. Note each of the four input patterns was mapped onto a particular activation value of the singleton hidden unit. These values were then mapped onto distributed patterns at the next layer of hidden units which were finally mapped into the required local representation at the output level . In princi ple, this trick of mapping patterns into activation values and then converting those activation values back into patterns could be done for any number of patterns, but it becomes increasingly difficult for the system to make the necessary distinctions as ever smal ler differences among activation values must be distingui shed. Figure 8 shows the network the system developed to do this job. The connection weights from the hidden units to the output units have been suppressed for clarity. (The sign of the connection, however, is indicated by the form of the connection -e.g., dashed lines mean inhibitory connections) . The four different activation values were generated by having relatively large weights of opposite sign . One input line turns the hidden unit full on, one turns it full off. The two differ by a relatively small amount so that when both turn on, the unit attains a value intermediate between 0 and 0.5. When neither turns on, the near zero bias causes the unit to attain a value slightly over 0.5. The connections to the second layer of hidden units is likewise interesting. When the hidden unit is full on, + +TABLE 7 + +Input Singleton Remaining Output Patterns Hidden Unit Hidden Units Patterns + +10 0 1 1 1 0 0010 11 .2 1 1 0 0 0001 00.6 .5 0 0 .3 1000 01 1 0 0 0 1 0100 + +Output Un its + +Hidden Units + +Input Un its + +FIGURE 8. The network illustrating the use of intermediate values in sol ving a problem. + +See text for explanation. + +the right-most of these hidden units is turned on and all others turned off. When the hidden unit is turned off, the other three of these hidden units are on and the left-most unit off. The other connections from the singleton hidden unit to the other hidden units are graded so that a distinct pattern is turned on for its other two values. Here we + +have an example of the flexibility of the learning system. + +Our experience is that there is a propensity for the hidden units to take on extreme values, but, whenever the learning problem calls for it, they can learn to take on graded values. It is likely that the propensity to take on extreme values follows from the fact that the logistic is a sigmoid so that increasing magnitudes of its inputs push it toward zero or one. This means that in a problem in which intermediate values are required, the incoming weights must remain of moderate size. It is interesting that the derivation of the generalized delta rule does not depend on all of the units having identical activation functions. Thus, it would be possible for some units, those required to encode information in a graded fashion, to be linear while others might be logistic. The linear unit would have a much wider dynamic range and could encode more different values. This would be a useful role for a linear + +unit in a network with h�8p9r\_dMaterial + +Symmetry + +Another interesting problem we studied is that of classifying input strings as to whether or not they are symmetric about their center. We used patterns of various lengths with various numbers of hidden units. To our surprise, we discovered that the problem can always be solved with only two hidden units. To understand the derived representation, consider one of the solutions generated by our system for strings of length six. This solution was arrived at after 1,208 presentations of each six-bit pattern with 'T1 = 0. 1. The final network is shown in Figure 9. For simplicity we have shown the six input units in the center of the diagram with one hidden unit above and one below. The output unit, which signals whether or not the string is symmetric about its center, is shown at the far right. The key point to see about this solution is that for a given hidden unit, weights that are symmetric about the middle are equal in magnitude and opposite in sign. That means that if a symmetric pattern is on, both hidden units will receive a net input of zero from the input units, and, since the hidden units have a negative bias, both will be off. In this case, the output unit, having a positive bias, + +." + +./ + +..... ..... + +..... ........ 9. 44 ..... + +> ./ ./ + +..... + ++ 8.3t /.3.1 7 ./ ./ ./ ./ .,. .,. .,. + +.,.. .,. .,.. ·9A4 + +.,. .,; + +..... ..... ..... + +.,. .,.. .,. + +..... ..... + +'Qoutput Y Unit .,; + +.,; .,; + +FIGURE 9. Network for solving the symmetry problem. The six open ci rcles represent the input units. There are two hidden units, one shown above and one below the input + +will be on. The next most important thing to note about the solution is that the weights on each side of the midpoint of the string are in the ratio of 1: 2:4. This insures that each of the eight patterns that can occur on each side of the midpoint sends a unique activation sum to the hidden unit. This assures that there is no pattern on the left that wi ll exactly balance a non-mirror-image pattern on the right. Finally, the two hidden units have identical patterns of weights from the input units except for sign. This insures that for every nonsymmetric pattern , at least one of the two hidden units wi ll come on and turn on the output unit. To summarize, the network is arranged so that both hidden units wi ll receive exactly zero activation from the input units when the pattern is symmetric, and at least one of them wi ll receive positive + +input for every nonsymmetric pattern. + +This problem was interesting to us because the learning system developed a much more elegant solution to the problem than we had previously considered. This problem was not the only one in which this happened. The parity solution di scovered by the learning procedure was also one that we had not discovered prior to testing the problem with our learning procedure. Indeed, we frequently discover these more elegant solutions by giving the system more hidden units than it needs and observing that it does not make use of some of those provided. Some analysis of the actual solutions discovered often leads us to the discovery of a better solution involving fewer hidden units. + +Addition + +Another interesting problem on which we have tested our learning algorithm is the simple binary addition problem. This problem is interesting because there is a very elegant sol ution to it, because it is the one problem we have found where we can rel iably find local minima and because the way of avoiding these local minima gi ves us some insight into the conditions under which local minima may be found and avoided. Figure 10 illustrates the basic problem and a minimal solution to it. There are four input units, three output units, and two hidden units. The output patterns can be viewed as the binary representation of the sum of two two-bit binary numbers represented by the input patterns. The second and fourth input units in the diagram correspond to the low-order bits of the two binary numbers and the first and third units correspond to the two higher order bits. The hidden units correspond to the carry bits in the summation. Thus the hidden unit on the far right comes on when both of the lower order bits in the input patter�yrig/Dtedf �t8li8J the one on the left comes + +difficult. Note that the middle bit should come on whenever an odd number of the set containing the two higher order input bits and the lower order carry bit is turned on . Observation wil l confirm that the network shown performs that task. The left-most hidden unit receives inputs from the two higher order bits and from the carry bit. Its bias is such that it will come on whenever two or more of its in puts are turned on . The middle output unit receives positive inputs from the same three units and a negative input of - 2 from the second hidden unit. This insures that whenever just one of the three are turned on, the second hidden unit wi ll remain off and the output bit wil l come on. Whenever exactly two of the three are on, the hidden unit wi ll turn on and counteract the two units exciting the output bit, so it wil l stay off. Final ly, when all three are turned on, the output bit will receive - 2 from its carry bit and + 3 from its other three inputs. The net is positive, so the middle unit wil l be on. Finally, the third output bit should turn on whenever the second hidden unit is on - that is, whenever there is a carry from the second bit. Here then we have a minimal network to carry out the job at hand. Moreover, it should be noted that the concept behind this network is general izable to an arbitrary number of input and output bits. In general , for adding two m bit binary numbers we wil l require 2m input units, m hidden units, and m+ I out- + +put units. + +Unfortunately, this is the one problem we have found that reliably leads the system into local minima. At the start in our learn ing trials on this problem we al low any input unit to connect to any output unit and to any hidden unit . We allow any hidden unit to connect to any output unit, and we allow one of the hidden units to connect to the other hidden unit, but, since we can have no loops, the connection in the opposite direction is disallowed. Sometimes the system wil l discover essentially the same network shown in the figure. 4 Often , however, the system ends up in a local minimum. The problem arises when the XOR problem on the low-order bits is not sol ved in the way shown in the diagram. One way it can fail is when the "higher" of the two hidden units is "selected " to sol ve the XOR problem. This is a problem because then the other hidden unit cannot "see " the carry bit and therefore cannot finally sol ve the problem. This problem seems to stem from the fact that the learning of the second output bit is always dependent on learning the first (because information about the carry is necessary to learn the second bit) and therefore lags behind the learn ing of the first bit and has no influence on the selection of a hidden unit to + +4The network is the same except for the highest order bit. The highest order bit is always on whenever three or more o f t h e input units are on. This is always learned first + +solve the first XOR problem. Thus, about half of the time (in this problem) the wrong unit is chosen and the problem cannot be solved. In this case , the system finds a solution for all of the sums except the 11 + 11 - 11 0 (3+3 = 6) case in which it misses the carry into the middle bit and gets 11 + 11 - 100 instead. This problem di ffers from others we have sol ved in as much as the hidden units are not "equipotential " here. In most of our other problems the hidden units have + +been equipotential, and this problem has not arisen. + +It should be noted, however, that there is a relati vely simple way out of the problem -namely, add some extra hidden units. In this case we can afford to make a mistake on one or more selections and the system can still solve the problems. For the problem of adding two-bit numbers we have found that the system always solves the problem with one extra hidden uni t. With larger numbers it may require two or three more. For purposes of illustration , we show the results of one of our runs with three rather than the minimum two hidden units. Figure 11 shows the state reached by the network after 3,020 presentations of each input pattern and with a learning rate of "Y/ = 0.5. For convenience, we show the network in four parts. In Figure 11 A we show the connections to and among the hidden units. This figure shows the internal representation generated for this problem. The "lowest" hidden unit turns off whenever either of the low-order bits are on. In other words it detects the case in which no low-order bit is turn on. The "highest" hidden unit is arranged so that it comes on whenever the sum is less than two. The conditions under which the middle hidden unit comes on are more complex. Table 8 shows the patterns of hidden units which occur to each of the si xteen input patterns. Figure lI B shows the connections to the lowest order output unit. Noting that the relevant hidden unit comes on when neither low-order input unit is on, it is clear how the system computes XOR. When both low-order inputs are off, the output unit is turned off by the hidden unit. When both low-order input units are on , the output is turned off directly by the two input units. If just one is on, the positive bias on the output unit keeps it on . Figure ll C gives the connections to the middle output unit, and in Figure 11 D we show those connections to the left-most, highest order output unit. It is somewhat difficult to see how these connections always lead to the correct output answer, but, as can be verified from the figures, the network is balanced so that this works . It should be pointed out that most of the problems described thus far have invol ved hidden units with quite simple interpretations. It is much more often the case, especially when the number of hidden units exceeds the mini mum number required for the task, that the hidden units are not readily interpreted. This fol lows from the fact that there is very little tendency for loealist representations to develop. Typically Copyrighted Material + +Output Un its 000 + +Input Units + +A + +Output Units + +Hidden Units + +Hidden Units + +o + +Output Un its + +OO� / , I\ '· '0 + +I\ \ Hidden + +·5 + +/ \ .• \ + +/ ' , Units + +0 + +/ \ \ I\ \ / \ 0 I \ '-J + +I \ I\ / \ + +0 + +6 0 6 + +o + +Input Units + +8 + +Output Units + +·· + +00 + +/1\\, 111\\ "1\ \ I I \ \ \ I1.,1\ \ + +., Hidden + +Units + +-- + + .:..' £":\ 0 II� \ I + 11 \_� -2 + +I \ ,-- \_\_ I I \ \ - - '3 + +Input Units + +c + +I, \' I I \' +2/ "2 '2\ \+2 + +66 66 + +Input Units + +D + +FIGURE 11 . Network found for Ihe summation problem. A: The conneclions from the input units to the three hidden units and the connections among the hidden units. B: The connections from the input and hidden units to the lowest order output unit. C: The connections from the input and hidden units to the middle output unit. D: The connec- + +TABLE 8 + +Input Hidden Unit Output Patterns Patterns Patterns + +00+ 00III 000 00+ 01 11 0 001 00+ 10 01 1 010 00+ 11 010 011 01+ 00 110 001 01+ 01 010 010 01 + 10 010 011 01 + 11 000 100 10 + 00 01 1 010 10 + 01 010 01 1 10 + 10 001 100 10 + II 000 101 11+ 00 010 01 1 11+ 01 000 100 11 + 10 000 101 11 + II 000 11 0 + +the internal representations are distributed and it is the pattern of activity over the hidden units, not the meaning of any particular hidden + +unit that is important. + +The Negation Problem + +Consider a situation in which the input to a system consi sts of patterns of n+ 1 binary values and an output of n values. Suppose further that the general rule is that n of the input units should be mapped directly to the output patterns. One of the input bits, however, is special . It is a negation bit. When that bit is off, the rest of the pattern is supposed to map straight through , but when it is on , the complement of the pattern is to be mapped to the output. Table 9 shows the appropriate mapping. In this case the left element of the input pattern is the negation bit, but the system has no way of knowing this and must learn which bit is the negation bit. In this case, weights were allowed from any input unit to any hidden or output unit and from any hidden unit to any output unit. The system learned to set all of the weights to zero except those shown in Figure 12 . The basic structure of the problem and of the solution is evident in the figure. Clearly the problem was reduced to a set of three XORs between the negation bit Copyrighted Material + +The T -C Problem + +Most of the problems discussed so far (except the symmetry problem) are rather abstract mathematical problems . We now turn to a more geometric problem-that of discriminating between a T and a C- independent of translation and rotation. Figure 13 shows the stimulus patterns used in these experiments . Note, these patterns are each made of five squares and differ from one another by a single square. Moreover, as Minsky and Papert (969) point out, when considering the set of patterns over all possible translations and rotations (of 90°, 180°, and 270°) , the patterns do not differ in the set of distances among their pairs of squares. To see a difference between the sets of patterns one must look, at least, at configurations of triplets of squares. Thus Minsky and Papert call this a problem of order three. 5 In order to facilitate the learning, a rather different architecture was employed for this problem. Figure 14 shows the basic structure of the network we employed. Input patterns were now conceptualized as twodimensional patterns superimposed on a rectangular grid. Rather than al lowing each input unit to connect to each hidden unit, the hidden units themselves were organized into a two-dimensional grid with each unit receiving input from a square 3 x 3 region of the input space. In this sense, the overlapping square regions constitute the predefined receptive field of the hidden units. Each of the hidden units, over the entire field, feeds into a single output unit which is to take on the value + +FIGURE 13. The stimulus set for the T-C problem. The set consists of a block T and a block C in each of four orientations. One of the eight patterns is presented on each trial. + +o o o + +o o Output Unit + +Hidden Un its + +Input Units + +FIGURE 14. The network for solving the T-C problem. See text for explanation. + +1 if the input is a T (at any location or orientation) and 0 if the input is a C. Further, in order that the learning that occurred be independent of where on the field the pattern appeared, we constrained all of the units to learn exactly the same pattern of weights. [n this way each unit was constrained to compute exactly the same function over its receptive field-the receptive fields were constrained to all have the same shape. This guarantees translation independence and avoids any possible "edge effects " in the learning. The learning can readily be extended to arbitrarily large fields of input units. This constraint was accompl ished by simply adding together the weight changes dictated by the delta rule for + +each unit and then chamzing all weil!hts + +e�actly the same amount. In + +this way, the whole field of hidden units consists simply of replications of a single feature detector centered on different regions of the input space, and the learning that occurs in one part of the field is automati- + +cally generalized to the rest of the field. 6 + +We have run this problem in this way a number of times. As a result, we have found a number of sol utions. Perhaps the simplest way to understand the system is by looking at the form of the receptive field for the hidden units. Figure 15 shows several of the receptive fields we have seen. 7 Figure 15A shows the most local representation developed. This on-center-off-surround detector turns out to be an excellent T detector. Since, as illustrated, a T can extend into the oncenter and achieve a net input of + 1, this detector wi ll be turned on for aT at any orientation. On the other hand, any C extending into the center must cover at least two inhi bitory cells. With this detector the bias can be set so that only one of the whole field of inhibitory units wi ll come on whenever a T is presented and none of the hidden units wi ll be turned on by any C. This is a kind of protrusion detector which differentiates between a T and C by detecting the protrusion of the T. The receptive field shown in Figure 15B is again a kind of T detector. Every T activates one of the hidden units by an amount + 2 and none of the hidden units receives more than + 1 from any of the C's. As shown in the figure, T's at 90° and 270° send a total of + 2 to the hidden units on which the crossbar lines up. The T's at the other two orientations receive +2 from the way it detects the vertical protrusions of those two characters. Figure 15C shows a more distributed representation. As illustrated in the figure, each T activates five different hidden units whereas each C excites only three hidden units. In this case the system again is differentiating between the characters on the basis + +of the protruding end of the T which is not shared by the C. + +Finally, the receptive field shown in Figure 150 is even more interesting. In this case every hidden unit has a positive bias so that it is on unless turned off. The strength of the inhibitory weights are such that if a character overlaps the receptive field of a hidden unit, that unit turns off. The system works because a C is more compact than a T and therefore the T turns off more units that the C. The T turns off 21 hidden units, and the C turns off only 20. This is a truly distributed + +6 A similar procedure has been employed by Fukushima (980) in his neocognitron and + +by Kienker, Sejnowski , Hinton , and Schumacher (985) . + +A + +c + +8. LEARNING INTERNAL REPRESENTATIONS 351 + +m[ + +:: ��r: + +i-1 -1 -1 + +-1 + +�1+ 2:- 1 + +0 -2 -2 -2 -2 -2 -2 + +B + +I::pf -1 1- 1 + +.. · .. ,· ,Jf� + +��:: :: ·· ·· + +-2 -2 -2 + +FIGURE 15 . Receptive fields found in different runs of the T-C problem. A: An oncenter-off-surround recept ive field for detecting T's. B: A vertical bar detector which responds to T's more strongly than C's. C: A diagonal bar detector. A T act ivates five such detectors whereas a Cactivates only th ree such detectors. D: A compact ness detector . This inhibitory receptive field turns off whenever an input covers any region of i ts receptive field . Si nce the Cis more compact than the T it turns off 20 such detectors + +whereas the T turns off 21 of them. + +representation. In each case, the solution was reached in from about + +5,000 to 10,000 presentations of the set of eight patterns. 8 + +It is interesting that the inhibitory type of receptive field shown in Figure 150 was the most common and that there is a predominance of inhibitory connections in this and indeed all of our simulations. This can be understood by considering the traject ory through which the learning typically moves. At first, when the system is presented with a + +8Si nce translation independence was bui ltinto the learning procedure, it makes no difference where the input occurs: the same thing will be learned wherever the pattern is presented . Thus, there are on�t5�pr@HiOO MWtIDfaP be presented to the system . + +difficult problem, the initial random connections are as likely to mislead as to give the correct answer. In this case, it is best for the output units to take on a value of 0. 5 than to take on a more extreme value. This follows from the form of the error function given in Equation 2. The output unit can achieve a constant output of 0.5 by turning off those units feeding into it. Thus, the first thing that happens in virtually every difficult problem is that the hidden units are turned off. One way to achieve this is to have the input units inhibit the hidden units. As the system begins to sort things out and to learn the appropriate function some of the connections will typical ly go positive, but the majority of the connections will remain negative. This bias for solutions involving inhibitory inputs can often lead to nonintuitive results in which hidden units are often on unless turned off by the input. + +More Simulation Results + +We have offered a sample of our results in this section. In addition to having studied our learning system on the problems discussed here, we have employed back propagation for learning to multiply binary digits, to play tic-tac-toe, to distinguish between vertical and horizontal lines, to perform sequences of actions , to recognize characters, to associate random vectors , and a host of other applications. In all of these applications we have found that the generalized delta rule was capable of generating the kinds of internal representations required for the problems in question. We have found local minima to be very rare and that the system learns in a reasonable period of time. Sti ll more studies of this type will be required to understand precisely the conditions under which the system wi ll be plagued by local minima. Suffice it to say that the problem has not been serious to date. We now turn to a + +pointer to some future developments. + +SOME FURTHER GENERALIZATIONS + +We have intensively studied the learning characteristics of the general ized delta rule on feed forward networks and semi linear activations functions. Interestingly these are not the most general cases to which the learning procedure is applicable. As yet we have only studied a few examples of the more fully generalized system, but it is relatively easy to apply the same learning rule to sigma-pi units and to recurrent net- + +works . We wi ll simply s�qg� here. + +The Generalized Delta Rule and Sigma-Pi Units + +It wi ll be recalled from Chapter 2 that i n the case of sigma-pi units + +we have + +(I7) + +where i varies over the set of conjuncts feeding into unit j and k varies over the elements of the conjuncts. For simplicity of exposition , we restrict ourselves to the case in which no conjuncts involve more than two elements. In this case we can notate the weight from the conjunction of units i and j to unit k by wkij ' The weight on the di rect connection from unit i to unit j would, thus, be wji; , and since the relation + +is multi plicative, Wkij = Wkj + +;' We can now rewrite Equation 17as + +OJ = Ij (L Wjh; 0h 0; ). ;.h + +We now set + +Taking the deri vative and simplifying, we get a rule for sigma-pi units + +strictly analogous to the rule for semilinear activation functions: + +!l.p wkij = 8 k o; oj . + +We can see the correct form of the error signal , 8, for this case by inspecting Figure 16. Consider the appropriate value of 8; for unit U; in the figure. As before, the correct val ue of 8; is given by the sum of the 8's for all of the units into which U; feeds , weighted by the amount of effect due to the activation of U; times the derivative of the activation function. In the case of semilinear functions, the measure of a unit's effect on another unit is given simply by the weight W connecting the fi rst unit to the second. In this case, the u, 's effect on Uk + +depends not only on Wk;j + +, but also on the value of Uj . Thus, we have + +8; = I'j (net; ) L8 k Wk;j OJ j ,k if u; is not an output unit and, as before, + +8; = .1 '; (net; )(t;-o;) + +if it is an output unit. Copyrighted Material + +&. &. J t + +FIGURE 16. The generalized delta rule for s igma - pi units. The products of activation values of individual units activate output units. See text for explanation of how the 8 + +values are computed in this case . + +Recurrent Nets + +We have thus far restricted ourselves to /eed/orward nets. This may seem like a substantial restriction, but as Minsky and Papert point out, there is, for every recurrent network, a feed forward network with identical behavior (over a finite period of ti me) . We wi ll now indicate how this construction can proceed and thereby show the correct form of the learning rule for the recurrent network. Consider the si mple recurrent network shown in Figure 17 A. The same network in a feedforward architecture is shown in Figure 17B. The behavior of a recurrent network can be achieved in a feedforward network at the cost of duplicating the hardware many times over for the feedforward version of the network . 9 We have distinct units and distinct weights for each point in time. For naming convenience, we subscri pt each unit with its unit number in the corresponding recurrent network and the time it represents. As long as we constrain the weights at each level of the feedforward network to be the same, we have a feedforward network which performs identically with the recurrent network of Figure 17 A. + +9Note that in this discussion, and indeed in our entire development here, we have assumed a discrete time system with synchronous update and with each connection + +involving a unit delay. + +A + +B + +· · · + +· · Time + +t+1 + +o + +FIGURE 17 , A comparison of a recu rrent network and a feedforward network with identical behavior, A: A completely connected recurrent network with two units, B: A feedforward network which behaves the same as the recurrent network , In this case, we have a separate unit for each time step and we requ ire that the weights connecting each layer of units to the next be the same for all layers, Moreover, they must be the same as + +the analogous weights in the recurrent case, + +The appropriate method for maintaining the constraint that all weights be equal is simply to keep track of the changes dictated for each weight at each level and then change each of the weights according to the sum of these individual ly prescribed changes. Now, the general rule for determining the change prescribed for a weight in the system for a particular time is simply CWf,lPighted � of an appropriate error + +measure 8 and the input along the relevant line both for the appropriate times. Thus, the problem of specifying the correct learning rule for recurrent networks is simply one of determining the appropriate value of 8 for each time. In a feedforward network we determine 8 by multiplying the derivative of the activation function by the sum of the 8's for those units it feeds into weighted by the connection strengths. The same process works for the recurrent network-except in this case, the value of 8 associated with a particular unit changes in time as a unit passes error back, sometimes to itself. After each iteration, as error is being passed back through the network, the change in weight for that iteration must be added to the weight changes specified by the preceding iterations and the sum stored. This process of passing error through the network should continue for a number of iterations equal to the number of iterations through which the activation was originally passed. At this point, the appropriate changes to all of the weights can + +be made. + +In general , the procedure for a recurrent network is that an input (generally a sequence) is presented to the system while it runs for some number of iterations. At certain specified times during the operation of the system, the output of certain units are compared to the target for that unit at that time and error signals are generated. Each such error signal is then passed back through the network for a number of iterations equal to the number of iterations used in the forward pass. Weight changes are computed at each iteration and a sum of all the weight changes dictated for a particular weight is saved. Finally, after all such error signals have been propagated through the system, the weights are changed. The major problem with this procedure is the memory required. Not only does the system have to hold its summed weight changes while the error is being propagated, but each unit must somehow record the sequence of activation values through which it was driven during the original processing. This follows from the fact that during each iteration while the error is passed back through the system, the current 8 is relevant to a point earl ier in time and the required weight changes depend on the activation levels of the units at that time. It is not entirely clear how such a mechanism could be implemented in the brain. Nevertheless , it is tantal izing to realize that such a procedure is potentially very powerful, since the problem it is attempting to solve amounts to that of finding a sequential program (like that for a digital computer) that produces specified input-sequence/ output-sequence pairs. Furthermore , the interaction of the teacher with the system can be quite flexible, so that, for example, should the system get stuck in a local minimum, the teacher could introduce "hints" in the form of desired output values for intermediate stages of processing. Our experience with recurrent net�Hmi�tePMII we have carried out some + +experiments. We turn first to a very simple problem in which the sys- + +tem is induced to invent a shift register to solve the problem. + +Learning to be a shift register. Perhaps the simplest class of recurrent problems we have studied is one in which the input and output units are one and the same and there are no hidden units. We simply present a pattern and let the system process it for a period of time. The state of the system is then compared to some target state. If it hasn't reached the target state at the designated time, error is injected into the system and it modifies its weights. Then it is shown a new input pattern and restarted. In these cases , there is no constraint on the connections in the system. Any unit can connect to any other unit. The simplest such problem we have studied is what we call the shift register problem. In this problem, the units are conceptualized as a circular shift register. An arbitrary bit pattern is first established on the units. They are then allowed to process for two time-steps. The target state, after those two time-steps, is the original pattern shifted two spaces to the left. The interesting question here concerns the state of the units between the presentation of the start state and the time at which the target state is presented. One solution to the problem is for the system to become a shift regi ster and shift the pattern exactly one unit to the left during each time period. If the system did this then it would surely be shifted two places to the left after two time units. We have tried this problem with groups of three or five units and, if we constrain the biases on al l of the units to be negative (so the units are off unless turned on) , the system always learns to be a shift register of + +this sort. + +IO Thus, even though in principle any unit can connect to any + +other unit, the system actually learns to set all weights to zero except the ones connecting a unit to its left neighbor. Since the target states were determined on the assumption of a circular register, the left-most unit developed a strong connection to the right-most unit. The system learns this relatively quickly. With T/ = 0.25 it learns perfectly in fewer than 200 sweeps through the set of possible patterns with either three- + +or five-unit systems. + +The tasks we have described so far are exceptional ly simple, but they do illustrate how the algorithm works with unrestricted networks. We have attempted a few more difficult problems with recurrent networks. + +10 If the constraint that biases be negative is not imposed, other solutions are possible. These solutions can involve the units passing through the complements of the shifted pattern or even through more complicated intermediate states. These trajectories are interesting in that they match a simple shift register on all even numbers of shifts, but do + +not match following an odd number of shifts. + +One of the more interesting involves learning to complete sequences of + +patterns. Our final example comes from this domain. + +Learning to complete sequences. Table 10 shows a set of 25 sequences which were chosen so that the first two items of a sequence uniquely determine the remaining four. We used this set of sequences to test out the learning abilities of a recurrent network. The network consisted of five input units (A, B, C, D, E) , 30 hidden units, and three output units (I, 2, 3) . At Time 1 , the input unit corresponding to the first item of the sequence is turned on and the other input units are turned off. At Time 2, the input unit for the second item in the sequence is turned on and the others are al l turned off. Then al l the input units are turned off and kept off for the remaining four steps of the forward iteration. The network must learn to make the output units adopt states that represent the rest of the sequence. Unlike simple feedforward networks (or their iterative equivalents) , the errors are not only assessed at the final layer or time. The output units must adopt the appropriate states during the forward iteration, and so during the back-propagation phase, errors are injected at each time-step by comparing the remembered actual states of the output units with their + +desired states . + +The learning procedure for recurrent nets places no constraints on the allowable connectivity structure. 11 For the sequence completion problem, we used one-way connections from the input units to the hidden units and from the hidden units to the output units . Every hidden unit had a one-way connection to every other hidden unit and to itself, + +> TABLE 10 25 SEQUENCES TO BE LEARNED AA 1212 AB1 223 AC 1231 ADl221 AEI 213 BA23 12 BB2323 BC2331 B02321 BE23 13 CA3112 CB3 123 CC3131 C03121 CE311 3 OA2112 OB2 123 OC2131 002121 OE2ll3 EA 13I2 EB 1323 EC 1331 EDl321 EEI3 13 + +1 1 The constraint in feed forward networks is that it must be possible to arrange the units into layers such that units do not influence units in the same or lower layers. In recurrent networks this amounts to the constraint that during the forward iteration, + +and every output unit was also connected to every other output unit and to itself. All the connections started with small random weights uniformly distributed between -0.3 and +0.3. All the hidden and output units started with an activity level of 0.2 at the beginning of each + +sequence. + +We used a version of the learning procedure in which the gradient of the error with respect to each weight is computed for a whole set of examples before the weights are changed. This means that each connection must accumulate the sum of the gradients for all the examples and for all the time steps involved in each example. During training, we used a particular set of 20 examples , and after these were learned almost perfectly we tested the network on the remaining examples to see if it had picked up on the obvious regularity that relates the first two items of a sequence to the subsequent four. The results are shown in Table 11. For four out of the five test sequences , the output units all have the correct val ues at all times (assuming we treat val ues above 0.5 as 1 and values below 0.5 as 0) . The network has clearly captured the rule that the fi rst item of a sequence determines the third and fourth, and the second determines the fi fth and si xth. We repeated the simulation with a different set of random initial weights, and it got all + +five test sequences correct. + +The learning required 260 sweeps through all 20 training sequences. The errors in the output units were computed as follows: For a unit that should be on, there was no error if its activity level was above 0.8, otherwise the derivati ve of the error was the amount below 0.8. Similarly, for output units that should be off, the deri vative of the error was the amount above 0. 2. After each sweep, each weight was decremented by .02 times the total gradient accumulated on that sweep plus 0.9 + +times the previous weight change. + +We have shown that the learning procedure can be used to create a network with interesting sequential behavior, but the particular problem we used can be solved by simply using the hidden units to create "delay lines" which hold information for a fi xed length of time before allowing it to influence the output. A harder problem that cannot be solved with delay lines of fixed duration is shown in Table 12 . The output is the same as before, but the two input items can arri ve at variable times so that the item arriving at time 2, for example, could be either the first or the second item and could therefore determine the states of the output units at either the fifth and sixth or the seventh and eighth times. The new task is equi valent to requiring a buffer that receives two input "words " at variable times and outputs their "phonemic realizations " one after the other. This problem was solved successfully by a network similar to the one above except that it had 60 hidden units and hal f of their possi ble iItM1iynnmetf>Ma� omitted at random. The + +TABLE 11 PERFORMANCE OF THE NETWORK ON FIVE NOVEL TEST SEQUENCES + +Input Sequence A D + +Desi red Outputs 2 2 + +Actual States of: + +Output Unit 1 0.2 0. 12 0.90 0.22 0. 11 0.83 Output Unit 2 0.2 0. 16 0. 13 0.82 0.88 0.03 Output Unit 3 0. 2 0.07 0.08 0.03 0.01 0.22 + +Input Sequence B E + +Desired Outputs 2 3 3 + +Actual States of: + +Output Unit 1 0.2 0. 12 0.20 0.25 0.48 0.26 Output Unit 2 0.2 0. 16 0.80 0.05 0.04 0.09 Output Unit 3 0.2 0.07 0.02 0.79 0.48 0.53 + +Input Sequence C A + +Desi red Outputs 3 2 + +Actual States of: + +Output Unit 1 0.2 0. 12 0. 19 0.80 0.87 0. 11 Output Unit 2 0.2 0. 16 0. 19 0.00 0. 13 0.70 Output Unit 3 0.2 0.07 0.80 0. 13 0.01 0.25 + +Input Sequence D B + +Desi red Outputs 2 2 3 + +Actual States of: + +Output Unit 1 0.2 0. 12 0. 16 0.79 0.07 0. 11 Output Unit 2 0.2 0. 16 0.80 0. 15 0.87 0.05 Output Unit 3 0.2 0.07 0.20 0.01 0. 13 0.96 + +Input Sequence E C + +Desired Outputs 3 3 + +Actual States of: + +Output Unit 1 0.2 0.12 0.80 0.09 0.27 0.78 Output Unit 2 0.2 0. 16 0.20 0. 13 0.01 0.02 Output Unit 3 0.2 0.07 0.07 0.94 0.76 0. 13 + +learning was much slower, requiring thousands of sweeps through all 136 training examples . There were also a few more errors on the 1 4 test examples, but the general ization was still good with most of the + +test sequences being coll!RJp)9tgRfd'lieM»terial + +TABLE 12 SIX VARIATIONS OF THE SEQUENCE EA \312 PRODUCED BY PRESENTING THE FIRST TWO ITEMS AT VARI ABLE TIMES + +EA-- 1312 -EA- 1312 E-A- 1J12 -E-A I312 + +E- -AI3l2 --EA\312 + +Note: With these temporal variations, the 25 sequences shown in Table 10 can be used to generate 150 different sequences. + +CONCLUSION + +In their pessimistic discussion of perceptrons, Minsky and Papert (1 969) finally discuss multilayer machines near the end of their book. + +They state: + +The perceptron has shown itself worthy of study despite (and even because of!) its severe limitations. It has many features that attract attention: its linearity; its intriguing learning theorem; its clear paradigmatic simplicity as a kind of paral lel computation . There is no reason to suppose that any of these virtues carry over to the many-layered version, Nevertheless, we consider it to be an important research problem to elucidate (or reject) our intuitive judgement that the extension is sterile. Perhaps some powerful convergence theorem wi ll be di scovered, or some profound reason for the failure to produce an interesting "learning theorem " for the multi layered machine + +wi ll be found. (pp. 231-232) + +Although our learning results do not guarantee that we can find a sol ution for all solvable problems, our analyses and results have shown that as a practical matter, the error propagation scheme leads to solutions i n virtually every case, In short, we bel ieve that we have answered Minsky and Papert's chal lenge and have found a learning result sufficiently powerful to demonstrate that their pessimism about learning in mul- + +tilayer machines was misplaced. + +One way to view the procedure we have been describing is as a parallel computer that, having been shown the appropriate input/ output exemplars specifying some function, programs itself to compute that function in general . Parallel computers are notoriously difficult to program. Here we have a mechanism whereby we do not actually have to know how to write the program in order to get the system to do it. + +Parker (1985) has emph�fflJIigHt-eB�rerial + +On many occasions we have been surprised to learn of new methods of computing interesting functions by observing the behavior of our learning algorithm. This also raised the question of generalization. In most of the cases presented above, we have presented the system with the entire set of exemplars. It is interesting to ask what would happen if we presented only a subset of the exemplars at training time and then watched the system generalize to remaining exemplars. In small problems such as those presented here, the system sometimes finds solutions to the problems which do not properly general ize. However, preli minary results on larger problems are very encouraging in this regard. This research is still in progress and cannot be reported here. This is + +currently a very active interest of ours. + +Final ly, we should say that this work is not yet in a finished form. We have only begun our study of recurrent networks and sigma-pi units. We have not yet appl ied our learning procedure to many very complex problems . However, the results to date are encouragi ng and + +we are continuing our work . + +PART III + +FORMAL ANALYSES + +Part III is focused on the formal tools employed in the study of PDP models and their application in the analysis of several specific aspects of + +PDP mechanisms. + +In Chapter 9, Jordan provides a very accessible introduction to linear algebra and its applications to the analysis of PDP models. This chapter is designed to be a tutorial for those who are not familiar with the basics of linear algebra. Most of the book can be read and understood without knowledge of linear algebra, but an understanding of this important tool will greatly enhance a reader's understanding of the mathematical discussions that can be found in several chapters of the + +book. + +In Chapter 10, Williams provides a useful analysis of activation functions. Throughout the book we employ several different activation functions. There is a question as to whether we will need to look for more complex activation functions to carry out some of the more complex computations. Williams shows that we will never have to consider + +activation functions more complex than the sigma pi function. + +In Chapter 11, Stone provides a useful analysis of the delta rule, which plays an important role throughout the book. Stone shows how a change of basis can be employed to reveal the internal workings of the delta rule. He shows that when there is no deterministic relationship between inputs and targets, the delta rule leads to a system whose outputs match the central tendencies of the target patterns. Finally, he + +In Chapter 12, McClelland analyzes the capacity limitations of two kinds of networks. He studies the effects of limitations of fan-in and fan-out on the capacities of standard pattern-association networks, and he explores the costs in units and connections of using programmable + +networks of the kind outlined in Chapter 16. + +Finally, in Chapter 13, Zipser and Rabin describe a computer simulation system, called P3, for building computer simulations of PDP models. P3 provides both a language for describing networks and an interface for interacting with these networks and observing their behavior. Chapter 13 gives as an example a description of how the + +competitive learning algorithm can be built in P3. + +In general, the chapters in this section are useful for two reasons. First, they describe several useful basic results-results that lie behind many of the simulation models described in other sections of the book. Second, and perhaps more importantly, they indicate some of the formal tools that are available for analyzing parallel networks, and show through example how these tools can be used to produce useful results. + +A + +Carol [�� I 1 21 + +8 + +FIGURE 1. + +37 72 + +Joe 1 75 + +8 1946 Mary [�?I + +Brad [�� I 155 + +to only three components, however. If, for example, we also wanted to keep track of Joe's shoe size and year of birth, then we would simply + +make a vector with five components, as in Figure lB. + +One important reason for the great utility of linear algebra lies in the simplicity of its notation. We will use bold, lower-case letters such as v to stand for vectors. With this notation, an arbitrarily long list of infor- + +mation can be designated by a single symbol. + +When a vector has no more than three components, it can be represented graphically by a point or an arrow in three-dimensional space. An example with three components is given in Figure 2 for the vector corresponding to Mary. Each axis in the figure corresponds to + +one of the three components of the vector. + +It will prove helpful to try and visualize vectors as points or arrows in two- and three-dimensional space in proceeding through this chapter in order to develop geometric intuition for the operations on vectors. Notice, however, that there is no fundamental distinction between such vectors and vectors with more than three components. All of the operations upon vectors described in later sections apply equally well to + +vectors with any finite number of components. + +In a parallel distributed processing model, many quantities are best represented by vectors. The pattern of numbers representing the activations of many processing units is one example. Other examples are the s�t of weights on the input lines to a particular processing unit, + +4 + +3 + +2 + +o�--�--�--�--�--��- 2 3 4 5 + +FIGURE 3. + +Addition of Vectors + +Two or more vectors can be added by adding their components. The vectors must have the same number of components to be added; other- + +wise the operation is undefined. + +Examples: + +Vector addition is associative (the vectors can be grouped in any manner) and commutative (the order of addition is unimportant) just like addition in ordinary algebra. This is true because if we consider one component at a time, vector addition is just addition in ordinary + +algebra. + +How can vector addition be represented graphically? Consider Figure 4, where lhe vectors vI - [ � 1 and. 2 - [ : 1 are being added. It can be + +seen that the sum v 1 + V 2 is a vector [ � 1 which lies between v 1 and v 2' + +Forming the parallelogram with sides v 1 and v 2, we see that the sum of Copyrighted Material + +3 + +2 + +2 + +FIGURE 4. + +4 5 + +the two vectors is the diagonal of this parallelogram. In two and three dimensions this is easy to visualize, but not when the vectors have more than three components. Nevertheless, it will be useful to imagine vector addition as forming the diagonal of a parallelogram. One implication of this view, which we will find useful , is that the sum of two vectors is a vector that lies in the same plane as the vectors being + +added. + +Example: Calculating averages. We can demonstrate the use of the two operations thus far defined in calculating the average vector. Suppose we want to find the average age, height, and weight of the four individuals in Figure lA. Clearly this involves summing the com- + +ponents separately and then dividing each sum by 4. Using vectors , this corresponds to adding the four vectors and then multiplying the resulting sum by the scalar 1/4. Using u to denote the average vector, + +u= ! II ��l + I !�l + I ��l + I :�ll = I �::�l · + +175 61 121 155 128 + +Using vector notation, if we denote the four vectors by v I, V 2, V 3, and + +v 4, then we can write the averaging operation as + +The vector u, then, is a vector whose components are the averages of the components of the four individual vectors. Notice that the same result is obtained if each vector is first multiplied by 1/4, and the resulting vectors are added. This shows that multiplication by scalars and vector addition obey a distributive law, as in ordinary algebra. + +LINEAR COMBINATIONS AND LINEAR + +INDEPENDENCE + +Linear Combinations of Vectors + +The average vector calculated in the last section is an example of a linear combination of vectors. In this section, we pursue this idea + +further. + +Consider the vectors v, = [ �], V 2 = [ �], and u = [ 1 �]. Can u be written as the sum of scalar multiples of v, and v 2? That is, can scalars + +c, and C2 be found such that u can be written in the form + +U = CIVI+C2V2? + +If so, then u is said to be a linear combination of the vectors v I and v 2. The reader can verify that c, = 3 and C2 = 2 witt work, and thus u is a + +linear combination of v, and v 2. + +This can also be seen directly in Figure 5, where these vectors are plotted. Remembering that multiplication by a scalar shortens or + +10 + +5 + +o�----�------�------�-- 5 10 15 + +lengthens a vector and that vector addition corresponds to forming the diagonal of a parallelogram, it seems clear that we can find scalars to adjust v 1 and v 2 to form a parallelogram that yields u. This is indicated in the figure. It also seems clear that, using positive scalars, any vector in the shaded area of the figure can be generated this way. By using both negative and positive scalars, any vector in the plane can be written as a linear combination of v 1 and v 2. This is true because multiplication by a negative scalar reverses the direction of a vector as well as shortening or lengthening it. The vectors v 1 and v 2 are said to span the plane, because any vector in the plane can be generated from these two + +vectors. + +In general , given a set v I> v 2 ••••• V II of vectors, a vector vis said to be a linear combination of the Vi if scalars el>e2 •...• ell can be found + +such that + +(1) + +The set of all linear combinations of the v, is called the set spanned by + +the v,. + +Exampk. The � vecto� [�I, [! I Md [ � I s� an ru thre� + +dimensional space since any vector v- [!I can be written as a linear + +combination v- a[i I +b [! 1+ c m The vecto� are ref erroo to + +as the standard basis for three-dimensional space (more on the idea of a + +basis in the next section) . + +Linear Independence + +To say that a set of vectors span a space is to say that all vectors in the space can be generated from the original set by linear combination. We have shown examples in which two vectors span two-dimensional space and three vectors span three-dimensional space. We might be led to expect that, in general, n vectors suffice to span n-dimensional space. In fact, we have been using the term "dimension" without defining what it means; it would seem that a good definition of n- + +To make this definition work, we would require that the same size space be generated by any set of n vectors. However, this is not the + +case, as can be easily shown. Consider any pair of collinear vectors, for example. Such vectors lie along a single line, thus any linear combination of the vectors will lie along the same line. The space spanned by these two vectors is therefore only a one-dimensional set. The collinear vectors [ � I and [ ; I are a good example. Any linear combina- + +tion of these vectors will have equal components, thus they do not span + +the plane. + +Another example is a set of three vectors that lie on a plane in three-dimensional space. Any parallelograms that we form will be in the same plane, thus all linear combinations will remain in the plane + +and we can't span all of three-dimensional space. + +The general rule arising from these examples is that of a set of n vectors, if at least one can be written as a linear combination of the others, then the vectors span something less than a full n-dimensional space. We call such a set of vectors linearly dependent. If, on the other hand, none of the vectors can be written as a linear combmation of the others, then the set is called linearly independent. We now revise the definition of dimensionality as follows: n -dimensional space is the set of vectors spanned by a set of n linearly independent vectors. The n + +vectors are referred to as a basis for the space. + +Examples: + +1. [ � + +I and [ ; I are linearly dependent. They span only a one- + +dimensional space. + +2. I: I and 1 � I are linearly independent. Thus they span the + +plane, a two-dimensional space. + +3. 1 � I, 1 � I, and 1-� I are linearly dependent since 7 times the + +first vector minus 4 times the second vector is equal to the third + +vector. + +4. [ i J.[ � I + +, an+ � I are linearly dependent. Clearly they =not + +span all of three-dimensional space, because no vector with a + +nonzero third component can be generated from this set. Copyrighted Material + +VECTOR SPACES + +Let us pause to reflect for a moment upon what a vector is. I have implied that a vector is a list of numbers, and I have also used the term to refer to a point or an arrow in space. Are both of these objects vectors, or is one just a heuristic representation for the other? Are there other objects that should be called vectors? Just what is a vector? + +As is often the case in mathematics, these kinds of questions are solved by being avoided. Consider the following definition of an + +abstract vector space, and try to decide what a vector is. + +Avector space is a set Vof elements, called vectors , with the follow- + +ing properties: + +• To every pair, u and v, of vectors in V. there corresponds a vector u + v also in V, called the sum of u and v, in such a way + +that addition is commutative and associative. + +• For any scalar c and any vector v in V, there is a vector cv in V, called the product of c and v, in such a way that multiplication by scalars is associative and distributive with respect to + +vector addition.l + +The answer to the question is that a vector is an undefined object in linear algebra, much like a line in geometry. The definition of a vector space simply lists the properties that vectors must have, without specifying what a vector must be. Thus, any set of objects that obey these properties can be called a vector space. Lists of numbers are vectors when addition is defined as adding components separately and scalar multiplication is defined as multiplying all the components by the scalar, because these operations fill all the requirements of a vector space. Arrows or points in space are also vectors when addition is defined geometrically as taking the diagonal of a parallelogram and scalar multiplication is defined as lengthening or shortening the arrow, because again, these operations fi ll the requirements of a vector space. A seemingly unrelated example of a vector space is the set of polynomials of order n, with addition and scalar multiplication defined in the + +obvious way. + +This sort of abstraction is common in mathematics. It is useful because any theorem that is true about a general vector space must be + +1 Ihave left out certain technicalities usually included as axioms for a vector space. These include the axiom that there must be a zero vector, and for every vector, there is + +true about any instantiation of a vector space. We can therefore discuss general properties of vector spaces without being committed to choosing a particular representation such as a list of numbers. Much of the discussion about linear combinations and linear independence was of + +this nature. + +When we do choose numbers to represent vectors, we use the following scheme. First we choose a basis for the space. Since every vector in the space can be written as a linear combination of the basis vectors, each vector has a set of coefficients c J, c 2 ••••• cn which are the + +coefficients in the linear combination. These coefficients are the numbers used as the components of the vector. As was shown in the previous section, the coefficients of a given vector are unique because + +basis vectors are linearly independent. + +There is a certain arbitrariness in assigning the numbers, since there are infinitely many sets of basis vectors, and each vector in th� space has a different description depending on which basis is used. That is, the coefficients, which are referred to as coordinates, are different for + +different choices of basis. The implications of this fact are discussed further in a later section where I also di scuss how to relate the coordi- + +nates of a vector in one basis to the coordinates of the vector in another basis . Chapter 22 contains a lengthy discussion of several + +issues relating to the choice of basis. + +INNER PRODUCTS + +As of yet, we have no way to speak of the length of a vector or of the similarity between two vectors . This will be rectified with the + +notion of an inner product. + +The inner product of two vectors is the sum of the products of the vector components. The notation for the inner product of vectors vand w is v . w. As with vector addition, the inner product is defined + +only if the vectors have the same number of components. + +Example: + +v. w = (3 . 1) + (- 1 . 2) + (2 . 1) = 3. + +The inner product is a kind of mUltiplication between vectors, although somewhat of a strange sort of multiplication, since it produces a single number from a pair of vectors. What does this single number + +"measure" ? + +Length + +As a special case, consider taking the inner product of a vector with itself. An example is the vector v = [ ! [ in Figure 7. The inner pro- + +duct of v with itself is + +v . v = 32+ 42= 25. + +Consider the right triangle in Figure 7 with sides corresponding to the components of v. and hypotenuse v itself. The Pythagorean theorem tells us that the square of the length of v is equal to the sum of the squares of the sides. Since this is exactly what is calculated by the inner product v . v, it appears that a reasonable definition of the length of a vector is the square root of the inner product of the vector with + +itself. Thus we define the length of a vector v, denoted by I + +Ivl l , as + +IIvll = (v' v)'h. + +Although the definition was motivated by an example in two dimensions, it can be applied to any vector. Notice that many of the + +properties we intuitively associate with length are included in this definition. For example, if a vector has larger components than another vector, it will be longer, because the squared components will contribute to a larger inner product. Multiplying a vector by a scalar produces a new vector whose length is the absolute value of the scalar + +times the length of the old vector: + +lIevll = !clllvll· + +This is a property that can be easily proved. Somewhat harder to prove is the so-called triangle inequality, which states that the length of the sum of two vectors is less than or equal to the sum of the lengths of + +the two vectors: + +Geometrically, the triangle inequality corresponds to the statement that one side of a triangle is no longer than the sum of the lengths of the + +other two sides. + +Thus, in the special case where the operands are the same vector, the inner product is closely related to the idea of length. What if the + +operands are different vectors? + +Angle + +The angle between two vectors v and w is defined in terms of the + +inner product by the following definition: + +v 'w + +cos (J =IIvll I + +Iwil + +(2) + +where (J is the angle between v and w. Note that all of the quantities on + +the right hand side of the equation are easily calculated for ndimensional vectors. At the end of this section, I will show geometrically why this formula is correct in two-dimensional space, using the + +ordinary geometrical definition of angle. + +Example. Find the angle (J between the vectors v I = [ � 1 and + +v2 = [ � I. First, we calculate the necessary inner product and lengths: + +must remember to divide the inner product by the lengths of the vec- + +tors involved to make such comparative statements. + +An important special case occurs when the inner product is zero. In + +this case, the two vectors are said to be orthogonal. Plugging zero into + +the right side of Equation 2 gives cos () == o. + +which implies that the angle between the vectors is 90°. Thus, orthog- + +onal vectors are vectors which lie at right angles to one another. + +We will often speak of a set of orthogonal vectors. This means that every vector in the set is orthogonal to every other vector in the set. That is, every vector lies at a right angle to every other vector. A good example in three-dimensional space is the standard basis referred to earlier. Although we will skip the proof, it is probably clear that any orthogonal set is linearly independent. Indeed, orthogonality is + +stronger than linear independence: whereas every orthogonal set is linearly independent, there are very many linearly independent sets of vectors that are not orthogonal. An example in two-dimensional space + +is the pair [ : 1 and [ � I· When we choose a basis for a space, we typi· + +cally choose an orthogonal basis. In fact, in much of classical physics and mathematics, there is not the slightest hint that a basis should be + +anything but orthogonal . + +Projections + +A further application of the inner product, closely related to the ideas of length and angle, is the notion of a projection of one vector onto another. An example is given in Figure 8. The distance x is the pro- + +jection of v on w, In two dimensions, we readily know how to calculate + +the projection. It is + +x.. IIvll cos () (3) + +where () is the angle between v and w, This formula generalizes , and + +for any vectors v and w, the projection of v on w is given by Equation 3. It is a scalar which can be thought of as indicating how much v is + +pointing in the direction of w . + +" + +FIGURE 8. + +There is a close relationship between the inner product and the projection. Using Equation 2, we can rewrite the formula for the projec- + +tion: + +x = \ + +Iv II cos 9 + +v 'w + +=IIv\l \lvll IIwll + +Thus, the projection is the inner product divided by the length of w. In particular, if w has length one, then IIwll = I, and the projection of v + +on wand the inner product of v and ware the same thing. This way of thinking about the inner product is consistent with our earlier comments. That is, if we hold the lengths of v and w constant, then we know that the inner product gets larger as v moves toward w. From the picture, we see that the projection gets larger as well. When the two vectors are orthogonal , the projection as well as the inner product are + +zero. + +Inner Products in Two Dimensions + +Equation 2 can be shown to be correct in two-dimensional space with the help of some simple geometry. Let v and w be two vectors in the plane, and 9 be the angle between them, as shown in Figure 9. Denote + +the x and y coordinates of v �nd w by V..J � Vy and wx, w + +y + +, respectively. + +COPYrighted Material + +FIGURE 9. + +v + +w + +Let I denote the projection of v on w. We have I = Ilv II cosO from geometry. We can break I into two pieces Ix and Iy as shown in the figure. I, can be computed from the diagram by noticing that triangles + +OAD and COB, in Figure 10, are similar triangles. Thus, the ratio of + +corresponding sides is constant: + +giving + +Iy Wy + +�= Ilwll' + +numbers. In what follows, cand Cj will be any scalars, and the v and w + +will be n -dimensional vectors. + +v·w= + +w·v + +C(v . w) = (e v) . w = v. (e w) + +w. (v I+ v 2) = w . V I + w . V 2 + +(4) + +(5) + +(6) + +The first theorem says simply that order is unimportant; the inner product is commutative. The second and third theorems show that the inner product is a linear function, as we will discuss at length in a later section. We can combine these two equations to get w. (eIVI + C2V2) = c) (w . VI) +C2 (w . V2). It is also well worth our while to use mathematical induction to generalize this formula, giving + +us + +(7) + +This important result tells us how to calculate the inner product of w + +and a linear combination of vectors. Another useful theorem is + +Iv . wi � IIvllllwll (8) + +This is known as the Cauchy-Schwartz inequality. It gives an upper + +bound on the inner product. + +ONE UNIT IN A PARALLEL DISTRIBUTED + +PROCESSING SYSTEM + +In this section, we show how some of the concepts we have introduced can be used in analyzing a very simple PDP model . Consider the processing unit in Figure 12 which receives inputs from the n units below. Associated with each of the n + 1 units there is a scalar activation value. We shall use the scalar u to denote the activation of the output unit and the vector v to denote the activations of the ninput units. That is , the ith component of v is the activation of the ith input unit. + +Associated with each link between the input uni ts and the output unit, there is a scalar wemwr;�& �g�� can think of the set of n + +FIGURE 12. + +FIGURE 13. + +weights as an n -dimensional vector w. This is the weight vector + +corresponding to the output unit. Later we will discuss a model with many output units, each of which will have its own weight vector. + +Another way to draw the same model is shown in Figure 13. Here we have drawn the n input units at the top with the output unit on the right. The components of the weight vector are stored at the junctions where the vertical input lines meet the horizontal output line. Which diagram is to be preferred (Figure 12 or Figure 13 ) is mostly a matter of taste, although we will see that the diagram in Figure 13 generalizes + +better to the case of many output units. + +Now to the operation of the model : Let us assume that the activation of each input unit is multiplied by the weight on its link, and that these products are added up to give the activation of the output unit. Using the definition of the inner product, we translate that statement + +into mathematics as follows: + +u =W ·v. + +9. INTRODUCTION TO LINEAR ALGEBRA 385 + +The geometric properties of the inner product give us the following picture to help in understanding what the model is computing. We imagine that the set of possible inputs to the model is a vector space. It is an n -dimensional space, where n is the number of input lines. + +The weight vector also has n components, thus we can plot the weight vector in the input space. The advantage of doing this is that we can now state how the system will respond to the various inputs. As we have seen, the inner product gives an indication of how close two vectors are. Thus, in this simple PDP model, the output activation gives + +an indication or measurement of how close the input vector is to the stored weight vector. The inputs lying close to the weight vector will yield a large positive response, those lying near 900 will yield a zero response, and those pointing in the opposite direction will yield a large negative response. If we present a succession of input vectors of constant length, the output unit will respond most strongly to that input vector which is closest to its weight vector, and will drop off in + +response as the input vectors move away from the weight vector. + +One way to describe the functioning of the processing unit is to say that it splits the input space into two parts, the part where the response is negative and the part where the response is positive. We can easily imagine augmenting the unit in the following way: if the inner product is positive, output a 1; if the inner product is negative, output a O. + +This unit, referred to as a linear threshold unit, explicitly computes + +which part of the space the input lies in. + +In some models, the weight vector is assumed to be normalized, that is, Ilwll = 1. As we have seen, in this case, the activation of the output + +unit is simply the projection of the input vector on the weight vector. + +MATRICES AND LINEAR SYSTEMS + +The first section introduced the concepts of a vector space and the inner product. We have seen that vectors may be added together and multiplied by scalars. Vectors also have a length, and there is an angle between any pair of vectors. Thus, we have good ways of describing + +the structure of a set of vectors . + +The usefulness of vectors can be broadened considerably by introducing the concept of a matrix. From an abstract point of view, matrices are a kind of "operator" �tftlitl{>ing from one vector space + +Addition of Matrices + +Matrices are added together by adding corresponding elements. Only matrices that have the same number of rows and columns can be added + +together. + +Example: + +[345] [-1 0 2 ] M + N= 1 0 1 +4 1 -1 = [ + +Notice that there is a close relationship between these definitions and the corresponding definitions for vectors. In fact, for fixed integers mand n, the set of all mx n matrices is another example of a vector space. However, we will not exploit this fact, rather, we will think about matrices in another way, in terms of functions from one vector + +space to another. This is the subject of the next section. + +Multiplication of a Vector by a Matrix + +We now link up vectors and matrices by showing how a vector can be multiplied by a matrix to produce a new vector. Consider the matrix W-[ � � :] and the vector v = [ � I. We wish to define a vector u + +which is the product of W and v . and denoted + +u = Wv-[ � � ;] m + +To define this operation, first imagine breaking the matrix into its rows. Each row of the matrix is a list of three numbers. We can think of the + +row as a three-dimensional vector and speak of the row vectors of the matrix. There are two such row vectors. Now consider forming the inner products of each of these row vectors with the vector v. This will yield two numbers. These two numbers can be thought of as a two- + +dimensional vector u, which is defined to be the product W v. Copyrighted Material + +components of the vector must be the same as the number of columns + +of the matrix. + +W(av) = aWv W (u + v) = Wu + Wv + +(9) + +(0) + +These equations are the counterparts to Equations 5 and 6. As in that section, they can be combined and generalized to general linear combi- + +nations: + +(1 1) + +In the next theorem, the matrices M and N must have the same + +number of rows and columns. + +Mv + Nv = (M + N)v + +ONE LAYER OF A PARALLEL DISTRIBUTED + +PROCESSING SYSTEM + +(12) + +I now generalize the simple model presented earlier to show how + +matrices can be used in analyzing PDP models . Consider Figure 17, which is the generalization of Figure 12 to the case of many output units. Suppose that there are m output units, each one connected to all + +of the n input units. Denote the activation of the output units by U b U 2, ...• Urn· Each output unit has its own weight vector Wi' separate from the other output units. As before, the activation rule + +Outputs: + +Inputs: + +u � W � v + +says that the activation of an output unit is given by the inner product + +of its weight vector with the input vector, thus, + +Ui = Wi ' v. + +If we form a matrix W whose row vectors are the Wi' then we can use + +the rule for matrix-vector multiplication to write all of the computations at once. Let u be the vector whose components are the Ui' Then + +u=Wv. + +This is a very succinct expression of the computation performed by the network. It says that for each input vector v. the network produces an output vector u whose components are the activations of the output + +units. + +Another way to draw the network is shown in Figure 18. which is the generalization of Figure 13 to the case of many output units. At each + +junction in the diagram there is a weight connecting an input unit with an output unit. 3 The weight vectors associated with each output unit appear on the horizontal lines. When drawn this way, it is clear why a matrix appears in the equation linking the output vector to the input + +vector: The array of junctions in the diagram is exactly the weight + +matrixW. + +Now let us attempt to understand geometrically what is being computed by the model. Each output unit is computing the inner product + +FIGURE 18. + +V 1 + +w ml + +W 12 + +W 21 + +W m2 + +Inputs + +appear in a multilayer system and thus have both an incoming weight vector and an outgoing weight vector, as shown in Figure 19. In this case, both views of matrix-vector multiplication can be useful : The unit can be thought of as matching its incoming weight vector to the current input using the inner product, and sending the result of this match + +multiplied by the outgoing weight vector to the next level. + +LINEARITY + +A distinction is often made between a linear system and a nonlinear system. In general, linear systems are relatively easy to analyze and understand, whereas nonlinear systems can be difficult. In this section, I will characterize linear systems. Nonlinear systems are defined simply as everything else. In a later section, I will give some specific examples + +of nonlinear systems. + +Suppose that there is a function f which represents a system in that + +for each input x to the system, the output y is given by + +y = j(x). + +The x and y might be scalars or they might be vectors, depending on the particular system. The function j is said to be linear if for any inputs X l and x2, and any real number c, the following two equations + +hold: + +f (ex) = c f (x). + +f (X l + X2) = f (X I) + f (X2 + +)' + +(13) + +(14) + +o + +o + +FIGURE 22. + +This equation can be easily generalized to give the strength of the con- + +nection between the jth element of v and the ith element of u: + +This formula calculates the inner product between the ith row of M and the jth column of N, which shows that P is equal to the product + +MN. + +This result can be extended to systems with more than two layers by induction. For example, in a three-layer system, the first two layers + +can be replaced with a matrix (as we have just seen) , and then that matrix can be multiplied by the matrix of the remaining layer to get a single matrix for the whole system. In general , the cascaded matrices of any n -layer linear system can be replaced by a single matrix which is + +the product of the n matrices. + +As a final comment, the definition of matrix multiplication may + +seem somewhat odd, especially since it would seem more straightforward to define it by analogy with matrix addition as the element-wise product. In fact, it would be perfectly acceptable to define multiplication as the element-wise product, and then to use another name for the operation we have discussed in this section. However, element-wise multiplication has never found much of an application in linear algebra. Therefore, the term multiplication has been reserved for the operation described in this section, which proves to be a useful definition, as the + +mappings of all other vectors in the domain are determined (cf. Equa- + +tion 15 ). + +In this section, let us special ize to the case of square matrices, that is, matrices with the same number of rows as columns. In this case, + +the domain and the range will have the same number of dimensions (because the vectors v and u must have the same number of components) , and the vectors in the domain and the range can be plotted in + +the same space. This is done in Figure 23 , where we have shown two + +vectors before and after multiplication by a matrix. + +In general , vectors in this space wi ll change direction as well as length when multipl ied by a matrix. However, as demonstrated by one of the vectors in Figure 23, there wi ll be some vectors that will change only in length, not direction. In other words, for these vectors, multiplication by the matrix is no different than multiplication by a simple scalar. Such vectors are known as eigenvectors. Each eigenvector v of a + +matrix obeys the equation + +Wv = AV (20) + +where A is a scalar. A is called an eigenvalue, and indicates how much v + +is shortened or lengthened after multiplication by W. + +Example: + +eigenvalues, then the n associated eigenvectors are linearly independent. Although the conditions under which a matrix has a full set of distinct eigenvalues are beyond the scope of this chapter, it is quite possible to have matrices with fewer than n eigenvalues, as in the case of the iden- + +tity matrix. + +I will not discuss how to find eigenvectors and eigenvalues for a particular matrix, but refer the reader to the books on linear algebra listed at the end of the chapter. There are several methods, all of which can be computationally expensive for large matrices. In a later section I will discuss how to construct a certain class of matrices given a set of + +desired eigenvectors. + +The goal now is to show how eigenvectors can be used. To do so, let us begin by assuming that we are dealing with the most favorable case: an n x n matrix W with n distinct eigenvalues }q , A 2•... • An . + +Denote the associated linearly independent eigenvectors by v\I V 2 ••••• VII. Recall that if we have a set of basis vectors for the domain of a matrix, and if we know the vectors in the range associated + +with each basis vector, then the mapping of all other vectors in the domain are determined. The eigenvectors of W form such a basis. This is because there are n eigenvectors, and they are linearly independent. Furthermore, we know the vectors in the range associated with + +each eigenvector Vi; they are simply the scalar multiples given by + +Wv = AV. + +To show how to take advantage of these observations, pick an arbitrary vector v in the domain of W. It can be written as a linear combi- + +nation of the eigenvectors, because the eigenvectors form a basis: + +We can now write: + +u =Wv + +Using linearity, + +If we next substitute for each of the quantities Wv i, using Equation 20: + +U = CIA lv l + C2A 2v 2 + ... + cn AnV n . + +(21) + +Algebraic Properties of the Transpose + +(W T) T= w + +(CW )T = cW T + +(M + N) T= MT +NT + +(MN )T = NTMT + +If a matrix is its own transpose, that i s i f W T = W. then the matrix is + +symmetric. + +Outer Products + +Before discussing outer products, let me attempt to ward off what could be a confusing aspect of the notation we are using. Consider, for example, the entity below. Is it a matrix with one column or is it a + +vector? + +The answer is that it could be either-there is no way of distinguishing one from the other based on the notation. There is nothing wrong with this failure to distinguish between vectors and n x 1 matrices for the following reason. In equations involving vectors and matrices , the same results will be obtained whether entities such as the one above are treated as vectors or as matrices . This is true because the algebra for vectors and matrices is exactly the same, as a review of the relevant earlier sections will show. Thus, as long as we are simply interested in calculating values and manipulating equations, there is no need to distinguish between vectors and n x 1 matrices. Rather, by treating them + +as the same thing, we have a uniform set of procedures for dealing with + +all equations involving vectors and matrices. + +Nevertheless, on the conceptual level , it is important to distinguish between vectors and matrices. The way we are using the terms, a vector is an element in a vector space, whereas a matrix can be used to define a linear mapping from one vector space to another. These are + +With this caveat in mind, we will conti{lue to take advantage of the uniformity of notation, bt.�fii'lWdMft{nOObn between a vector and an + +in the previous section, the i ,j t,h element of W is equal to the product u, vi ' which is the product of the activation of the jth input unit and the ith output unit. Both of these quantities are available in a physically circumscribed area on the link joining these two units. Thus, the weight on that link can be changed by autonomous local processes. The Hebb rule is often referred to as a local learning rule for this reason. To summarize, we have established a procedure for finding a matrix W which will associate any particular pair of input and output vectors. Clearly for every pair of vectors, we can find a different weight matrix to perform the association. What is less obvious is that the same matrix can be used for several pairs of associations. Let us assume that + +we are given n n-dimensional output vectors Ub U 2 , + +. + +.. , Un which + +we want to associate with n n -dimensional input vectors + +vI, V 2 ' . + +. . , V n. In other words, for each i , we wish to have + +Let us further assume that the vectors v, form a mutually orthogonal + +set and that each vector v, is of unit length. That is, we assume + +T11 if i=.i vj Y j = 0 otherwise. + +We now form a set of matrices W, using the learning scheme + +developed above: + +Finally, we form a composite weight matrix W which is the sum of + +the W, : + +W=W 1+ ... +W,+ . . . +Wn• + +We already know that, for example, W \ above will associate V I and U I. It is also true that W will perform all such associations. Thus, for + +arbitrary i : + +Wv , = (W\ + .. . + W, + ... + Wn h, + +=(U \V \T + ... + u ·v .T +. .. + Uv T)y . I I + +nn I + +=(u \v th, + =U\ (vtv, ) + + (u ,ylh, + + u, (ylv, ) + + ++ (u ny!h, + Un (v!v , ) + +The property of orthogonality was crucial here, because it forced the disappearance of all terms involving vectors other than Uj in the next to last step. The reader may find it useful to justify the steps in this + +derivation. + +When the set of input vectors is not orthogonal , the Hebb rule will not correctly associate output vectors with input vectors. However, a modification of the Hebb rule, known as the delta rule, or the Widrow-Hoff rule, can make such associations. The requirement for the delta rule to work is that the input vectors be linearly independent. The delta rule is discussed further in Chapter 11, and at length in Kohonen + +(977) . + +Earlier it was discussed how, at least for square matrices, knowledge of the eigenvectors of a matrix permits an important simplification to be made. The matrix multiplication of a vector can be replaced by scalar multiplication (cf. Equation 21) . I will now show that the Hebbian learning scheme fits nicely with the notion of eigenvectors. Suppose that we wish to associate vectors with scalar copies of themselves. This is what is done, for example, in an auto-associator like those discussed in J. A. Anderson et al . (977) ; see Chapters 2 and 17. In other + +words , we want the vectors U ; to be of the form A; v i where vi are the input vectors. Let us further assume that the n scalars Ai are distinct. + +Using the outer product learning rule, we have + +where + +If we now present the vector vI to the matrix W thus formed, we have + +WV i = (W I + ... + WI + . . . + Wn hi + +=(A IV IV { + . .. + Ajvjvl + ... + A n v n v!h, + +=0 + .. . + Ai v, (V lv j ) + ... + 0 + +This equation shows that vI is an eigenvector of W with eigenvalue Ai ' Let me summarize. When we calculate a weight matrix W using the + +Hebbian learning rule and associate input vectors to scalar multiples of themselves, then those input vectors are the eigenvectors of W. It is + +important to note that the matrix W need not even be calculated-as was stated in the section on eigenvectors, once we have the eigenvectors and eigenvalues of a matrix, we can throw away the matrix. All input-output computatiditPK4§'I"dcMft�rW using Equation 21. This + +approach is in contrast to a scheme in which we first calculate a matrix W from the input vectors, and then calculate the eigenvectors from the matrix W. Here, the eigenvectors are avai lable in the statement of the + +problem. + +Why should one want to associate vectors with scalar copies of themselves? Essentially, the answer is that a system which learns in this way will exhibit the desirable property of completion. That is, when par- + +tial versions of previously learned vectors are presented to the system, it will be able to produce the whole vector. Readers desiring more details on how this is done should consult Anderson et at . (1977) . + +MATRIX INVERSES + +Throughout this chapter, I have discussed the linear vector equation u = Wv . First, I discussed the situation in which v was a known vector + +and W a known matrix. This corresponds to knowing the input to a system and its matrix, and wanting to know the output of the system. Next, I discussed the situation in which vand uwere known vectors, and a matrix W was desired to associate the two vectors . This is the + +learning problem discussed in the previous section. Finally, in this section, I discuss the case in which both u and W are known, but v is + +unknown . There are many situations in which this problem arises, + +including the change of basis discussed in the next section. + +As we will see, the solution to this problem involves the concept of a matrix in verse. Let us first assume that we are dealing with square matrices. The inverse of a matrix W, if it exists, is another matrix + +denoted W- l that obeys the following equations: + +W-l W=I + +WW- l =I + +where I is the identity matrix. + +Example: + +[ 1 'hl W = -1 1 {2 3 + +W- l -- + +2 + +Copyrighted Materi 1 + +3 + +1 3 + +2 3 + +v + +FIGURE 26. + +We now want to show how to find the coordinates of a vector v ir. new basis Y h Y 2 , ... , Y n • These coordinates are simply the coef + +cients Cj in the equation + +(2 + +Let us form a matrix Y whose columns are the new basis vectors : + +and let v· be the vector whose components are the Cj . Then Equati + +23 is equivalent to the following equation: + +v = Yv · (2 + +where v· is the unknown. The solution to the problem is now clear: . use the inverse matrix y-I to calculate the unknown vector as in t + +previous section: + +v· = y- 1v. + +Example. Letting Y I = [\_! I and Y2 = [ I� I, we have Y = [\_! I, + +-2 --1 3 3 + +and y- I = 2 2 + +3 3 + +w\* v· .. U · + +y - t y + +v • U w + +FIGURE 28. + +Luckily, we already know how to make each of these + +transformations- they are given by the equations: + +v = yV · u =WV + +u · = y- IU. + +Putting these three equations together, we have + +u· = y- Iu + += y- I Wv + += y- IWyv· . + +Thus, W· must be equal to y-I WY. Matrices related by an equation of + +the form W· = y-IWY are called similar. + +One aspect of this discussion needs further elaboration. We have been treating matrices as linear operators on a vector space. However, as the results of this section make clear, a matrix is tied to a particular basis. That is, the numbers in the matrix are just as arbitrary as the numbers used for representing vectors. When the basis changes, the numbers change according to the equation W· = y-IWY. The under- + +lying mapping, which remains the same when the matrix W is used in the original basis and the matrix W· is used in the new basis, is called a linear traniformation. The same linear transformation is represented by + +different matrices in different bases . + +It is interesting to recast the results on eigenvectors in terms of a + +change of basis. For sOfflSP.w�mJVMJrerN§ consider changing basis to + +the linear structure of the vectors shows that it is this linear structure that is relevant to the behavior of the model , and not the particular + +basis chosen to describe the vectors. + +NONLINEAR SYSTEMS + +The use of nonlinearity occurs throughout this book and throughout the literature on parallel distributed processing systems (Anderson et aI., 1977; Grossberg, 1978; Hopfield, 1982; Kohonen, 1977) . In this section, I will indicate some of the reasons why nonlinearities are deemed necessary. 8 Although these reasons are based on the desire for behaviors outside the domain of linear models, it should be stated that linear systems have a great deal of power in themselves, and that many of the nonlinearities represent comparatively small changes to underlying models which are linear. Other models are more fundamentally nonlinear. Further discussions of nonlinear mathematics can be found + +in Chapters 10 and 22. + +One simple nonlinearity has already arisen in the discussion of a PDP system with one output unit. Such a system computes the inner product of its weight vector and the input vector. This is a linear system, given the linearity of the inner product. The geometrical properties of the inner product led us to picture the operation of this system as computing the closeness of input vectors to the weight vector in space. + +Suppose we draw a line perpendicular to the weight vector at some point, as in Figure 29. Since all vectors on this line project to the same point on the weight vector, their inner products with the weight vector are equal . Furthermore, all vectors to the left of this line have a smaller inner product, and all vectors to the right have a larger inner product. Let us choose a fixed number as a threshold for the unit by requiring that if the inner product is greater than the threshold, the unit outputs ai , otherwise it outputs a O. Such a unit breaks the space into + +two parts by producing a different response to vectors in the two parts. This use of a threshold is natural in using the unit to classify patterns as belonging to one group or another. The essential point is that the threshold permits the unit to make a decision. Other units in a larger + +8 Since nonlinear systems in general are systems that are defined as "not linear," it is important to understand clearly what "lineat" means. A review of the section on linearity + +\ + +FIGURE 29. + +\ , , \ \ + +\ W + +\ \ + +> \ , \ \ + +system that take their input from this unit could choose completely different behaviors based on the decision. Notice also that the unit is a categorizer: All input vectors that are on the same side of the space + +lead to the same response. + +To introduce a threshold into the mathematical description of the processing unit, it is necessary to distinguish between the activation of the unit and its output. A function relating the two quantities is shown in Figure 30. It produces a one or a zero based on the magnitude of the activation. It is also possible to have a probabilistic threshold. In this case, the farther the activation is above the threshold, the more + +OUTPUT + +o + +ACTIVATION + +likely the unit is to have an output of one, and the farther the activation is below the threshold, the more likely the unit is to have an output of zero. Units such as these are discussed in Chapters 6 and 7. The threshold unit is a good example of many of the nonlinearities that are to be found in PDP models. An underlying linear model is modified with a nonlinear function relating the output of a unit to its activation. Another related example of such a nonlinearity is termed subthreshold summation. It is often observed in biological systems that two stimuli presented separately to the system provoke no response, although when presented simultaneously, a response is obtained. Furthermore, once the system is responding, further stimuli are responded to in a linear fashion. Such a system can be modeled by endowing a linear PDP unit with the nonlinear output function in Figure 31. Note that only if the sum of the activations produced by vectors exceeds T + +will a response be produced. Also, there is a linear range in which the system responds linearly. It is often the case in nonlinear systems that there is such a linear range, and the system can be treated as linear pro- + +vided that the inputs are restricted to this linear range. + +One reason why subthreshold summation is desirable is that it suppresses noise. The system will not respond to small random inputs + +that are assumed to be noise. + +All physical systems have a limited dynamic range. That is, the response of the system cannot exceed a certain maximum response. This fact can be modeled with the output function in Figure 32, which shows a linear range followed by a cutoff. The system will behave linearly until the output reaches M, at which point no further increase can occur. In Figure 33, a nonlinear function is shown which also has a + +OUTPUT + +T + +ACTIVATION + +FIGURE 32. + +FIGURE 33. + +M + +OUTPUT + +ACTIVATION + +M-------- --.. ....... + +OUTPUT + +ACTIVATION + +maximum output M. This curve, called a sigmoid, is a sort of hybrid between Figure 31 and Figure 32. It combines noise suppression with a + +limited dynamic range. Chapter 8 shows how such units are necessary for certain kinds of interesting behavior to arise in layered networks. + +To summarize, I have described some of the ways in which linear systems are modified to produce nonlinear systems that exhibit certain desired behaviors. All of these systems have an important linear component and are sometimes referred to as semilinear. Furthermore, several of the systems have a linear range in which the nonlinearities can be ignored. The next chapter discusses more fundamentally non- + +FURTHER READING + +Halmos, P. R. (1974) . Finite-dimensional vector spaces. New York: Springer-Verlag. For the more mathematically minded. An excellent + +account of linear algebra from an abstract point of view. + +Kohonen, T. (1977) . Associative memory: A system theoretic approach. + +Berlin: Springer-Verlag. This book has a short tutorial on linear algebra. The di scussion of associative memory depends heavily on the + +mathematics of linear algebra. + +Strang, G. ( 1 976) . Linear algebra and its applications. New York: Academic Press . A general textbook treating most of the essentials of linear algebra. It is especially good in its treatment of computational topics. A good place to find out about calculating matrix inverses and + +eigenvalues. + +vary is the same as the range of values over which the output of the unit (its activation) may vary. Another is that time may be ignored as a variable. The activation function of a unit will be taken to be a function that computes the output of the unit (at a fixed but unspecified time) as a function of its inputs (at a presumably slightly earlier but unspecified time). Thus, given a unit with n inputs whose activation values range over the set A, the activation function a for this unit is just a function from A n (the set of ordered n -tuples of elements of A) + +to A, denoted a :An-A. + +In order to avoid cluttering the presentation, detailed proofs of the results have been omitted; in their place are short sketches indicating the key steps. A more rigorous and abstract formulation of the basic concepts introduced here, along with detailed proofs of the results, may + +be found in Williams (1983). + +EXAMPLES OF ACTIVATION RULES + +The following are some examples of activation functions from which + +models have been constructed. + +Example 1. A = (0,11 (the two-point set), a=fog, where g is linear into JR and f: JR-A is a thresholding function. (The operator 0 between two functions here denotes composition in a right-to-left manner.) A unit using this activation function is called a threshold logic unit or a linear threshold unit and is the basis of the simple perceptron + +(Rosenblatt, 1962; Minsky & Papert, 1969). + +Example 2. A = JR, a linear (Kohonen, 1977). + +Example 3. A = I (the closed unit interval [0,1)), a=fog, where gis linear into JR and f is nondecreasiI-., into I. This is a commonly used variant of Example 1. Let liS call this a quasi-linear activation function. The function f is sometinu:!s called a squashing function for obvi- + +ous reasons. + +Example 4. A = I, a= fog. where f is nondecreasing into I and g + +is a multilinear function into JR of the form + +g(X\, ... ,xn) = X\X2+XJX4+ ... +Xn-lxn + +(where n is assumed to be even). Such an activation function is suggested by Hinton(1981 b). Note that this is similar to Example 3 Copyrighted Material + +A + +IX = 0 + +", ... + +"""',' """',' + +., + +B c + +FIGURE 3. a (x\, + +X2) = max(O,xI+x2-l). A: Three-dimensional plot. The cube is + +bounded by the planes where each coordinate is 0 or I. B: Contour plot. C: Some sections along xI' Note that the three-dimensional plot of this function consists of two planar surfaces. Clearly, each section along xI is a nondecreasing function; by symmetry the same is true of each section along x2' Thus this function is uniformly nondecreasing. Copyrighted Material + +A + +a + +�X2 + +X, + +a=l + +�------------'-� + +X 1 + +8 c + +FIGURE 4. a (X!, + +X2 + +) = xl+x2-xlx2 + +' A: Three-dimensional plot. The cube is bounded + +by the planes where each coordinate is 0 or I. B: Contour plot. C: Some sections along xl' Note that each section along xl is a linear function with nonnegative slope; by symmetry the same is true of each section along x2' Thus this function is uniformly non- + +decreasing. + +A + +a + +�X2 + +X, + +Cl + +Cl = .5 + +Cl = 25 + +on + +o + +Cl = + +=.75 + +B + +1 + +� + +c + +FIGURE 5. a(xJ,x2) = max(xJ,x2)' A: Three-dimensional plot. The cube is bounded by the planes where each coordinate is 0 or 1. B: Contour plot. C: Some sections along xI' Note that the three-dimensional plot of this function consists of two planar surfaces. Note also that each section along xI is a nondecreasing function; by symmetry the same + +A + +a- a = 0 + +--,,-, a= 25� + +I + +a = .5 I + +B + +L-----------------�� + +Xt + +c + +FIGURE 7. a (xIoX2) - xl+x2-2xlx2' A: Three-dimensional plot. The cube is bounded by the planes where each coordinate is 0 or I. B: Contour plot. C: Some sections along XI ' Note the saddle shape of the three-dimensional plot of this function. Also note that the sections along XI are linear functions with slopes ranging from 1 to -I; by symmetry the same is true of the sections along Xl' Thus this function is monotonic-in-context but + +not uniformly monotonic. + +A + +k::x + +' + +XI + +o Ot = 0 o + +Ot =----..... + +B + +I .751 I I I + +X, �-----------------L�X, + +c + +FIGURE 8. ex (x1,X2) = Ih(xl+x2)' A: Three-dimensional plot. The cube is bounded by the planes where each coordinate is 0 or 1. B: Contour plot. C: Some sections along x I' Note that the three-dimensional plot of this func�on consists of a single planar surface. Each section along xI is a linear function with'slo\>e 'h, as is each section along x2, by + +symmetry. Thus this function is uniformly nondecreasing. + +A + +(l + +--��� :� + +\,. "i C! = .5 5 + +C! .2 I5 + +(l = 0 I + +8 c + +FIGURE 9. cdx),x2) = (2x'I- t)2(2x'2- t)2. A: Three-dimensional plot. The cube is bounded by the planes where each coordinate is 0 or I. B: Contour plot. C: Some sections along xI' Note that the sections along XI are parabolas of varying widths. Evidently, this function is not monotonic-in-context since, for example, when x2- 0, a first + +decreases and then increases as X I increases. + +The mapping from Boolean expressions to real algebraic expressions + +is defined by replacing: + +1. True by 1. 2. False by O. + +3. The disjunction operator by addition. 4. The conjunction operator by multiplication. S. The negation operator by subtraction from 1. + +6. Xi by Xi, for each i. + +For example, applying this function to the Boolean expression X,X2+ X, yields the real expression XI (I-x 2) + (I-XI). It should be emphasized that this is a function defined only on formal expressions; two expressions that are equivalent under Boolean algebra will not, in general, be mapped to the same real algebraic expression or even equivalent real algebraic expressions. In other words, it is not a map- + +ping from Boolean functions to real functions. + +A standard result from Boolean algebra is that any Boolean function may be expressed in a certain canonical form, called the disjunctive normal form. A simple prescription for this form is as follows: Form a disjunction of terms, each of which is the result of applying the verticesto-Boolean-expressions function described above to those vertices ofln for which the function takes on the value true. For example, the disjunctive normal form for the Boolean function /3(XbX2) = X,+X2 is + +X,X2+ X,X2+ X,X2· + +A closely related result for multilinear functions is the following: + +Lemma. For any function assigning arbitrary real numbers to the vertices of P there is a unique multilinear function agreeing with + +the given function on these vertices. + +This function is formed in a manner generalizing the prescription given above for the disjunctive normal form: For each vertex of I + +n, + +form the corresponding Boolean conjunct; then apply the other function described above to turn each of these conjuncts into a real expression; finally, form the sum of these individual expressions with each one weighted by the value cf the given function at the corresponding vertex. It will be convenient to dub the result the vertex normal form for the given function. For example, the vertex normal form for a multi- + +linear function a of two variables is + +a (X "X2) = a (O,O)(l-x:)(I-x2)+a(O,O(I-x,)x2 + ++a (l,O)x,(1-x2)+a (l,l)x,x2. Copyrighted Material + +This lemma has the following immediate consequence: + +Theorem 1. Given any Boolean function, there is a unique multi- + +linear activation function realizing it. + +In contrast, not every Boolean function can be realized by a quasilinear activation function. Those Boolean functions that can be so realized are called linearly separable. It is easily shown that any linearly separable Boolean function is necessarily uniformly monotonic, but the converse is not true. A simple example of a function that is not linearly separable is the XOR function t31(X\.X2) = X1X2+X1X2. The easiest way to see that it is not linearly separable is to observe that it is not uniformly monotonic. An example of a function that is uniformly + +monotonic but not linearly separable is + +t32(X\.X2,X3,x4) = X1X2+ X3X4· + +Our next result, also a consequence of the lemma, shows that the very general class of all activation functions may be represented up to vertex-equivalence by the narrower class of multilinear activation + +functions. + +Theorem 2. Every activation function is vertex-equivalent to a + +unique multilinear activation function. + +The next result suggests that monotonicity-in-context is enjoyed by a + +fairly wide variety of activation functions. + +Theorem 3. Every sigma-pi activation function is monotonic-in- + +context. + +This is an easy consequence of three facts: (a) that a multilinear function is linear in each variable when the other variables are held constant; (b) that a linear function is monotonic; and (c) that the com- + +position of monotonic functions is monotonic. + +The following result characterizes uniform monotonicity for multi- + +linear activation functions. + +Theorem 4. A multilinear activation function is uniformly monotonic if and only if its restriction to vertices is uniformly monotonic. + +The key step in the proof of this result is the observation that a multilinear function may be built up inductively through linear interpolation, starting with the values at the vertices. This follows from the fact that a multilinear function is linear in each variable when the other variables are held constant. The remainder of the proof consists of verifying that each step of this inductive construction preserves uniform Copyrighted Material + +monotonicity. This result may be extended to the sigma-pi case as well, under certain mild restrictions, using the fact that a strictly + +increasing function has a monotonic inverse. + +Corollary. Let a = fog be a sigma-pi activation function, where g is multilinear and f is a squashing function. If f is strictly increasing, then a is uniformly monotonic if and only if its restriction to ver- + +tices is uniformly monotonic. + +The results presented up to this point would seem to suggest that the class of multilinear activation functions provides us with sufficient power that we need not consider the more general class of sigma-pi activation functions. However, from the standpoint of uniform monotonicity, there may be some drawbacks in restricting ourselves to multilinear activation functions. One such potential drawback is that a uniformly nondecreasing multilinear activation function may have some negative weights. For example, the Boolean function {3 (X 1 ,X 2) = Xl + X 2 corresponds, by Theorem 1, to the multilinear activation function a (Xl,x2) = X\+X2-x\X2, which requires a negative weight even though it is uniformly nondecreasing. But what if a more general sigma-pi activation function were to be used? Is there a sigma-pi realization of this same Boolean function for which all weights are nonnegative? Of course there is in this case: The sigma-pi activation function a (Xl,x2) = min (xl+ x2, n is one such realization; many others could be devised. (These two realizations of the OR function are displayed in Figures 4 and 6.) It seems reasonable to suspect that + +the following is true: + +Cor/iecture. Every uniformly nondecreasing activation function is vertex-equivalent to a sigma-pi activation function with nonnegative + +weights. + +Note that any sigma-pi activation function with nonnegative weights is certainly uniformly nondecreasing. The conjecture is that the converse is true (up to vertex equivalence). Under the assumption that the uniformly nondecreasing activation function is Boolean-like (as in the preceding example), the conjecture is indeed valid, as the following theorem shows. In fact, the conclusion may be made even stronger in + +this case. + +Theorem 5. Every uniformly nondecreasing Boolean-like activation function is vertex-equivalent to a sigma-pi activation function whose + +weights are all 0 or 1. + +The essential step in the proof of this result is showing that any uniformly nondecreasing �t.�a/may be expressed as a + +disjunction of conjunctions containing no negated factors. Once such an expression is available, the desired sigma-pi activation function is obtained by converting this Boolean expression to a real expression and + +then composing this with the function j(z) = min (z ,1). + +This theorem may be generalized to cover arbitrary senses of uniform monotonicity by running any inputs for which the activation function is nonincreasing through the "inverter" j(x) = I-x. Thus the general class of all uniformly monotonic Boolean-like activation functions may be represented up to vertex-equivalence by a narrower class + +of sigma-pi activation functions of a certain form. + +It is instructive to contrast the sigma-pi activation functions which result from applying Theorems I and 5 to a particular uniformly monotonic activation function. Consider the Boolean function of six variables IHXJ,X2,x3,X4,XS,X6) - X1X2+ X�4+ XsX6' Theorem I realizes this using the vertex normal form, which, after simplification, + +becomes + +Q l(Xl,x2,x3,X4,xS,x6) = xlx2+xJX4+XsX6 + +- xlx�JX4 - xlx� sX6 - xJX4XsX6 + ++xlx�JX4XsX6' + +In contrast, Theorem 5 implies a realization of this same function by + +the gating activation function + +Q2(Xl,x2,x3,x4,x5,x6) = min(xlx2+XJX4+XsX6, n. + +CONCLUSION + +As suggested in the introduction, the ideasand results presented here represent an exploratory set of concepts intended to help in understanding PDP networks. There is a clear need for a general language and set of concepts for describing and understanding PDP computation, both at the local, individual unit level, as explored here, and at the level of whole networks. (In fact, the greatest need is for a means of describing and understanding the relationship between computation at these two levels.) Whether the ideas contained in this chapter can extend naturally to become a useful framework for understanding the behavior of whole networks is difficult to foresee. One way that this gap between local and global computation might be bridged is by dealing with questions of learning in such networks. The goal of learning is generally to cause the ne���\$te�Xfa,erra5ticular global behavior, but + +CHAPTER }} + +An Analysis of the Delta Rule + +and the Learning of Statistical Associations + +G. o. STONE + +The development of parallel distributed processing models involves two complementary enterprises: first, the development of complete models with desired operating characteristics� and second, the in-depth analysis of component mechanisms and basic principles. The primary objective in modeling is the development and testing of complete systems. In general these models are complex and their behavior cannot be fully deduced directly from their mathematical description. In such cas�s, simulation plays an important role in understanding the properties of a model. Although simulations are useful in determining the properties of a specific model, they do not, on their own, indicate how a model should be modified when a desired behavior is not achieved. An understanding of basic principles and a collection of potential mechanisms with known properties provide the best guides to the + +development of complex models. + +This chapter provides an analysis of one of the most popular components-namely, the error correction learning rule developed by Widrow and Hoff (1960). This learning rule which has been analyzed and employed by a number of authors (Amari, 1977a, 1977b; Kohonen, 1974, 1977; Sutton & Barto, 1981), has been called the Widrow-Hoff rule by Sutton and Barto (1981) and is generally referred to as the delta rule in this book. This rule is introduced in Chapter 2, discussed extensively and generalized in Chapter 8, and employed in models discussed in a number of chapters-most notably Chapters 17 and 18. In the present chapter I show how concepts from linear algebra Copyrighted Material + +where, as usual, bold letters indicate vectors, uppercase indicates matrices and the superscript T indicates the transpose of a vector or matrix. This learning rule was described in some detail in Chapter 9 and that discussion will not be repeated here. It was shown there that if the input vectors are normalized in length so that ip . ip = 1 and are orthogonal, the product rule will, after the presentation of all of the + +input/ output patterns, lead to the following weight matrix: + +If the input vectors are orthogonal, there will be no interference from storing one vector on others already stored so that the presentation of + +input ip will lead to the desired output tp' that is, + +Wip = tp + +for all patterns p from 1 to P. Unfortunately, we cannot always insure that the input vectors are orthogonal. Generally, the storage of one input/ output pair can interfere with the storage of another and cause crosstalk. For this case a more sophisticated learning rule is required. Fortunately, as we saw in Chapter 8, the delta rule is a rule that will work when the input patterns are not orthogonal. This rule will produce perfect associations so long as the input patterns are merely linearly independent (see Chapter 9) and will find a weight matrix which will produce a "least squares" solution for the weight matrix when an exact solution is not possible (i.e., the input patterns are not linearly + +independent). In matrix notation the rule can be written as + +W (n) = W (n - 1) + 1)8 (n)j T (n ) (1) + +where W (n) is the state of the connection matrix after n presentations, i (n) is the input presented on the nth presentation, 1) is a scalar constant which determines the rate of learning, and 8 (n) is the difference + +between the desired and actual output on trial n , such that + +IS (n ) = t (n ) - W (n - l)i (n ) (2) + +where t (n) is the desired output (or target) for presentation n and W (n - l)i (n ) = 0 (n) is the output actually produced on that presentation. W (0) is assumed to be the matrix with all zero entries. In other words, the weight matrix is updated by adding the outer product of the response error and the input. (See Chapter 9 for discussion of outer product.) Proofs concerning the convergence of this recursion to the optimum weight matrix (in the sense outlined above) are provided by + +The Delta Rule in Pattern-Based Coordinates + +To this point we have discussed the delta rule for what Smolensky (Chapter 22) has called the neural or unit level of representation. Before proceeding, it is useful to consider the form that the rule takes in the conceptual level of representation in which there is one vector component for each concept. In general, the input and output patterns correspond to an arbitrary set of vectors. Interestingly, it is possible to show that the delta rule applies only to the "structure" of the input and output vectors and not to other details of the representation. In a linear system, it is only the pattern of correlations among the patterns + +that matter, not the contents of the specific patterns themselves. + +We can demonstrate this by deriving the same learning rule following a change oj basis from the unit basis to the pattern basis. Since a detailed discussion of the process whereby bases can be changed is given in Chapter 9 and, in more detail, in Chapter 22, I will merely sketch tl1e concept here. Each pattern over a set of units corresponds to a vector. If there are N units, then the vector is of dimension N. In the unit basis, each element of the vector corresponds to the activation value of one of the units. Geometrically, we can think of each unit as specifying a value on a dimension and the entire vector as corresponding to the coordinates of a point in N-dimensional space. Thus, the dimensions of the space correspond directly to the units (this is why it is called the unit basis). Now, a change of basis amounts essentially to a change in coordinate system. This can be accomplished through rotation, as well as other linear transformations. Converting to the pattern basis merely involves transforming the coordinate system so that the patterns line up with the axes. Figure 1 illustrates a simple case of this process. In Figure lA we give the geometric representation of the patterns. Pattern 1, PI, involves two units, each with activation value + 1. Pattern 2, P2, has activation values < + 1 ,- 1 >. The patterns described + +in the unit basis are + +Figure 1 B shows the same two vectors, but now expressed with respect to a new coordinate system, the pattern coordinate system. In this case the axes correspond to the patterns not the units. The vectors + +corresponding to patterns 1 and 2 now become + +\* 1 = [?] and p + +\* 2" [A]· + +A Unit 2 + +-1--------�------- + +-1 + +B -1 + +Pattern 1 <+1,+1> + +Unit 1 + +Pattern 2 < +1,-1 > + ++1 + +< 0,+1 > + +-1 + ++1 + +FIGURE 1. An example of conversion from unit-based coordinates into pattern-based + +coordinates. + +In general, conversion to a new basis requires a matrix P which specifies the relationship between the new and old coordinate systems. For each vector, Pi' we write the new vector p\* i as P\* i = Pp i' If all of the vectors and matrices of the original system are converted into the new basis, we simply have a new way to describe the same system. For present purposes we have !wo tran"formation matrices, one that Cbpyngnred MaTerial + +transforms the input patterns into a coordinate space based on the input patterns, which we denote P /, and one that transforms the target patterns into a coordinate space based on the target patterns, P r. In this case, we have i\*; = P/i; for the input vectors and t\*, = Prt, for the target vectors. Moreover, since the output vectors must be in the same space as the target vectors we have 0\*; = Pro,. We must also transform the weight matrix W to the new basis. Since the weight matrix maps the input space onto the output space, both transformations must be involved in transforming the weight matrix. We can see what this transformation must be by considering the job that the weight matrix must do. Suppose that in the old bases Wi = 0 for some input i and output o. In the new bases we should be able to write W\*i\* = 0 + +\* + +Thus, W\*P/i = Pro and PT"IW\*P/i = 0 = Wi. From this we can readily see that P T" I W\*p / = Wand finally, we can write the appropriate + +transformation matrix for W as + +W\* = PrWP[I. + +We can multiply both sides of Equation 1 by P r on the right and P [I + +on the left. This leads to + +PrWp[ l (n) = PrWp[l(n- 1) + PT1}8(n)ir(n)p/1 + +which, by substitution, can be written as + +W\* (n) = W\* (n - 1) + 1/8\* (n ) [ P [I i \* (n ) r P /1, + +where + +8 \* (n ) = t\* (n ) - W\* (n - 1) i\* (n ). + +(3) + +Finally, by rearranging we have + +(4) + +where the matrix C, given by C = (p/I )Tp[l, is a matrix which holds the correlational information among the original input patterns. To see this, recall that we are changing the input patterns into their pattern basis and the target patterns into their pattern basis. Therefore, the vector i\*j consists of a 1 in the jth cell and zeros eve�ywhere else. Thus, since i· = P/l i\* j' we see that P /1 must be a matrix whose j th column is th� j th original input vector. Therefore, C is a matrix with the inner product of the input vectors i I and i j occupying the ith row and j th column. This inner product is the vector correlation between + +the two patterns. Copyrighted Material + +We have finally constructed a new description which, as we shall see, allows many insights into the operation of the delta rule which are normally obscured by the internal structure of the patterns themselves. Instead, we have isolated the critical interpattern structure in the + +matrix C. + +One advantage of this new description is that the output the system actually produces-even when it does not match any target exactly-can easily be interpreted as the weighted average of the various target patterns. The value in each cell of the output vector is the coefficient determining the amount of that target in the output. In this case the + +sum squared error for input/output pattern p, given by + +Ep = L (t\*j - O"jP' + +measures the error directly in terms of the degree to which each target pattern is present in the output, rather than the degree to which each unit is present. It should be noted, of course, that this new patternbased error function is related to the old unit-based error by the same + +change of basis matrices discussed above. + +It might be observed further that under this description, the perfect associator-which results when the input and output patterns are linearly independent -will be the identity matrix, I, in which the main diagonal has a 1 in each entry and all other entries are O. It should be noted, however, that the preceding analysis of this new description has assumed the input and target output patterns were linearly independent. If they are not, no such pattern basis exists. However, there is an analogous, but somewhat more complex, development for the case in + +which these vectors cannot form a legitimate basis. + +I will now demonstrate some of the useful insights which can be gained through this analysis by comparing the unit and pattern basis descriptions for a sample learning problem. The upper portion of Figure 2 gives the representations of the four input/ output patterns to be learned in the unit basis. These patterns are all linearly independent and were generated under the constraint that each pattern has unit length and that the input patterns have the correlation structure given in the + +matrix shown in the figure. + +Figure 3 shows the states of Wand W\* after one, four, and eight sweeps through the four input/ output patterns. While inspection of the unit-based representations gives no direct information about the degree of learning and crosstalk between targets, this information is explicit in the pattern-based representation. For example, one can discern that the error for the pairs with highly correlated inputs (pairs 1 and 2) is greater at each stage than that for the pairs with slightly correlated input + +.36 .20 49 .44 Xl -.0 1 + +> .28 .09 .55 + +.25 .48 -.48 .56 X3 .18 -.28 .0 4 -.22 + +1 + +.... Yl + +3 + +.... Y3 + +.57 + +-.10 .05 -.66 .12 . 30 .23 -.08 X2 .08 -.45 .47 .50 -.36 + +.50 + +-.1 1 + +-.10 -.08 .40 .03 .27 .36 .27 X4 .0 1 -.56 -.7 1 .6 1 -.54 + +.24 + +1.00 .75 0 0 + +2 + +-.07 -.39 + +.... + +.74 Y2 -.2 1 46 -. 1 9 + +4 + +.47 .17 + +.... + +-.2 1 Y4 .0 1 -.66 -.5 1 + +c== .75 1.00 0 0 + +o 0 1.00 .25 o 0 .25 1.00 + +FIGURE 2. Key-target pairs and the key correlation structure. + +patterns (pairs 3 and 4). Moreover, there is no intrusion of targets associated with orthogonal inputs. In addition, the intrusion of targets from correlated pairs is least for the pair most recently learned, pairs 2 and 4. (The patterns were presented in order 1-2-3-4 on each sweep.) Finally, it is clear from inspection of the pattern-based weight matrix that after eight sweeps the patterns have been almost perfectly learned. The pattern-based formulation also allows a more detailed analysis of the general effect of a learning trial on the error. We can define the + +.. potential error" to pattern j, a J \* as + +Since the vectors i\* j and i\* [ consist of a 1 and the rest zeros, the entire expression i\* [e i\* j reduces to Ckj' the entry in the k th row and + +jth column of matrix e. Thus, Equation 6 becomes simply + +(7) + +In other words, the decrease in error to the jth input/output pair due to a new learning trial is a constant times the error pattern on the new learning trial. The constant is given by the learning rate, Tt, times the correlation of the currently tested input and input from the learning trial. Thus, the degree to which learning affects performance on each test input is proportional to its correlation with the pattern just used in learning. Note that if Tt is small enough, the error to the presented pat- + +tern always decreases. In this case Equation 7 can be rewritten + +8k -en) = 8k -(n - D(1 - 'rjCkk)' + +Recalling that Ckk is given by i[ik, the length of the kth input vector, we can see that the error will always decrease provided 11 - Tt i[ik I < 1. To summarize, this exercise has demonstrated that a mechanism can often be made more conceptually tractable by a judicious transformation. In this case, expressing the possible input and output representations in the appropriate pattern bases clarified the importance, indeed the sufficiency, of the input "structure" (i.e., the pattern of inner products among the input vectors) in determining the role of the input representations in learning. Furthermore, converting the weight matrix into a form from which the errors at any stage of learning can be read directly allowed us to "see" the learning more obviously. The result has been a clearer understanding of the operation of the delta rule for + +learning. + +STATISTICAL LEARNING + +In this section we extend our analysis of the delta rule from the case in which there is a fixed target output pattern for each input pattern to the case in which sets of input patterns are associated with sets of output patterns. We can think of the sets as representing categories of input and outputs. Thus, rather than associate particular input patterns with particular output patterns, we analyze the case in which categories bf input patterns are associated with categories of output patterns. This, for example, might be the case if the system is learning that dogs bark. The representation for dog might differ on each learning trial with respect to size, shagginSi§p�htW8iNtatb;;afepresentation for the bark + +might vary with regard to pitch, timbre, etc. In this case, the system is simultaneously learning the categories of dog and bark at the same time + +it is learning the association between the two concepts. + +In addition, when we have category associations, statistical relationships between the input and output patterns within a category can be picked up. For example, the system could learn that small dogs tend to have high-pitched barks whereas large dogs may tend to have low- + +pitched barks. + +In order to analyze the case of statistical learning, we now treat the input/ output pairs of patterns as random variables. In other words, each time pattern ij is selected as input, its entries can take different values. Similarly, the target output for pair j, Ij will have variable entries. The probability distributions of these random variables may take any form whatsoever, but they are assumed not to change over time. Moreover, we can consider the entire set of input/ output pairs to form a single probability distribution. We then assume that on each trial an input/ output pair is randomly sampled from this overall proba- + +bility distribution. + +We proceed with our analysis of statistical learning by computing the expected or average change in the weight matrix following a presentation. From Equations 1 and 2 we get the following form of the delta + +rule: + +W (n) = W (n - 1) + .,., [t (n ) - W (n - 1) i (n ) ] i T (n ). + +Simplifying and taking the expected value of each side we have + +Note, we may take + +E[W (n - 1)i{n)i T (n)] = E[W (n - 1)]E[i{n)i T (n)] + +since each trial is assumed to be statistically independent of all preceding trials, upon which W (n - 1) depends. Letting R J = E [Ii T] be the pattern of statistical correlations among the input patterns and R JO = E hi T] be the statistical correlations between the input and tar- + +get patterns, we can rewrite Equation 7 as + +E[W (n) ] = E[W(n- 1)](1 - .,.,RJ) + .,.,RJO. + +If we solve the recursion by replacing W (n - I) with an expression in terms of W (n - 2) etc. down to W (0) and assuming that W (0) = 0, the matrix of all 0 entries, we can write the expected value of the weight + +matrix after n trials as + +E(W(n) ] = 7)RJOt(I - 7)R, )i. + +(9) + +i-O + +Fortunately, in the limit, this matrix reduces to a simpler form. To see this, we must introduce the concept of the pseudo-inverse of a matrix. This is a matrix which, unlike the inverse, is certain to exist for all matrices, but which has a number of properties in common with an true inverse. (See Chapter 9 for a discussion of matrix inverses and the conditions under which they exist.) In particular, it is the true inverse, if the true inverse exists. The pseudo-inverse of a matrix B, designated + +B+, is given by + +B+ = 7)BTr, (I - 7)BBT)l i-I + +provided 7) is sufficiently small. (See Rao & Mitra, 1971, and Kohonen, 1977, 1984, for a full discussion of the pseudo-inverse.) In order to convert Equation 9 into a form that includes the expression for the pseudo-inverse, we observe that since the square matrix R, = EUiT] has independent rows and columns, we can select a matrix P such that ppT = R, and P also has linearly independent rows and columns. Since the generalized inverse of P, P+, is also the true inverse of P, it satisfies (P T )-Ip T = I. Thus, taking the limit as + +n-oo of Equation 9 and substituting P, we can write + +00 + +limE(W(n)] = E(Woo] = RJO (pT )-1 (7)pT:E (I - 7)ppT F1. (10) + +n-oo i=\ + +Now, by substituting in for the pseudo-inverse of P and simplifying we + +get + +Since the rows and columns ofR, are linearly independent, R,I = Rt. + +So we finally get + +(12) + +Now we wish to show that, after training, the system will respond appropriately. Without further restrictions, we can demonstrate a minimal appropriateness of the response, namely, we can show that E [W J ] = E [t ]. In other words, we can show that the mean output of the system, after learning, is the mean target. Since the test trials + +and learning trials are statistically independent we can write + +that, given a particular input, the system will produce an output equal to the average of the targets paired with that input. In this sense, sys- + +tematic covariation of input/ output pairs will be learned. + +The Delta Rule and Multiple Linear Regression + +Some readers may have already noticed the similarity of the learning task we have been analyzing to the problem encountered in multiple linear regression. In a linear regression problem the objective is to predict, to the degree possible, one variable, say y, from a set of variables x. In these problems we typically wish to find a set of coeffi- + +cients, b, such that + +(where Xo is taken to be 1) and the sum-squared error + +is minimized. This is precisely the problem that the delta rule seeks to solve. In this case, each element of the target vector for input/ output + +pair (p tp + +) is analogous to a to-be-predicted observation Yj; our predic- + +tion variables x j are analogous to our input vectors ip + +; our regression + +coefficients b correspond to a row of the weight matrix W; and the intercept of the regression line, bo, corresponds to the bias often assumed for our units (cf. Chapter 8). In our typical case the target vectors have many components, so we are simultaneously solving a multiple regression problem for each of the components of the target vectors. Now, the standard result from linear regression, for zero-mean random variables, is that our estimate for the vector b, b is given by + +where X is the matrix whose columns represent the values of the predictors and whose rows represent the individual observations. (Again, we take the first column to be all Is.) Now, note from Equation 12 + +that the delta rule converges to + +This equation is the strict analog of that from linear regression theory. 2 If we assume that each output unit has a bias corresponding to the intercept bo of the regression line, we can see that the delta rule is, in effect, an iterative method of computing the best, in the sense of least + +squares, linear regression coefficients for our problems. + +SUMMARY + +To summarize, this chapter has shown that close examination of the delta rule reveals a number of interesting and useful properties. When fixed patterns are being learned, the rule's operation can be elucidated by converting from a unit-based description to a pattern-based description. In particular, the analysis showed that the correlations between the input patterns, and not the specific patterns used, determined their effect on the learning process. Thus, any alteration of the specific input patterns that does not alter the correlations will have no effect on learning by a linear delta rule. It was also shown that expressing the inputs and outputs in terms of the patterns being learned facilitated analysis of the learning process by allowing one to read directly from the output produced the degree to which each target was present in the + +output generated by a given input pattern. + +When the patterns being learned are variable, it was noted that the final weight matrix could be expressed simply in terms of the intercorrelations among the input patterns, RI, and the correlations between the input and output patterns, RIO' It was also shown that when several reasonable requirements for the distribution of the input/ output random variables are met, the delta rule will learn the pattern of covariation between the inputs and targets. Finally, we showed that the delta rule carries out the equivalent of a multiple linear regression from the input patterns to the targets. Those familiar with linear regression should conclude from this both the power of the rule and its weaknesses. In particular, wherever a linear regression is insufficient to provide a good account of the relationship between input and target patterns, the system will perform poorly. The solution to this problem is to have nonlinear units and intermediate layers of hidden units. Chapter 8 is a detailed discussion of the generalized delta rule and its + +application to these situations. + +2 Actually, there is a slight difference in convention between our development and that typical of linear regression. In our case, the stimulus vectors are the column vectors, whereas in linear regression the predictor variables are the rows of the matrix X. Thus this equation differs by a transposition from Equation 12. This has no consequences for + +the points made here. Copyrighted Material + +The preceding discussion does not, by any means, provide a complete analysis of the delta rule. Rather, it illustrates two important ideas. First, that a basic principle (in this case, the use of patternbased, rather than unit-based representations) can provide valuable insights into the operation of a useful mechanism; and second, that the analysis of component mechanisms which were designed for one use + +can often reveal new applications. + +CHAPTER 12 + +Resource Requlrements of + +Standard and Programmable Nets + +1. L. McCLELLAND + +In several places in this book we have examined the capabilities of various models of parallel distributed processing. We have considered models that are guaranteed to do one thing or another-to learn, say, up to some criterion of optimality or to settle into global states with probabi lities proportional to the goodness of the states. In later chapters, we describe various models of psychological or neurophysiological processes and consider how well they account for the data. The models, then, are held up against various criteria of computational, + +psychological, and sometimes physiological adequacy. + +In this chapter I raise another question about PDP models . I consider the resources they require, in terms of units and connections, to carry out a particular amount of work. This issue is touched on in various other places in the book, particularly Chapter 3. There we showed that a distributed model can often perform even an arbitrary mapping with less hardware than a local model would require to do the same + +task. + +In this chapter I continue this line of thinking and extend it in various ways, drawing on the work of several other researchers, particularly Willshaw (1971, 1981). The analysis is far from exhaustive, but it focuses on several fairly central questions about the resource requirements of PDP networks. In the first part of the chapter, I consider the resource requirements of a simple pattern associator. I review the analysis offered by Willshaw (1981) and extend it in one or two small ways , and I consider how it might be possible to overcome some Copyrighted Material + +FIGURE 1. A pattern associator consisting of a set of input units (across the bottom) and output units (a)ong the right side), with a connection from each input unit to each + +output unit. + +he assumed that the threshold of each output unit is set equal to the number of active input units. Given this assumption, only those output units with switched-on connections from all of the active input + +units will reach threshold. + +Now we can begin to examine the capacity of these networks. In particular, we can ask questions like the following. How many input units (n/) and output units (no) would be needed to allow retrieval of + +the correct mate of each of r different input patterns? + +The answer to such a question depends on the criterion of correct retrieval used. For present purposes, we can adopt the following criterion: All of the correct output units should be turned on, and, on the average, no more than one output unit should be turned on spuriously. Copyrighted Material + +We want to keep this number less than 1. Adopting a slightly more + +stringent criterion to simplify the calculations, we can set + +or + +I + +I n + +lo I mj � Pon + +Rearranging, we get + +For small positive x, logO-x ) = -x. If we restrict ourselves to cases where mj mol nj no < .1-that is, reasonably sparse patterns in the sense that m < nl.JTO-the approximation will hold for the right-hand side of + +the equation, so that taking logs we get + +We can solve this for r, the number of patterns, to obtain + +(1) + +Now, -log 1- [ n + +� I �, I ranges upward from .69 for very sparse patterns + +where mj = 10g2no' Using .69 as a lower bound, we are safe if we say: + +or + +This result tells us that the number of storage elements (that is, connections, nj na) that we need is proportional to the number of associations we wish to store times the number of connections (mj ma) activated in storing each association. This seems about right, intuitively. In fact, this is an upper bound rather greater than the true number of storage elements required for less sparse patterns, as can be seen by plugging values of mj greater than log2na into Equation 1. + +It is interesting to compare Wilishaw nets to various kinds of local representation. One very simple local representation would associate a single, active input unit with one or more active output units. Obviously, such a network would have a capacity of only nj patterns. We can use the connections of a Willshaw net more effectively with a distributed input if the input and output patterns are reasonably sparse. For instance, in a square net with the same number n of input and output units and the same number m of active elements in each, if n = 1000 and m = 10, we find that we can store about 7,000 associations instead of the 1,000 we could store using local representation over + +the input units. + +Another scheme to compare to the Willshaw scheme would be one that encodes each pattern to be learned with a single hidden unit between the input and output layers. Obviously a net that behaved perfectly in performing r associations between mj active input elements and ma active output units could be handcrafted using r hidden units, each having m, input connections and ma output connections. Such a network can be economical once it is wired up exactly right: It only needs r (m;+mo) connections. However, there are two points to note. First, it is not obvious how to provide enough hardware in advance to handle an arbitrary r patterns of m, active input units and mo active output units. The number of such patterns possible is approximately (n, mil m, !)(no mol mo 1) , and if we had to provide a unit in a,dvance for each of these our hardware cost would get out of hand very fast. Second, the economy of the scheme is not due to the use of local representation, but to the use of hidden units. In many cases even more economical representation can be achieved with coarse-coded hid- + +den units (see Chapter 3 and Kanerva, 1984). + +Randomly Connected Nets + +Returning to the standard Wilishaw net, there are several minor difficulties with Willshaw's scheme. First, it assumes that each input unit sends one and only one connection to each output unit. In a neural network, we might aSSCDP¥r\_diMHI�rMllit sends out a randomly + +distributed array of connections to the set of output units without any guarantee that each output unit actually receives a connection. Second, the analysis depends on a rather strict and sharp threshold for output unit activation. In a random net rather than a fully connected net, we could not actually guarantee that a given output unit would in fact receive mj inputs� and in realistic nets, we would expect there to be some inherent variability in the activations of the units. Thus, we would not be able to guarantee that all correct units would exceed the + +sharp threshold, nor that all incorrect units would fall below it. + +However, it turns out that we can reformulate the problem just slightly and get a handle on networks that have these properties. Assume that we have a square network of n input and n output units and that we wish to store associations between m active input units and m active output units. Suppose each input unit has f output connections which fall where they may among the n output units so that the output units have an average of f inputs each. Note again that the connections are randomly distributed without restriction so that there is + +no guarantee that input unit i projects to output unit j. + +To study the performance of this net, imagine storing some number , of patterns using the Willshaw learning scheme. During testing, we will examine the number of active inputs each output unit that should be turned on will receive and the number of active inputs each unit that should not be turned on will receive, and we will then calculate the signal-detection measure of sensitivity d' (Green & Swets, 1966) as an index of the ability of inputs reaching each output unit to distinguish between units that should be on and units that should not be on. Since d' is independent of the threshold, this measure allows us to bypass the + +question of the threshold itself. + +Let us first consider what happens in our random network as we train it with pairs of patterns using Willshaw's scheme. Pick an arbitrary connection in our net between an arbitrary input unit and an arbitrary output unit. Now, consider learning an arbitrary pattern. The probabi lity that a particular input unit will be on is m/ n. Similarly, the probability that a particular output unit will be on is m/ n. The probability that the units joined by the particular connection we are considering will be one of the ones turned on in learning a particular pattern, then, is m2/ n2 just as before. The rest of the earlier analysis still applies, and + +we get + +This is exactly the same value that we had before in the original Willshaw model, and it is independent of f, the number of connections Copyrighted Material + +each unit makes. This factor will become important soon, but it does not affect the probability that a particular connection will be on after + +learning r patterns. + +Now consider what happens during the testing of a particular learned association. We activate the correct m input units and examine the mean number of quanta of activation that each output unit that should be on wi ll receive. The m active input units each have f outputs, so there are mf total "active" connections. A particular one of these connections reaches a particular output unit with probability lin, since each connection is assumed to fall at random among the n output units. Thus, the average number of active connections each output unit receives will simply be mf In. For output units that should be on, each of these connections will have been turned on during learning, so mfln is the average number of quanta that unit will receive. Assuming that n is reasonably large, the distribution of this quantity is + +approximately Poisson, so its variance is also given by mfl n. + +Units that should not be on also receive an arbitrary connection from an active input unit with probability lin, but each such connection is only on with probability Pon' Thus , the average number of quanta such units receive is (mf In )Pon' This quantity is also approximately Pois- + +son, so its variance is also equal to its mean. + +Our measure of sensitivity, d', is the difference between these means divided by the square root of the average of the variances. That is, + +d' =mf I n (I - Pon ) + +J(mfln)(l + Pon)/2 + +Simplifying, this becomes + +, ..Jm1Tii 1 - Pon d= mfln JO + Pon )/ 2 + +We can get bounds on the true value of d' by noting that the denominator above cannot be greater than 1 or less than .Jiii . The largest value of the denominator sets a lower bound on d', so we find that + +d' � .Jmf/n (t - Pon)' + +Substituting for 1 - Pon, we obtain + +d' � .J mf / n[ 1 - :: r. (3) + +the units that should be on and false alarm to less than 1 % of the units + +that should be off. 1 + +How big would a net have to be to meet these specifications? Assuming a fully connected net, and consulting Equation 4, we find that we need to set n equal to a value near about 106 to get r large + +enough. + +This number of units is not a serious problem since estimates of the number of units in the brain generally range upward from 1010 (see Chapter 20). However, individual units are not general ly assumed to have enough connections for this scheme to work as stated. If there are 1,000 to 10,000 connections per unit, as suggested in Chapter 20, we are off by two to three orders of magnitude in the number of con- + +nections per unit. + +Given this limitation on fan-out, we had better consult Figure 2. The figure indicates that the maximum capacity of a net with a fan-out of 1,000 and a d' of 5 is only about 150 patterns. With / - 10,000 we get up to a capacity of about 15,000 patterns, but we are still well short of the mark. It seems, then, that the fan-out of neurons drastically + +limits the capacity of a distributed network. + +A simple method for overcoming the fan-out limitation. But all is not completely lost. It turns out that it is a relatively simple matter to overcome the fan-out limitation. The trick is simply to use multiple layers of units. Let each input unit activate a set of what we might call dispersion units, and let each output unit receive input from a set of collection units. Let the / outgoing connections of each of the dispersion units be randomly distributed among the "dendrites" of the collection units. A miniature version of this scheme is illustrated in Figure 3. Note that it is assumed that each dispersion unit is driven by a sin gle input unit, and each collection unit projects to a Single output unit. Collection units are assumed to be perfectly linear so that the net input to each output unit is just the sum of the net inputs to the collector units that project to it. Assuming each input unit and each dispersion unit has a fan-out of /, the effective fan-out of the input and disper- + +sion layers together becomes /2 + +. Simi larly, the set of collection units + +feeding into each output unit col lect an average of /2 connections. To construct an associator of 1 million input units by 1 million output units assuming each unit has a fanout of 1,000, we will need 1 billion dispersion units and 1 billion collection units. The number of connections between the dispersion units and the collection units would be on + +the order of 1012, or 1 trillion connections. + +I It should be pointed out that any intrinsic noise in the units would reduce the actual + +FIGURE 3. A diagram of a multilayer network consisting of an input layer, a dispersion layer, a collection layer, and an output layer. The network serves to square the effective + +fan-out of each input unit, relative to the simple two-layer case. + +The network would require about 20% of human cortex, based on the estimate that there are lOs neurons under each square millimeter of the brain and that there are about lOS square millimeters of cortical surface. This might be a little tight, but if the fan-out were 10,000, the network would fit handily. In that case, it would only require about 2 + +percent of the 1010 units. + +There are, of course, a lot of reasons to doubt that these figures represent anything more than a first-order estimate of the capacity of real associative networks. There are several oversimplifications, including for example the assumption that the dispersion units are each driven by a single connection. We must also note that we have assumed a two-layer net along with an extremely simple learning rule. The intermediate layers postulated here merely serve to provide a way of overcoming the fan-out limits of individual units. However, as was pointed out in Chapters 7 and 8, a multilayer net can often learn to construct its own coding schemes that are much more efficient than the random coding schemes used here. Even simple two-layer nets can + +profit if there are somedcf���}bed M1t + +�?ra + +fetwork and if they use a + +sensible learning rule, as shown in Chapter 18. Thus random nets like the ones that have been analyzed in this section probably represent a lower limit on efficiency that we can use as a benchmark against which + +to measure "smarter" PDP mechanisms. + +Effects of Degradation and the Benefits of Redundancy + +One virtue of distributed models is their ability to handle degradation, either of the input pattern or of the network itself. The d' analysis allows us to tell a very simple story about the effects of degradation. In this section I will just consider the effects of degradation by removal, either of a random fraction of the pattern or of a random fraction of the connections in the network; effects of added noise will be considered later on. In the case of removal, we can think of it either in terms of presenting an incomplete pattern or actually destroying some of the input units so that parts of the pattern are simply no longer represented. Consider the case of a network that has already been trained with some number of patterns so that Pan can be treated as a constant. Then we can write the equation relating d' to m, f, and n as + +d' � k.Jmf!n. + +Now, suppose that during testing we turn on only some proportion PI of the m units representing a pattern. The m in the above equation becomes mpI, so we see that the sensitivity of the network as indexed by d' falls off as the square root of the fraction of the probe that is presented. Similarly. suppose some of the connections leading out of each unit are destroyed. leaving a random intact proportion Pi of the mf active connections. Again. the sensitivity of the network will be proportional to the square root of the number of remaining connections. Thus, performance degrades gracefully under both kinds of + +damage. + +Another frequently noted virtue of distributed memories is the redundancy they tend naturally to provide. The ability of simple distributed memories to cope with degraded input patterns is really just a matter of their redundancy, as Willshaw (1981) pointed out. For. if a network is fully loaded, in the sense that it can hold no more associations and still meet some predetermined standard of accuracy with complete patterns, it will not be able to meet that same criterion with degradation. The only way to guard against this problem is to load the network lightly enough so that the criterion can still be met after subjecting the network or the inputs to the specified degree of degradation. Copyrighted Material + +PROGRAMMABLE PATTERN ASSOCIATORS + +In this section, I extend the sort of analysis we have performed on simple associator models to the resource requirements of connection information distribution (CID) networks of the type discussed in + +Chapter 16. + +The mechanism shown in Figure 4 is a distributed CID mechanism. The purpose of this network is to allow connection information stored in a central associative network to be used to set connections in several local or programmable networks in the course of processing so that more + +Central Input Units + +Central Output Units� + +'- + +Local Input Units + +CA Units + +o + +FIGURE 4. A connection information distribution (CID) network consisting of two local, programmable networks; a central, standard network; and a set of connection activation (CA) units. Each local input unit projects to the corresponding central input unit, and each CA unit projects to the corresponding connection in both local networks. Central output units turn on CA units relevan tto processing the patterns they program the local modules to process. �MlWe'ri8# are a few examples of each type. + +than one input pattern can be processed at one time. The mechanism works as follows: One or more patterns to be processed are presented as inputs, with each pattern going to the input units in a different programmable network. The input pattern to each local net is also transmitted to the input units of the central associative network. When more than one pattern is presented at a time, the input to the central network is just the pattern that results from superimposing all of the input patterns. This pattern, via the connections in the central associative network, causes a pattern of activation over the central output units. The central output pattern, of course, is a composite representation of all of the input patterns. It is not itself the desired output of the system, but is the pattern that serves as the basis for programming (or turning on connections) in the local, programmable networks. The local networks are programmed via a set of units cal led the connection activation (CA) units. The CA units act essentially as switches that turn on connections in the programmable networks. In the version of the model we will start with, each CA unit projects to the one specific connection it corresponds to in each programmable network, so there are as many CA units as there are connections in a single programmable net. In the figure, the CA units are laid out so that the location of each one corresponds to the location of the connection it commands in + +each of the programmable networks. + +To program the local networks, then, central output units activate the CA units corresponding to the connections needed to process the patterns represented on the central output units. The CA units turn on the corresponding connections. This does not mean that the CA units actually cause activation to pass to the local output units. Rather, they simply enable connections in the programmable nets. Each active local input unit sends a quantum of activation to a given local output unit if + +the connection between them is turned on. + +The question we will be concerned with first is the number of CA units required to make the mechanism work properly. In a later section, we wilI consider the effect of processing multiple items simultane- + +ously on the resource requirements of the central network. + +Connection Activation Unit Requirements + +Consider a CID mechanism containing programmable networks of n; by no units in which we wish to be able to associate each of s different output patterns with each of s different input patterns arising at the same time in different local networks. Input and output patterns consist of rn; by rno active units, respectively. Fol lowing the assumptions Copyrighted Material + +for Willshaw nets, we assume binary units and connections, and we assume that output units are turned on only if they receive m quanta of + +activation. + +Now, let us consider how many CA units are needed to implement this mechanism. For now we bypass the bottom-up activation of CA units and assume instead that we know in advance which connections need to be turned on. If each local network must be as complex as a standard network capable of processing r different patterns, we are in serious trouble. In the previous analysis of Willshaw networks, we found that the number of connections we needed to process r associa- + +tions of m by m active units was + +It looks as though the number of connections required in each local network grows linearly with the number of known patterns times the content of each. If we had one CA unit for each programmable connection, a programmable version of our square I-million-pattern associator would require 1012CA units, a figure which is one or two orders of magnitude larger than conventional estimates of the number of units in the brain. Just putting the matter in terms of the cost we must bear to use programmable connections, it appears that we need n 2 CA units just to specify the connections needed for a standard net that could do the same work with just the connections between n input and n output + +units. 2 + +However, things are not nearly as bad as this argument suggests. The computation I just gave misses the very important fact that it is generally not necessary to pinpoint only those connections that are relevant to a particular association. We can do very well if we allow each CA unit to activate a whole cohort of connections, as long as (a) we activate all the connections that we need to process any particular pattern of interest, and (b) we do not activate so many that we give rise + +to an inordinate number of spurious activations of output units. + +The idea of using one CA unit for a whole cohort of programmable connections is a kind of coarse coding. In this case, we will see that we can reap a considerable benefit from coarse coding, compared to using one CA unit per connection. A simple illustration of the idea is shown in Figure 5. The figure illustrates CA units projecting to a single one + +2 Many readers will observe that the CA units are not st rictly necessary. However, the specificity of their connections to connections in local networks is an issue whether CA units are used as intermediaries or not. Thus, even if the CA un its were eliminated, it would not change the relevance of the following results. In a later section, the CA units and central output units will be collapsed into one set of units; in that case, this analysis + +will apply directly to the numI>edJfYllf}hlWl¥'lf.Mt�pe required. + +o o o o + +o + +o + +FIGURE 5. A programmable network with 8 input units and 8 output units and 64 programmable connections. Each of the 16 connection activation units is assumed to project to a random set of 4 programmable connections. These connections are only drawn in for two of the CA units. The sets of connections are chosen without replacement so that each connection is programmed by one and only one CA unit. Whenever a CA unit is + +on it turns on all of the connections it projects to. + +of two programmable networks. Note that a given CA unit must activate the same connections in each programmable net when there is + +more than one. + +One Pattern at a Time + +To see how much this scheme can buy us, I will start by considering the case in which we want to program some local nets to process a single pattern. We ask, how small a number nCQ of CA units can we ge� Copyrighted Material + +by with, assuming that each one activates a distinct, randomly selected + +set of ni nol nco connections? + +First of all, the number of CA units that must be activated may have to be as large as mi mo, in case each of the different connections required to process the pattern is a member of a distinct cohort. Second, for comparability to our analysis of the standard network, we want the total fraction of connections turned on to allow no more than an average of 1 output unit to be spuriously activated. As before, this + +constraint is represented by + +[ 1 I �i Pon �;; • + +As long as mi � log2n;, .5 will be less than the right-hand side of the expression, so we will be safe if we keep Pon less than or equal to .5. Since we may have to activate mimo CA units to activate all the right connections and since we do not want to activate more than half of the + +connections in all, we conclude that + +From this result we discover that the number of CA units required does not depend at all on the number of connections in each programmable network. Nor in fact does it depend on the number of different known patterns. The number of known patterns does of course influence the complexity of the central network, but it does not affect the number of CA units. The number of CA units depends on mimo, the number of connections that need to be turned on per pattern. Obviously, this places a premium on the sparseness of the patterns. Regard- + +less of this , we are much better off than before. + +Several Patterns at a Time + +So far we have considered the case in which only one item is presented for processing at a time. However, the whole point of the connection information distribution scheme is that it permits simultaneous processing of several different patterns. There is, however, a cost associated with simultaneous processing, since for each pattern we need to turn on all the connections needed to process it. In this situation, we will need to increase the total number of CA units to increase the specificity of the set of connections each association requires if we are to keep the total fractiWSP9f;g1W�a�hat have been turned on + +below .5. Formally, assume that we know which s patterns we want to process. Each one will need to turn on its own set -of mimo CA units out of the total number nca of CA units. The proportion of connec- + +tions turned on will then be + +Im,mo ]S p, on =1- 1- --nca + +This formula is, of course, the same as the one we saw before for the number of connections activated in the standard net with s, the number of different patterns to be processed simultaneously, replacing r, the number of patterns stored in the memory, and with nca, the number of connection activation units, replacing nino, the total number of connections. Using Pon = .5 and taking the log of both sides we get + +-.69 = slog 1 1\_ m�:o ]. + +Invoking the 10g (1- x) = -x approximation, we obtain + +nca � 1.45sm 2. + +This formula underestimates nca slightly for s < 3. With this caveat, the number of CA units required is roughly proportional to the number of patterns to be processed at one time, times the number of connec- + +tions needed to process each pattern. + +Overlapping the Programmable Networks + +In Chapter 16, the CID scheme we have been considering thus far was generalized to the case where the programmable networks overlapped with each other. This allowed strings of letters starting in any of a large number of input locations to correctly activate units for the corresponding word at the appropriate location at the next higher level. Here I will consider a more general overlapping scheme using distributed representations in the overlapping local networks. A set of three overlapping local networks is illustrated in Figure 6. In this scheme, both the input and the output units can play different roles depending on the alignment of the input pattern with the input units. In consequence, some of the connections also play more than one role. These connections are assumed to be programmable by a number of different CA units, one for each of the connection's different roles. Obviously, this will tend to increase the probability that a connection will be turned Copyrighted Material + +[J .J J Y .J Y .J .J + +� y y y y y .J Y () + +LY y y y y .J .J Y lY � pr P' y � � � + +y 15 � � � � .J � LY y ,;J .J Y 15 ;Y L.Y J ,;J y ,Y .J J J .J Y � Y lY y y y ;J y y y y 5 Y Y Y Y Y J Y Y J J Y + +Y;J ;J ;J � y y y J Y Y Y {) + +Y J J Y Y J Y Y Y Y Y J + +,Y rY )' ,Y lY lY L.Y � ,;J ,;J � ,;J {) + +y L.Y Y ;J LY [Y Y Y J Y LY Y + +Y Y LY y lY lY y lY () Y Y -0 LY y lY lY y l5 + +y Y l5 J � ;J l5 � y15 Y y y ;J y y + +0 0000000 00 0 + +FIGURE 6. Three overlapping programmable networks of 8 x 8 units each. The networks overlap every four units, so the input and output units can participate in two dif- + +ferent, partially overlapping networks. + +on, and therefore will require a further revision of our estimate of the + +number of CA units required. + +Unfortunately, an exact mathematical analysis is a bit tricky due to the fact that different junctions have different numbers of opportunities to be turned on. In addition, input patterns in adjacent locations will tend to cross-activate each other's output units. If the patterns to be processed are wel l separated, this will not be a problem. Restricting our attention to the well-separated case, we can get an upper bound on the cost in CA units of allowing overlapping modules by considering the case where all of the connections are assumed to play the maximum number of roles. This number is equivalent to the step size or grain, + +example, for four-letter words, if the increments in starting places of successive overlapping networks were one letter wide, g would be 4. Assuming that the connections turned on for each slice of a pattern are independent of those turned on by each other slice, it is easy to show + +that the formula for Pan becomes + +Pan � 1 - 1 \_\_ , \_0 , [ m· mI + +Sg + +nco + +and the number of CA units required to keep Po" less than .5 is approx- + +imated by + +The cost goes up with the number of patterns to be processed simul- + +taneously times the grain of the overlap. + +Summary of CA Unit Requirements + +In summary , the number of CA units required to program a programmable network depends on different variables than the number of connections required in a standard associator. We can unify the two analyses by noting that both depend on the number of patterns the net must be ready to process at any given time. For the standard associator, the number is r, the number of known patterns; for the programmable net, the number is sg , the number of patterns the net is programmed for times the grain of overlap allowed in the starting locations + +of input patterns. + +This analysis greatly increases the plausibility of the CID scheme. For we find that the "initial investment" in CA units needed to program a set of networks to process a single association is related to the content of the association or the number of connections required to allow each of the active input elements to send a quantum of activation to each of the active output elements. Incorporating a provision for overlapping networks, we find that the investment required for processing one association is related to the content of the association times the grain of the overlap. This cost is far more reasonable than it looked like it might be at first, and, most importantly, it does not depend on + +the number of patterns known. + +An additional important result is that the cost of programming a set of networks grows with the number of patterns we wish to program for at one time. This cost seems commensurate with the linear speedup we + +would get by being abtc + +o b�dh + +��CJM + +�lJ + +��,1 patterns simultaneously. + +The somewhat intangible benefit to be derived from mutual constraint among the patterns would come over and above the simple linear throughput effect. However, this benefit, as we shall see in the next section, is balanced by the extra cost associated with the possibility that there might be spurious patterns in the intersection of input elements + +of the presented patterns. + +The Cost of Simultaneous Access + +So far, we have proceeded as though we already knew what patterns to prepare each local module for. However, the CID mechanism was intended to allow several inputs to access the central network simultaneously and thereby program the local networks in the course of processing. This simultaneous access costs something; in this section we consider how much. The discussion here is relevant to the general issue of the C:lsts of simultaneous access to a PDP network, as well as to the + +specific question of the capacity requirements of CID. + +For simplicity I will begin by considering local representations at the central output level. That is, I will assume that each central output unit represents a different pattern and that it is switched on only when all of + +the central input units corresponding to its pattern are active. + +Now, recall that a central input unit is switched on if the corresponding unit is active in any of the programmable nets. Thus, what the central output units actually see is the pattern of activation that results from the superimposition of the input patterns presented for simultaneous processing. The effect of this is that there is some possibility that ghosts of patterns not actually presented wil l show up in the result. This is just the kind of situation that is described in Chapter 16 when similar words such as SAND and LANE are presented to each of two programmable networks for simultaneous processing. When the activation patterns of the two words are superimposed, the central word units for LAND and SANE get turned on just as strongly as the central word units for SAND and LANE. Thus, the programmable networks end up being programmed to process any one of these four words, rather than + +just any one of the two actually presented. + +Is there anything that can be done to control the number of different patterns that show up when several patterns are superimposed? In fact, there/is. If we increase the number of input units in each programmable network or if we reduce the number of input units active in each pattern, we will reduce the possibility of spurious patterns showing up + +in the superposition. + +To get a quantitative grip on this matter, assume that the input patterns are random selections of m out of the n input units as we have been assuming throughout. The probability that a spurious pattern is present in the superposition of s patterns can now be easily calculated. First, we calculate the probability that a randomly selected unit will be + +on; this is just + +The probability that a particular spurious pattern is fully represented in the set of units activated by the s patterns is just this number to the power m, and the average number of such patterns out of r known patterns is just this probability times r - s. Thus, the average number of + +spurious patterns present in the superposition is + +Assuming r » s, we can simplify by replacing r - s with r. If we take acceptable performance to be an average of one or fewer spurious patterns present and therefore of spurious CP units active, we get + +Rearranging and taking logs , + +log [ 1- (! )! 1= slog(1 - mi n). + +Several things are apparent from this equation. First, the number of patterns that can be processed at one time increases with the number of input units. The effect is approximately linear as long as m/ n � .1. Second, though i t i s not quite as straightforward, s tends to increase with a decrease in m. For example, suppose n = 5,000 and r = 10,000. In this case, when m drops from 1,000 to 500, s increases from 21 to about 37; if m drops to 100, s goes up to about 120. Third, for a fixed m and n, especially for large m, we can make very large changes in r with only minimal impact on s. Thus, if we have, say, + +n = 10,000 and m = 1,000 with r = 106 + +, we get s = 43; if we reduce r + +to lOS, we only get an increase of 2 in s, to 45. + +If we allow overlapping local networks , and we assume that the patterns are random with independent subparts, we need only replace s in the preceeding equation with sg . While this is a fairly steep cost, it is still the case that reasonably moderate values of n (about 2. 5xlOS + +) + +would be sufficient to process 10 out of 106 known patterns of size + +Simultaneous Access to Distributed Representations + +The results just described, it must be remembered, depend on the use of local representations at the central output level . What happens if we consider simultaneously accessing distributed representations instead? Obviously this question remains relevant to general questions about simultaneous access, as well as to the situation that would arise using distributed central output units in CID. Furthermore, we should note that the central output units in Figure 4 simply mediate a mapping from one distributed representation-on the central input units-to another-on the CA units. The present analysis describes what would happen if we simply collapsed these two sets of units into one, activat- + +ing the connections directly from the central output units. + +We consider a case exactly like the one we were just considering, except that now the output representation is not a single unit per pattern, but mo active units on out of no central output units. We consider two somewhat separate questions. First, if we superimpose + +several input patterns, what effect does this have on d ' + +at the central + +output level , relative to the case where only a single pattern is shown ? Second, what is the probability that ghosts of whole patterns not + +presented will show up in the output of the central network ? + +To begin our analysis of the first question, recall from Equation 2 the + +expression for d' in random nets with full fan-out (n = j): + +d'= .rm; 1 - Pon + +I .J ( 1 + Pon )/ 2 . + +We first ask, what is the effect on d' of turning on spurious input units with probabi lity p , in addition to the m units representing a particular pattern to be processed? The number M; of input units that wi ll then + +be on is + +M; == mj + (nj - mj )p. + +Consider first, output units that should not be on. These will receive M; active inputs, and each of these connections will be on with probability Pon . The output units that should be on will receive mj inputs on the input lines whose connections were turned on in learning the presented pattern plus (nj - mj )p inputs to connections that will have been turned on in learning other patterns with probabi lity Pon ' The numerator for our revised expression wi ll then simply reduce to its old value, with the (n; - mj )p term canceling out. However, there will be + +an increase in variance, and hence a decrease in d ' + +. The denominator + +means, which are, also as before, equal to the means. The expression + +for d' therefore becomes + +d' = m + +( 1 - Pan ) J (m; + m;pon + 2(n; - m;)p 1/ 2 + +We get a simpler expression if we approximate by replacing Pan in the denominator with its maximum value of 1; this gives us a slight overestimate of the variance and therefore a slight underestimate of d': + +> d' � ( 1- Pan ) ? m.j m; +( n; - m; )p . + +The variance goes up with the mean number of spuriously activated units, and d' goes down with the effect of this on the square root of the + +variance. + +To determine the effect of presenting several patterns on d', we note that from the point of view of the units that belong to one of the patterns, all the units activated by the other patterns are spurious. The + +number of such units is + +1 - ( 1 - m;/ ny - I + +Inserting this for p in the previous equation gives + +d' = m + +( 1 - Pan ) .Jm; + (n; - m; )[I - ( 1- m;/ ny- I] + +Using this equation we can examine the effects of increasing s on the value of d'. Not too surprisingly, d' does go down as s goes up, but + +the effect is relatively benign. For example, with n = 106 + +, r = 106 + +, + +m = 1,000, and s = 1, d' is about 11.6. It drops to half that value at s= 4, and drops much more gradually thereafter. With n = 2 x 106 units and the same values of r and m, we can get an acceptable value + +of d' (� 6) with s as high as 16. + +The final issue we will consider is the possibility that new spurious output patterns have been introduced in the superposition of the s output patterns simultaneously activated in processing the s mput patterns. For simplicity, we will just consider the probability of a "ghost," given that all and only the correct ma units are active for each of the s patterns. The analysis is entirely the same as the one we gave before for the probabi lity of ghosts showing up in the input patterns. We get an + +average of one ghost when + +1� r [ 1 - (1 - m/ n ) S 1m • + +As before, the number of simultaneous patterns we can tolerate increases with n and decreases with m and is relatively insensitive to + +the value of r. + +In general , it appears that the probabi lity of ghosts occurring can be kept small with sufficiently large dedication of resources, but these trade off approximately linearly with s. With fixed n, we must simply + +make the patterns sparser or tolerate some loss of sensitivity. + +Discussion + +This analysis of the resource requirements of networks like the eIn model has discovered a number of basic results. In essence, the picture is really a very simple one. The resource requirements of eIn depend on the number of programmable networks one wants to program for at once. The number of connections needed in each local network depends on the number of patterns to be programmed for and is independent of r. the number of known patterns. In the central network, the number of units required to keep spurious activations under control grows with s, as does the number of units required to keep ghosts from emerging in the input and output patterns. It is worth noting, also, that the probabi lity of ghosts increases as we increase m. The fact that the resource requirements of the local networks are independent of the number of patterns known is obviously important. Relative to the central network, it means that the local networks are very cheap. The number of distinct inputs that are needed to program them is quite reasonable, and, as I will explain, we can even get by with far fewer units in the local networks than we need at the central level . On the other hand, the results concerning the costs of simultaneous access to the central network are much less encouraging for the eIn scheme. Using local or distributed representations in the central module, the unit requirements grow with the product of s and r-a very expensive proposition since the number of central connections will + +then grow as sr2. + +However, there are several important further observations. One is that, at fixed numbers of units and patterns known, the degradation of sensitivity as a function of s is rather gradual . And, given a lightly loaded network, one can take s up to reasonable values without catastrophe. Simultaneous access by multiple patterns is very much like degradation: a network can handle it without a noticeable decrement of function if it is lightly loaded. A second observation concerns the limits of coarse coding. Fot[�l1teYw!5le9jaF of m essentially amounts + +to a question of how coarse the code is: Large m corresponds to very coarse coding, and small m corresponds to very fine coding. As we saw in Chapter 3, the ability to represent several patterns at a time goes down as the coding gets coarser. For simultaneous processing we need sparse patterns, with each unit serving as a rather sharply tuned con- + +junctive detector. + +The final observation is that large costs are associated with simultaneous access to the central network. This fact has lead me to the view that it is probably most reasonable to imagine that we must probably restrict simultaneous access, except perhaps in the case of small, compact and well-differentiated subpatterns like letters. I incorporated this idea of restricted access in the programmable blackboard model of reading by assuming that we program successive parts of the programmable blackboard sequentially, using only the contents of the spotlight of attention to access the central network; but that the local networks so programmed continue to process and hold patterns of activation and to allow those patterns to interact with one and other after the spotlight of attention has moved on. In this way we get the best of both worlds: sequential access to central knowledge, combined with interactive parallel processing of several stimuli in the programmable nets. Another point is that it may be a good idea to dissociate the inputs to the local networks and the inputs to the central networks . Throughout this chapter and Chapter 16, I have assumed that the units in each local network would be isomorphic to units in the central network. However, there is no reason for them to be. The central network needs much higher "resolution " (n proportional to r) than the local networks (n proportional to s ) . Thus, the units in the programmable modules need only provide a few primitive clues to which of the s patterns are to be represented in their outputs , while the units in the central network + +would require a much higher-resolution representation. + +CONCLUSION + +This chapter has indicated how Willshaw's fruitful analysis of simple pattern associator models can be extended in several directions. These extensions have lead to several interesting observations , particularly into the effects of limited connectivity (Mitchison, personal communication, 1984) and into the capacity requirements of programmable networks. A large number of issues remain to be explored. I hope that this discussion and elaboration of Willshaw's analysis will aid in this + +ACKNOWLEDGMENTS + +This work was supported by Contract N-0001 4-82-C-0374 , NR 667- 483 with the Personnel and Training Research Programs of the Office of Naval Research, by a grant from the System Development Foundation to the Institute for Cognitive Science at UCSD, and by an NIMH Research Scientist Career Development Award (MH-00385) . This chapter was developed in response to a number of questions raised by Geoff Hinton and Scott Fahlman about the resource requirements of programmable nets. I thank Dave Rumelhart for several useful discussions and for encouraging me to pursue the issues descri bed herein. The material descri bed in the section entitled "Randomly Connected Nets" was developed in col laboration with Dave, and the application of the d' analysis to the problem of simultaneous access to a distributed + +memory network was Dave's suggestion. + +CHAPTER 13 + +P3: A Parallel Network Simulating System + +D. ZIPSER and D. RABIN + +Research on parallel distributed processing is to a large extent dependent upon the use of computer simulation, and a good deal of the researcher's time is spent writing programs for this purpose. Virtually all the PDP systems described in this book require special-purpose computer programs to emulate the networks under study, In writing programs of this type, it is usually found that the basic algorithms of the PDP network are easy to program but that these rather simple "core" programs are of little value unless they are embedded in a system that lets the researcher observe and interact with their functions. These user interface programs are generally tedious and very time consuming to write. What is more, when they are directed toward one particular system they can be quite inflexible, making it difficult to easily modify the PDP network being studied. Also, because of the time involved, particularly for interactive graphics programs, the researcher often makes do with very limited facilities for analyzing the performance of the network. In this chapter we will describe a general-purpose parallel system simulator called P3. It was developed with PDP research explicitly in mind and its major goal is to facilitate simulation by providing both the tools for network description and a powerful user interface that can be used with any network described using the tools. There are many problems to be faced and tradeoffs to be made in designing such a system but in the process of doing this we feel that not only has a useful system been developed, but also that we have learned a great + +In P3 networks, each computing element, called a unit, contains a computer program that reads inputs from connections and sets outputs on other connections, possibly also modifying some local state parame- + +ters. The major components of P3 are: + +• The plan language, which describes the collection of units in a model and specifies the connections between them. This + +description is called a "plan." + +• The method language, an extension to LISP, which implements the internal computational behaviors of the units in a model. + +• The constructor, which transforms the plan and associated methods into a computer program and, when run, simulates the + +network. + +• The simulation environment, which provides an interactive display-oriented facility for observing and testing P3 models. + +Input to units described in a P3 plan can come only from other units in the plan. That is, there is no "outside world" in a P3 plan language description of a network. This means that at the level of description of the P3 plan language, the P3 network is closed. Access to the outside world must occur inside a unit through its method. Methods may access the world outside the P3 system through any available computer peripheral. The only thing that methods are not allowed to do is to reconfigure with the P3 system itself or communicate with other methods through "underground connections" not mentioned in the P3 + +plan. + +In any simulation, the relationship between real and modeled time is of key importance. A real unit, such as a neuron, would read inputs continuously and update its outputs asynchronously, but this cannot be simulated exactly on a digital computer. Many simulations use a simple synchronous approximation to real time. However, sometimes this produces unwanted artifacts and a closer approximation of asynchrony is required. Often, in fact, what the investigator really wants to do is to experiment with the effect of different kinds of time simulation on the network under study. Since there is no way for the system designer to know in advance all the possible ways that the investigator will want to handle time, some strategy has to be used that allows great flexibility. The approach taken by P3 is that this flexibility can come through the methods that can use conditional updating. The P3 system itself is completely synchronous and updates all units on each cycle. Since updating a unit involves invoking its method, the question of whether or not the outputs of ��I"5R!mDe on any P3 cycle can be + +decided by the method. For example, to model asynchronous updating, each unit can have an additional input that controls whether or not it is updated on a cycle. Then the decision as to which units are to be updated can be given to a control unit that is connected by a separate line to the update inputs of all the other units. The method program inside this control unit decides which units in the network will be updated on each cycle. Note that this approach is very flexible since small changes in the method program of the control unit can imple- + +ment a large range of possible update time schemes. + +A typical P3 plan might contain a large number of simple neuron-like units forming the core of the network together with a few special purpose units to generate input to the core network and control its function. The master control unit, used above to implement asynchronous updating, is an example of this kind of special-purpose unit. They can also be used to sequence simulated experiments and to interpret output of other units. How all this can be done will become clearer as we describe the use of P3 in detail. They key point here is that the P3 "style" is to include within the P3 plan all aspects of the simulation including input to and control of the core network. This approach simplifies the problem of constantly having to interfere special-purpose + +routines to a general-purpose modeling environment. + +It often happens that n�tworks are modular, that is, made up of distinct subnetworks. P3 facilitates the use of modularity by allowing subnetworks to be treated as single processing units. This feature is of particular use when several P3 units are used to simulate a single object such as a "realistic" neuron. The modular feature also facilitates "topdown" and "structured" definition of the plan even when the underly- + +ing networks are not particularly modular. + +The P3 plan language has an additional feature that is not directly concerned with describing the functional aspects of a parallel network. Every unit in a P3 plan has a location in a three-dimensional Euclidean reference frame call P3 space. This means that every P3 plan not only describes a network, but it also describes a geometrical structure. Since the functioning of a P3 network does not depend on its geometrical structure, it might seem odd to go to all the trouble of describing the geometry. There are two main reasons for locating P3 units in space. The first reason is to facilitate visualizing a P3 network while observing its function during the simulation of a model. The units can be placed so that they appear at the same relative positions on the computer display during simulation as they have in the investigator's conceptual image of the model. The second reason to give each unit a position in space is to make it possible to specify connections between units implicitly on the basis of their spatial locations rather than explicitly. This latter feature is of particular importance when modeling systems in Copyrighted Material + +which the connectivity is described in terms of geometrical relations. This is often the case when dealing with realistic neuronal modeling, + +especially of primary sensory processing s tructu res. + +The P3 Plan Language + +The job of the P3 p lan language is to describe the units and connections that constitute the network being simulated. To do thi s , the language uses a small but rich set of s ta tements that make it possible to succinctly describe large groups of complex, connected units. The three fundamental constituents of the plan language are the UNIT TYPE, UNI T, and CONNECT s ta temen ts . The UNIT TYPE s ta teme nt name s and describes a kind of unit. The UNIT statement instantiates and names actual units. This statement can instantiate either a single unit or a whole array of units of the same type. The CO NNECT st ate ment makes connections. Since the statement can be used inside of loops , a single connect statement can make an arbitrarily large number + +of connection s using the available array features. + +A unit in P3 can have any number of inputs and outputs together with any number o f parameters. Before the start of a si mula tion , values must be given to all parameters and to a ll outputs. Each value is always a single computer word in length. The interpretation of thi s word depends on how the methods use it. As the simulation proceed s, these initial values are continuously updated. Taken together, the values of the parameters and the outputs constitute the state of the sy stem at any time during simulation. The major difference between parameter values and output values is that outputs are a vai lable to other units in a network through connections, while the value of parameters can only be read by the unit to which they belong. P3 units can have two classes of parameter s: unit parameters and terminal parameters. The unit parameters apply to the whole unit, for example, the threshold in a linear threshold unit. The terminal parameters are associated with individual inputs or outputs and correspond, for example, to + +weights. + +An impor tant function of the P3 plan language is to de scribe the connections between units. Since units can have multiple inputs and outputs there has to be some way to name them so that the CO N NECT statements will know which connections to make. These names are also used within the method programs to read inputs and set outputs. + +The basic form of the CONNECT stateme nt is + +(CONNEC T < un it -name > OU TPU T < output-name> TO < unit-re�hlflM1Ie1Jainput-name > ) + +For units with only a few inputs or outputs each input or output can be given a separate name. When a unit has a large number of inputs or outputs it is more convenient to group them together in input or output arrays. The individual items in these arrays are referenced by giving the array name and a set of subscript values. These arrays can be used + +in iterative statements in plans and methods. + +An output value can serve as input to any number of units, i.e., the fan-out is arbitrarily large. Each individual input can receive only one value. This is easy to enforce as long as it is known that just one connection is to be made to each input. This works well in many cases but it often happens that it is very hard or impossible for the programmer to know exactly how many connections will be made. This is the case, for example, when connection decisions are being made implicitly by some computational procedure such as "connection by location" or random connection. To overcome this, P3 secretly treats each individual input as an array and automatically adjusts its size to fit the num ber of inputs. This process is transparent to the programmer which means that multiple connections can be made freely to a single input. There is a special iteration statement in the method lang uage to access these multiple inputs. Each individual input that actually gets generated is called a TERMINAL and there are procedures for associating parame- + +ters with terminals and initializing their values. + +The method programs that im plement the internal functionings of units are written in the form of ordinary computer programs in an appropriate language. In the current implementation, which runs on the Symbolics 3600, the language is LISP. In order to allow the methods to use the values of inputs and parameters in their computations, a set of special access statements is incorporated into this system and is available to LIS P programs. These statements make it possible for methods to read and set inputs, out puts, and parameters more or + +less as if they are ordinary variables. + +In order to illustrate how P3 works, we will describe a model of a simple competitive learning network of the type described in Chapter S. The basic network contains two types of units: a pattern generator to supply stimuli and a cluster of com petitive learners connected to it, which spontaneously discover some features of the patterns. Since learning is spontaneous and does not require a teacher, the functioning of the network is simple and straightforward. Thr. pattern generators sequentially produce output patterns that serve as input stimuli to the cluster units. Each pattern is an activation vector specifying which of the in puts are active and which are not. Each cluster unit prod uces an output indicating its res ponse to the current stimulus which is transmitted to all other members of the cluster to create a "winner take all" network. The cluster unit which wins is the only one that learns and it Copyrighted Material + +uses the weight redis tribution procedure described in the competitive + +learning chapter, that is, + +aWl} =CI 0if uni tj loses on stimulus k + +g...!!... - gWi} if unit j wins on stimulus k + +nk + +where Clk is e qual to 1 if in stimulus pattern Sk, element; in the lower layer is active and zero otherwise , and nk is the number of acti ve ele- + +ments in patte rn Sk (thus nk = l:Clk)' + +i + +The first step in creating a P3 plan is to supply the UNI T TYPE statements. The UNIT TYPE statement for the pattern generator is + +given below: + +(unit type dipole + +parameters flag i 1 j 1 i2 j2 outputs (d array i j) + +method < update routine code in lisp> ) + +In this, and all our other examples, words in italics are part of the P3 plan language while the nonitalicized words are supplied by the user. The UNIT TYPE statement gi ves the type a name that will be used throughout the plan. The name for the pattern generator type is "dipole." There are five parameters that are used internally for pattern generation . The technicalities of the use of these parameters is irrelevant here. The UNIT TYPE statement describes the output of the unit. This ou t put is a two-dimensional array of lines called "d." This array of outputs is the retina on which stimulus patterns are generated which serves as an input to the competitive learning cluster units. The "i" and "j" that follow the word array are dummy variables that tell P3 how many dimensions the array has. The actual size of the array is variable and is initialized when we instantiate units of the type dipole. Note that the unit type dipole had no inputs since it is itsel f the source + +of patterns. + +The second basic unit type is the competitive learning unit, which in our plan we call "competitor." The unit type statement for it is given + +below: + +(unit type competitor parameters p g flag + +inputs (C array i j terminal parameters W) + +(i-A) outputs (o-A) + +Note that the input array"C" of this unit corresponds exactly in form to the output array "d" of the dipole unit described previously. This correspondence will make it possible to make one-to-one connections between the output of dipole type units and the input of competitor type units. Also notice that a terminal parameter "W" has been associ- + +ated with the input array"C." The competitor unit needs an additional + +input called "i-A" which will receive information from the outputs of all + +the other members of the cluster. + +We have described the two unit types we will need. We can now go ahead and instantiate units of these types. The statement that creates a + +pattern generator unit of type dipole is shown below: + +(unit stimulus of type dipole at (@ 000) + +outputs (d array (i 0 5) (j 0 5»» + +The unit statement names the unit it is creating. This is the name of a real unit that is actually going to exist in our model and it is the name that will be referred to when this unit is connected to other units. For P3 to build such a unit, it has to be told the type. There can be any number of units of the same type and they can all have different names. Since every real unit in P3 has a location in P3 space, we must specify it in the unit statement that instantiates the unit. The at clause is used for this. The at is followed by a location specifier that simply evaluates to the x-, y-, and z-coordinates of the unit in P3 space. For simplicity we locate the pattern generator at the origin of P3 space which will initially be located at the center of the display window when we simulate the model. Since we are building a real unit, we have to give a size to its array of output lines. This is done in the outputs clause of the UNIT statement. Each subscript specifier consists of a subscript name and initial value, which in the current implementation must be 0, and final value, which in this example is 5 for both the "i " and the "j" subscripts. This statement will generate a 6 x 6 array of output lines on + +connector" d." + +Now that we have a source of patterns, we need to create a cluster of units that will receive these patterns. The statement that instantiates + +these units is given below: + +(unit cluster array (k 0 - cluster-size 1) of type competitor at (@ ( ... k (+ cluster-size 4»)( + cluster-size 10) 0) + +initialize (g = 0.05) + +inputs (C array (i 0 (- stimulus-size 1)(j 0 (- stimulus-size 1)) + +In this case, we are not instantiating a single unit but an array of units. In the competitive learning model, the learning cluster always consists Copyrighted Material + +of two or more units, so we want a way to vary the number of units in a cluster. In the first line of the unit statement we give the name cluster to the array and then we indicate the size of the array with a subscript specifier. The name of this subscript is "k"; its initial value is O. Its final value is one less than the global constant "cluster-size." The value of cluster-size, which will occur at various points in the plan, is set by a statement at the beginning of the P3 plan that determines the value of global constants. This feature means that we can change the parameters such as cluster-size globally throughout the plan by only fiddling with a single value. The upper bound of the stimulus input line array has also been set with the use of a global constant "stimulus-size" rather than with an integer as was done previously. Also notice that the variable "k" is used in an at clause to place each unit of the array at + +a different place in P3 space. + +Our next task is to connect the units together in the appropriate fashion. We have two classes of connections: those that go from the stimulus generator to the learning cluster and those that interconnect the units within the learning cluster. Each of these classes of connections has many individual connections within it, but these individual connections can be specified algorithmically in such a way that only a few CONNECT statements are needed to generate the entire network. What is more, the algorithmic specification of these connections makes it possible to change the size of the cluster or the size of the stimulus array without altering the CONNECT statements at all. The code required to connect the stimulus to the learning cluster is given below: + +{for (k 0 (+ 1 k}) + +exit when (> k cluster-size) do + +{for (i 0 (+ 1 j)} + +exit when (> i stimulus-size) do + +{for (j 0 (+ 1 j» + +exit when (> j stimulus-size) do (connect unit stimulus output d i j to unit (cluster k) input C i j + +terminal initialize (W - (si:random-in-range + +0.0 (! I 2.0 (expt (+ stimulus-size 1) 2»»»» + +There are three nested loops. The first ranges over each member of the cluster, and the next two range over each dimension of the stimulus array. Inside these three nested loops is a single CO NNECT statement. The CO N NEC T statement has the job of initializing the value of any terminal parameters. In our model we have a very important terminal parameter, "W," the weight between a stimulus line and a cluster unit, which we �byR�il1Matl!n;lt random value which sums + +to one for the whole input array. This is accomplished by setting the + +initial value of "W" with a LISP function that evaluates to the required quantity. In general, in a P3 plan wherever a number is required, a function (in our case a LISP function) that evaluates to a number can replace the number itself. The sum of the random numbers generated by our simple LISP function is not exactly one, but only averages one. This is satisfactory for the competitive learning algorithm because it is self-normalizing and will force the sum to one in the course of learning. The connections that link the members of a cluster are a bit more complex. Each member of the cluster must receive input from all other members except itself. The code for doing this in a completely + +general way for clusters of any size is given below: + +{for (k 0 (+ 1 k» + +exit when (> k cluster-size) do + +{for G 0 (+ 1 j» + +exit when (= j k) do + +(connect unit cluster k output o-A to unit cI uster j input i-A» + +{for G (+ k 1) (+ 1 j» + +exit when (> j cluster-size) do (connect unit cluster k output o-A to unit cluster j input i-A») + +The idea here is that we first connect each unit to those units whose subscripts are lower than it and then to each unit whose subscript is higher than it. This requires two separate loops, each with its own CONNECT statement, both nested within an outer loop that ranges over all units in the cluster. Note that this is a case of making multiple connections to a single input line. We don't have to know how many connections there are because within the method there is code that will examine all connections on this line to decide if the unit has won. This feature is very useful and can be applied whenever a method needs to + +know the value of an input but not its originating unit. + +We have now specified all the features of a plan that describes the + +basic competitive learning network. Of course, this plan can only be + +used to construct a running model if we have available the appropriate method programs. Since these are ordinary computer programs written in LISP, we won't analyze them in detail. The code for the methods used here is given in the appendix of this chapter, which shows a complete plan for a simulation of competitive learning. It is worthwhile, however, to see how the method language accesses the inputs and outputs of the units about which we have been saying so much in the + +The only difference between the arguments to a P3 method and the arguments to a normal LISP function is that the P3 arguments are accessed by special access functions. For example, to get the value of a + +parameter, the following form is used: (read-un it-parameter flag) + +This form returns the current value of flag. To read an input from an + +array of input lines the following form can be used: + +(read-input (C i j» + +In this case the value of "i" and "j" must be bound at the point in the program where an expression using them occurs. There are corresponding forms for reading terminal parameters, setting outputs, + +and setting parameter values. + +The P3 Simulation System + +The P3 simulation system is the environment in which models in P3 are simulated. It is highly interactive and makes extensive use of the window system and the "mouse" pointer of the Symbolics 3600. The first step in simulating a model is to compile the methods and construct the plan. The constructor is a program similar in purpose to a compiler. However, the input is a P3 description of a network, rather than a computer language description of a program. The output of the constructor is a data structure containing all the relevant information about the network that can be used by the P3 simulation system to run a simulation of the model. As with any form of computer programming, a model must be debugged before it can be simulated. There are really two + +levels of debugging for network models. First, the user wants to know + +that the network that has been created is connected up in the way + +intended. Once this has been established, the actual functioning of the + +network can be debugged. P3 provides tools for both of these phases + +of the debugging process. + +To check the correctness of connections, P3 provides a display that shows each unit in the model at its location in P3 space. The user interacts with this display with a mouse pointing device. Clicking on a particular unit provides a menu that enables the user to trace out any of the connections emanating from that unit. This facil ity for tracing out connections, one at a time, has proved much more useful than simply presenting a user with the wiring diagram of the model. Once the user is convinced that the constructed model corresponds to the envisioned network, the job of anal:ebMRt'¥PRJ�99n9Ji the model can begin. + +Analyzing the running of a complex simulation is a demanding task. It is in this analysis that we have found that all the features of the P3 system come together and begin to justify their existence. Because every object in the model has a location in P3 space that corresponds to the user's mental image of the network, the simulation system can display values representing the state of the system at locations on the screen that have meaning to the user. This means that during the course of a simulation, meaningful patterns of P3 variables can be displayed. This approach is widely used in analyzing the function of parallel systems. What P3 has done is to standardize it and relieve the user of the need to implement the details of this display strategy for + +each new model. + +In the current implementation of P3, each object in the model is represented at its designated location by a small rectangular icon. By the use of a mouse pointer driven menu system, the user can assign the icon representing a unit the variable whose value is to be displayed. Thus, for example, the icons representing the input terminals of a cluster unit in our example can be assigned either the value of the input to that terminal or the value of the weight on that terminal. These assignments can be made or changed at any time during a simulation run. They can be set to be updated continually as a simulation proceeds, or they can be examined in detail when the simulation is temporarily interrupted. The current P3 implementation displays the relevant state values at two possible levels of precision. The approximate value of the state value is indicated by the degree of darkening of the icon. There are five levels of intensity. Their range is under user control and can be changed at any time. This enables the user to adjust the range so that the difference between the lightest and the darkest icons will optimize the information content of the display. There is also a high precision display that permits the exact value of any P3 variable to be + +examined. + +Figure 1 shows how the screen of the Symbolics 3600 looks after 588 P3 cycles of simulation of a competitive learning model with a 6 x 6 stimulus array and a dipole stimulus. There are six windows displayed and each shows a different aspect of the simulation. Window A shows the three units in the model at their respective positions in P3 space. The upper narrow rectangle is the pattern generator. It is not displaying any value. The lower two rectangles represent the two cluster units. They are displaying the approximate value of their outputs by the size of the contained black rectangle. Clearly the unit on the left has a lower output value than the one on the right. Window B shows the output of the pattern generator unit, which was called "stimulus" in the plan. The lines form a square array because that is the way they were specified in the plan. The two dark rectangles show the current dipole Copyrighted Material + +In addition to the special functions of P3, the user also has available all the powerful program development tools of the Symbolics 3600. For example, suppose that the user believes that an observed bug is due to an error in the code of a method. It is possible to interrupt the simulation, go directly to the editor buffer that contains the method code, alter it, recompile the alteration, and then return to the simulation at exactly the point at which it was interrupted. This facility has + +proved invaluable in debugging. + +As we work with the P3 simulation system, we constantly find new features that are useful in the analytical process. We view the implementation of each of these new analytical techniques as analogous to adding a new instrument to a laboratory. Thus, we call the features of P3 that enable the user to analyze a functioning model "instruments." Each of these instruments can be called up at any time. Every instrument has a window that displays the results of the instrument's analysis. For example, one instrument is the "strip chart recorder" used in Figure 1. The strip chart recorder has a probe that can be connected to any particular state variable of any unit. Since multiple instances of any instrument can be created, any number of strip charts can be running at the same time. In addition to instruments that display the values of variables, we also envision a class of instruments that record these variables. Clearly, it is very important for a serious modeler to be able to record the results of a simulation. The instrument concept will enable the modeler to record just those variables required. This is a very important feature since simply recording the entire state of the model as it develops in time would produce an + +overwhelming flow of data. + +Performance + +So far we have said nothing about the speed at which simulations run. This is a problem of tremendous importance for PDP models. Big models inherently run slowly on serial computers. Generally, parallel programming systems like P3 stress ease of model definition and simulation. How much penalty must we pay in model performance? There is always some performance penalty for a general-purpose system. For any given piece of computer hardware, it is generally possible to write a specially tailored program that will run some particular model faster than any general system will run it. However, this special tailoring itself takes considerable time and makes it much harder to change the details of the model structure. Thus, we envision that programs like P3 will be useful in the early stages of model development when the size Copynghted Material + +of the models are modest and there is frequent need for changes in structure. When the structure and parameters of a model have been decided upon and it is necessary to scale the model up and have it run extremely rapidly. it may in some cases be advantageous to write a spe- + +cial program to implement the model. + +The general-purpose systems, however, have several things going for them with respect to model performance. First of all, since the data structure has the same form for models, it is possible to put a lot of effort into optimizing running speed for the particular hardware on which the system is implemented. This optimization only has to be done once rather than for each model. A second way in which generalpurpose systems can improve performance is through the use of special-purpose hardware. The models generated by the P3 system are inherently parallel models and map well to some parallel computer architectures. The one way to get blinding speed from parallel models is to implement real parallelism in parallel computers. In some cases, array processors can also be highly beneficial. Since all the P3 models are of the same sort. a constructor can be made that will provide the appropriate data structures to run any P3 model on these kinds of hardware. This will make the hardware transparently available to the user of systems like P3. This, we believe, is a significant plus, since it is notoriously difficult to program any particular application for array + +processors or truly parallel hardware. + +In conclusion, the P3 system illustrates some of the general issues that arise in any attempt to simulate PDP models, and provides a number of useful tools that can greatly facilitate model development. General-purpose systems like P3 have promise for speeding and facilitating the programming of parallel models and the ultimate ability to + +run these models very fast using specialized hardware. + +APPENDIX A + +'" '" '" + +'" P3 Plan for Competitive Learning + +'" (NOTE the use of the "plan constant" and "include" statements.) + +'" '" + +•••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• + +'" + +'" Unit types + +•••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• + +'" + +;;; ........ Dipole pattern generator ...... .. + +(unit type dipole + +parameters flag il j1 j1 i2 j2 + +outputs (d array i j) + +include dipole-generator) ... (see code file on p. 506) + +;;; .......... Learning unit ....... . + +(unit type competitor parameters p Q flag + +inputs (C array i j terminal parameters W) + +(i-A) outputs (o-A) + +include comp-learn) ... (code on p. 504) + +•••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• + +'" + +'" Unit instances + +•••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• + +'" + +(plan constant stimulus-size = 6) (plan constant cluster-size = 2) + +;;; ........ Dipole pattern generator········ + +(unit stimulus of type dipole + +at (@ 000) + +;;; ........ Learning units ...... .. + +(unit cluster array (k 0 (- cluster-size 1) of type competitor at (@ (. I (+ cluster-size 4» (+ cluster-size 10) 0) + +initialize (q = 0.05) + +inputs (C array (i 0 (- stimulus-size 1) GO stimulus-size») + +..................................................................... + +Connections + +..................................................................... + +;;;u + +...... Stimulus to both clusters ....... . + +(for (k 0 (+ 1 k» + +exit when ( =k cluster-size) do + +(for (j 0 (+ 1 j» + +exit when ( =i stimulus-size ) do + +(for G 0 (+ 1 j) + +exit when ( =j stimulus-size) do + +(connect unit stimulus output d i j to unit cluster k input C i j + +terminal initialize + +(W = (si:random-in-range + +0.0 (! / 2.0 (expt (+ stimulus-size 1) 2»»»» + +;;; ....... Interconnect the clusters to implement competition ....... . + +(for (k 0 (+ 1 k» + +exit when ( =k cluster-size 1) do + +(for G 0 (+ 1 j» + +exit when ( =j k) do + +(connect unit cluster k output o-A to unit cluster j input i-A» + +for G (+ k 1) (+ 1 j» + +exit when ( =j cluster-size 1) do (connect unit cluster k output o-A to unit cluster j input i-A») + +APPENDIX B + +'" ,,, '" + +'" Competitive Learning: Methods + +'" + +•••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• ", + +to, Method for unit in cluster of competitive learners + +•••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• to, + +method + +(let «imax (input-dimension-n C 1) Gmax (input-dimension-n C 2» + +(win t) (N 0» + +;; ........ Is this a learning iteration? •••••••• + +(cond + +;; ........ No ....... . + +;; Accumulate the weighted sum of the pattern inputs into ;; unit parameter p, and set the competition output p-A to + +;; that value + +«> (read-unit-parameter flag) 0) + +(loop initially (set-unit-parameter p 0) + +for i from 0 below imax do + +(loop for j from 0 below jmax do (set-unit-parameter p + +(+ (read-unit-parameter p) + +(. read-terminal-parameter (C i j) W) + +(read-input (C i j»»» finally (set-output o-A (read-unit-parameter p») + +;; .......... Yes •••••••• + +;; Figure out whether this unit wins on this cycle. Winning ;; requires that this unit's parameter p be greater than those ;; for the other units of this type. Those values are available + +;; on the terminals of input i-A. + +;; NOTE: On iteration 0, everything is 0, so no unit thinks it + +;; wins, and hence all avoid learning. + +(t + +;; ........ Find out whether we won ....... . + +;; Win was initialized to t in the let at the top level of this method. + +(for-terminals k of input i-A + +(if « .. (read-unit-parameter p) (read-input (i-A terminal k») + +(setq win nil)) + +(when win + +;; ........ Accumulate sum of all inputs into N ....... . + +;; This will become a normalizing constant. (loop for i from 0 below imax do (loop for j from 0 below jmax do + +(setq N (+ N (read-input (C i j»»» + +;; .. •• .... Compute new weights ....... . ;; But only if the total input was greater than O. + +(if (> NO) + +(loop with q-factor = (read-unit-parameter g) + +for i from 0 below imax do (loop for j from 0 below jmax do + +;; ........ Compute one new weight ........ + +(let· (old-weight + +(read-terminal-parameter + +(C i j) W» (new-weight + +> (+ old-weight (. g-factor + +;; Update the terminal parameter to the new weight + +(set -termi nal-parameter (C i j) W + +new-weight»») ) + +;; ........ Flip the iteration-parity flag ....... . + +(set-unit-parameter flag 1»» + +•••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• + +, " + +", Dipole pattern generator method + +•••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• + +method + +;; ........ Do we need a new pattern on this iteration? ....... . + +(cond + +;; ........ Yes. Erase old dipole and make new one ........ . + +« < (read-unit-parameter flag) l) + +Oet « imax (- (output-dimension-n d 1) 2» (jmax (- (output-dimension-n d 1) 2») + +(set-output (d (read-unit-parameter i 1) (read-unit-parameter i 1) 0) (set-output (d (read-unit-parameter i2) (read-unit-parameter i2» 0) + +(set-unit-parameter i 1 (+ (random imax) 1» (set-unit-parameter jl (+ (random jmax 1) + +(cond «> (random 2) 0.5 (cond «> (random 2 0.5) + +(set-unit-parameter i2 (+ (read-unit-parameter il) 1)) + +(t + +(set-unit-parameter i2 (- (read-unit-parameter i 1 1) ) + +(set-unit-parameter i2 (read-unit-parameter j 1») + +(t + +(cond «> (random 2) 0.5) + +(set-unit-parameter i2 (+ (read-unit-parameter j 1) 1)) + +(t + +(set-un it-parameter i2 (- (read-un it-parameter j 1) 1»» + +(set-un it-parameter i2 (read-unit-parameter i 1»» (set-output (d (read-unit-parameter il) (read-unit-parameter j 1) 1) (set-output (d (read-unit-parameter i2) (read-unit-parameter j2» 1) + +(set-unit-parameter flag 1») + +References + +Ackley, D. 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S., 94, 560 description of, 363 Abstraction models of memory, examples of, 428-429 199-206 main concepts of, 426-428 comparison of experimental and as major aspect of PDP model s, + +simulation results, 203-205 51-52 + +other findings on, 205-206 results of, 429, 439-442 summary of training and test rules , examples of, 425-426 stimuli, 202-203 three-dimensional plots, 429, + +Whittlesea's experiments on, 201 - 430-438 (Figs.) 202 views of, 423-425 Ackley, D. H., 264, 306, 313, 317 , Activation rule. See Activation + +335,507, 510, 393, 562 functions + +ACP model, 32, 124, 127 Activation vector of harmony Activation functions theoretical model , 21 5-216 examples of Active representation in PDP + +gating activation function, 426 models. See PDP models, active + +semilinear, 52, 324-328 representation in + +quasi-linear, 425 Addition problem, simple binary, quasi-multilinear, 426 341 -346. See also Deltarule, + +Algebra, linear. See Linear algebra Algebraic properties of inner products, 382-383. See also + +Vectors + +Allman, J.. 34 7, 374. 375. 553, 554 Alternative activity patterns, 82-83 AM. See Monocular occlusion Amari, S. A., 42, 45, 444, 507, 489. + +495, 553 Ambiguity + +> lexical. 302-304 structural, 304-305 + +and shading of feature patterns, + +305-306 + +Ambiguous characters, 8, 155-157. See also Reading, programmable + +blackboard model of Amnesia. See also Memory, a distributed model of + +anterograde, 504, 505-506. 512-513 bitemporal, basic aspects of, 505- + +506 + +conclusions on, 52 7 description of, 503-505 + +neurochemistry of synaptic change. hypothetical account of, 50 7-509 paradox of, resolution to, 506-50 7 quantitative model, formulation of, + +509 + +relation to other accounts of, 510- + +5/l + +residual learning in, 518-524 simulations, 511-518 + +anterograde amnesia, 512-513 lost memories, recovery of, 515- + +516 + +retrograde amnesia, 513-515 retrograde and anterograde amnesia, correlation of, 51 3 + +studies on, 516-518 summary of, 518 + +spared learning in. 207-208, 518, + +524-526 + +Anandan, P., 322, 508 , 550, 554 AND function, 429. See also Boolean function + +Anderson. C. W., 539, 554 + +Anderson, J. A., 33 , 42, 56,62,66, 68 ,80, 82, 101 ,406, 409, 410, 418, 507,510, 51 1, 8, 173, 183, 200,226,277, 311, 380, 389, 394,399,431,551, 553, 554, + +561,564 + +Anderson, J. R., 32, 124, 127, 25 1, 46 1 ,507, 173,106,209, 524, + +549, 554, 558 Anlezark, G. M., 477, 554 + +Annealing, simulated. See Simulated + +annealing Aragon, C. R., 235, 508 Arbib, M. A., 362, 577 + +Arbitrary mapping, implementing. + +96- 104 + +grapheme strings. 97·99, 102 sememe units, 97-98, 99 , 10 1·102 three-layer network, 97-98 . See also Boltzmann machines Arguments, missing, filling in, 301- 302. See also Case role assignment, model of + +Ary . M., 477, 564 Asanuma, H., 35 7, 554 Asynchronous update vs. synchronous update, 61 ATN. See Augmented transition + +network parsers + +Attention + +networks for focusing, 114·1 18 shifting focus of, 147·151 Augmented transition network parsers (A TN), 11 9 + +Auto·associative paradigm. See also Memory, a distributed model of + +definition of, 55 , 161 modification of, 211-212 + +Back'propagation simulator , description of, 328 ·330 Bagley, W. C., 58, 98, 1 06 , 554 + +Bahl, L. R., 293, 508 Baker, J. F., 34 7, 554 Baker, R. G., 24, 515 + +Boolean function (continued) linearly separable functions, 440 mapping from expressions, 439 neurons treated as devices, 424-425 + +XOR function , 429 + +Bottom-up approach to analysis of information processing systems , {3 units, simulations of (App.), 469- 470. See also {3-coefficient model + +Bunt, A. H., 35 7, 566 + +Bybee, 1. L., 221, 247. 249, 250, 251.254, 255,256,556 + +123 CA. See Connection activation unit + +Bottom-up presentation of harmony Caan, W., 368, 571 + +theory, 199, 213-26 1. See also Cajal, S. Ramon y, 336, 350, 358, Harmony theory 359,361, 363,36 7, 556 Bottom-up processing system, 51 Caminiti, R., 377-378, 560 matrix representation of, 57-58 Canonical feature detectors, 114 + +Boycott, B. B. , 336, 558 Caplan, C. J. , 478, 570 Brachman, R. 1., 313, 555 Carew, T. J., 552, 561 Brain. See Cerebral cortex, anatomy Carlson, M., 275, 573 and physiology of; Cerebral Carman , 1. B., 350, 556 cortex, questions about Carnes , K. M. , 477, 554 + +computation in Carpenter, P. A., 153, 16 1, 549,564, + +Brain damage. See also Amnesia; 577 + +Damage, effects of on a network Carrol l, Lewis, 97 graceful degradation and, 29, 134 Cascade model, 42 + +neuropsychological investigation of Case role assignment, model of patients with, 134-135 architecture of, 27 7-289 + +simulated effects of, 304-313 case role representation, 286-288 Brain state in a box model (BSB), semantic microfeatures, 278-283 66-68 sentence processing and learning, + +Branch. M., 435, 571 detai ls of, 288-289 + +Brayton, R. K., 381. 382, 575 sentence-structure units, 283-286 + +Bresnan , J .• 274, 559, 564 descriptions of, 3-4 Brightman, M. W., 336, 572 discussion of, 313-325 Broadbent, D. E., 1 2 1 , 508, 97, 532, context-sensitive coding, + +555 iteration. and center embedding, + +Brock, L. G., 36 7, 555 323-325 + +Brodmann, K., 345, 346, 555 fixed-length, 320-322 Brodmann's areas of the neocortex, limitation myths, 322-323 + +345-346. See also Cerebral meaning, representation of. 315- + +cortex, anatomy and physiology 316 + +of model. basic features of, 314-315 Brooks. C. McC.. 336 , 553 parsers, conventional interfacing + +Brooks. L. R .• 171.556 with,317-318 Brown, P .• 295 recursion, 318-320 Brown , R .• 219, 241, 556 goals of, 276-277 Bruce, C. J., 368. 556. 558 studies on , 277 + +Brugge. J. F .• 356, 563 multiple constraints on, 272-275 BSB model . See Brain state in a box studies on. 273. 275, 277 + +COHORT model (continued) cerebral cortex in, 387-389 + +resolution of, 101-106 Computational temperature (n, 211 Cole, K. S., 364, 556 Computational viewpoint on PDP + +Cole, R. A., 58, 61, 98, 99, 100, models, 397-398 + +107,111, 556, 557 Conel, J. LeRoy, 358, 557 Collins, A. M., 85, 508 Confabulation , as a stable pattern, 81 Colonnier, M., 348, 361, 557, 571 Conjuncti ve encoding, 90-91, 96. Colon Osorio, F. c., 424, 510 See also Coarse coding; Coltheart, M., 102, 508 Distributed representations Competence theorem, 226-229 CONNECT statements for P3 Competitive inhibition, 21. See also system, 495-496. See also P3 + +Phoneme identification , factors system + +influencing Connection activation system, 130- + +effect of at phoneme level, 89-90 134 + +Competitive learning Connection activation unit (CA) . architecture of competitive learning See also Connection information system, 162- 166 distribution mechanism basic components of, 151-15 2 definition of, 132-134 + +characteristics of, 166- 167 multiple pattern processing, 477- + +conclusions on , 190 478 + +definition of, 147 requirements of, 474-476 + +dipole experiments, results of, single pattern processing, 476-477 170-177 summary of requirements, 480-48 1 correlated teaching inputs, 182- Connection information distribution 183 (CID) mechanism , 473-486, letter similarity effects, 182 129-134, 137, 139-140 number of elements, effect of per benefits of, 164-166 + +serial position , 181-182 central knowledge store in, 130-134 position-specific letter detectors, computer simulation of word 180-18 1 recognition using, 134-136 word detection units, 18 1 extensions of, 167-168 + +word perception model, 177-180 resource requirements of, 473 -486, + +formal analysis of, 168-170 166-167 + +geometric interpretation of, 164- Connectionist models, 72 166 Connolly, M., 353, 355, 566 history of, 152- 159 Connors, B. W., 364, 369, 557 horizontal and vertical lines, Constructor, as major component of experiments with, 184-190 P3 system, 489. See also P3 + +mechanism of, 159 system + +neural-like processing systems, Content-addressable memory, 79-80 160- 16 1 Continuity and uniqueness in P3 simulation system constraints in depth perception, + +methods (App. B), 504-506 19-20 + +plans for (App. A), 502-503 Cool ing schedule, 244-245. See also + +Completion task. example of. 206- Electricity problem-solving; 208 Simulated annealing Computational level. 121 Coombs. 1. S .• 367. 555 + +Cooper, L. N., 42, 180, 508, 480, 487, 489, 499, 555, 557, 573 + +Corkin, S., 519, 524, 556 Cortical areas of the neocortex, Brodmann's cortical parcellation + +scheme, 345 input systems, 346 + +irregularities within, 353·356 thalamus, as gateway to cerebral + +cortex, 349·352 + +topographic representation, 352· + +353 + +output systems, 356·357 Cortical plasticity, processes that modulate, 476·478 Cotton, S., 99, 105, 557 + +Cottrell, G., 165, 277, 3lJ, 314, 557 + +Coulter, 1. D., 357, 570 Cowan,1. 0., 381, 389,578 Cowan, W. M., 350, 351, 556, 572 + +Cowey, A., 363, 576 Crain, S., 274, 557 Crane, A. M., 350, 572 + +Crick, F. H. c., 296, 297, 509, 351, + +384, 387, 557 + +Critical or sensitive period of plasticity, 473·484 + +cortical plasticity, processes that + +modulate, 476·477 effect of environment on, 478 hypothesis for, 483·484 + +ocular dominance statistics, 474· + +476 + +other examples of, 477·478 Crosstalk, 139·142. See also Reading, programmable blackboard model of Crow, T. 1., 476, 477, 554, 557 Crowder, R. G., 64, 94, 209, 557 Cynader, M., 475, 476, 478, 492, + +498, 557, 558 + +in Boltzmann machines, 304·313 + +Daniel, P. M., 354, 558 Daniels, 1. D., 477, 554 Darien·Smith, J., 480, 574 Davis, E., 432, 558 + +Daw, N. W., 497, 500, 558, 577 Deacedo, B. S., 519, 524, 556 Decay process in increments to + +weights, 181. See also Memory, a + +distributed model of Decision·making and freezing in + +harmony theory + +coherent interpretation, robustness + +of, 240 + +idealized task, 238·239 + +phase transitions, computational significance of, 236·237 symmetry breaking, 237·238 thermodynamic limit, 239 + +Deep dyslexia, 102 + +Degradation, effects of and benefits of redundancy, 472. See also Standard pattern associators Deliberate conscious control (DCC> , 543-545. See also PDP approach, + +reflections on + +Delta rule, 43, 53, 62, 63, 363, 417· + +418 + +Delta rule, analysis of. See also Delta rule, generalized and multiple linear regression, + +457·458 + +in pattern-based coordinates, 447· + +453 + +statistical learning and, 453·457 + +summary of, 458·459 in vector notation, 445·447 Delta rule, generalized, 149 application of, 327·328 conclusions on, 361·362 general cases, 352·361 recurrent nets, 354·361 and gradient descent, 322·324 + +Dahlstrom, A., 350, 553 problem of, 318·323 Damage, effects of on a network, 29, XOR problem, 319·321 + +134, 472. See also Amnesia; for semilinear activation functions Boltzmann machines; Brain in feedforward networks, 324·328 + +Delta rule, generalized (continued) simulation results, 328-330, 352 encoding problem, 335·339 negation problem, 346-347 + +parity, 334-335 + +simple binary addition problem, + +341-346 symmetry, 340-341 T-C problem, 348-352 XOR problem, 330-334 use of to determine size and direction of changes in connections, 179-181 generalized, 209 + +DeMarzo, P. M. , 241, 242, 509 Demps ter, A. P., 293, 509 + +Dendrites , studies on , 381-382. See also Cerebral cortex, questions + +about computation in + +Denes , P., 87, 558 + +de Riboupierre, F., 385, 553 de Ribou pierre, Y. , 385, 553 Derthick, M., 298, 299, 509, 313 Desimone, R., 368, 374, 556, 558 Di pole experiments for competitive learning mechanisms, 170-174 formal analysis of, 174-177 homogeneous stimulus patterns , + +191·193 + +Distal landmarks for biologically plausible models of place + +arbitrary pairing, implementing, + +96-104 + +binding problem, 88-90 coarse coding, 91-96 con junctive encoding, 90-91 Distributed view-field model for goal location , 449-460. See also Place recognition and goal location, biologically plausible models of + +descri ption of, 451-453 network used in, 450-451 P3 simulation of, 453-454 Symbolics 3600 LISP machine, use of for, 454-456 + +problems of, 451 properties of, 453 testing of, 453 Dobson, V., 97, 100 Dostrovsky, J., 435, 571 Dowling, J. E. , 336, 558, 578 Drager, U. c., 490, 558 Dretske, F., 195, 509 Duckrow, R. B., 477, 561 Duda, R. 0., 380, 558 Dukes, K., 61, 110, 570 Durham, D. , 500, 558 + +Dynamic functional system, 41 Dynamical systems, perspective of PDP models as, 397-398 + +recognition and goal location , 445 Eccles, 1. C., 336, 367, 370, 553, + +Distributed representations. See also 555, 558 + +Memory, a distributed model of; Edelman, G. M. , 387, 558 Schemata, concept of Edmonds , D., 153, features of Ehrlich , S., 163, 573 + +generalization effects, 82·85 Eichenbaum, H., 385, 519, 524, 556, + +memory, 79·81 565 + +new concepts, 86·87 Eigenvalues . See Eigenvectors and + +status of, 78·79 eigenvalues + +structure in representations and Eigenvectors and eigenvalues, 399· processes, 104·108 403. See also Matrices and linear + +constituent structure, systems + +representing, 105·106 Eimas , P. D. , 94, 473, 558, 560 + +sequential symbol processing, Eisen , M. , 456, 509 106·108 Elbaum, c., 499, 573 + +summary on , 108·109 Electricity problem·solving, 240·250 technical details of, 87·104 Electroencephalography (EEG), 335 Copyrighted Material + +Freezing and decision-making in harmony theory. See Decisionmaking and freezing in harmony + +theory + +Freund, T. F., 363, 576 Friedlander, M. J. , 351 , 560 + +Fry, D. B., 94, 560 Fuchs, A. F., 357, 566 + +Fujimura, 0., 62, 473, 560, 569 Fujisaki, H., 77, 94, 560 + +Fukushima, K. , 42, 152, 162, 300, + +313,350, 509 + +Future directions for PDP, 54 7-552 Fuxe, K., 350, 364, 553, 560 Fuzzy map theory, 432-433. See also Place recognition and goal location, biologically plausible + +models-of + +Gallistel, C. R., 141, 509 Gamma factor in bitemporal amnesia, 50 7 Ganong, W. F., 60, 78, 560 Garey, L. J. , 348, 497, 500, 555, + +560,5 77 Garnes, S., 61, 555 Garrett , M. F., 274, 559 Garrud, P., 434, 466, 569 Gary-Bobo, E., 476, 478, 556 + +Gati, I. , 499, 560 + +Gating activation function, 426. See also Activation functions Gee, J., 60, 63, 107, 115, 561 Gelatt, C. D., Jr ., 48, 235, 287, 511 Geman, D., 148,264,271,278,289, + +509 + +Geman, S., 148,264,268,271,278, + +289, 509 + +Generalization, 30, 85. See also Memory, a distributed model of Glaser, E. M., 366, 577 Glass, L., 494, 571 Glorioso, R. M., 424, 510 Gluck, M. A., 383, 552, 561 Glushko, R. J., 43, 510, 171, 561 Goal location. See Place recognition and goal location, biologically + +plausible models of Goldman-Rakic, P. S., 350, 572 Goodness-of-fit function, 14- 16, 31 , 32-33, 35-36. See also Schemata, + +concept of + +Graceful degradation, 29, 134. See also Damage, effects of on a + +network Gradient descent + +and delta rule, 322-324 use of to solve hard optimizing problems on conventional computers, 287-288 + +Grapheme strings, 97-99, 102. See also Arbitrary mapping, + +implementing Gray, E. G., 339, 361, 561 Green, D. M., 466, 510, 225, 561 + +Green, K., 96, 569 Greenberg, Z., 254 Greenway, A. P., 477, 554 Grinvald, A., 385, 561 + +Grosjean, F., 60, 63, 99, 100, 105, 10 7, 114, 11 5, 55 7, 561 Gross, C. G., 368, 556, 558 Grossberg, S., 42, 53, 70, 116, 146, 152, 162, 164, 167,418,510,90, + +389, 494, 535, 556, 561 Grossberg's models, 70-71 Guillery, R. W., 351, 561 Gutnick, M. J., 364, 369, 55 7 + +Georgopoulos, A. P., 377-378, 560 Haggard , M., 85, 576 Gernsbacher, M. A., 79,559 Hale, B. L., 159, 563 Gerstein, G. L. , 385, 560 Halle, M., 24, 508, 168, 56 1 Gibbs sampler, research with, 264 Halmos, P. R., 422, 510 Gibson, E. J., 198 Hamiltonian function (fl), 211 + +Gilbert, C. D., 356, 358, 366, 385, Hamori, J., 351, 577 + +480, 560, 561, 577, 578 Hard learning, example of, 299-303. Ginsburg, H. P., 241, 509 See also Boltzmann machines Copyrighted Material + +Horizontally hierarchical networks, + +21 7 + +Houde, J. , 353, 355, 566 Houser, C. R., 351, 562 + +Hubel, D. H., 340, 353, 356, 367, 373, 474, 475, 483, 497, 500, + +562, 563, 566, 578 + +Huberman , B. A., 313, 511, 389, 562 Hughlings-Jackson, J., 41, 141-142 Human information processing. See also PDP approach, reflections on + +essential properties of, 537 new understanding of, 545-546 Human memory. See Memory, a distributed model of; Memory, retrieving information from Hummel , R. A., 285, 286, 511, 514 + +Hunt, S. P., 364, 559 + +Huppert, F. A., 516, 517, 563 6-hydroxydopamine (6-0HDA), + +477-496 + +Identity/ role combinations, 1 06. See also Case role assignment, model of; Distributed representations + +Imbert, M., 476, 478, 556 Imig, T. J. , 356, 563 + +Implementational (physiological) level of distributed memory, 121 Inner products . See also Vectors algebraic properties of, 382-383 in two-dimensional space, 380-382 + +Input units, definition of, 48 Interactive activation model of word perception, 43, 71 -72, 177-180, 216-2 1 7,125-129, 137-1 38 Interactive model of reading (Rumelhart) , 43, 122 + +Interactive models, representation of in matrix form, 57, 59-61. See also Interactive activation model + +of word perception layered systems , 60 one-step system, 60 single-level , 60 + +associators� Reading, + +programmable blackboard model of� Standard pattern associators Interference of memories, 208-209. See also Memory, a distributed + +model of + +Internal representations. See Delta rule. generalized� Representation, + +learning of IS-A hierarchy, 105 Isenberg, D .• 7. 511 + +Isomorphism hypothesis. See also PDP models, neural and conceptual interpretation of of conceptual and neural levels. + +395-396 + +failure of in nonlinear models, + +422-424 + +levels and localized damage, 413- + +416 + +levels, learning of connections and, + +416-418 + +in linear systems, 411 -413 Iverson, L. L., 340, 563 + +Jackson , J. H., 41, 141,511 Jacoby, L. L. , 171, 172, 192, 193, + +556,563 + +Jakimik, J., 61 , 98, 99, 100, 107, + +111, 557 Jelinek, F., 293, 508 Jenkins, 1. J., 473, 569 Jenkins, W. M. , 385, 563 Johnson, D. S., 235, 508 Johnson, E., 324, 563 Johnston, D., 477, 562 + +Johnston, J. C., 159, 160, 563, 574 Jones, E. G., 351 , 352, 35 7, 363, + +563,564 + +Jones, R. S., 56, 406, 409, 410, 418, 507,173, 226, 311 , 551 , 554 + +Jouvet, M. , 350, 555 Julesz, B., 18, 511 + +Just, M. A., 153, 161,549, 564,577 + +Interference of patterns, 139-142. 387, 569, 570, 578 See also Programmable pattern Kahneman, D., 536, 564 Copyrighted Material + +Kaiserman·Abramof, I. R., 336, 361, + +365,571 + +Kalaska, J. F., 378, 560 + +Kandel, E. R., 333, 364, 507, 552, + +561 , 564, 576 Kanerva, P., 76, 465, 51 1 Kant, E., 17, 19,564 + +Kaplan, R. M., 119, 516,274,559, + +564 + +Kasamatsu, T., 476, 477, 492, 497, + +564 + +Kawamoto, A. H., 101, 511,277, + +311,564 + +Kawashima , T., 77, 94, 560 Keele, S. W. , 171, 183, 200, 203, + +572 + +Kelly,1. P. , 480, 560 Kewley·Port, D. , 85, 564 + +Kienker, P. K., 302 , 350, 511,515 Kinematics of the dynamical system, 398·399, 400·403. See also PDP models, neural and conceptual + +interpretation of + +Kirkpatrick, S., 148, 235, 287, 511 + +Kisvardy, Z. F .• 363, 576 Klatt, D. H., 59, 60,62. 564 + +Kliegl, R., 273. 567 Knapp, A., 173, 200, 564 Knowledge atoms definition of. 202 + +and electricity problem·solving, 242 Koch, C., 365, 381, 383, 564. 565 Kohonen. T .. 42. 45. 62. 63. 152, 406.409, 418, 422. 424, 425, 444, 446,455,461, 5Il. 222, + +226, 380, 565 Konishi, M., 473, 565 Kratz, K. E., 490, 565 Krnjevfc, K .• 339. 565 + +Kubie. J. L., 435. 441. 445, 447. + +565.570 + +Kucera. H., 74. 240, 565 + +Kuczaj, S. A., 219, 220. 221. 253, + +257. 258, 565 Kuffler, S. W .• 367. 565 Kuipers, B., 433, 565 + +Kuperstein, M .• 385, 565 Kupperman, B.; 478, 572 Kurtzman. H. S., 275, 565 Kuypers. H. G. 1. M., 352, 571 + +Laird, N. M., 293, 509 + +Lakoff, G., 97 + +LaManna , 1. c., 477, 561 Lamperti, 1., 277, 511 Lane, H. L., 91 , 565 Lang, K., 127, 510 Lang, M., 511 + +Language acquisition device (LAD), 217. See also Verbs , learning past + +tenses of Larkin, 1. H., 24'1 , 512 Larsson, K., 350, 553 Lashley , K. S., 41,512 + +Law of mass action, 509·510. See + +also Amnesia + +Layered systems in interactive + +models , 60 Lazarus, J. H. , 94, 572 Le. See Locus coeruleus Leaky learning model. 179 + +Learnability theorem, 235·236, 260 Learning. See also Boltzmann + +machines; Delta rule, generali zed; Memory, a distributed model of; Neural plasticity and learning + +in Boltzmann machines easy and hard, 290-299 hard, example of, 299-303 learning algorithm, derivation of, + +31 5 - 318 + +establishing features through, 258· + +260 + +in symbolic and subsymbolic paradigms, 261·262 Learning machine (Minsky and Edmonds), 153-154 Learning paradigms, 54-57 + +Learning rule, general form of, 52·53 + +Leavitt, R. Y., 351, 563 Le Cun, Y .• 322, 512 Lehiste, 1.,61. 565 + +Kullback, S., 294, 511 Lenneberg, E. H .• 473, 565 Kuno, M .• 336, 565 Copyrighted MMMfa/U. R.• 63, 559 + +Letter-perception model. See Interactive activation model of + +word perception + +LeVay, S .• 350. 353. 355,361.374. 497.500.563. 565. 566 Levels of analysis. 121·129. See also Isomorphism hypothesis Marr's levels. 122-124 + +other notions of levels. 124-127 reductionism and emergent properties. 127-129 Levin. 1. A.. 43. 85, 512. 90. 566 Levin's proteus model. 43 Levine. R. D., 227, 512 Lewis. B. , 341, 566 Lewis, C. H. , 251. 512 LGN cells. 480 + +Liberman. A. M .• 61. 62. 73. 92, 94, 95. 473. 560. 566. 569, 573. 576 + +Lichten. W .• 63. 569 Licklider, 1. C. R., 106, 566 Lieberman. F .• 489. 557 Limited fan-out. See Fan-out. limited; Standard pattern + +associators + +Limited increment hypothesis. 520. + +See also Amnesia Lin, C. S .• 351. 560 Lindsay. P. H .• 8. 206. 512 + +Linear algebra + +matrices and linear systems + +basis for vector space, change of. + +413 + +description of, 385-386 eigenvectors and eigenvalues , + +399·403 linearity. 393 matrices. 386-390 matrix inverses , 410-413 matrix multipl ication and multilayer systems. 395-399 one-layer PDP system. 390-393 PDP systems, 2 examples. 406- + +410 + +vectors + +basic operations of. 367-370 concepts , use of in analysis of simple PDP model, 383-385 description of, 365·366 inner products, 375 linear combinations and independence, 370-373 vector spaces, 374-375 Linear models, simple, 61-63. See + +also Linear algebra auto-associator version of, 63 pattern associator, 63 simple linear associator, 62 + +weaknesses of, 63 + +Linear threshold units, 63-66, 425, 224. See also Activation + +functions perceptron, 65 XOR function, 64-65 + +LISP programming language, 124 use of in P3 system, 492, 496-497 Llinas, R., 364, 370, 558, 566 Local representations, 77, 85, 96 Locus coeruleus (LC), 476-4 77, 493 + +Loeb, G. E., 383, 566 + +Loftus , E. F., 85, 508, 208, 566 Logical computation. notion of. See + +Activation functions Logogen model, 43, 192-193 Loomis. L. H .• 402, 566 + +Lorente de No, R., 344. 358, 566 + +Lovins. 1. B., 62, 560 Luce, R. D., 75. 93. 195, 566 Luce choice rule. appl ication of, 90· + +91, 195 + +Lund, J. S., 35 7, 358, 361, 366, 374, + +566,5 73 + +Lund, R. D., 336, 35 7, 566 Luria, A. R., 41,79, US, 512 Luria's dynamic functional system, + +41 + +Lynch , J. c., 366, 56 7 + +transposes and the outer product, Ma , S. -K., 388, 56 7 403-405 Macchi, G., 350, 567 nonlinear systems, 418·420 Macrodescription of harmony + +Copyrighted Mat9lrgranism. 246-258 + +problem sol ving for, 246-247 one-layer PDP system. 390-3Q� productions and expertise, 251-253 transposes and outer prod uct, 403- + +schemata. 253 405 + +approximation , 256-258 Matrix inverses. 410-413. See also for rooms, 255-256 Matrices and linear systems two-choice model , 253-255 Matrix mapping, algebraic properties MacWhinney, 8.. 273, 274, 554.56 7of, 389-390. See also Matrices + +Macy, A., 481, 567 and linear systems + +Magistretti. P. 1., 364, 569 Maunsell.1. H. R., 345,352,353, + +Mann, V. A., 95, 118. 56 7 356. 500. 568, 577 + +Mapping from expressions. 439. See Maximum-likelihood model , 292-294 also Boolean function McCarthy, J., 157-158, 512 Marcus. M. P., 317, 324, 567 McClelland, 1. L.. 20, 22, 24, 27, 28. Marin, O. S. M., 134,514 42,43,71 , 79, 85, 120, 121, 133, Marin-Padilla, M., 363, 567 177, 199,202,216,321,512. Mark, R. F., 490, 555 514,8,58.59, 63, 69. 71. 75, 77. Marr, D., 18, 19.20.42, 113, 116, 80,90, 119, 123, 126, 127. 130. 117.121-122,123,196,283,512, 131,135,138,140, 141, 142, 63, 119.378,567 170,172,195, 217, 370,380, Marr's levels of analysis. 122-124. 381,383, 394.532.558,559, + +See also Levels of analysis 568, 574 + +Marrocco, R. T., 480, 567 McClurkin, 1. W .• 480, 567 Marshall, 1. c., 102,508 McConkie, G. W., 161, 163, 568, + +Marshall. W. H .• 352, 579 573 + +Marslen-Wilson, W. D., 43. 512. 63. McCulloch, W. S., 152,424.512 77, 79,80, 97, 98, 99, 275, 56 7 McDermott, D., 432.568 Martin , K. A. c., 363, 56 7, 576 McGeoch, L. A .• 235, 508 Massaro, D. W .• 77, 81, 86. 94, 567. McGill. J. , 145, 575 + +568,5 71 McGuinness, E. , 374, 375. 553 Massey, T., 378. 560 McNaughton , B. L. , 448, 568 Matrices and linear systems. See also MD. See Monocular deprivation Linear algebra Medin, D. L., 171, 181,200.205. + +basis for vector space, change of, 536, 568 + +413-418 Meditch , J. S., 456,512 + +descriptions of, 385-386 Memory, a distributed model of. See eigenvectors and eigenvalues, 399- also Distributed representations; 403 Memory, retrieving information + +examples of PDP systems, 406-410 from + +linearity, 393-395 conclusions on, 214-215 + +matrices, 386 detailed assumptions of, 176-182 addition of. 387-389 experimental results of simulations matrix mapping. algebraic repetition and familiarity effects, + +properties of, 389-390 192-199 + +scalars, multiplication by, 386 representation of general and matrix inverses. 41 0-413 specific information, 199-206 + +Memory, a distributed model of Miller, W., 254 + +extensions of model (continued) Milner, B., 504, 506, 510, 514 , 569 + +interference and fan effects, 208- Minciacchi, D., 350, 56 7 + +209 Minsky , M., 65, 76, 96, 111-1l3, memory blends, 208 153, 154, 157-158, 160, 233, 29 1, regularities of behavior, 319,321, 334, 348, 354, 36 1, emergence of, 207 424, 513, 18, 19, 535,569 semantic memory , emergence of Mitchell, D. E., 475, 558 + +from episodic traces , 206 Mitchinson, G., 296, 297, 468, 486, + +general properties of, 173- 175 509 + +modular structure, 174-1 75 Mitra , S. K. , 455, 513 paltern of activation, 175 Miyuwaki , K., 473, 569 + +hidden units, augmenting model Models, simi larities and differences + +with, 209-214 between, 4-5 + +model 's behavior, key aspects of, Modifications of patterns of + +182- 192 interconnectivity in PDP models, + +relation to basic concept in, 176 52-53. See also Learning theories of, 2-3, 170-1 71 Modular structure of memory, 79, Memory, retrieving information 174- 175. See also Memory , a from. See also Distribu ted distributed model of representations, fealures of; Molinari, M. , 35, 567 + +Memory, a distributed model of Monocular deprivation (MD) , 474, + +content addressability, 25-29 475 + +de fault assignment, 29-30 00 shift under, 48 7 + +graceful degradation, 29 rearing, 489 + +spontaneous generalization , 30-31 Monocular occlusion (AM) , 474 Mercer, R. L., 293, 508 Monotonicity concepts for acti vation Merzenich , M. M., 385, 386, 38 7, functions, 427-428. See also 563, 569 Activation functions Mesulam, M. M., 350, 569 Monotonicity-in-context , 426-428 Metropol is, N., 230, 277, 513 Montero, V. M., 351, 569 Meyer, D. R. , 352, 579 Moran, 1., 374 , 558 Michael , C. R. , 36 7, 368, 569 Morrell, F. , 379, 569 + +Micro- and macrolevels of harmony Morris, R. G. M., 434, 466, 569 theory, 203-204, 210 Morrison, J. H., 364, 569 Microdescription , problem-solving Morton , J., 43, 513, 97, 106, 192, + +of, 246. See also Electricity 570 + +problem-solving Moser, M. G., 313, 570 + +Microfeature, 80-81 Motor control + +Microfeatures, semantic. See example of multi ple constraints in, + +Semantic microfeatures 4-6 + +Microstructure of cognition, 12-13 PDP models for, examples of, 13- + +Miezin, l, 374, 375, 553 18 + +Miller, D. T. , 536, 564 finger movements in ski lled + +Miller, G. A., 63, 106, 323, 566, 569 typing , 14-16 + +Miller, J. L., 62, 96, 569reaching for objects, 16-18 Miller, J. P., 381, 382, 569, 575 Mountcastle, V. B., 356, 366, 373, + +Moussouris , J., 289, 513 Mower, G. D., 478, 570 + +Mozer, M. C, 68, 127, 507, 513 , 125, 139, 140, 142, 5 70 Muller, R. U. , 435, 441, 445, 44 7 , + +565, 5 70 + +Multiple linear regression and the delta rule, 457·458. See also Delta rule, analysis of Multiple simultaneous constraints, 4·9, 58, 124, 272·2 75 mutual constraints, 7 operation of in syntax and + +semantics , 6-7 duplication of connection + +information , need for to exploit , + +124 + +role assignment, use of in , 272-2 75 simultaneous mutual constraints in + +word recognition , 7-9 + +speech perception, role of in, 124 Munro, P. W., 42, 180, 508, 480, 487, 489, 495, 496, 555, 570 + +Murray, E. A. , 35 7, 570 Mutt, V., 364, 560 + +groups of neurons behavior in cerebral cortex, 365-366 neurons wi thout many spines, 361 neurons wi th spines, 360-361 si ngle·neuron behavior in cerebral + +cortex, 364- 365 special cell types , 362-364 Network damage. See Damage , + +effects of on a network; Graceful + +degradation + +Neural and conceptual interpreta tion of PDP models. See PDP models , + +neural and conceptual interpretation of Neural-like processing systems , common learning paradigms in, + +1 60·16 1 Neural modeling, 130 + +Neural nets, biological limits on storage capacity of, 469-470. See + +also Fan-out, limi ted Neural or unit level of + +representation. See Pattern-based + +coordinates , delta rule in Neural plasticity in cerebral cortex, 385·38 7. See also Cerebral + +Nadel, L. , 435, 445, 510, 52 7, 571, cortex , questions about 576 computation in Nakatani, L., 61 , llO, 570 Neural plasticity and learning Nathan, P. W. , 514, 515 , 574 critical period , effect of Nativism vs. empiricism, 139·142 environment on, 478 Nauta, W. J. H. , 334, 342, 570 critical period of, 473·4 78 NE. See Norepinephrine ocular domi nance , measuring Necker cube, ll, 13, 16, 28. See also changes in, 474·4 76 + +Schemata, concept of plasticity· modulating processes , + +Neely, R. B., 63, 122, 573 476·4 78 + +Negation problem, 346-348. See also discussion of, 471·473, 494·499 Delta rule, generalized existing modification rules, state + +Neisser, U., 81, 11 3. 11 6, 212 , 513 , dependence and, 494·496 515 global modulators as dynamic + +Nelson, R. J. , 352, 354, 385, 477, variables, 496·497 569, 570 predictions for, 497·499 Nelson, S. B., 477, 554 experimental data on, comparison + +Neocortical neurons, nature of with, 489·494 + +cell types in, 358·360 ocularity state and its effect on, + +Neural plasticity and learning + +(continued) + +state dependencies of plasticity, + +484-489 + +PDP models, learning rate as factor + +in. 472 + +single-unit learning. focus on, 471 + +summary of, 501 terminology. 473 + +visual cortex, ideas described with respect to ocular dominance in, + +499-501 + +Neural processing in cerebral cortex . 378-381. See also Cerebral cortex , questions about computation in + +Neural realism, lack of in PDP models, 136-13 8 + +Neurons. See also Cerebral cortex, anatomy and physiology of; Neocortical neurons. nature of behavior in the cerebral cortex + +isomorphism. failure of in, 411-414 quasi-linear systems with, 418-422 + +use of. 41 8-42 1 + +limited dynamic range and, 420- + +42 1 + +subthreshold summation , 420 Nonpyramidal cel ls. 358-360. See also Neocortical neu rons, nature + +of + +Norepinephrine (NE) , 476-477, 478, + +480, 493 + +as potential modulator of neural plasticity, 476-477. 491-494, 497 + +Normal rearing (NR) . 474 Norman, D. A .. 8, 9, 14, 15, 79, 11 6. 133, 206, 512, 513 , 51 4, 18, 19, 53 7, 539, 540. 543, 545, 555, + +570, 574 + +Norris, D. , 63, 100, 57/ NR. See Normal rearing Nusbaum , H. C. 110. 57/ + +groups of neurons, 365-366 Ochs, M. T. , 385, 563 single neuron , 364-365 Ocular dominance (OD) + +classical description of, 335-33 7 class, 484 + +connections between, in brain, histograms, 475, 479. 489, 490 132-133 shift, under MD. 48 7 communication among, 132 statistics , 474-4 76 + +continuous output of, 133- 134 Ocular dominance index. 481-483, + +graceful degradation of. 134 484, 490 + +neocortical , 358-365 vs. responsivity plot, 491 + +number of, 131 Ocularity plane, power of as tool in speed of, 130-131 theoretical analyses of ocular systems, 131- 132 dominance plasticity, 483-484 treated as devices, 424-425 (see Ocularity state and its effect on also Boolean function) plasticity, 478-480. See also without many spines, 361 Neural plasticity and learning + +with spines , 360-361 ideal neuron. 479-480 Newell , A., 108, 195, 513 ocularity plane, 480-484 Newsome, W. T. , 347, 356, 554, 568 plasticity, state dependence of, + +Newtonian mechanics, 125 484-489 + +Nicholson , C. , 364, 566 OD. See Ocular dominance Ninteman , F. W., 493, 572 Oden, G. C. , 77, 275, 568, 571 Nonlinear systems. See also PDP ODH. See Ocular dominance, + +models, neural and conceptual histogram + +interpretation of 001. See Ocular dominance index dist ributed, natural competition in, 6-0HDA. See 6-hydroxydopamine 414-428 . d Oh�awa l., 481, 491, 560, 567 Copynghte Matena + +Oja, E., 489, 557 + +O'Keefe, J., 434, 435, 445, 448, 466, + +568, 569, 571 O'Kusky, 1., 348, 571 Olson, C. R. , 475, 571 Olson, L. , 350, 553 + +Olton, D. S., 435, 522, 554, 571 One-layer PDP systems , use of matrices in analyzing, 390-393 . See also Matrices and linear + +systems + +One-layer perceptron , 111 -113 limitations of, 11 2- 11 3 One-step system in interactive + +models, 60 + +Optimization problems, use of linear programming for, 284-286 Organization of Behavior, 53, 152 + +Ortony, A., 19, 32, 574 + +Output units definition of, 48 + +as major aspect of PDP models, 46, + +48 -49 + +system), 453-454 + +competitive learning methods (App. + +B), 504-506 + +description of, 364, 488-489 major components of, 489-490 performance of, 500-501 + +plan for competitive learning, (App. + +A), 502- 503 + +plan language of, 490, 49 1 -497 simplified diagrams of, 454-455, + +464 + +simulation system, 497- 500 typical plan for, 490 Parity networks, 159, 160 Parity problem, 334-335 See also Delta rule, generali zed Parker, D. B., 322, 36 1, 513 PARSIFAL (Marcus ), 31 7 Parsing in PDP models, 31 7-323 Part/ whole hierarchy, 105 + +Past-tense acquisition , three stages of, 21 9-221. See also Verbs , learning past tenses of + +Patte, P., 38 7, 556 + +Pattern of activation , in distributed + +P3 system. See Parallel process model of memory, 175 programmer memory traces as change in + +PABLO. See Reading, programmable weights, 176 + +blackboard model of mental state as, 176 + +Palay, S. L., 338, 571 prior, retrieval as reinstatement of, + +Palmer, R. G. , 296, 511, 513 176 + +Palmer, S. E. , 11 7, 513 and response strength, 1 94- 195 Pandemonium, 42 Pattern association paradigm , + +Pandya, D. N., 352, 571, 573 defin ition of, 55 + +Papert, S., 65, 76, 96, 11 1-1 13, 158, Pattern associators. See also + +160, 233, 29 1, 319, 32 1, 334, Programmable pattern associators; 348, 354, 361 , 424, 513 , 535, 569 Standard pattern associators; Paradigms of learn ing Verbs , learn ing past tenses of associative, 54-55 basic properties of, 33-37, 226-228 + +regularity discovery, 55 definition of, 161 + +Paradiso, M. A., 477, 554 learning regular and exceptional + +Parallel distributed processing. See patterns in, 226 + +PDP. models, attractive properties of, 38 + +Parallel Models of Associative Memory, restrictions of, 228-233 + +33, 533 Pattern-based coordinates, delta rule + +Pattern completion device, use of Boltzmann machine as, 289-290. See also Boltzmann machines Pattern of connectivity as major aspect of PDP models, 46, 49-5 1 + +Patterson , K. , 102, 508 + +PDP approach and cognitive science + +conclusions on, 1 45- 146 natural applications of, 144 + +objections to + +analysis, wrong level of, 121-127 cognitive approach, lack of, 120- + +121 + +problems of, 543-545 new directions in, 545-546 strengths of, 535-539 + +description , levels of, 538-539 human information processing, essential properties of, 53 7 + +schema, 536-53 7 useful result of, 537-538 weaknesses of, 539-543 + +evaluative structure , need for, + +541 -542 + +multiple systems, required for, + +542-543 + +cognitive theories, constraints of, type-token problem , 539-540 + +129- 136 variables, 540-541 + +conscious knowledge and explicit PDP models, active representation + +reasoning, 143- 145 in, 31 -40, 175-1 76 human vs. rat intelligence, 143 local vs . distributed, 32 + +lack of neural realism in, 136- 1 38 pattern associator models attractive + +Marr's levels, 122-124 properties of, 38 nativism vs. empiricism, 139- 142 pattern associ ators, 33-37 other notions of levels, 124-127 structure of ensemble of patterns, + +reductionism and emergent extracting, 39-40 + +properties, 127-129 PDP models and the brain. See also weaknesses of, 111- 120 Cerebral cortex , anatomy and status of various models, 144- 145 physiology of; Cerebral cortex , PDP approach , introduction to questions about computation in active representation in, 31 -40 relationship between, 328-330 as alternati ve to serial models, 12- models of neural mechanisms, + +13 330-331 + +appeal of, 3-4, 10- 12 neurophysiology relevant to, 32 7- + +examples of 328 + +memory retrieval , 25-31 PDP models, future directions for, + +motor control , 13- 17 54 7-552 + +perception, 1 8-24 PDP models, general framework for history of, 41 -44 bottom-up processing, 57-59 local vs . distributed representation, conclusions on, 74-76 + +32-33 hierarchical organizations, 57 pattern associator models interactive models , 59-60 attractive properties of, 38 learning paradigms, 54-57 ensemble of patterns, extracting major aspects of, 46-54 structure from, 39-40 activation rule, 51-52 learning multiple patterns, 37-38 learning rule, 52-54 learning rules of, 36- 37 propagation rule, 51 workings of, 33-36 sigma-pi units, 73-74 PDP approach, reflections on synch ronous vs . asynchronous + +versions, specific + +brain state in a box model (BSB) , + +66·68 + +Feldman and Ballard ' s units , 72 Grossberg's units, 70·7 1 interactive activation model, 71 linear threshold units, 63·66 simple linear models, 61·63 thermodynamic models, 68·70 PDP models, learning rate as factor in, 472·4 73. See also Neural plasticity and learning PDP models , neural and conceptual + +interpretation of conclusions on , 429·431 consideration of, 390·391 distributed nonlinear models, natural competition in, 424·429 as dynamical systems, 39 7·398 interpretations, 391 ·396 + +isomorphism hypothesis, fail ure of in nonlinear models, 422·424 + +kinematics , 400·403 + +kinematics and dynamics, 398·399 + +learning connections and + +isomorphism of levels, 41 6·418 linear systems, isomorphism of + +levels in, 41 1·413 + +localized damage and, 413·416 nonlinearity, quasi·linear systems + +with, 418·422 + +pattern coordinates, 406·41 1 vector space, structure of, 403·406 + +Pearlmutter, B., 298 Pearson , 1. c., 385, 575 Peck, C. K. , 475, 571 + +Peptides in the cerebral cortex, 340 + +Perez, R. , 494, 571 + +Perception, examples of for PDP + +models + +familiar patterns and, 20· 23 novel patterns, completion of, 23· + +25 + +stereoscopic vision, 18-20 Perceptrons (Rosenblatt) , 154· 15 8 convergence procedure, 41 ·42 , 65, + +learning rule, 53, 154·15 7 parallel reorganizing elements, + +158·159 + +Perceptua l processing, centrality of, 197·198. See also Harmony + +theory + +Perkel, D. H., 381, 571 Perkel, D. J., 381 , 571 Perrett, D. I., 368, 571 Perry, 1., 195, 508 Peterhans, E., 376, 578 + +Peters , A., 336, 338, 361, 363, 365, + +559, 571, 572 Petersen , S. E. , 34 7, 554 Petitjean, F., 350, 555 + +Pettigrew, J. D., 476, 477, 487, 490, + +492, 555, 564 + +Phase transitions, computational significance of, 236·237 Phill is, J. W. , 339, 565 + +Phoneme identification , factors + +influencing + +categorical perception, 84, 88·95 detectors, retuning of by context, + +95· 97 + +lexical effects on , 77· 78 factors influencing, 78-80 simulations, summary of, 97 trading relations, 84·88 + +use of phonotactic rules in, 81 ·81 Phonemic restoration effect, 20 + +Piaget, J., 17, 19, 572 Piercy, M., 516, 51 7, 563 Pillsbury, W. B., 20, 513 Pinker, S., 21 7, 572 Pinto-Hamuy, T. , 352, 579 Pisoni, D. B., 60, 77, 92, 94, 100, + +572, 574 + +Pitts, W, 15 2, 424, 512 + +Place-field model. See also Place recognition and goal location , biologically plausible models of + +description of, 436-441 goal location , 449 properties of, 439·440 + +scope of, 448 + +shape and size, 445-446 + +Place recognition and goal location, biologically plausible models of � -coefficient constants (App.) , + +46 7-468 + +�-coefficient model , 460-466 � units (App.) , 469-4 70 conclusions on , 466 distal landmarks , 445 + +distributed view-field model, 449- + +460 + +goal location, 449 + +location parameters, 441 -443 model , description of, 436-441 properties of, 439-440 place-field location , 446-448 place-field model, scope of, 448 place-field shape and size, 445-446 + +place recognition, 434-436 simulated experiments, 443-445 Plan language, as major component of P3 system, 489, 490, 49 1-497 creating P3 plan for, 493-497 + +features of, 490 functions of, 491-493 Plasticity, neural . See Neural + +plasticity Podgorny, P., 501 , 575 + +Poggio, T., 18, 19, 20, 42, 117,512 , 513, 129, 365, 381, 383, 564, + +565, 572 Poincare, H., 213, 513 + +Pollack, 1. B. , 277, 278, 31 1, 314, + +578 + +reading. See Reading, + +programmable blackboard model + +of + +Programmable pattern associators. See also Connection information distribution mechanism; Reading, programmable blackboard model + +of + +CA units, requirements of, 474-476 CID networks, requi rements of, + +473-474 + +conclusions on, 486 discussion of, 485-486 distributed representations , simultaneous access to, 483-485 multiple pattern processing, 477- + +478 + +overlapping, 478-480 + +simultaneous access , cost of, 481- + +482 + +single pattern processing, 476-477 summary of CA requirements, + +480-48 1 + +Proskauer, C. c. , 336, 361, 363, 571, + +572 Prototypes + +> coexistence of and repeated exemplars, 189- 192 + +learning from exemplars, 182-184 multiple, nonorthogonal, 184- 188 Pyramidal cells, 358-360. See also Neocortical neurons, nature of + +Porrino, L. J., 350, 572 Quasi-linear activation function , 52, Poschel, B. P. H. , 493, 572 425. See also Activation + +Posner, M. I., 171, 183, 200, 203, functions + +572 Quasi-linear systems with Powell , T. P. S., 344, 348, 350, 351 , nonlinearity, 418-422. See also 352, 556, 560, 563, 564, 572, 5 73 Nonlinear systems; PDP models, + +Prince, D. A., 364, 369, 557 neural and conceptual Principles of Neurodynamics, 41-42, interpretation of + +154 Quasi-local interpretations, 394-395. Probabi lity theory, 209-2 10 See also PDP models, neural and Processing units, set of for PDP conceptual interpretation of + +model , 46-48 Quasi-multilinear activation function , + +vs. one-unit-one-concepl 426. See also Activation + +Rader, R. K., 497, 5 77 conspiracies of, /57-/59 Rail, W., 336, 381 , 382, 569, 572, Realizability theorem, 230-235 575 Receptor, cartoon of, 508-509. See + +Ralston, H. 1., 336, 572 also Amnesia + +Ramachandran , V. S., 478, 572 Recurrent networks, 354-360. See Ranck, J. B. , Jr., 435, 441 , 445, 44 7, also Delta rule, generalized 565, 570 performance of, 359-360 Random-dot stereograms, 18 sequence completion , learning of, + +Rao, C. R. , 45 5, 513 358-359 + +Rauschecker, J. P. , 476, 478, 576 shift register problem and, 357-358 Rawlins, J. N. P., 434, 466, 569 Recursion, 11 9-120, 318-320 Rayner, K., 153 , 161 , 163, 164, 275, Reddy, D. R., 63, 107, 122, 573 560, 572, 573 Reductionism, PDP models as + +Reading, programmable blackboard exercise in, 127- 129 + +model of (PABLO) Redundancy, benefits of, 472 . See ambiguous characters, 155-157 also Standard pattern associators + +amount of feedback, effect of Reese, T. S., 336, 572 + +display length on, 159-161 Regularity detector paradigm, 1 61 + +cm computer simulation , results Reich , P. A. , 323, 573 of, 136- 141 Rei lly, D. L., 499, 573 conclusions on, 168-169 Reitboek, H. 1. P., 385, 573 connection information Relaxation searches, use of parallel distribution , networks to perform , 283-290 benefits of, 164- 166 learning, difficult and easy, 290-292 computer simulation of word maximum likelihood models, 292- + +recognition using, 134-136 294 + +cost of, 166-167 optimization problems and, 284· + +extensions of, 167-/68 286 + +mechanism, details of. /29-136 pattern completion, 289·290 (see also Programmable pattern . probabilistic decisions, use of to associators) escape from local minima, 287 - + +description of, 2, 125 288 + +fixations, sequences of, /61-164 simulated annealing, appl ication of fixations, single and multiple, 153- to Hopfield nets , 288·289 155 Relaxation system, 135- 136 interactive activation model , Relearning, speed of in Boltzmann + +bottom-up activations of word machines, 308-310 + +units in cm version of, /3 7-138 Repetition and famil iarity effects, + +interference and crosstalk, 139-1 41 /92- /99 + +PABLO simulation model alternative interpretation of, 193- + +coarse coding, 146-14 7 /94 + +details of, /5/-153 pattern action and response feedback, 147 strength, 194-195 + +focus of attention , shifting, /47- time-accuracy curves, effects of /5/ experimental variables on , /95- + +.overlappirig slots in, 143-14 7 /99 + +Repp, B. H., 95, 118, 56 7, 573 Representation , distributed. See Distributed representation Representation of environment as major aspect of PDP models, 53- + +54 + +Representation vector of harmony + +theory, 213-214 Representational features of + +harmony theoretical model , 213 - + +214 + +Representation , learning of. See Boltzmann machines; + +Competitive learning; Delta rule, + +general ized + +Representation , learning of new in + +harmony theory + +procedure and abstract features, + +258-260 + +in symbolic and subsymbolic + +paradigms , 26 1 + +Reproduction trial s , 520. See also + +Amnesia + +Residual learning skills in amnesia, + +518-524. + +Retinocentric feature detectors , 11 4 Retrograde amnesia, 505-506, 513- + +515 + +Reverse learning , occurrence of, + +See also Reading, programmable + +blackboard model of Rolls, E. T., 368, 571 Rosch , E., 171, 573 Rose, J. E., 345, 573 Rosen, I., 357, 554 + +Rosenblatt, F. , 41 , Ill , ]52, 153 - 154, 15 5- 157, 158, 29 1, 424, 514, + +226, 289, 535, 573 + +Rosenbluth, A. W., 230, 277, 513 Rosenbluth, M. N., 230, 277, 513 + +Rosenfeld, A., 285, 514 Rosenthal , M., 477, 561 Ross , B. H., 206, 554 RS. See Reverse suture Rubin, D. S., 293, 509 Rudnicky, A., 58, 55 7 + +Rule of propagation as major aspect of PDP models, 46, 51 Rumelhart, D. E. , 6, 9, 14, 15 , 20, 22, 24, 43, 71, 11 6, 1 20 , 121, 130, 133, 177, 199, 202, 216, 300, 32 1, 512, 51 4, 7, 18, 19, 31 , 59, 71 , 75, 77, 90, 170, 195, 21 7, 316, 380, 394, 532, 539, 540, + +545, 568, 573, 574 Russell, W. R., 514, 515, 574 + +Ryder, 1. M., 7, 511 + +296-298 Sachs, M. B. , 383, 574 Reverse suture (RS) , 474, 48 7-488, Saffran, E. M., 134, 514 489 Said, S., 364, 560 Reverse suture paradigm, time Sakaski , K., 370, 558 + +course of, 489-490. See also Salasoo, A., 60, 100, 197, 198, 559, + +Visual cortex, developmental 574 + +models of Sal vert , D., 350, 555 Ribak, C. E., 363, 572 Samuel , A. G. , 95, 160, 574 Riley, M. S. , 24 1, 264, 514, 515 Sanderson , K. 1., 480, 574 Rinzel, J., 381 , 382, 569, 575 Sayers , F. c., 324, 563 + +Ritz, S. A., 56, 406, 409, 410, 41 8, Scalars, multiplication by, 367, 386. 507, 1 73, 226, 311 ,399, 551, 554 See also Matrices and linear + +Roberts, E. , 351, 562 systems ; Vectors Rock, I., 11 7, 5 1 4 Schacter, D., 519, 574 + +Rocke! , A. 1., 344, 573 Schaffer, M. M., 17/, 200, 536, 568 Rockland, K. S., 352, 366, 374, 573 Schank, R. c. , 6, 9, 201, 202 , 514, + +Role-assignment model . See Case 18, 19, 3]4, 574 + +role assignment, model of Scheibel , A. B., 351 , 574 Role-specific letter un its, I�/J#fghted n§�P5WcfJ, M. E. , 351, 574 + +Sentence processing in PDP 418, 507, 173, 226, 311, 399, + +networks. See Case role 55 J, 554 + +assignment, model of Simon, H. A., 24 1, 508 Sentence-structure (SS) Simple binary addition problem, representation , 283-286. See also 34 1 ·346. See also Delta rule, + +Case role ass ignment, model of generalized + +Sequential symbol processing, 106- Simulated annealing, 287, 288-289, 108 313. See also Cool ing schedule; + +Sequential thought processes in PDP Harmony theory + +models. See also Recurrent Simulation system environment, as networks; Sequential symbol major component of P3 system, + +processing; Seriality, emergent 489 , 497-500 + +account of mental processing, Singer, W. , 476, 478, 575, 576 development of, 38-39 Single·level interactive model , 60 conclusions on, 53-57 Single-shot algorithms, 380. See also consciousness, contents of, 39 Cerebral cortex, questions about + +control , problem of, 39-40 computation in + +conversations , 42-44 Single-unit learning, focus on , 472. external representations and formal See also Neural plasticity and + +reasoning, 44-48 learning important aspects of, 47 Singley, 209 + +role of language in, 47 Skirboll, L. R. , 350, 577 mental models and, 40-42 Slater, P. c., 513, 515, 576 mental simulations and practice, 42 Siobin, D. 1., 221, 24 7, 249, 250, summary of, 48 251 ,254,255, 256, 556 thinking, goal direction in, 48 Siowiaczek, L. M., 120, 571 tic-tac-toe example of, 48-53, 54 Smal l, S. L. , 277, 3/4, 55 7, 576 + +Seriality, emergent, 247 , 249. See Smith , D. c., 490, 565 also Electricity problem-solving Smith , E. , 24, 515 Settlage, P. H., 352, 579 Smith , P. T. , 24, 515 + +Shall ice, T., /45, 543, 570, 575 Smolensky, P. , 12 5, 24 1, 259, 264 , Shankweiler, D. , 92, 94, 566 277, 289, 447 , 514, 515 Shannon , C. E., 195, 267 , 515 Sokolov, 1. L., 274, 56 7 Sharma, v. K. , 477, 561 Somogyi , P. , 362, 363, 56 7, 576 Shaw, G. L., 385, 575 Spared learning in amnesia, 518-519, Shepard, R. N. , 198, 515, 501, 536, 521-524. See also Amnesia 575 Spear, P. D., 490, 565 Shepherd, G. M., 336, 381, 382, Speech , fundamental aspects for 572, 575 development of TRACE model Sherk , H., 350, 374, 566 architecture for TRACE model, + +Sherman , S. M., 351, 560 importance of, 63-64 + +Shiffrin, R. M., 197, 198, 559, 574 context effects , left and right, 60 + +Shlaer, R., 494, 571 cues , sensitivity of, 62 Sickels, E. R. , 324, 563 lack of boundaries , 60, 61 Sigma-pi units, 72, 73·74, 426 speech signal , noise and generalized delta rule for, 353 indeterminacy in, 62-63 + +Spencer, W. A., 364, 576 Spoehr, K. , 24, 515 + +Spoken word recognition , study of, + +97- 98 + +Spontaneous learning (Rosenblatt) , + +15 5- 156 + +Squashing function , 425 , 485-489. See also Activation functions; Ocularity state and its effect on + +plasticity + +Squire, L. R., 505 , 510, 513, 515, 516, 51 7, 525, 52 7, 556, 576 Standard pattern associators. See also Programmable pattern associators + +conclusions on , 486 degradation, effects of, 472 limited fan-out, effects of, 468-472 programmable nets , resource requirements, 465-468 redundancy, benefits of, 472 resource requirements of, 460, + +46 1 -465 + +computations of, 463-465 Stanford, L. R., 351, 560 + +State of activation as major aspect of + +PDP model , 46, 48 State space (S) , 398·399. See also Kinematics of the dynamical + +system + +coordinate system for, 400 of general nonlinear activation + +model, 402 pattern view of, 406 + +unit coordinates for, 400-401 Statistical learning, analyzing case of, 453·457. See also Delta rule, + +analysis of Steedman, M., 274, 55 7 Sternberger, 1. P., 248, 576 Sternberg, S. , 13 3, 51 5, 402, 566 Stevens, K. N. , 61, 168, 561, 5 76 Stimulus equivalence, problem of, + +11 3·1 14 + +Stochastic generative model, 293· + +294, 31 3 Stochastic units, 81 + +Structure in representations and processes , 104· 108 constituent structure, 105·106 sequential symbol processing, 106- + +108 + +Studdert-Kennedy, M., 92, 94, 566, + +576 + +Subsymbol ic and symbolic + +paradigms, learning in, 261 ·262 Subth reshold summation , 420. See also Nonlinear systems, use of + +Summerfield, Q., 85, 576 Sur, M. , 352, 354, 385, 56 9 , 570 Surround effects in visual cortex, 374-3 77. See also Cerebral cortex, questions about computation in + +Sutton , R. S., 43, 53, 57, 444, 508, 515 , 383, 539, 554, 576 Swanson , L. W. , 350, 576 Swets, 1. A., 466, 510, 225, 56 1 Swinney , D. A., 109 , 577 Symbol ic and subsymbolic + +paradigms, learning in, 26 1 ·262 Symmetry problem , 340·34 1. See also Delta rule, generalized Synapses in the cerebral cortex , basi c types , 338·339 + +Synaptic change, neurochemistry of, 50 7·509. See also Amnesia + +Synchronous update vs . asynchronous update, 61 Syntactic processing in PDP models, + +31 7·323 + +Szentagothai, 1., 351, 361, 577 + +T-C problem, 348·352. See also Delta rule, generalized Tabula rasa, 139, 141 Takeuchi, A., 489, 495, 553 Talbot , W. H., 366, 56 7 Tank, D., 389, 562 Tash, 1., 92, 572 Teitelbaum , P. , 142, 515 Tel ler, A. H., 230, 277, 513 + +Strang, G., 41 1, 422, 515 Tel ler, E., 230, 277, 513 Strange, W. , 473, 569Copyrighted �aum , J. M. , 63 , 554 + +Terminal parameters, 49 1 . See also 57-59 + +P3 system Top-down theoretical strategy Terrace, H. S., 183, 515 pursued in harmony theory, 196, + +Theorems, harmony, (App.) 199-213 + +Boltzmann machines, second-order Torre, V., 11 7 , 51 3, 129, 365, 381, + +observables and, 273 - 275 565, 572 harmony function H, cogn itive Touret , M., 350, 555 + +systems and, 267-268 Touretzky, D., 322, 548, 577 terminology, 268-269 TRACE model of speech perception overview of definitions, 264-267 compared to Fanty's parser, 321- + +proofs of, 275-28 1 322 + +retrieving information from H, conclusions on , 120-121 269-272 deficiencies of, 119-120 storing information in H, 2 72-273 descri ption of, 2, 58-59, 64-68, Thermal equilibrium of network, 123- 124, 143, 153- 154 + +290- 29 1, 313 phoneme identification , factors + +Thermodynamic limit, 239 influencing + +Thermodynamic models, 68-70 categorical perception , 84, 88- 95 Boltzmann machines , 68, 69 lexical effects of on , 77-81 harmony theory, 68 phoneme detectors, retuning of + +Thibadeau, R., 161, 549, 577 by context, 95- 97 + +Thomas , G. 8. , Jr., 276, 515 simulations, summary of, 97 Thompson , H., 6 0 , 6 3 , 8 4 , 107, 577 trading relations, 84-88 + +Thompson , R. F. , 383, 552, 561 use of phonotactic rules in, 81 -83 Th ree-dimensional plots , 429, 430- phoneme units, context-sensitive + +438. See also Activation tuning of, 68-69 + +functions programmable version of, 167-168 Three-layer network, 97-98. See also speech, fundamental aspects for, + +Arbitrary mapping, implementing 59-63 + +Th ree-level interactive model, 59 spoken word recognition, study of, Three-stage learning curve, 240-245. COHORT model , 98- 101, 102, + +See also Verbs , learning past 103 + +tenses of word segmentation , lexical basis + +Th reshold logic unit, 425. See also of, 106-115 + +Acti vation functions word segmentation simulations, + +Tic-tac-toe, as example of sequential summary of, 115-11 7 + +thought processes in PDP models , successes, summary of, 117-/19 48-53, 54 TRACE I model , 69, 70- 71 , 75, 76 Tigges , J., 348, 577 TRACE II model , 69, 70, 71 - 75, + +Tigges, M. , 348, 577 76, 102, 110 Timing Travis, A. M., 352, 579 problem of, 378-380 Tri bus , M., 227, 512 of sensory stimulation , 383-384 T'so, D. Y., 385, 577 temporal binding, 383-385 Turner, M. R., 385, 560 Timney, B. N., 475, 558 Tversky , A., 499, 560 + +TombOl , T., 35/, 36 /, 363, 577 Two-dimensional space, inner Top-down approach , 12 3 products in, 380-382. See also + +Top-down processing syst��ghted MateYfifl.ors + +Verbs, regular, 245-246 , 24 7, 254- 257, 2j8-260. See also Verbs, learning past tenses of Verbrugge, R., 473, 569 Vertical and horizontal lines, experiments with, 184-190 Vertical ly hierarchical networks, 217 + +Videen, T. 0. , 497, 577 + +View-field model. distributed. See Distributed view- field model + +Vincent, S. R., 350, 577 + +Visual cortex , developmental models + +of. 489-494 + +alternating monocular occlusion , + +490, 491 + +norepinephrine, role of, 492-494 responsi vity, relation of to connectivity, 490, 492 reverse suture paradigm, time course of, 489-490 Visual system, 282-283. See also Boltzmann machines + +Vital-Durand. F .• 497. 500. 555, 577 + +Voight, H. F. , 383, 574 Volman, S. F., 36 7, 574 von der Heydt. R .• 376. 578 von der Malsberg, C .• 42. 1 47. 15 2. 162, 164, 51 6. 384. 489. 494. 578 Von Neumann architecture. 534-535. See also PDP approach , + +reflections on + +Von Neumann computer metaphor. + +195 + +Vygotsky. L. S. , 43, 47, 578 + +Walker, A. E., 349, 578 Walker, E. C. T., 7, 511 Walker, J. A .• 435. 554 Wall. J T., 385, 569 + +Waltz, D. L., 277. 278, 3lI, 314. + +578 + +Warren, R. M .• 20, 516 Webster. H. de F .• 338, 571 Weight-decay. use of in Boltzmann + +machine. 298·299. Weller. R. E. , 345, 578 + +Welsh, A., 43 , 512 , 63, 77, 79, 80, + +Werbl in , F. S., 336, 578 Wessels, J, 99, 104, 577 Westrum, L. E. , 336, 578 + +Whitteridge, D. , 354, 363, 558, 56 7, + +576 + +Whittlesea, B. W. A., 171, Ill, 200, 201, 202, 203, 204, 556, 578 Wickelfeature representation + +(Wickelgren) blurring, 238-239 details of, 234-239 + +Wickelgren , W. A., 62, 181 , 233, 510, 5lI, 527, 578 Wickelphones, 233-234, 236-238 + +Widrow, G., 3 2 1 , 516 + +Widrow- Hoff rule, 53, 291 -292 . See + +also Delta rule + +Wiener, 534 + +Wiesel, T. N., 340, 353, 356, 358, 366, 36 7, 373, 374, 385, 474, 475,483, 497, 500, 561, 562, + +563, 566, 577, 578 Williams, R. J., 425, 516 + +Willshaw, D. J. , 42, 97 , 100, 460, 46 1, 465-466, 468, 472, 475, 516 + +Wi lls haw nets, 46 1 -465 + +comparison of to various kinds of local representation , 465 difficulties with, 465-468 Wi lson , H. R., 381, 389, 578 Winston, P. H., 32, 51 6, 524, 578 + +Wise, R. A., 493, 578 Wise, S. P., 35 7, 564 Wolverton , G. S., 161, 568 Wood, C. c., 102, 516, 551, 578 Woods , W., 11 9, 516. 322. 578 Woolsey, C. N., 352, 579 + +Woolsey , T. A., 355, 500. 558. 579 Word identification simulations in TRACE, summary of. lI5- 1 17 Word-order and semantic cues to role assignment. 293-300. See also Case role assignment. model + +of + +Word perception model (McClelland & Rumelhart). See Interactive activation model of word + +Word segmentation , lexical basis of for TRACE, 106-1 15 identification , word, 112- 115 nonwords , end of, 11 1-112 short sentence example, J 15 word inputs, single and multiple, + +107-1 11 Wu, T. Y., 350, 577 Wyatt, H. J., 500, 558 + +XOR problem, 319-32 1, 330-334. See also Delta rule, generalized + +Yin, T. C. T. , 366, 56 7 Young, E. D., 383, 574 + +Zadeh , L. A., 423, 516 Zeki, S. M., 368, 374, 577, 579 Zipser, D., 97, 300, 51 4, 432, 43 7, 438, 440, 442, 443, 444, 44 7, 579 + +Zola, D., 161, 568 + +Zucker, S. 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b/lit-marker2/david-rumelhart-james-mcclelland-pdp-research-group-parallel-distributed-process-vol-2/david-rumelhart-james-mcclelland-pdp-research-group-parallel-distributed-process-vol-2.md @@ -0,0 +1,14805 @@ +Table of Contents Preface to Volume 2 + +Addresses of the PDP Research Group + +IV PSYCHOLOGICAL PROCESSES + +14 Schemata and Sequential Thought Processes in PDP Models + +D.E. Rumelhart, P. Smolensky, J.L. McClelland, and G.E. Hinton + +15 Interactive Processes in Speech Perception: The TRACE Model + +J.L. McClelland and J.L. Elman + +16 The Programmable Blackboard Model of Reading + +J.L. McClelland + +17 A Distributed Model of Human Learning and Memory + +J.L. McClelland and D.E. Rumelhart + +18 On Learning the Past Tenses of English Verbs + +D.E. Rumelhart and J.L. McClelland + +19 Mechanisms of Sentence Processing: Assigning Roles to Constituents + +J.L. McClelland and A.H. Kawamoto + +21 Open Questions About Computation in Cerebral Cortex + +T.J. Sejnowski + +22 Neural and Conceptual Interpretation of PDP Models + +P. Smolensky + +23 Biologically Plausible Models of Place Recognition and Goal Location + +D. Zipser + +24 State-Dependent Factors Influencing Neural Plasticity: A Partial Account of the Critical Period + +P.W. Munro + +25 Amnesia and Distributed Memory J.L. McClelland and D.E. Rumelhart + +VI CONCLUSION + +26 Reflections on Cognition and Parallel Distributed Processing + +D.A. Norman + +Future Directions + +Preface + +The chapters in this volume continue the explorations of parallel distributed processing that we began in Volume I . The accompanying table lays out the organization of both volumes . Part IV , which begins this volume , presents parallel distributed processing (POP ) models of psychological processes, and Part V explores the biological mechanisms of parallel distributed processing in the brain . Part VI provides a brief retrospective discussion of the whole book and our thoughts about + +future directions . + +The various parts of this book are interrelated , but they can generally be read in any order , and indeed most of the chapters can be under stood without reference to the rest of the book . However , readers may find it useful to read some of the chapters in Part I before delving into the specific topics covered in the chapters of Parts IV and V . A discus sion of the contents of each chapter and the background that is relevant to, it may be found in the introductory section at the beginning of each + +part of the book . + +Primary support for both volumes of the book came from the System Development Foundation and the Office of Naval Research . The System Development Foundation has provided direct support for the POP research group through a grant to Norman and Rumelhart , and has also supported several of the individual members of the group (Crick , Hin ton , Sejnowski , and Zipser ) . ONR contracts that have contributed support include NOOO14 -79 -C -O323 , NR 667 -437 ~ NOOO14 - 85 -K -O450 , NR + +667 - 548 ~ and NOOO14 - 82 -C -O374 , NR 667 -483 . + +x PREFACE + +VOLUME II + +Health, through a Career Development Award- PHS-MH -OO385- to McClelland and postdoctoral fellowships to Paul Smolensky and Paul Munro under Grant PHS-MH -14268 to the Center for Human Informa tion Processing at UCSD. Smolensky received support in the form of a fellowship from the Alfred P. Sloan Foundation , and some of McClelland 's work was supported by a grant from the National Science Foundation (BNS-79-24062) . These and other sources of support for specific individuals or projects are acknowledged in the appropriate + +chapters. + +Once again we would like to acknowledge the support of the Institute for Cognitive Science at UCSD and of all of the people at UCSD and elsewhere who have helped us bring this work to completion . These people are mentioned individually in the acknowledgments section of + +Volume I, which applies to both volumes. + +December 1985 + +I. THE POP PERSPECTIVEII. BASIC MECHANISMSIII. FORMAL ANALYSES + +1. The Appeal of POP 2. A Framework for POP + +3. Distributed Representations 4. General Issues + +5. Competitive Learning 6. Harmony Theory 7. Boltzmann Machines + +8. Learning by Error Propagation + +9. Linear Algebra 10. Activation Functions 11. The Delta Rule + +12. Resource Requirements 13. Parallel Network Simulator + +IV. PSYCHOLOGICAL PROCESSES + +V. BIOLOGICAL MECHANISMS VI. CONCLUSION + +14. Schemata and POP 15. Speech Perception 16. Model of Reading 17. Learning and Memory 18. Morphology Acquisition 19. Sentence Processing + +20. Anatomy and Physiology 21. Computation in the Brain 22. Neural and + +Conceptual Levels 23. Place Recognition 24. Neural Plasticity 25. Amnesia + +26. Reflections Future Directions + +David E. Rumelhart LA JOLLA, CALIFORNIA + +Addresses of the PDP Research Group + +Chisato Asanuma + +Francis H. C. Crick + +Jeffrey L. Elman + +Geoffrey E. Hinton + +Michael I. Jordan Department of Computer and + +Information Science University of Massachusetts + +Amherst , MA 01003 + +Carnegie-Mellon University Pittsburgh, PA 15213 + +Salk Institute P .O . Box 85800 San Diego , CA 92138 + +Salk Institute P .O . Box 85800 San Diego , CA 92138 + +Department of Linguistics + +University of California , San Diego + +La Jolla , CA 92093 + +Department of Computer Science + +Carnegie - Mellon University Pittsburgh , P A 15213 + +ADDRESSES OF THE POP RESEARCH GROUP . . XII + +James L. McClelland + +Paul W. Munro + +Institute for Cognitive Science University of California, San Diego + +La Jolla, CA 92093 + +Donald A. Norman + +Intellicorp + +1975 EI Camino Real West Mountain View, CA 94040 + +Daniel E. Rabin + +David E. Rumelhart + +Terrence J. Sejnowski + +Paul Smolensky + +Center for Adaptive Systems Department of Mathematics + +Gregory O. Stone + +Institute for Cognitive Science University of California, San Diego + +La Jolla, CA 92093 + +Ronald J. Williams + +lnsitute for Cognitive Science University of California, San Diego + +La Jolla, CA 92093 + +David Zipser + +University of Pittsburgh Pittsburgh, P A 15260 + +Boston University Boston, MA 02215 + +Department of Computer Science + +University of Colorado Boulder , CO 80309 + +Department of Psychology Carnegie-Mellon University Pittsburgh, PA 15213 + +Department of Information Science + +Institute for Cognitive Science University of California , San Diego + +La Jolla , CA 92093 + +Department of Biophysics Johns Hopkins University Baltimore , MD 21218 + +PSYCHOLOGICAL PROCESSES + +The chapters in this section are designed to show how parallel distrib uted processing has changed the way we think about the mechanisms of cognition . Each chapter describes a model of some mental process. Each shows how the model captures some basic aspects of the process. And each offers an alternative to other, earlier ways of thinking about + +aspects of the process. + +The models described in these chapters were motivated by a number of different considerations. Quite often , they were motivated by the feeling that parallel distributed processing mechanisms provide a very natural and appropriate set of mechanisms for dealing with some aspect of cognition that has not been dealt with successfully by other approaches. Quite often , they were motivated by an attempt to meet computational challenges posed by the processes they address. And quite often , they were motivated by attempts to extend the domain of POP models, to encompass processes and phenomena we did not know + +how to model at the outset. + +The first chapter of the section, Chapter 14, explains how parallel distributed processing can take us beneath the surface of schemata, to a level of description that allows us to see how we can preserve the desirable characteristics of schemata and at the same time make them more flexible , more sensitive to context, more adaptable. This chapter also begins to show how POP mechanisms can be used as the building blocks from which we may construct sequential thought processes, such + +PART IV + +2 PSYCHOLOGICAL PROCESSES + +The next two chapters consider issues in perception. Chapter 15 presents a model of speech perception and shows how it provides a unified framework for capturing a number of aspects of speech. Here, the goal was to develop a model that accounts in detail for psychological data on the process of speech perception and, at the same time , to begin to deal with several computational problems that make the extension of POP models to speech a challenging and stimulating task. The model introduces a processing structure called the Trace, a dynamic working memory, in which units that stand for hypotheses about the contents of an utterance at different points in time can interact. The parallel distributed processing that occurs in the Trace allows the model to account for contextual influences on phoneme identification , and the simple competitive interactions among hypotheses representing competing interpretations of the same portion of an utterance allow the model to segment and identify the words in an utterance in a simple and integrated fashion. The model accounts for a wide range of data in a direct and coherent way, and shows how POP mechanisms offer new ways of interpreting several phenomena, such as categorical perception + +and the perception of phonologically regular nonwords. + +The model described in Chapter 15 purchases its parallel processing capabilities by duplicating the same hardware to cover each time-slice of the Trace. This idea seems incorrect~ in general, it seems more plausible to view the Trace not as a fixed processing structure, but as one that is dynamically configured in the course of processing, using knowledge of contingencies between hypotheses to construct the Trace on the fly . Chapter 16 develops a model called the Programmable Blackboard Model of Reading (PABLO for short) that does just this, though for printed , as opposed to spoken input . This model is based on the idea of connection information distribution- roughly , the idea is to use information stored in one part of a processing system to set or program connections in another part of the same system. Two related simulation models based on this idea are applied to a number of aspects of reading that could not be addressed by the interactive activation + +model of word recognition , which was described in Chapter 1. + +Neither TRACE nor PABLO really extend above the word level to deal with the larger syntactic and semantic structures that organize words into sentences~ these levels are considered in Chapter 19, which + +we will describe a bit more below. + +Chapters 17 and 18 describe distributed models of different aspects of learning and memory. Chapter 3 (on Distributed Representations) provides useful background for these chapters, as well as for Chapter 19. Chapter 17 considers an existing dilemma for models of memory - whether to store summary representations in memory or whether to store an enumeration of specific experiences. The chapter + +INTRODUCTION TO PART IV 3 + +points out that with distributed representations, you can have it both ways. In the model, the (long-term) memory trace of an event is the change or increment to the connections that results from the event. Functional equivalents of summary representations (e.g., prototypes) emerge naturally from the superimposition of memory traces of specific events. Traces of recent or often-repeated events can coexist with the summary representation. The chapter also illustrates that the same composite memory trace can learn several different prototypes from exemplars, without ever being informed - and indeed, without having to "figure out " - which exemplars belong to each category. The model uses the delta rule (examined in Chapters 2, 8, and 11) for adjusting connection strengths and has some advantages over some distributed memory models, but it contains no hidden units, and so is not capable of overcoming what we call the "linear predictability constraint" on the set of patterns it can learn. At the end of the chapter, we illustrate with a simple example simulation how the model can be extended with hidden units that are trained with the aid of the generalized delta rule + +discussed in Chapter 8. + +Chapter 18 draws out some other implications of distributed models of learning and memory. It considers how knowledge underlying the lawful use of language might be represented in a PDP model and how that knowledge might be acquired. More generally, it shows how distributed representations provide an alternative to the conventional view that linguistic knowledge is represented in the form of explicit (though inaccessible) rules. The chapter considers a paradigm case of rule learning from the language acquisition literature - the acquisition of the past tense by children acquiring English as their first language. This case is often cited as an instance of rule acquisition par excellence because of the fact that children "regularize" irregular verbs at one stage, often saying "goed," for example. The model we describe in this chapter exhibits this and many other aspects of the acquisition process, and it does this by using very simple learning mechanisms. Lawful behavior emerges from the superposition of changes to connection strengths. The representation of the rules of past-tense formation is implicit in the resulting connection strengths and is acquired without the aid of any device that relies on the formulation and testing of + +explicit but inaccessible rules. + +Many of the chapters we have been describing deal with aspects of language, but none of them get much beyond the processing of individ ual words. Does this indicate that PDP models are inappropriate for capturing higher levels of language structure and processing? We think not . Indeed, one of our goals has been to work toward the development of PDP models of sentence processing. As Chapter 19 indicates, much of the groundwork has now been laid. That chapter describes a 4 PSYCHOLOGICAL PROCESSES + +distributed model that brings the benefits of parallel distributed pro cessing to the processing of simple sentences , and shows how a POP network can be configured to produce a representation that can capture the underlying case structure of simple sentences . The model exhibits a number of very nice properties . It can assign arguments of sentences to the appropriate case roles based on word - order information , based on the mutual selectional constraints imposed by the different words in the sentence , and based on word - order and mutual constraints working together ~ it can choose the appropriate " case frame " for a verb on the basis of the content and configuration of the arguments in the sen tence ~ it can choose the appropriate reading of a semantically ambigu ous word based on constraints imposed by the other arguments in the sentence ~ it can fill in default values for missing arguments ~ and it can generalize its case - role assignments to novel verbs if it is given a representation of some of the semantic features of the verb . The model has not yet reached the stage where it can process sentences with embedded clauses , but we suggest three ways in which it might be extended to do so , including one that relies on the use of the connec tion information distribution mechanism described in Chapter 16 and one that involves " true " recursion . These suggestions indicate that POP mechanisms are capable of processing recursively defined struc - + +tures , contrary to prevalent belief . + +Similarities and Differences Between Models + +Each of the models described in these chapters differs in detail from + +all of the others . One model uses continuous - valued , asynchronous units ~ several others use continuous , sychronous units ~ still others use stochastic units . In some models , activation values can range from 1 to - 1 ~ in others , they can only range from 1 to 0 , or slightly below O . All the models , however , are examples of the class of POP models , as described in Chapter 2 , and their minor differences are in most cases incidental to their behavior . Where these detailed assumptions seem to make a difference , we point it out , but in general , we do not think that + +much hinges on these differences . + +One characteristic that differentiates some of the models from the others requires some comment : The models in Chapters 15 and 16 use local representations , while the models in the other chapters use distrib uted representations . Even this does not reflect a fundamental differ ence in the philosophy of the models ~ rather , they reflect differences in the points we wanted to make and the issues we wanted to raise in the different chapters . In fact , we believe that both the TRACE model and + +INTRODUCTION TO PART IV 5 + +the models described in Chapter 16 could be made more efficient by the use of distributed rather than local representations, for reasons discussed in Chapters 3 and 12. It is also true that nearly all of the models can be seen as either local or distributed , depending on one's point of view. They are local, in the sense that each unit generally stands for a particular conceptual object or feature, or perhaps a (coarse coded) conjunction of features. They are distributed , in the sense that any given stimulus object- a phoneme, a word, a sentence, a sceneproduces a pattern of activation over a very large number of units. Whether we see the models as distributed or local is primarily a matter + +of whether we are looking at the forest or the trees. + +Stepping Stones + +Most of the models we present represent the result of a long series of explorations. In some cases, we learned a great deal from our earlier attempts, and the problems we had with them lead natually to better formulations . In other cases, our early attempts were failures we did not know at first how to overcome. For example, an early version of the model of past tense learning could be made to produce overgeneralization errors, but it could only process verbs consisting of a consonant, a vowel, and a consonant. It took us two years to formulate a better + +representation. + +We think the models we describe in these chapters demonstrate progress in the development of POP models of psychological processes. But none of the models is the final word. Each model has its weaknesses, as well as its strengths. We have not solved all the problems~ rather, we have suggested an approach that shows promise of leading us closer to their solution . We offer these models in that spirit : as stepping stones along the way to a deeper understanding of the + +microstructure of cognition . + +Schemata and + +Sequential Thought Processes in PDP Models + +CHAPTER 14 + +D. E. RUMELHART, P. SMOLENSKY, J. L. McCLELLAND + +One of our goals for this book is to offer an alternative framework for viewing cognitive phenomena. We have argued that talk at the level of units and activations of units is the preferable way to describe human thought . There is, however, already an established language for discussing cognitive phenomena. In this chapter we wish to address the relationship between some of the key established concepts and our parallel distributed processing models. There are many important concepts from modern cognitive science which must be explicated in our framework . Perhaps the most important , however, is the concept of the schema or related concepts such as scripts, frames, and so on. These large scale data structures have been posited as playing critical roles in the interpretation of input data, the guiding of action, and the storage of knowledge in memory. Indeed, as we have argued elsewhere (cf. Rumelhart , 1980) , the schema has, for many theorists, become the basic building block of our understanding of cognition . Yet, the POP language we are proposing is devoid of terms such as schemata, scripts, frames, and so forth . Instead, we have proposed building blocks at a much more microlevel - at the level of units, activations, and similar "low-level" concepts. Interestingly , it was struggling with the concept of the schema and some of its difficulties that led one of us (OER) to an exploration of POP models to begin with . It was therefore with + +and G. E. HINTON + +8 PSYCHOLOGICAL PROCESSES + +some priority that we began to develop an interpretation of the schema + +in the language of parallel distributed processing . 1 + +Perhaps the first thought that comes to mind is to map the notion of the schema onto the notion of the unit . This does , indeed , capture some of the important aspects of the schema . In particular , the unit is an element , like the schema , which monitors its inputs searching for a good fit and takes on a value which represents how well its inputs fits its own internal criteria . However , such an identification misses much of what makes the schema a powerful conceptual tool . In particular , there is no analog to the variable or default values . There is no notion of the internal structure of the schema nor many of the other important aspects of schemata . Moreover , the scale is wrong . Schema theorists talk of schemata for rooms , stories , restaurants , birthday parties , and many other high -level concepts . In our parallel distributed processing models , units do not tend to represent such complex concepts . Instead , units correspond to relatively simple features or as Hinton ( 1981a ) calls them microfeatures . If we are to do justice to the concept of the schema ~ we are going to have to look beyond the individual unit . We are going to have to look for schemata as properties of entire networks rather than single units or small circuits . In the following sections we show how features of networks can capture the important features of schemata . Since our interpretation is clearest in the subset of POP models that can be characterized as constraint satisfaction networks , it will be useful to first describe that class of models and provide a + +language for talking about their properties . + +PARALLEL DISTRIBUTED PROCESSING MODELS AS + +CONSTRAINT SA TISF ACTION NETWORKS + +It is often useful to conceptualize a parallel distributed processing network as a constraint network in which each unit represents a hypothesis of some sort (e.g ., that a certain semanti .c feature , visual feature , or acoustic feature is present in the input ) and in which each connection represents constraints among the hypotheses . Thus , for example , if feature B is expected to be present whenever feature A is , + +1 All of the authors have contributed to the ideas expressed in this chapter. Smolensky's slightly different framework is sketched in Chapter 6. Hinton 's view of the microstructure of symbols is sketched in J. A . Anderson and Hinton (1981, pp. 29-32), and McClelland (1981) shows how POP networks can be employed to fill default values (see the discussion in Chapter 1) . While we all agree with the flavor of the current dis- + +14. SCHEMATA AND SEQUENTIAL THOUGHT 9 + +there should be a positive connection from the unit corresponding to the hypothesis that A is present to the unit representing the hypothesis that B is present . Similarly , if there is a constraint that whenever A is present B is expected not to be present , there should be a negative con nection from A to B. If the constraints are weak , the weights should be small . If the constraints are strong , then the weights should be large . Similarly , the inputs to such a network can also be thought of as con straints . A positive input to a particular unit means that there is evi dence from the outside that the relevant feature is present . A negative input means that there is evidence from the outside that the feature is not present . The stronger the input , the greater the evidence . If such a network is allowed to run it will eventually settle into a locally optimal state in which as many as possible of the constraints are satisfied , with priority given to the strongest constraints . 2 The procedure whereby such a system settles into such a state is called relaxation . We speak of the system relaxing to a solution . Thus , a large class of POP models , including the interactive activation model of word perception , are con straint satisfaction models which settle on locally optimal solutions + +through the process of relaxation . + +Figure 1 shows an example of a simple 16-unit constraint network . Each unit in the network represents a hypothesis concerning a vertex in a line drawing of a Necker cube .3 The network consists of two intercon nected subnetworks - one corresponding to each of the two global interpretations of the Necker cube . Each unit in each network is assumed to receive input from the region of the input figure - the cube - corresponding to its location in the network . Each unit in the Figure is labeled with a three letter sequence indicating whether its ver tex is hypothesized to be front or back (F or B) , upper or lower (U or L ) , and right or left (R or L ) . Thus , for example , the lower left -hand unit of each subnetwork is assumed to receive input from the lower left -hand vertex of the input figure . The unit in the left -hand network represents the hypothesis that it is receiving input from a lower left hand vertex in the front surface of the cube (and is thus labeled FLL.) , whereas the one in the right subnetwork represents the hypothesis that it is receiving input from a lower left vertex in the back surface (BLL ) . + +2 Actually, these systems will in general find a locally best solution to this constraint satisfaction problem. It is possible under some conditions to insure that the "globally" best solution is found through the use of stochastic elements and a process of annealing + +(cf. Chapters 6 and 7 for a further discussion). + +3 J. A. Feldman (1981) has proposed an analysis of the Necker cube problem with a somewhat different network. Although the networks are rather different, the principles are the same. Our intention here is not to provide a serious account of the Necker cube + +10 PSYCHOLOGICAL PROCESSES + +FIGURE 1. A simple network representing some of the constraints involved in perceiv- + +Since there is a constraint that each vertex has a single interpretation , these two units are connected by a strong negative connection. Since the interpretation of any given vertex is constrained by the interpretations of its neighbors, each unit in a subnetwork is connected positively with each of its neighbors within the network . Finally , there is the constraint that there can only be one vertex of a single kind (e.g., there can only be one lower left vertex in the front plane FLL ) . There is a strong n~gative connection between units representing the same label in each subnetwork. Thus, each unit has three neighbors connected, positively , two competitors connected negatively, and one positive input from the stimulus . For purposes of this example, the strengths of connections have been arranged so that two negative inputs exactly balance three positive inputs. Further , it is assumed that each unit receives an excitatory input from the ambiguous stimulus pattern and that each of these excitatory influences is relatively small. Thus, if all three of a unit 's neighbors are on and both of its competitors are on, these effects would entirely cancel out one another~ and if there was a small input from the outside, the unit would have a tendency to come on. On the other hand, if fewer than three of its neighbors were on and both of its + +ing the Necker cube. + +14. SCHEMATA ANDSEQUENTIAL THOUGHT 11 + +competitors were on, the unit would have a tendency to turn off, even + +with an excitatory input from the stimulus pattern. + +In the last paragraph we focused on the individual units of the networks. However, it is often useful to focus not on the units, but on entire states of the network. In the case of binary (on-off or 0-1) units, there is a total of 216 possible states in which this system could reside. That is, in principle, each of the 16 units could have the value either 0 or 1. In the case of continuous units, in which each unit can take on any value between 0 and 1, the system can, in principle, take on any of an infinite number of states. Yet, because of the constraints built into the network, there are only a few of those states in which the system will settle. To see this, consider the case in which the units are updated asynchronously, one at a time. During each time slice, one of the units is chosen to update. If its net input exceeds 0 its value will be pushed toward 1, otherwise its value will be pushed toward 0, using the activa- + +tion rule from the word perception model: + +Q} (I + 1) = Q} (t) + net} a} (t) otherwise. I net} (1 - a) (t net} > 0 + +Here, a) (t) stands for the activation of unit j at time t , and net) (t) stands for the net input to unit j at t . netj (t) is simply the sum of the + +excitatory and inhibitory influences on unit j : + +ej (t) + r. Wjiai (t) i~j + +where ej (t) is the external input to unit j at t and Wji is the weight on + +the connection to unit j from unit i . + +Imagine that the system starts with all units off. A unit is then chosen at random to be updated. Since it is receiving a slight positive input from the stimulus and no other inputs, it will be given a positive activation value. Then another unit is chosen to update. Unless it is in direct competition with the first unit, it too will be turned on. Eventually, a coalition of neighboring units will be turned on. These units will tend to turn on more of their neighbors in the same subnetwork and turn off their competitors in the other subnetwork. The system will (almost always) end up in a situation in which all of the units in one subnetwork are fully activated and none of the units in the other subnetwork are activated. That is, the system will end up interpreting the Necker cube as either facing left or facing right. Whenever the system gets into a state and stays there, the state is called a stable state or a + +Figure 2 shows the output of three runs of a simulation based on this network. The size of the square indicates the activation values of each 12 PSYCHOLOGICAL PROCESSES + +Run 2 Run 3 + +Left Subnet + +Right Subnet + +Right Subnet + +Left Subnet + +FIGURE 2. Three runs of a simulation based on this network. The size of the square indicates the activation value of each unit. The units are arranged in the shape of the subnetwork with each square shown in its position corresponding to the vertex of the cube from which it is receiving input. The states are shown after every second update. + +14. SCHEMATA AND SEQUENTIAL THOUGHT 13 + +unit . The units are arranged in the shape of the subnetwork with each square shown in its position corresponding to the vertex of the cube from which it is receiving input . The system begins with a zero activa tion value on all units - represented by single dots . Then , once each time slice , at most one unit is changed . On each run the system winds up in a state in which each unit has a value of either 0 or 1 (designated by a large square ) . The first two runs are most typical of the system . In this case , the inputs are low relative to the strength of the con straints among units . When low inputs are involved , the system virtu ally always winds up either in the state in which all of the units in the left -hand network are turned on and all of the units in the right -hand are off or vice versa . These final stable states correspond to the interpretations of a left -facing and right -facing cube as illustrated in the figure for the first and second run respectively . The third example of simulation results is much more aberrant and was generated with a high input value . With a high input value , the system can occasionally get a third interpretation of the Necker cube . This is the " impossible " cube with two front faces illustrated in the figure . Thus , of the 216 possible states of the system , only two are ever reached with low input values and only three are ever reached at all . The constraints implicit in the pattern of connections among the units determines the set of possible stable states of the system and therefore the set of possible interpreta - + +tions of the inputs . + +Hopfield ( 1982 ) has shown that it is possible to give a general account of the behavior of systems such as this one (with symmetric weights and asynchronous updates ) . In particular , Hopfield has shown that such systems can be conceptualized as minimizing a global measure which he calls the energy of the system through a method of gradient descent or , equivalently , maximizing the constraints satisfied through a method of hill climbing . In particular , Hopfield has shown that the sys tem operates in such a way as to always move from a state that satisfies fewer constraints to a state that satisfies more constraints , where the + +measure of constraint satisfaction is given by 4 + +G (t ) = LLW ;ja ; (t ) aj (t ) + Linputi (t ) aj (t ) . i j i + +4 Note, the question of what to :call this constraint satisfaction function is difficult . Hopfield uses the negation of this function and, by analogy to thermodynamics, calls it energy. This system can thus be said to settle into states of minimum energy. Similarly , Hinton and Sejnowski (Chapter 7) use the same terminology . Smolensky (Chapter 6) has a similar function which he calls harmony to emphasize that increasing values correspond to more harmonious accounts of the inputs. In this chapter we have chosen to use the language of constraint satisfaction and call the function G for measure of the + +Essentially, the equation says that the overall goodness-of -fit is given by the sum of the degrees to which each pair of units contribute to the goodness plus the degree to which the units satisfy the input constraints. The contribution of a pair of units is given by the product of their activation values times the weights connecting them. Thus, if the weight is positive, each unit wants to be as active as possible- that is, the activation values for these two units should be pushed toward 1. If the weight is negative, then as least one of the units should be 0 to maximize the pairwise goodness. Similarly , if the input constraint for a given unit is positive, then its contribution to the total goodness-of -fit is maximized by being the activation of that unit toward its maximal value. If it is negative, the activation value should be decreased toward O. Of course, the constraints will generally not be totally consistent. Sometimes a given unit may have to be turned on to increase the function in some ways while decreasing it in other ways. The point is that it is the sum of all of these individual contributions that the system seeks to maximize. Thus, for every state of the system- every possible pattern of activation over the units - the pattern of inputs and the connectivity matrix W determines a value of the goodness-of-fit function . The system processes its input by moving upward from state to adjacent state until it reaches a state of maximum goodness. When it reaches such a stable state or fIXed point it will stay in that state and it can be said to have "settled" on a solution to the constraint satisfaction problem or alternatively , in our present case, "settled into an interpretation " + +of the input . + +It is important to see, then, that entirely local computational operations, in which each unit adjusts its activation up or down on the basis of its net input , serve to allow the network to converge towards states that maximize a global measure of goodness or degree of constraint satisfaction. Hopfield 's main contribution to our present analysis was to point out this basic fact about the behavior of networks with sym- + +metrical connections and asynchronous update of activations. + +In general, since there are so many states, it is difficult to visualize the goodness-of -fit function over which the system is moving . In the present case, however, we can get a reasonably good image of this landscape. To begin, we can limit our consideration to those states in which a particular unit is either on or off since the system always ends up in such states. We can consider the states arrayed along two dimensions. One dimension corresponds to the number of units turned on in the left subnetwork and the other dimension corresponds to the number of units turned on in the right subnetwork. Thus, at (0,0) we locate the state in which no units are turned on. Clearly, by the above + +14 PSYCHOLOGICAL PROCESSES + +14. SCHEMATA ANDSEQUENTIAL THOUGHT 15 + +equation such a state will have zero goodness of fit . 5 At (8,8) we have the state in which all of the units are turned on . At location (8,0) we have the state in which the units on the left network are all turned on and those on the right network are all off . At position (0,8) we have the state in which those in the left network are all off and those in the right network are all on . Each of those locations contain unique states. Now , consider the location ( 1,0) in which one unit from the left subnetwork and zero units in the right subnetwork are turned on . There are eight different states, corresponding to the eight different units in the left subnetwork that might have been turned on . In order to plot the goodness -of -fit landscape for this state space, we have plotted only the states at each location of the two -dimensional space with highest goodness -of -fit - i .e., the best state at each location . Figure 3 shows the landscape . In the figure , we are viewing the goodness landscape from about the (0,0) corner , the start state . Thus , the peak to the right corresponds to the goodness of the state in which all of the units in the left subnetwork are turned on and all in the right subnetwork are turned off . The peak at the upper left portion of the figure + +; I + +I I ifr' + +'. + +goodness :.': + +~'~:~:~"."~~.:~ .,' . ' .; : . ' . " ':.: . ' : . . + +(0 ,8) ':~ + +(8 ,0) + +::::::::::~\_\_;~I'~~ .\ s of ' + +(0,0) :\t 0\ uf ' \ "' A.IO{~ + +bf ' e \.'V' + +\f' \ e\\ su + +FIGURE 3. The goodness -of -fit surface for the Necker -cube network . The low point at the (0,0) corner corresponds to the start state . The peaks on the right and left correspond to the standard interpretations of the Necker cube , and the peak in the center + +corresponds to the impossible Necker cube illustrated in the previous figure . + +s Note , zero goodness -of -fit is not the minimum goodness -of -fit attainable . In general , goodness -of -fit can be negative as well as positive . When there is negative goodness -of - + +16 PSYCHOLOGICAL PROCESSES + +corresponds to the state (0,8) . The two peaks in the graph at (8,0) and (0,8) correspond to the two primary interpretations of the Necker cube. It should be clear that if we start a system at (0,0) and allow it to "hill climb " it will almost always end up at one of these two peaks. It might be noted, that there are three smaller peaks right in the middle of the surface. These local peaks are very hard to get to because the system is almost always swept from the start state uphill to one of the two major peaks. It is possible, by having large input values, to reach location (4,4) . This peak corresponds to the impossible Necker cube illustrated + +in the previous figure . + +The input to the system can be conceptualized as systematically modifying or sculpting the goodness landscape. This effect is illustrated in Figure 4. In this case, the same landscape has been plotted, except the units corresponding to the interpretation of the Necker cube as facing to the left receive more input than the corresponding units on the other subnetwork. (This could perhaps be done by slightly shading that face of the Necker cube.) What we see is a "sloping" goodness surface with the peak associated with the interpretation of the Necker cube + +as left facing. + +To summarize, then, there is a large subset of parallel distributed processing models which can be considered constraint satisfaction models. These networks can be described as carrying out their infor mation processing by climbing into states of maximal satisfaction of the + +FIGURE 4. The distortions of the goodness landscape when a large input is given to the units corresponding to the front face of a left-facing cube. The figure shows only one + +14. SCHEMATA ANDSEQUENTIAL THOUGHT 17 + +constraints implicit in the network . A very useful concept that arises from this way of viewing these networks is that we can describe the behavior of these networks, not only in terms of the behavior of individual units, but in terms of properties of the network itself . A primary concept for understanding these network properties is the goodness-of-fit landscape over which the system moves. Once we have correctly described this landscape we have described the operational properties of the system- it will process information by moving uphill toward goodness maxima. The particular maximum that the system will find is determined by where the system starts and by the distortions of the space induced by the input . One of the very important descriptors of a goodness landscape is the set of maxima which the system can find , the size of the region that feeds into each maximum , and the height of the maximum itself . The states themselves correspond to possible interpretations , the peaks in the space correspond to the best interpretations , the extent of the foothills or skirts surrounding a particular peak determines the likelihood of finding the peak, and the height of the peak corresponds to the degree that the constraints of the network are actually met or, alternatively , to the goodness of the interpre- + +tation associated with the corresponding state. + +CONSTRAINT SATISFACTION AND SCHEMATA + +In the previous section we recounted a perspective on parallel distrib uted processing systems. In this section we address, again, the nature of the schema and relate it to constraint satisfaction systems and POP models. We will proceed by first recounting some of the history of the concept of schemata, then by offering an interpretation of the schema in terms of POP models, by giving a simple example; and finally showing how the various properties attributed to schemata are, in fact, prop- + +erties of the PDP networks of the kind we have been discussing. + +The schema, throughout its history , has been a concept shrouded in mystery. Kant's (1787/ 1963) use of the term has been provocative but difficult to understand. Bartlett 's (1932) usage has long been decried for its vagueness. Piaget (1952) used the term schema, but it was diffi cult to come up with a consistent interpretation of Piaget's own views on the matter. Throughout most of its history, the notion of the schema has been rejected by mainstream experimental psychologists as being too vague. As a result, the concept ot- the schema was largely shunned until the mid-1970s. The concept was then revived by an attempt to offer a more clearly specified interpretation of the schema in + +terms of explicitly specified computer implementations or, similarly, formally specified implementations of the concept. Thus, Minsky (1975) postulated the concept of the frame, Schank and Abelson (1977) focused on the concept of the script, and Bobrow and Norman (1975) and Rumelhart (1975) developed an explicit notion of the schema. Although the details differed in each case, the idea was essentially the same. Perhaps Minsky (1975) was clearest in the motivation: + +> It seems to me that the ingredients of most theories both in artificial intelligence and in psychology have been on the whole too minute , local, and unstructured to account- either practically or phenomenologically- for the effectiveness of common sense thought . The "chunks" of reasoning, language, memory, and 'I perception" ought to be larger and more structured, and their factual and procedural contents must be more intimately connected in order to explain the apparent power and speed of + +mental activities. (p. 211) + +18 PSYCHOLOGICAL PROCESSES + +Minsky and the others argued that some higher-level "suprasentential " or, more simply, conceptual structure is needed to represent the complex relations implicit in our knowledge base. The basic idea is that schemata are data structures for representing the generic concepts stored in memory. There are schemata for generalized concepts underlying objects, situations, events, sequences of events, actions, and sequences of actions. Roughly, schemata are like models of the outside world . To process information with the use of a schema is to determine which model best fits the incoming information . Ultimately , consistent configurations of schemata are discovered which, in concert, offer the best account for the input . This configuration of schemata + +together constitutes the interpretation of the input . + +Different theorists have proposed more or less concrete specifications of the exact nature of these higher-level structures, but somehow none of them has ever really been adequate. None of them ever captured all of the qualitative characteristics that schemata were supposed to have. For example, a schema is supposed to be a kind of generative thing , which is flexible but which can produced highly structured interpretations of events and situations. Many representational formats have been proposed in an attempt to meet these criteria . For example, Rumelhart (1975) chose as a representation for the schema, a notation rich in generative capacity, namely, the rewrite rules from generative linguistics. Although the generativity of the rewrite rules and the idea that the structure is I' constructed" in the process of interpretation is well captured by the rewrite rules, the nonprocedural character of such a system seems wrong. Some more active representation seems 14. SCHEMATAND SEQUENTIAL THOUGHT 19 + +necessary. Moreover , the important notions of "default values," variables, and so forth are poorly represented by the rewrite notation . Min sky (1975) and Schank and Abelson (1977) employed passive data structures with slots and explicit default values. These representations are better but are not active and seem to lack the flexibility and generativity that the schema requires. Rumelhart (1977) proposed a representation in which schemata are special kinds of procedures. This view was most completely explicated in Rumelhart (1980) . Attempts to build explicit models employing this view, however, have proven + +unsuccessful. The representation is simply too unwieldy . + +It should be clear from the foregoing that there are two distinct ways in which the term schema can be used. On the one hand, it is used to refer to an idea which is common to the work of Kant , Bartlett , Piaget, Minsky , Schank and Abelson, Norman and Bobrow, Rumelhart and Ortony , and many others. This is an idea that has evolved over the years and through the eyes of many different theorists. Many people have sought to clarify and further develop the idea. On the other hand, the term schema is used to refer to one of a large number of instantiations of the general idea of the schema. These explicit schema models are always only pale representations of the underlying intuitions . Whenever a new instantiation of the schema idea is developed, a new perspective is offered on the underlying idea. What we hope to do in this chapter is to propose an alternative to the conventional representation of the schema and at the same time , through the development of a new perspective on schemata, sharpen the idea and develop a system which better captures our intuitions of the nature of the human + +information -processing system. + +One important feature of schemata proposed by Rumelhart and Ortony (1977) has never actually been included in any implementation of the idea. This involves the nature of variable constraints and the filling of default values. The variable constraints associated with each variable serve two functions . On the one hand, they are important for determining whether a particular candidate is an allowable assignment for a variable and, if the variable remains unfilled , are used in the assignment of a default value. These constraints should not be considered absolute. Rather it was proposed that variable constraints should be considered as distributions of possible values. The nearer to the mode of the distribution , the better the variable filler . Moreover , the mode could itself be considered the default value. Importantly , however, there are interdependencies among the possible slot fillers . If one variable is filled with a particular value then it changes the default for the other variables. It was therefore proposed that the variable constraints (and the fillers of the default values) should be considered multivariate distributions in which the default value for a particular + +20 PSYCHOLOGICAL PROCESSES + +variable is determined by the values filling the other slots. This idea was difficult to integrate with any of the conventional semantic networks or similar representational formats for schemata. As we shall + +see, this is a central feature of the POP analog to schemata. + +If schemata are to work as a basis for models of cognitive processing, they must be very flexible objects- much more flexible than they really ever have been in any actual implementations . This is a sort of dilemma. On the one hand, schemata are the structure of the mind . On the other hand, schemata must be sufficiently malleable to fit around most everything. None of the versions of schemata proposed to date have really had these properties. How can we get a highly structured schema which is sufficiently rich to capture the regularities of a situation and to support the kinds of inferences that schemata are supposed to support and at the same time is sufficiently pliable to adapt to + +new situations and new configurations of events? + +On our current view, the answer is simple. Schemata are not "things." There is no representational object which is a schema. Rather, schemata emerge at the moment they are needed from the interaction of large numbers of much simpler elements all working in concert with one another. Schemata are not explicit entities, but rather are implicit in our knowledge and are created by the very environment that they are trying to interpret - as it is interpreting them. 6 Roughly, the idea is this: Input comes into the system, activating a set of units. These units are interconnected with one another, forming a sort of constraint satisfaction network . The inputs determine the starting state of the system and the exact shape of the goodness-of -fit landscape. The system then moves toward one of the goodness maxima. When the system reaches one of these relatively stable states, there is little ten- + +dency for the system to migrate toward another state. + +The states themselves are the product of the interaction among many groups of units. Certain groups, or subpatterns of units tend to act in concert. They tend to activate one another and, when activated, tend to inhibit the same units. It is these coalitions of tightly interconnected units that correspond most closely to what have been called schemata. The stable pattern as a whole can be considered as a particular configuration of a number of such overlapping patterns and is determined by + +6 Hofstadter (1979) expresses essentially the same view in his book Godel, Escher, Bach + +when the Anteater says: + +My "symbols" are ACTIVE SUBSYSTEMS of a complex system., and they are composed of lower-level active subsystems . . . They are therefore quite different from PASSIVE symbols., external to the system, such as letters of the alphabet of musical notes, which sit there immobile , waiting for an active system to process them. + +the dynamic equilibrium of all of these subpatterns interacting with one another and with the inputs. Thus, the maxima in the goodness-of -fit space correspond to interpretations of the inputs or, in the language of schemata, configurations of instantiated schemata. In short, they are those states that maximize the particular set of constraints acting at the moment . Depending on the context and the inputs, the system will be closer to one or another of the peaks in the goodness-of -fit function at the outset and will usually find the closest one. This interpretation , we believe, captures almost all of the important aspects of the schema with a view that is at once more flexible than the previous interpretations and yet highly structured. The degree of structure depends on the tightness of the coupling among the coalitions of units which correspond to the schemata in question. Thus, the language of schemata and schema theories should be considered an approximation to the language of POP. In those cases in which there are coalitions of units that tend to work together, we have a rather close correspondence to the more conventional notion of a schema. In those cases in which the units are more loosely interconnected, the structures are more fluid and less schema-like . Often, knowledge is structured so that there are relatively tight connections among rather large subsets of units. In + +these cases, the schema provides a very useful description. + +One important difference between our interpretation of schemata and the more conventional ones is that in the conventional story, schemata are stored in memory. Indeed, they are the major content o/ memory. In our case, nothing stored corresponds very closely to a schema. What is stored is a set of connection strengths which, when activated, have implicitly in them the ability to generate states that correspond to instantiated schemata. This difference is important - especially with regard to learning. There is no point at which it must be decided to create this or that schema. Learning simply proceeds by connection strength adjustment, according to some simple scheme such as those we discuss in various places in this book. As the network is reorganized as a function of the structure of its inputs, it may come to respond in a + +more or less schema-like way. + +We now turn to an example to illustrate the various aspects of these PDP networks and show that many of those features that prompted the invention of schemata in the first place are present in these networks. At the same time , we show that certain features that are problematic with conventional representations of schemata are better dealt with in + +the POP language. + +14. SCHEMATA ANDSEQUENTIAL THOUGHT 21 + +22 PSYCHOLOGICAL PROCESSES + +An Example + +Consider our knowledge of different kinds of rooms. We all have a clear idea of what a typical kitchen or bathroom or living room or bedroom or office looks like . We know that living rooms have sofas and easy chairs, but they don't usually have ovens or bathtubs and that offices have desks and typewriters, but they don't usually have beds. On the other hand, kitchens, living rooms, and offices might all very well have telephones, carpets, etc. Our default bathroom is very small, our default kitchen is somewhat larger but still probably small relative to our default living room. We chose our knowledge of rooms and types of rooms as the primary example to illustrate the POP representation of schem~ta. To begin, we need a constraint network that embodies the constraints implicit in our knowledge of rooms. We built our constraint network in the following way. We chose a set of 40 descriptors of rooms. These descriptors are listed (in Table 1. We asked two subjects to imagine an office and then, for each of the 40 descriptors asked if the descriptor was accurate of that office . We then asked subjects to imagine a living room and asked about the 40 descriptors again. We then asked about a kitchen, a bathroom, and a bedroom. After finishing these five types of rooms we asked subjects to imagine another office , etc. We collected a total of sixteen judgments of the 40 descriptors on each of the five room types. This data served as the basis for creating our network . 7 In principle , we could imagine presenting each !of these 80 room descriptions to the system and have it + +TABLE! + +THE FORTY ROOM DESCRIPTORS + +door small very-large + +typewriter clock coffee-cup coffeepot + +toilet + +desk + +dresser oven + +carpet floor -lamp fi replace toaster bathtub clothes-hanger + +~ef rigerator television computer + +ceiling large telephone books sofa drapes cupboard + +windows \'ery-small bookshelf picture ashtray + +7 This was not designed to be a formal experiment of any kind . Rather it was concep tualized as a method of Quickly getting a reasonable data base for building an example . Some slight modifications in the data base were made in order to emphasize certain + +14. SCHEMATA ANDSEQUENTIAL THOUGHT 23 + +learn according to one or another learning rule we have discussed . Rather than doing that , however , we simply set the weights according + +to the following equation : + +P (Xi = 0 & Xj = l )p (Xi = 1 & Xj = 0) + +Wi. = - In . J P (Xi = 1 & Xj = l )p (Xi = 0 & ~j = 0) + +This equation is derived from a Bayesian analysis of the probability that unit Xi should be on given unit Xj is on and vice versa (see Hinton & Sejnowski , 1983 ) . Four aspects of the weight equation should be + +noted : + +. If the two units tend to be on and off together (i .e., the proba bility that Xi = Xi is much greater than the probability that + +Xi ~ Xi ) ' then the weight will be a large positive value . + +. If , on the other hand , the probability that the two units take on different values (i .e ., Xi ~ Xi ) is much greater than the proba bility that they take on the same values (i .e., Xi = X j ) , then the + +weight takes on a large negative value . + +. If the two units come on and off independently (i .e., if P (Xi = VI & Xj = V2) = P (Xi = VI )P (Xj - V2) ) , then the weight + +between the two units is zero . + +. The weights are symmetric (i .e., Wi) = W)i ) . + +In addition , each unit has a bias (constant input ) which is given by + +. P (Xi = 0) blGSi = - In ( - 1) . P Xi - + +Note that if the unit is usually off , it has a negative bias ~ if it is usually on , it has a positive bias ~ and if it is equally often on or off , it has a zero bias . 8 The weight . matrix estimated by this means is shown in Figure 5 . ~ he figure uses the method of Hinton and Sejnowski (Chapter 7) to display the weights . Each unit is represented by a square . The name below the square names the descriptor represented by each square . Within each unit , the small black and white squares represent the weights from that unit to each of the other units in the + +8 With a finite data base some of the probabilities mentioned in these two equations might be O. In this case the values of weights are either undefined or infinite . In estimating these probabilities we began by assuming that everything occurs with some very small probability (.00001) . In this way the equation led to finite values for all + +14. SCHEMATA ANDSEQUENTIAL THOUGHT 25 + +units in the network. We consider this example to be a simplified case. It is possible to imagine hidden units which respond to patterns among the input units. In the general case, we, of course, recognize that hidden units would be required to give different coalitions enough coherence. As we have pointed out elsewhere in the book (cf. Chapter 2 and Chapter 8) , multilayer systems containing hidden units are sometimes required to carry out certain computations. In the present instance, however, the existence of hidden units would not change the basic properties of the network which we wish to illustrate . Such higher-level units are not required for the basic schema-like behavior of these networks and, in no case should such a unit be confused with a schema. It should also be noted that we have chosen a rather high level of abstraction for this example. We have taken such features as has television as a microjeature. In a more realistic example, we would expect television to itself be a particular pattern over a set of units that are used to represent many different varieties of television . There might be many variations on the television pattern corresponding to variations among televisions. Moreover , since televisions in bedrooms may be systematically different (perhaps smaller) than televisions in living rooms, we would expect that these correlations would be picked up and there would be a context dependency between the particular version of television and the remaining objects in the room. In such a case the units that participate in the representation of television would play the role of a slot in a schema, and the particular pattern of activation on + +these units would represent the characteristics of the slot filler . + +Figure 6 shows several examples of the processing of this network. These runs started by "clamping" one of the descriptors on (that is, by setting the value to 1 and not letting it change) and then letting the system find a goodness-of -fit maximum . In the first example, the descriptor oven was clamped on. In such a case, we expect that the system will bring those units most tightly bound to the oven unit on and turn off those units negatively correlated to oven or other units that it turns on. On the assumption that oven is a central feature of the kitchen schema, the pattern the system eventually turns on is just that which might be said to correspond to the default kitchen schema. The strengths of each of the 40 units is shown along with the "goodness-of - fit " of the state after every 20 updates. The system begins with oven and ceiling on and then adds coffee-cup (weakly) , then sink and refrigerator, concludes that the room is small, adds toaster and coffeepot and finally ends up at a maximum with ceiling, walls, window, small, telephone, clock, coffee-cup, drapes, stove, sink, refrigerator, toaster, cupboard, coffeepot, and oven. In other words, it finds the default or prototype kitchen. Similarly , runs of the system starting with desk, bathtub, sofa, or bed clamped lead to goodness maxima corresponding to the prototype or default office , + +26 PSYCHOLOGICAL PROCESSES + +bathroom , living room , or bedroom , respectively . It is, as previously noted , these maxima that we believe correspond roughly to instantia tions of schemata for kitchens , offices , bathrooms , living rooms , and bedrooms . The system receives input in the form of having some of the descriptors clamped from the outside . It then finds the best interpretation of the input through this process of hill climbing . As it climbs , the system " fills in " the relevant descriptors of the scene in + +Question . + +In the case of the network we created for this example , there are essentially five maxima - one corresponding to each of the different room types . There are 240 possible binary states in which the system could potentially settle , but , in fact , when it is started by clamping exactly one descriptor , it will only settle into one of five states . This roughly corresponds to the view that this data base contains five schemata defined over the set of 40 descriptors . There are, as we shall see, numerous subschemata which involve subpatterns within the whole + +pattern . + +00000000000000000000 oven . . . . . . . . . . . . . . . . . . . computer . . . . . . . . . . . . . . . . . coat - hanger . . . . . . . . . . . . . scale . . . . . . . . . . . . . . . . toilet . . . . . . . . . . . . . . . . . bathtub . . . . . . . . . . . . . . . . . . television . . . . . . . . . . . . . . . . dresser . . 000000000000000000 coff ee- pot . . 0000000000000000 cupboard . 000000000000000000 toaster . 0000000000000000000 refrigerator 0000000000000000000 sin k . . . . . . . . . 000000000 stove . . . . 0 0 00000000000000 drapes . . . . . . . . . . . . . . . . . . fire - place . . . . . . . . , . . . ash - tray . c cOD 000000000000000 coffee - cup . . . . . . . . . . . . . . . . . . . easy - chair . . . . . . . . . . . . . . . . sofa . . . . . . . . . . . . . . . floor - lamp . . . . . . . . . . . . picture ooooooDDDDDDDD clock . . . . . . . . . . . . . . . . . . desk - chair . . . . . . . . . . . . . . . books . . . , . . . . carpet . , . . . . . . . . . . . bookshelf . . , . . . . . . . . . . . . . . typewriter . . . . . . . . . . . . . . . oed + +: . . ~ ~ c coo 0 0 ~ 0 ~ 0 C?C?C? ~~~khone . . . . . . . . . . . . . . . . . . . very - small . . . . ODD D D D D 000000000 small . . . . . . . . . . . . . . . . . . . . medium . . . . . . . . . . . . . . . . large . . . . . . . . . . . . . . very - large . . c c c c 0000000000000 window . . . . . . . . . . . . door 0000000000000000000 walls DDDDDDDDDDDD 0 0000000 ce i Ii n g + +FIGURE 6. Five runs of the network from five different starting places. In each case, the unit ceiling and one other is clamped on . The clamping of ceiling represents informa tion indicating that room is the domain of discussion . The other clamped units are oven, desk, bathtub , sQ(a , and bed in the five runs . In each case, the system settles on a proto - + +36 PSYCHOLOGICAL PROCESSES + +amount of drapes added to the schema (i .e., to the activation value for the drapes unit ) . The second axis corresponds to the amount of window added. The third axis, of course, corresponds to the goodness-of -fit for each of the states. It should be noted that the low points on the graph correspond to those cases in which one of the two units of the window subschema is on and the other is off . The high points on the graph, corresponding to goodness maxima, occur when either neither (at the origin) or both of the units are on. The case where neither is on corresponds to a slightly higher peak than when both are on. Thus, the default office probably doesn't have a window, but if the input indicates that either one of the units (window or drapes) is on, turning the other one on is best. To conclude, large schemata such as the office schema can be conceptualized as consisting, in part, of a configuration of subschemata which mayor may not be present as wholes. Having parts of these subschemata is worse than having either the entire subschema + +or none of it . + +Schemata represent knowledge at all levels. They should represent encyclopedic knowledge rather than definitional information . This amounts to the claim that all coherent subpatterns should be considered schemata as well as the whole stable pattern. It also suggests that knowledge of all sorts should be represented in the interconnections + +among the constituent units. + +Schemata are active processes. This is obviously true of the the POP system we are describing. They are a kind of organic element + +which grows and fulfills itself within its environment . + +Schemata are recognition devices whose processing is aimed at the evaluation of their goodness-of-fit to the data being processed. This feature is obviously also a part of the idea outlined here. The goodness-of -fit is roughly determined by the height of the peak in goodness space. The processing of the system is aimed toward climbing uphill along the goodness-of -fit gradient. The stable points correspond to local maxima in this space. The height of the peak corresponds to + +the goodness-of -fit . + +Some additional features of our interpretation . There are three major difficulties with the conventional representation of schemata that are naturally overcome in the POP approach. In the conventional approaches, decisions must be made about which aspects of a given 14. SCHEMATA AND SEQUENTIAL THOUGHT 37 + +schema are constant and which are variable. The POP solution is essentially that all aspects are variable~ some aspects are simply more tightly constrained than others. Secondly, in a conventional representation , one has to decide exactly which aspects of the situation are part of the schema and which are not. In our PDP approach, units may cohere more or less strongly to their mates and in this sense be more or less a part of the schema. Finally , on the conventional view a decision must be made about whether a certain set of relationships should be put together to form a schema at all. Again, in the POP formulation no such decision needs to be made. One can have schemata of varying degrees of existence. The rigidity of the schema is determined by the tightness of bonding among the units that constitute the schema. The tighter the bond, the more strongly the constituent elements activate one another, and the more rigid the structure. The weaker the bonds, the more fluid the structure, and the more easily a system can flow among states. This degree of fluidity depends on the shape of the goodness-of-fit landscape. Tightly rigid schemata have sharp peaks in goodness space~ fluid schemata with many variable parts correspond to rounded hilltops . The goodness landscape, in turn , depends on the knowledge base that lies beneath it . If the knowledge is tightly inter constrained so that one part strongly predicts other parts, then we have a rigid schema. We can't easily get just part of it active. If part of it becomes active, the part will pull in the whole and suppress the activity of aspects that are not part of it . On the other hand, if the knowledge is only loosely interrelated, the schema will be a relatively weak organizer of the information and will be a pressure for structuring the input , but it will flow easily from one pattern to another. Moreover , within a schema itself , some aspects will be tightly bound together while other aspects will be only more loosely tied to the body of the schema. Input situations that demand an interpretation that breaks up the tightly bound clusters are going to be more difficult for the system to attain than those that require breaking up much more loosely interconnected + +elements. + +Finally , we point out one way in which these ideas about schemata might be elaborated to overcome one apparent deficiency of the network we have thus far been considering. The network uses a fixed set of units to represent each type of object that might be present in a particular instantiation of a schema. This is clearly an oversimplification since it is often necessary to be able to think about two different instantiations of the same subschema within a larger overall schema- for example, there is often more than one chair in a living room. To capture such situations, it is necessary to imagine that the network may contain several subsets of units, each capable of representing a different possible chair. The subsets would correspond to different roles the + +different chairs might play in the overall room schema. This would also allow the representation to capture the assignment of a particular + +object to a particular role. + +In the previous section we offered an interpretation of the schema in terms of the emergent properties of simple POP networks. From there, we believe that we can make contact with much of the cognitive science literature . There are central issues, however, which remain difficult to describe within the PDP framework . We have particularly in mind here, the process of thinking , the contents of consciousness, the role of serial processes, the nature of mental models, the reason for mental simulations, and the important synergistic role of language in thinking and in shaping our thought . These issues are especially important because these are issues that PDP approaches do not, on first blush, seem to have much to say about. In this section we attack some of those problem areas. We don't claim to have solutions to them, rather we can outline a story that represents our current understanding of these processes. The story is overly simplistic but it does give an idea + +of where we are in our thinking on these critical issues. + +It should be noted here that the account of mental processing we have been developing offers an interesting perspective on the relations between parallel and serial processing. The " parallel" in "parallel distributed processing" is intended to indicate that, as a basic architectural design principle , processing is carried out, in so far as possible, in parallel. Parallel algorithms are employed rather than serial ones. At the same time , however, the "distributed " in "parallel distributed processing" brings a serial component to POP systems. Since it is patterns of activations over a set of units that are the relevant representational format and since a set of units can only contain one pattern at a time , there is an enforced seriality in what can be represented. A given set of units can, however, be seen as representing a sequence of events. Since we assume that the system is moving toward a maximum goodness solution every time a new input comes into the system, the system operates in the following way. An input enters the system, the system relaxes to accommodate the new input . The system approaches a relatively stable state which represents the interpretation of the input by the system. The system then occupies this state until the stimulus conditions change. When a new input arrives, the system relaxes to a new state. Looking at the system over a short time frame, it is dominated + +38 PSYCHOLOGICAL PROCESSES + +PARALLEL DISTRIBUTED~ PROCESSING MODELS AND + +THINKING + +One common critique of the kind of model we have sketched so far is that it can't really change without external prodding. Suppose that we are in a fixed stimulus environment . In this case, the system will relax into ah interpretation for that environment and stay there. Our conscious experience will be of a fixed interpretation of a fixed stimulus . Until the world changes there is no change to the system nor to the contents of our consciousness. Obviously this is an incorrect + +14. SCHEMATA ANDSEQUENTIAL THOUGHT 39 + +by the relaxation process in which all units work cooperatively to "discover" an interpretation of a new input . Looking over a somewhat longer time frame, we see the system as sequentially occupying a series of relatively stable states- one for each change in input . Roughly, if we imagine that the relaxation process takes on the order of a few tenths of a second and that the time spent in essentially the same stable state is on the order of a half of a second or so, we could see events requiring less than about a half second to be essentially a parallel process, and those requiring several seconds to involve a series of such + +processes and therefore to have a serial component. + +The Contents of Consciousness + +It isn't necessary for the arguments that follow , but for the sake of concreteness, we suppose that there is a relatively large subset of the total units in the system whose states of activity determine the contents of consciousness. We imagine that the time average of the activities of these units over time periods on the order of a few hundred mil liseconds correspond to the contents of consciousness. Since we imagine that our systems must be such that they reach equilibrium in about this amount of time , the contents of consciousness are dominated by the relatively stable states of the system. Thus, since consciousness is on the time scale of sequences of stable states, consciousness consists of a sequence of interpretations - each represented by a stable state of the system. Typically , consciousness contains a single interpretation (i.e., a single pattern representing its inputs) and consists of a sequence of such interpretations . On occasions in which the relaxation process is especially slow, consciousness will be the time average over a dynamically changing set of patterns and thus would be expected to lead to + +"fuzzy" or unclear phenomenal impressions. + +The Problem of Control + +conclusion. How can such a system do something? Perhaps the first thing that comes to mind is that the environment never really is fixed . It is always changing and therefore the contents of our consciousness must always be changing to interpret the current state of affairs. A good example of this might be the movies. We sit in the movies and watch. Our system reaches a sequence of interpretations of the events on the screen. But, since the movie is always continuing , we are driven to continue to interpret it . Surely, what is true of a movie is also true of life - to some extent. This may be part of the story, but it would appear to be rather more passive than we might want. We don't just sit passively by and let the world change and then passively monitor it . + +Rather we act on the world . + +A second answer to the problem of a system fixated on a particular interpretation becomes apparent in realizing that our interpretation of an event often dictates an action which, in turn , changes the environ ment. The environmental change can then feed back into the system and lead to another interpretation and another action. Figure 14 illustrates how this feedback loop can continuously drive the system from state to state. A paradigm case for this is playing a game. We can imagine that we are playing a game with someone~ our input consists of a board configuration , and we settle into a state which includes a specification of a response. It would be quite easy to build a relaxation network that would take as input a description of a current board situation and produce, as part of the state to which it relaxed, a specification of the response. It would simply require that, for each game situation, the system relaxes to a particular state. Certain units of the state represent the action (or class of actions) that should be taken. Upon taking these actions, the opponent makes a play which in turn leads to a new set of constraints to which the system relaxes. In this way, the system can make a sequence of moves. Indeed, as we describe below, we have built such a network that can play tic-tac-toe. Other more complex games, such as checkers or chess require rather more effort , of course, but can, in principle, be dealt with in the same way. Although this is a much more activist view, it is still a "data-driven" view. The system is + +entirely reactive- given I am in this state, what should I do? + +40 PSYCHOLOGICAL PROCESSES + +Men tal Models + +Suppose, for arguments sake, that the system is broken into two pieces- two sets of units. One piece is the one that we have been discussing, in that it receives inputs and relaxes to an appropriate state that includes a specification of an appropriate action which will , in turn , + +14. SCHEMATA AND SEQUENTIAL THOUGHT 41 + +Interpretation Network + +change the inputs to the system. The other piece of the system is similar in nature, except it is a ,t model ,t of the world on which we are acting. This consists of a relaxation network which takes as input some specification of the actions we intend to carry out and produces an interpretation of ,t what would happen if we did that." Part of this specification would be expected to be a specification of what the new stimulus conditions would be like . Thus, one network takes inputs from the world and produces actions~ the other takes actions and predicts how the input would change in response. This second piece of the system could be considered a mental model of the world events. This second portion , the mental model of the world, would be expected to be operating in any case, in as much as it is generating expectations + +In this way, the out- + +FIGURE 14 . The inputs to the POP system should be considered as partially due to the + +effects that the output of the system has had on the environment . + +put of the system can drive it from state to state . + +about the state of the world and thereby " predicting" the outcomes of + +actions. + +Now, suppose that the world events did not happen. It would be possible to take the output of the mental model and replace the stimulus inputs from the world with inputs from our model of the world . In this case, we could expect that we could "run a mental simulation" and imagine the events that would take place in the world when we performed a particular action. This mental model would allow us to perform actions entirely internally and to judge the consequences of our actions, interpret them, and draw conclusions based on them. In other words, we can, it would seem, build an internal control system based on the interaction between these two modules of the system. Indeed, as we shall show, we have built a simple two-module model of tic-tac-toe which carries out exactly the process and can thereby " imagine" playing tic-tac-toe. Figure 15 shows the relationships between the interpretation networks, the inputs, the outputs, and the network representing a + +model of the world and the process of " mental simulations." + +42 PSYCHOLOGICAL PROCESSES + +Mental Simulations and Mental Practice + +One nice feature of this model is that it ties into the idea of mental simulations and learning through mental practice . Performance in the task involves two parts - a system that determines what to do in any given situation and a system that predicts what will happen if any given action is carried out . If we have a reasonably good model of the " world " we could learn from our model the various consequences of our actions - just as if we were carrying them out in the real world . It may very well be that such a feature accounts for the improvement that + +occurs in mentally practicing complex motor tasks . + +Conversations : Actual and Imagined + +Imagine a situation in which we had a relaxation network which would take as input a sentence and produce an interpretation of that sentence as well as the specifications for a response to that input . It is possible to imagine how two individuals each with such a network could carry out a conversation . Perhaps , under appropriate circumstances they could even carry out a logical argument . Now , suppose that we don ' t actually have another participant , but instead have a mental model of the other individual . In that case , we could imagine carrying + +Inte rpretati on Network + +Internal Units Input Output + +From + +Environment Environment + +Model of World + +Internal Units + +0 t t Input u pu U . U "t nl s nits + +14. SCHEMATA AND SEQUENTIAL THOUGHT 43 + +To + +out a conversation with someone else. We could hold an imaginary argument with someone else and perhaps even be convinced by it ! Indeed, this brings up the last move that we wish to suggest. Suppose that we don't have a model of another person at all. Suppose that instead we simply use our one single model to both produce and react to imagined linguistic inputs. This description is, it would seem, consistent with Vygotsky's (1934/ 1962) view of thinking and is consistent with the introspections about a certain kind of thinking and "internal speech." Note, this does not suggest that thinking is simply internal speech. More generally, thinking , as we have argued, involves a sequence of states of consciousness. There are a number of ways of controlling that sequence. One way involves running "mental simulations." Another way involves recycling linguistic inputs. Note, this gives language an interesting, almost Whorfian , role however. Suppose that the interpretation that led to the production of the internal speech was much richer than the linguistic forms could possibly suggest. Thus, + +FIGURE 15. The relationships among the model of the world ., the interpretation net- + +work ., the inputs., and the outputs for the purpose of mental simulations. + +the linguistic forms pick out aspects of the entire interpretation to emphasize. Once this emphasis has taken place and the new input has been processed, the next state will be strongly affected by the new input and our new interpretation will be shaped, to some extent, by the words we chose to express our first idea. Thus, our thinking about a topic will be, sometimes strongly, affected by the language tools we + +have for expressing our ideas. + +44 PSYCHOLOGICAL PROCESSES + +External Representations and Formal Reasoning + +If the human information -processing system carries out its computations by "settling " into a solution rather than applying logical operations, why are humans so intelligent ? How can we do science, mathematics, logic, etc.? How can we do logic if our basic operations are not logical at all? We suspect the answer comes from our ability to create artifacts- that is, our ability to create physical representations that we can manipulate in simple ways to get answers to very difficult + +and abstract problems. + +The basic idea js that we succeed in solving logical problems not so much through the use of logic, but by making the problems we wish to solve conform to problems we are good at solving. People seem to have three essential abilities which together allow them to come to logical conclusions without being logical. It is these three abilities that have allowed us to accomplish those uniquely human achievements of + +formal reasoning. These abilities are: + +. We are especially good at pattern matching. We seem to be able to quickly "settle" on an interpretation of an input pattern. This is an ability that is central to perceiving, remembering, and comprehending. Our ability to pattern match is probably not something which sets humans apart from other animals, but is probably the essential component to most cognitive behavior. + +. We are good at modeling our world . That is, we are good at anticipating the new state of affairs resulting from our actions or from an event we might observe. This ability to build up expectations by " internalizing " our experiences is probably crucial to the survival of all organisms in which learning plays a + +key role. + +. We are good at manipulating our environment . This is another version of man-the-tool-user, and we believe that this is perhaps the crucial skill which allows us to think logically, do mathematics and science, and in general build a culture . + +Roughly speaking, the view is this: We are good at "perceiving" answers to problems. Unfortunately , this is not a universal mechanism for solving problems and thinking , but as we become more expert, we become better at reducing problem domains to pattern-matching tasks (of the kind best accomplished by PDP models) . 9 Thus, chess experts can look at a chess board and "see" the correct move. This, we assume, is a problem strictly analogous to the problem of perceiving anything. It is not an easy problem, but it is one that humans are especially good at. It has proven to be extraordinarily difficult to duplicate this ability with a conventional symbol-processing machine. However, not all problems can be solved by immediately " seeing" the answer. Thus, few (if any) of us can look at a three-digit multiplication problem (such as 343 times 822) and see the answer. Solving such problems cannot be done by our pattern-matching apparatus, parallel processing alone will not do the trick ~ we need a kind of serial processing mechanism to solve such a problem. Here is where our ability to manipulate our environment becomes critical. We can, quite readily, learn to write down the two numbers in a certain format when given such a problem. + +Moreover, we can learn to see the first step of such a multiplication problem. (Namely, we can see that we should enter a 6 below the 3 + +and 2.) + +14. SCHEMATA AND SEQUENTIAL THOUGHT45 + +343 822 + +Especially important here is our ability to manipulate the environment so that it comes to represent something . This is what sets human intellectual accomplishments apart from other + +animals . + +343 822 6 + +We can then use our ability to pattern match again to see what to do next . Each cycle of this operation involves first creating a representa tion through manipulation of the environment , then a processing of this ( actual physical ) representation by means of our well - tuned percep tual apparatus leading to a further modification of this representation . + +9 As we have argued before , it is because experts have such a powerful pattern matching capability that expert systems that rely only on pattern matching (albeit not + +By doing this we reduce a very abstract conceptual problem to a series of operations that are very concrete and at which we can become very good. Now this applies not only to solving multiplication problems. It applies as well to solving problems in logic (e.g., syllogisms) , problems in science, engineering, etc. These dual skills of manipulating the environment and processing the environment we have created allow us to reduce very complex problems to a series of very simple ones. This ability allows us to deal with problems that are otherwise impossible. This is real symbol processing and, we are beginning to think , the primary symbol processing that we are able to do. Indeed, on this view, + +the external environment becomes a key extension to our mind . + +There is one more piece to the story. This is the tricky part and, we think , the part that fools us. Not only can we manipulate the physical environment and then process it , we can also learn to internalize the representations we create, "imagine" them, and then process these imagined representations- just as if they were external. As we said before, we believe that we are good at building models of our environment so that we can anticipate what the world would be like after some action or event takes place. As we gain experience with the world created by our (and others') actions we develop internal models of these external representations. We can thus imagine writing down a multiplication problem and imagine multiplying them together. If the problem is simple enough, we can actually solve the problem in our imagination and similarly for syllogisms. Consider, for example, a simple syllogism: All A are B and no Care B. We could solve this by drawing a circle for A , a larger circle including all of the A 's around the first circle to represent the B's, and a third disjoint circle standing for the C's. We could then "see" that no A 's are C. Alternatively , we need not actually draw the circles, we can merely imagine them. We believe that this ability to do the problem in our imagination is derivative from our ability to do it physically, just as our ability to do mental multiplication is derivative from our ability to do multiplication with pencil and paper. The argument that external representations playa crucial role in thought (or, say, in solving syllogisms) is sometimes challenged on the ground that we don't really have to draw Venn diagrams (or whatever) to solve them since we can solve them in our head. We argue that the major way we can do that is to imagine doing it externally . Since this imagination is, we argue, dependent on our experience with such representations externally, the argument that we can solve them mentally loses its force against the view that external symbols are important for thought processes. Indeed, we think that the idea that we reason with mental models is a powerful one precisely because it is about this process of + +It is interesting that it is apparently difficult to invent new external representations for problems we might wish to solve. The invention of a new representation would seem to involve some basic insight into the nature of the problem to be solved. It may be that the process of inventing such representations is the highest human intellectual ability . Perhaps simply creating an external representation sufficient to support problem solving of a particular kind is evidence of a kind of abstract thinking outside of the simple-minded view sketched here. That may be, but it seems to us that such representational systems are not very easy to develop. Usually they are provided by our culture . Usually they have evolved out of other simpler such systems and over long periods of time . Newer ones, when they are developed, usually involve taking an older system and modifying it to suit new needs. One of the cri tical aspects of our school system would seem to be teaching such representational schemes. The insights into the nature of the problem become embedded in the representations we learn to use to solve the + +problems. + +Language plays an especially tricky and interesting role in all of this. Perhaps the internal / external issue is not too important with language. The notion we have here is one of " self-instruction ." This follows Vygotsky's (1934/ 1962) view, we believe. We can be instructed to behave in a particular way. Responding to instructions in this way can be viewed simply as responding to some environmental event. We can also remember such an instruction and "tell ourselves" what to do. We have, in this way, internalized the instruction . We believe that the process of following instructions is essentially the same whether we have told ourselves or have been told what to do. Thus, even here, we have a kind of internalization of an external representational format (i.e., language) . We don't want to make too much of this point since we recognize that the distinction between external and internal when we ourselves produce the external representation is subtle at best, but we don't really think it differs too much from the case in which we write something down and therefore create a real, physical, viewable representation. Saying something out loud creates a hearable representation . There are interesting cases in which people talk to themselves (for example, solving difficult problems in noisy environments leads people to literally talk to themselves and instruct themselves on the + +problems they are solving) . + +Before leaving this topic, one more important aspect of external representations (as opposed to internal representations) should be noted. External representations allow us to employ our considerable perceptual/ motor abilities in solving abstract problems. This allows us to break problems into a sequence of relatively simple problems. Importantly , once an external representation is created, it can be + +14. SCHEMATA AND SEQUENTIAL THOUGHT 47 + +Our discussion thus far has left one central issue undiscussed, namely, the role of goals in thought and problem solving. Clearly it is not the case that the same perceptual stimulus always drives the system to react in a consistent way. Rather, our goals or intentions interact with the stimuli (internal and external) that provide the inputs to the thinking process. Further , goals organize whole sequences of thoughts into a coherent problem-solving activity , and the notion that there is a hierarchy of goals is certainly important for understanding these + +coherent sequences. + +While we have not stressed the importance of goals, it is not difficult to see how they could be incorporated into our framework . Goals can be explicitly represented as patterns of activation and can thus provide one source of input to the thinking process. Nor is it difficult to imagine how a POP network could learn to establish specific subgoal pat- + +terns in response to particular superordinate goals and inputs. + +48 PSYCHOLOGICAL PROCESSES + +reinterpreted without regard to its initial interpretation . This freedom allows us to discover solutions to problems without "seeing" our way to the end. We can inspect intermediate steps and find alternative solutions which might be better in some ways. In this way, we can discover new features of our representations and slowly extend them and make + +them more powerful . + +Goal Direction in Thinking + +Summary + +These ideas are highly speculative and detached from any particular POP model. They are useful, we believe, because they suggest how POP models can be made to come into contact with the class of phenomena for which they are, on the face of it , least well suited- that is, essentially sequential and conscious phenomena. Even in these + +cases, however, they lead us to view phenomena in new ways. + +An Example + +14. SCHEMATA AND SEQUENTIAL THOUGHT 49 + +Line Detector Units + +Response + +Board Units + +Units + +Therefore , to illustrate the notion of thought as mental simulation more concretely, we created two relaxation networks that can be connected together to mentally simulate playing a game of tic-tac-toe. The two networks are very similar . The first is a system which, given a pattern representing the board of a tic-tac-toe game, will relax to a solution state that fills in an appropriate response. The second module is nearly identical to the first ~ it takes as input a board position and a move and settles to a prediction of the opponent's responding move. In short, it is a "mental model" of the opponent. When the output of the first is fed, as input , to the second and the output to the second is fed, as input , to the first , the two networks can simulate a game of tic-tac-toe. Figure 16 illustrates the basic structure of the tic-tac-toe playing network . The network consists of a total of 67 units. There are nine units representing the nine possible responses. These are indicated by the nine dots at the top of the figure . There is one unit for each of the nine possible moves in tic-tac-toe. Since only one response is to be + +made at a time , these units are mutually inhibitory . This is indicated by the heavy black line feeding back from the top plane in the figure to itself . There are a total of 18 units representing the board configuration . These are divided into two groups of nine: one group for the positions of the friendly or player pieces on the board and one group representing the positions of the opponent's pieces. Since if any square is occupied, it is not a possible move, each board unit strongly inhibits its corresponding output unit . This strong inhibition is indicated by the heavy black lines connecting the board units to the response units. In addition to these 9 output units and 18 input units, there is a total of 40 hidden units which detect patterns in the board units and activate the various response alternatives. These 40 units can be divided into eight classes corresponding to the eight possible ways of getting three x 's or o 's in a row. In the figure , one of each such category of units is illustrated. The receptive field of each unit is indicated by the line inside the circle representing that unit . Thus, there is one unit for each of the three horizontal lines, one for each of the three vertical lines, and one for each of the two possible diagonal lines. For each of the eight classes of hidden units, there are five different pattern types that dif ferent units are responsive to. For example, some units are responsive to empty regions. That is, they respond just in case none of the board units from which it receives inputs is turned on. This is implemented by making them be inhibited by any activity in their receptive field and by giving them a negative threshold. We call this an empty line detector. All things being equal, it is better to move into an empty row, column , or diagonal~ therefore these units weakly activate their respective output units. At the start of the game these are the only units which are active and therefore the sole criterion for the first move is the number of possible strings of three the square is a member of. Since the center square intersects the largest number, it will usually be chosen by the system for its first move. On later moves, there are other units feeding into the decision, but these units also contribute . Another unit type will respond whenever two or more units of the same kind occur in its regions. This is the kind of unit illustrated in the figure . It receives strong inhibitory input from one set of board units (in this case the opponent's pieces) and excitatory inputs from the other set. It has a rather high positive threshold so that it will not come on until at least two units are on in its row. We call this a friendly doublet detector. Whenever this unit comes on it means that the system can make a winning move by playing in that row. Therefore, it is strongly positively connected to its respective output units. If such a move is possible, the system will make it . There are similar units which respond to two or more units from the representation of the opponent's pieces are active in its receptive field . We call this an opponent doublet detector. If such a + +50 PSYCHOLOGICAL PROCESSES + +unit comes on, it means that the opponent could win by a move in this region, so it excites its response units very strongly as well. Unless there is a winning move somewhere else, the blocking response will become the most active. Finally , there are units which respond to one or more friendly pieces or one or more opponent pieces in an otherwise open line. We call these friendly singleton and opponent singleton detectors. It is generally good to extend your own singleton or block an opponent's singleton if there is nothing more pressing, so these units also activate their respective output units, only rather more weakly than the units detecting doublets. Thus, the net input arriving at any given unit is the weighted sum of all of these urgencies detected by the hidden units. Because of the direct inhibition from the board units, only those response units corresponding to open squares receive positive input . The mutual inhibition insures that the strongest unit will usually win . In order that this system truly climb in overall goodness-of -fit , all weights are symmetric and the update is done asynchronously at random. This means that when there isn't much difference between the possible response alternatives, a weaker one will sometimes get the upper hand and win the competition . This never happens, however, when a unit is receiving very strong input , as with the case of an open + +double for a win or to be blocked. + +The simplest case is when the system simply is given a board position , settles on a move, is given the next board position incorporating the opponent's response, settles on a move for that position, etc., until a game is finished . This involves only one network and presumably would be the basic modality for the system to run in. Figure 17 shows a sample run of such a situation . The activation levels of each of the 67 units is shown in each column . Successive activation states are shown from left to right . At the start, it should be noted that there is a friendly piece in the center square and two enemy pieces, one in each corner of the upper row. It is the system's move. The system starts with the units corresponding to the board position clamped on and all other units off . The figure shows the strengths for each of the units after every 50 asynchronous updates. By the second time slice, the system is beginning to extract the relevant features of the board position. The five groups of eight units shown in each column following the response units and board position display the line-detector units. Each group of eight is laid out with three units across the top corresponding to the top, middle, and bottom lines from left to right . The second row of the eight corresponds to the left and right diagonals, and the bottom row of each eight corresponds to the left , middle , and right columns. Thus, we see that the system has, by the second time slice, begun to discover that the bottom row is empty, that it has a singleton in the middle row, that the opponent has a singleton in the left column , and + +14. SCHEMATA ANDSEQUENTIAL THOUGHT 51 + +own responding to the environmental process of generating a sequence of stimuli . This is a very common form of control of sequential behavior and involves no special mechanism. The case of "mental simulations " involves a bit more machinery. We need a "model of the world " to predict the environment 's response to any action that might be taken. In the case of tic-tac-toe, this involves a network which models the opponent. In general, the model of the opponent may be arbitrarily different from that used by the system to make its own response. In our case, however, it is sufficient to build an identical network for the opponent. The only difference is that in the opponent's network , the board is interpreted differently : The opponent's board position of the original network setup drives the friendly board position in the model of the opponent, and the friendly board position in the original network drives the opponent board position in the model of the opponent. Figure 18 shows a run of the system "mentally simulating " the play of a game. The state of the units are shown after every 100 updates. First, the state of the original network is shown as it settles on its move, then the state of the model of the opponent is shown as it settles on its move. This continues until the game reaches a conclusion. In this instance, the "simulated player" makes a "mistake" in its response to the system's opening. Successive moves show the system + +taking advantage of its own mistake and winning the game. + +We have argued in this book that the analysis of psychological phenomena in terms of units, activations of units, connections among units, and the action of large coalitions of such units leads us to many insights that have not been possible in terms of the language that has recently been more popular in cognitive science. In that sense, we may be perceived as throwing out the insights gained from the more conventional language and concepts. We are not throwing out such insights. In this chapter, we attempt to show the relationship between two such insights and our models. At start, we argue that the concept of the schema has a correspondence in the PDP framework . In particular, we argue that a schema is best viewed as a coalition of units which cohere and that configurations of such coalitions determine the interpretations that the system can attain. These stable states correspond to instantiated configurations of schemata that can be characterized in terms of goodness-of-fit maxima that the system can move into . Such processing systems, we argue, have all of the features of schemata and more. Among the advantages of this view is that the + +14. SCHEMATA ANDSEQUENTIAL THOUGHT 53 + +CONCLUSION + +schema becomes much more fluid and flexible and able to accommodate itself to inputs. In more conventional representations there is a strong distinction between variables and slots and the bulk of the schema. Under our interpretation an aspect of the schema is more or less a variable. Even central aspects of the schema can be missing and the system can still find a reasonably low energy stable state. If very rigid schemata are implicit in the knowledge base, this will show up as narrow peaks in the goodness landscape. If more fluid and variable schemata are required, the landscape will contain broad plateaus which allow for a good deal of movement in the region of the maximum . + +We see the relationship between our models and schema theory as discussed by other researchers as largely a matter of levels of analysis. This is roughly analogous to the relationship between the level of discussion of fluid dynamics and an underlying level of description involv ing statistical mechanics. It is often useful to theorize at the level of turbulence and different kinds of turbulence, and such a description will do for many purposes. However, we can often run up against phenomena in which our high-level descriptions will not do, we must describe the system in terms of the underlying processes in order to understand its behavior. Another feature of this example is our understanding of the phenomena of emergent properties. Turbulence is not predicted by the knowledge of the elements of the system~ it is inherent in the interactions among these elements. Similarly , we do not believe that single-unit activity is the appropriate level of analysis. Properties of networks ., emerge" from the interactions of the elements. Indeed, such properties as goodness maxima, etc., are emergent in just this way. In general, we see cognitive phenomena as emergent from the interactions of many units. Thus, we take the symbolic level of analysis to provide us with an approximation to the underlying system. In many cases these approximations will prove useful~ in some cases they will be wrong and we will be forced to view the system from the level of units + +to understand them in detail. + +We also discussed the relationship between POP models and the more conventional sequential processing systems. We believe that processes that happen very quickly - say less than .25 to .5 secondsoccur essentially in parallel and should be described in terms of parallel models. Processes that take longer, we believe, have a serial component and can more readily be described in terms of sequential information -processing models. For these processes, a process description such as a production would, we imagine, provide a useful approximate description. We would caution, however, that when one chooses a formalism such as production systems and attempts to use it not only to describe the conscious sequential processes that occur at this slow time scale, it is important not to fall into the trap of assuming that the + +56 PSYCHOLOGICAL PROCESSES + +14. SCHEMATA AND SEQUENTIAL THOUGHT 57 + +microstructure of these sequential processes should also be described in the same terms . Production systems have the power of Turing machines and people often attempt to describe phenomena at this faster time scale in terms of the same sequential formalism that seems appropriate for the slower time scale . We believe that it will turn out that this approach is wrong , that the power of the formalism has led us astray . In these cases we suspect that the unit level of analysis will be + +required . + +Finally , we showed how the important notion of mental models and the related notion of mental simulations play important roles in the sequential behavior of a POP system . We illustrated this point with a system which could use a " model of its opponent " to " mentally simu late " a tic - tac - toe game . We suspect that this process will turn out to be important when we begin to apply our models to temporally + +extended reasoning and problem - solving tasks . + +ACKNOWLEDGMENTS + +This research was supported by Contracts NOOO14 - 79 -C -O323 , NR 667 - 437 and NOOO14 - 85 - K - O450 , NR 667 - 548 with the Personnel and Training Research Programs of the Office of Naval Research , by grants from the System Development Foundation , and by a NIMH Career + +Development Award ( MHOO385 ) to the third author . + +Interactive Processes in + +Speech Perception: The TRACE Model + +CHAPTER 15 + +J. L. McCLELLAND and J. L. ELMAN + +Consider the perception of the phoneme / g/ in the sentence She received a valuable gift . There are a large number of cues in this sen tence to the identity of this phoneme . First , there are the acoustic cues to the identity of the / g/ itself . Second , the other phonemes in the same word provide another source of cues , for if we know the rest of the phonemes in this word , there are only a few phonemes that can form a word with them . Third , the semantic and syntactic context further constrain the possible words that might occur , and thus limit still further the possible interpretation of the first phoneme in gift . + +There is ample evidence that all of these different sources of infor mation are used in recognizing words and the phonemes they contain . Indeed , as R . A . Cole and Rudnicky ( 1983 ) have recently noted , these basic facts were described in early experiments by Bagley ( 1900 ) over 80 years ago . Cole and Rudnicky point out that recent work (which we consider in detail below ) has added clarity and detail to these basic findings but has not lead to a theoretical synthesis that provides a satis factory account of these and many other basic aspects of speech + +perception . + +In this chapter , we describe a model that grew out of the view that the interactive activation processes that can be implemented in POP + +This chapter is a condensed version of the article 'IThe TRACE Model of Speech Perception" by J. L. McClelland and J. L. Elman, which appeared in Cognitive Psychology, 1986, 18, 1-86. Copyright 1986 by Academic Press, Inc. Adapted with permission. + +15. THE TRACE MODEL59 + +models provide a natural way to capture the integration of multiple sources of information in speech perception . This view was based on the earlier success of the interactive activation model of word percep tion ( McClelland & Rumelhart , 1981 ~ Rumelhart & McClelland , 1982 ) in accounting for integration of multiple sources of information in + +recognizing letters in words . + +In attempting to apply the ideas embodied in the interactive activa tion model of word perception to speech , it soon became apparent that speech provided many challenges . The model we have come up with , the TRACE model , is a response to many of these challenges and demonstrates how they can be met within the PDP framework . After we developed the model , we discovered many aspects of its behavior that are consistent with facts about speech . Thus , we were gratified to discover that the search for a mechanism that was sufficient to meet many of the challenges also lead to a model that provided quite close accounts of a number of basic aspects of the literature on speech per - + +ception . + +In what follows , we begin by reviewing several facts about speech that played a role in shaping the specific assumptions embodied in TRACE . We then describe the structure of the TRACE model and the salient features of the two versions we have developed to handle dif ferent aspects of the simulations . Following this , we describe how the model accounts for a considerable body of psychological data and meets some of the computational challenges facing mechanisms of speech per ception . The discussion section considers some reasons for the success of the model , explains its limitations , and indicates how we plan to + +overcome these in future work . + +SOME IMPORTANT FACTS ABOUT SPEECH + +Our intention here is not to provide an extensive survey of the nature of speech , but rather to point to several fundamental aspects of speech that have played important roles in the development of the TRACE model . A very useful discussion of several of these points is + +available in Klatt ( 1980 ) . + +Temporal Nature of the Speech Stimulus + +It does not , of course , take a scientist to observe one fundamental characteristic of speech : It is a signal that is extended in time . This differentiates speech perception from most other perceptual applications + +60 PSYCHOLOGICAL PROCESSES + +of PDP models, which have generally been concerned with visual + +stimuli . + +The sequential nature of speech poses problems for the modeling of contextual influences, in that to account for context effects, it is necessary to keep a record of the context. It would be a simple matter to process speech if each successive portion of the speech input were processed independently of all of the others, but, in fact, this is clearly not the case. The presence of context effects in speech perception requires a mechanism that keeps some record of that context, in a form that + +allows it to influence the interpretation of subsequent input . + +Left and Right Context Effects + +A further point , and one that has been much neglected in certain models, is that it is not only prior context, but also subsequent context, that influences perception. (This and related points have recently been made by Grosjean & Gee, 1984~ Salasoo & Pisoni, 1985~ and Thompson, 1984) . For example, Ganong (1980) reported that the identifica tion of a syllable-initial speech sound that was constructed to be between Igl and 1 kl was influenced by whether the rest of the syllable was 1 Isl (as in kiss) or 1 1ft 1 (as in gift) . Such right context effects (Thompson, 1984) indicate that the perception of what comes in now both influences and is influenced by the perception of what comes in later. This fact suggests that the record of what has already been presented cannot be a static representation but should remain in a malleable form , subject to alteration as a result of influences arising + +from subsequent input . + +Lack of Boundaries and Temporal Overlap + +A third fundamental point about speech is that the cues to successive units of speech frequently overlap in time . The problem is particularly severe at the phoneme level. A glance at a schematic speech spectrogram (Figure 1) clearly illustrates this problem. There are no separable packets of information in the spectrogram like the separate feature bun- + +dles that make up letters in printed words. + +Because of the overlap of successive phonemes~ it is difficult ~ and we believe counterproductive , to try to divide the speech stream up into separate phoneme units in advance of identifying the units. A number of other researchers (e.g., Fowler, 1984~ Klatt , 1980) have made much + +re + +> u z w : =) a w ~ u - + +TIME + +15. THE TRACE MODEL 61 + +FIGURE 1. A schematic spectrogram for the syllable bag, indicating the overlap of the information specifying the different phonemes. (From "The Grammars of Speech and Language" by A. M . Liberman , 1970, Cognitive Psychology, 1, p. 309. Copyright 1970 by + +Academic Press, Inc. Reprinted by permission.) + +the same point . A superior approach seems to be to allow the phoneme identification process to examine the speech stream for characteristic patterns , without first segmenting the steam into separate units . + +The problem of overlap is less severe for words than for phonemes , but it does not go away completely . In rapid speech , words run into each other , and there are no pauses between words . To be sure , there are often cues that signal the locations of boundaries between words stop consonants are generally aspirated at the beginnings of stressed words in English , and word initial vowels are generally preceeded by glottal stops , for example . These cues have been studied by a number of investigators , particularly Lehiste (e.g ., Lehiste , 1960 , 1964 ) and Nakatani and collaborators . Nakatani and Dukes ( 1977 ) demonstrated that perceivers exploit some of these cues , but found that certain utter ances do not provide sufficient cues to word boundaries to permit reli able perception of the intended utterance . Speech errors often involve errors of word segmentation (Bond & Garnes , 1980 ) , and certain seg mentation decisions are easily influenced by contextual factors ( R . A . Cole & Jakimik , 1980 ) . Thus , it is clear that word recognition cannot count on an accurate segmentation of the phoneme stream into separate word units , and in many cases such a segmentation would perforce exclude from one of the words a shared segment that is doing double + +Context Sensitivity of Cues + +A fourth major fact about speech is that the cues for a particular unit vary considerably with the context in which they occur. For example, the transition of the second formant carries a great deal of information about the identity of the stop consonant / b/ in Figure 1, but that for mant would look quite different had the syllable been big or bog instead of bag. Thus, the context in which a phoneme occurs restructures the + +cues to the identity of that phoneme (Liberman , 1970) . + +Not only are the cues for each phoneme dramatically affected by preceding and following context, they are also altered by more global factors such as rate of speech (J. L. Miller , 1981) , by morphological and prosodic factors such as position in the word and in the stress contour of the utterance, and by characteristics of the speaker such as size and shape of the vocal tract, fundamental frequency of the speaking voice, and dialectical variations (see Klatt , 1980, and Repp & Liber- + +man, 1984, for discussions) . + +A number of different approaches to the problem have been tried by different investigators. One approach is to try to find relatively invariant - generally relational - features (e.g., Stevens & Blumstein, 1981) . Another approach has been to redefine the unit so that it encompasses the context , and therefore becomes more invariant (Fujimura & Lovins , 1982~ Klatt , 1980~ Wickelgren , 1969) . While these are both sensible and useful approaches, the first has not yet succeeded in establishing a sufficiently invariant set of cues, and the second may alleviate but does not eliminate the problem: Even units such as demisyllables (Fujimura & Lovins , 1982) , context-sensitive allophones (Wickelgren , 1969) , or even whole words (Klatt , 1980) are still influenced by context . We have chosen to focus instead on a third possibility: that the perceptual system uses information from the context in which an utterance occurs to alter connections dynamically, thereby effectively allowing the context to retune the perceptual + +mechanism in the course of processing. + +Noise and Indeterminacy in the Speech Signal + +To compound all the problems alluded to above, there is the additional fact that speech is often perceived under less than ideal circumstances. While a slow and careful speaker in a quiet room may produce sufficient cues to allow correct perception of all of the phonemes in an utterance without the aid of lexical or other higher-level + +15. THE TRACE MODEL63 + +constraints , these conditions do not always obtain . People can correctly perceive speech under quite impoverished conditions if it is semanti cally coherent and syntactically well -formed (G . A . Miller , Heise , & Lichten , 1951) . This means that the speech mechanisms must be able to function , even with a highly degraded stimulus . In particular , as Grosjean and Gee ( 1984) , Norris ( 1982) , and Thompson ( 1984) have pointed out , the mechanisms of speech perception cannot count on accurate information about any part of a word . As we shall see , this fact poses a serious problem for one of the best current psychological models of the process of spoken word recognition , the COHORT model + +of Marslen - Wilson and Welsh ( 1978) . + +Many of the characteristics that we have reviewed differentiate speech from print - at least , from very high quality print on white paper - but it would be a mistake to think that similar problems are not encountered in other domains . Certainly , the sequential nature of spoken input sets speech apart from vision , in which there can be some degree of simultaneity of input . However , the problems of ill -defined boundaries , context sensitivity of cues, and noise and indeterminacy are central problems in vision just as much as they are in speech (cf . Ballard , Hinton , & Sejnowski , 1983~ Barrow & Tenenbaum , 1978~ Marr , 1982) . Thus , though the model we present here is focused on speech perception , we would hope that the ways in which it deals with the challenges posed by the speech signal will be applicable in other + +domains . + +The Importance of the Right Architecture + +All of the considerations listed above played an important role in the formulation of the TRACE model . The model is an instance of a POP model , but it is by no means the only instance of such a model that we have considered or that could be considered . Other formulations we considered simply did not appear to offer a satisfactory framework for dealing with these central aspects of speech (see Elman & McClelland , 1984, for discussion ) . Thus , the TRACE model hinges on the particu lar processing architecture it proposes for speech perception as well as on the POP mechanisms that implement the interactive activation + +processes that occur within it . + +Sources of TRACE 's architecture. The inspiration for the architecture of TRACE goes back to the HEARSAY speech understanding system (Erman & Lesser , 1980~ Reddy , Erman , Fennell , & Neely , 1973) . HEARSAY introduced the notion of a Blackboard , a structure similar + +64 PSYCHOLOGICAL PROCESSES + +to the Trace in the TRACE model . The main difference is that the Trace is a dynamic processing structure that is self -updating , while the Blackboard in HEARSAY was a passive data structure through which autonomous processes shared information . The architecture of TRACE also bears a resemblance to the neural spectrogram proposed by Crowder ( 1978 ~ 1981 ) to account for interference effects between successive + +items in short -term memory . + +THE TRACE MODEL + +The TRACE model consists primarily of a very large number of units , organized into three levels , the feature , phoneme , and word levels . Each unit stands for an hypothesis about a particular perceptual object - feature , phoneme , or word - occurring at a particular point in time defined relative to the beginning of the utterance . Thus , the + +TRACE model uses local representation . + +A small subset of the units in TRACE II , the version of the model with which we will be mostly concerned , is illustrated in Figures 2 , 3, and 4 . Each of the three figures replicates the same set of units , illus trating a different property of the model in each case . In the figures , each rectangle corresponds to a separate processing unit . The labels on the units and along the side indicate the spoken object (feature , phoneme , or word ) for which each unit stands . The left and right edges of each rectangle indicate the portion of the input the unit spans . At the feature level , there are several banks of feature detectors , one for each of several dimensions of speech sounds . Each bank is repli cated for each of several successive moments in time , or time slices . At the phoneme level , there are detectors for each of the phonemes . There is one copy of each phoneme detector centered over every three time -slices . Each unit spans six time slices , so units with adjacent centers span overlapping ranges of slices . At the word level , there are detectors for each word . There is one copy of each word detector cen tered over every three feature slices . Here , each detector spans a stretch of feature slices corresponding to the entire length of the word . Again , then , units with adjacent centers span overlapping ranges of + +slices . + +Input to the model , in the form of a pattern of activation to be applied to the units at the feature level , is presented sequentially to the feature -level units in successive slices , as it would be if it were a real stream of speech . Mock -speech inputs on the three illustrated dimen sions for the phrase tea cup (/ tik " p / ) are shown in Figure 2. At any instant , input is arriving only at the units in one slice at the feature + +system. These continuing interactions permit the model to incorporate right context effects and allow the model to account directly for certain aspects of short-term memory, such as the fact that more information can be retained for short periods of time if it hangs together to form a + +coherent whole. + +Processing takes place through the excitatory and inhibitory interactions of the units in the Trace. Units on different levels that are mutu ally consistent have mutually excitatory connections, while units on the same level that are inconsistent have mutually inhibitory connections. All connections are bidirectional . Thus, the unit for the phoneme Ikl centered over Feature-Slice 24 (shown in Figure 3) has bidirectional excitatory connections to feature units that would be activated if the input contained that phoneme centered on Time-Slice 24. It also has bidirectional excitatory connections to all the units at the word level for words containing Ikl at Time -Slice 24. The connections of illustrative feature- and word-level units are shown in Figure 4. Units on the same level are mutually incompatible, and hence mutually inhibitory , to the extent that the input patterns they stand for would overlap with each other in time . That is to say, units on the same level inhibit each other in proportion to the extent of the overlap of their temporal spans, or windows. At the feature level, units stand for the content of only a single time slice, so they only compete with units standing for other values on the same dimension (see Figure 4) . At the phoneme and word level, however, there can be different degrees of overlap, and hence of mutual inhibition . The extent of the mutual inhibition between the I kl in Slice 24 and other phoneme-level units is indicated in Figure 3 by the amount of shading that falls over the rectangle for the other unit . Similarly , the extent of mutual inhibition between the unit for I kA pi starting in Slice 24 and other word-level units is indi - + +cated in Figure 4. + +68 PSYCHOLOGICAL PROCESSES + +Context -Sensitive Tuning of Phoneme Units + +The connections between the feature and phoneme levels determine what pattern of activations over the feature units will most strongly activate the detector for each phoneme. To cope with the fact that the features representing each phoneme vary according to the phonemes surrounding them, the model uses multiplicative connections of the kind proposed by Hinton (1981b) and discussed in Chapters 4 and 16. These multiplicative connections essentially adjust the connections from units at the feature level to units at the phoneme level as a function of activations at the phoneme level in preceding and following time slices. + +15. THE TRACE MODEL69 + +For example, when the phoneme I tl is preceded or followed by the vowel Iii , the feature pattern corresponding to the It I is very different than it is when the It I is preceded or followed by another vowel, such as la / . Accordingly , when the unit for Iii in a particular slice is active, it changes the pattern of connections for units for It / in preceding and + +following slices . + +TRACE I and TRACE II + +In developing TRACE and in trying to test its computational and psychological adequacy , we found that we were sometimes led in rather different directions . We wanted to show that TRACE could process real speech , but to build a model that did so, it was necessary to worry about exactly what features must be extracted from the speech signal , about differences in duration of different features of different phonemes , and about how to cope with the ways in which features and feature durations vary as a function of context . Obviously , these are important problems , worthy of considerable attention . However , con cern with these issues tended to ohscure attention to the fundamental properties of the model and the model 's ability to account for basic + +aspects of the psychological data obtained in many experiments . + +To cope with these conflicting goals , we have developed two dif ferent versions of the model , called TRACE I and TRACE II . Both models spring from the same basic assumptions , but focused on dif ferent aspects of speech perception . TRACE I was designed to address some of the challenges posed by the task of recognizing phonemes from real speech . This version of the model is described in detail in Elman and McClelland (in press) . With this version of the model , we have been able to show that the TRACE framework could indeed be used to process real speech - albeit from a single speaker uttering isolated monosyllables at this point . We have also demonstrated the effi cacy of the idea of using multiplicative connections to adjust feature to -phoneme connections on the basis of activations produced by sur - + +rounding context . + +The second version of the model , TRACE II , will be the main focus of this chapter . We developed this version of the model to account for lexical influences on phoneme perception and for what is known about on -line recognition of words , though we will use it to illustrate how certain other aspects of phoneme perception fallout of the TRACE frame work . This version of the model is actually a simplified version of TRACE I . Most importantly , we eliminated the connection -strength adjustment facility , and we replaced the real speech inputs to TRACE I + +70 PSYCHOLOGICAL PROCESSES + +with mock speech. This mock-speech input consisted of overlapping but contextually invariant specifications of the features of successive phonemes. Thus, TRACE II sidesteps many of the issues addressed by TRACE I, but it makes it much easier to see how the mechanism can account for a number of aspects of phoneme and word recognition. A number of further simplifying assumptions were made to facilitate examination of basic properties of the interactive activation processes + +taking place within the model. + +Implementation Details + +The material in this section is included for completeness, but the basic line of development may be followed without reading it . Readers uninterested in these details may wish to skip to the section on factors + +influencing phoneme identification . + +Units and their dynamics. The dynamic properties of the units in TRACE are the same as those used in the interactive activation model of visual word perception~ these are described in detail in Chapter 2. In brief , the model is a synchronous model, in that all the units update their activation at the same time , based on the activations computed in the previous update cycle. Each unit takes a sum of the excitatory and inhibitory influences impinging on it . Each influence is essentially the product of the output of the influencing unit and the weight on the connection between it and the receiver. If this net input is positive~ it drives the activation of the unit upward in proportion to the distance left to the fixed maximum activation level; if the net input is negative, it drives the activation of the unit down in proportion to the distance left to the fixed minimum . Activations also tend to decay back to their resting activation level, which was fixed at 0 for all units. The output of a unit is 0 if the activation is less than or equal to O~ otherwise it is + +equal to its activation. + +TRACE I . The inputs to TRACE I are sets of 15 parameter values extracted at 5 msec intervals from syllables spoken by a male native speaker of English. The bulk of the TRACE I simulations have been done with a set of CV syllables consisting of an unvoiced stop consonant (I pi , I t/ , or I k/ ) followed by one of the vowels I ai , I ii , and I ul , as in the words shah, tea, and who. At the feature level, TRACE I consists of detectors for each of eight different value ranges on each of the 15 input parameters. There is a complete set of detectors for each 5 msec time slice of the input . Since there are 100 slices, the model is + +15. THE TRACE MODEL 71 + +There are no word - level units in TRACE I . However , there are phoneme - level units for each successive 15 msec time slice of the speech . The connections from the feature to the phoneme units were determined by using the perceptron convergence procedure ( see Chapter 2 ) under two different conditions . First , in the invariant con nections condition , a single set of connection strengths was found for each phoneme , using tokens of the phoneme spoken in all different contexts . In the context - sensitive connections condition , separate sets of connection strengths were found for each stop consonant in the con - + +text of each of the vowels . + +TRACE I can be tested either using the invariant connections or using the multiplicative context - sensitive connections described above . In the latter case , the weights coming into a particular phoneme are weighted according to the relative activation of other phonemes in the surrounding context . Consider an arbitrary phoneme unit which we will designate , for now , the target unit . The strengths of the connec tions coming into this unit can be designated by the vector w , where the elements of the vector are just the individual weights from each feature unit to the phoneme unit . This vector is the average over all context phonemes k of the context - specific weight vectors appropriate for the target phoneme in the context of k , where the contribution of each of these context - specific weight vectors is proportional to the exponential of the activation of phoneme k summed over the time slices adjacent to the target phoneme unit ( see Elman & McClelland , + +1986 , in press , for further details ) . + +TRACE II . Inputs to TRACE II are not real speech , but mock speech of the kind illustrated in Figure 2 . The mock speech is a series of specifications for inputs to units at the feature level , one for each 25 msec time slice of the mock utterance . These specifications are gen erated by a simple computer program from a sequence of to - be presented segments provided by the human user of the simulation pro gram . The allowed segments consist of the stop consonants / b / , / p / , Id / , It / , / g / , and / k / ~ the fricatives / s / and / S / ( sh as in ship ) ~ the liquids / II and / r / ~ and the vowels / a / ( as inpot ) , / i / ( as in beet ) , / u / ( as in boot ) , and / A / ( as in but ) . / A / is also used to represent reduced vowels such as the second vowel in target . There is also a I' silence I' segment represented by 1 - / . Special segments , such as a segment half - + +way between / b / and / p / , can be constructed as well . + +A set of seven dimensions is used in TRACE II to represent the feature - level inputs . Of course , these dimensions are intentional sim plifications of the real acoustic structure of speech , in much the same way that the font used by McClelland and Rumelhart ( 1981 ) in the interactive activation model of visual word recognition was an + +72 PSYCHOLOGICAL PROCESSES + +intentional simplification of the real structure of print . Each dimension is divided into eight value ranges . Each phoneme has a value on each dimension ~ the values on the vocalic , diffuseness , and acuteness dimensions for the phonemes in the utterance ItikA pi are shown in Figure 2. The dimensions and the values assigned to each phoneme on each dimension are indicated in Table 1. Numbers in the cells of the table indicate which value on the indicated dimension is most strongly activated by the feature pattern for the indicated phoneme . Values range from 1 (very low ) to 8 (very high ) . The last two dimensions were altered for the categorical perception and trading relations simula - + +tions , as described below . + +Values are assigned to approximate the values real phonemes would have on these dimensions and to make phonemes that fall into the same phonetic category have identical values on many of the dimen sions . Thus , for example , all stop consonants are assigned the same values on the power , vocalic , and consonantal dimensions . We do not claim to have captured the details of phoneme similarity exactly . Indeed , one cannot do so in a fixed feature set because the similarities vary as a function of context . However , the feature sets do have the property that the feature pattern for one phoneme is more similar to the feature pattern for other phonemes in the same phonetic category (stop , fricative , liquid , or vowel ) than it is to the patterns for phonemes + +TABLE 1 + +PHONEME FEATURE VALUES USED IN TRACE II + +PHONEME POW VOC DIF ACU CON VOl BUR + +15. THE TRACE MODEL 73 + +in other categories. Among the stops, those phonemes sharing place of articulation or voicing are more similar than those sharing neither + +attribute . + +The feature specification of each phoneme in the input stream extends over 11 time slices of the input . The strength of the pattern grows to a peak at the sixth slice and falls off again , as illustrated in Figure 2. Peaks of successive phonemes are separated by six slices . Thus , specifications of successive phonemes overlap , as they do in real + +speech (Fowler , 1984~ Liberman , 1970) . + +Generally , there are no cues in the speech stream to word boundaries - the feature specification for the last phoneme of one word overlap with the first phoneme of the next in just the same way feature specifications of adjacent phonemes overlap within words . However , entire utterances presented to the model for processing - be they indi vidual syllables , words , or strings of words - are preceded and followed by silence . Silence is not simply the absence of any input ~ rather , it is a pattern of feature values , just like the phonemes . Thus , a ninth value on each of the seven dimensions is associated with silence . These values are actually outside the range of values that occurred in the phonemes themselves so that the features of silence are completely + +uncorrelated with the features of any of the phonemes . + +TRACE II contains a unit for each of the nine values on each of the seven dimensions , in each time slice of the Trace . At the phoneme level , each Trace contains a detector for each of the 15 phonemes and a detector for the presence of silence . The silence detectors are treated like all other phoneme detectors . Each member of the set of detectors for a particular phoneme is centered over a different time -slice at the feature level , and the centers are spaced three time -slices apart . The unit centered over a particular slice receives excitatory input from feature units in a range of 11 slices , extending both forward and backward from the slice in which the phoneme unit is located . It also sends excitatory feedback down to the same feature units in the same range + +of slices . + +The connection strengths between the feature -level units and a particular phoneme -level unit exactly match the feature pattern the phoneme is given in its input specification . Thus , as illustrated in Figure 3, the strengths of the connections between the unit for / k/ centered over Time -Slice 24 and the units at the feature level are exactly proportional to the pattern of input to the feature level pro duced by an input specification containing the features of / k/ centered + +TRACE II also contains detectors for the 211 words found in a com puterized phonetic word list that met all of following criteria : (a) The word consisted only of phonemes in the list above ~ (b) it was not an 74 PSYCHOLOGICAL PROCESSES + +inflection of some other word that could be made by adding ed , s , or ing ~ and ( c) the word together with its ed , s , and ing inflections occurred with a frequency of 20 or more per million in the Kucera and Francis ( 1967 ) word count . It is not claimed that the model ' s lexicon is an exhaustive list of words meeting these criteria since the computer ized phonetic lexicon was not complete , but it is reasonably close to this . To make specific points about the behavior of the model , detec tors for the following three words not in the main list were added : blush , regal , and sleet . The model also has detectors at the word level + +for silence ( I - I ) , which is treated like a one - phoneme word . + +Presentation and processing of an utterance . Before processing of an utterance begins , the activations of all of the units are set at their resting values . At the start of processing , the input to the initial slice of feature units is applied . Activations are then updated , ending the initial time cycle . On the next time cycle , the input to the next slice of feature units is applied , and excitatory and inhibitory inputs to each unit resulting from the pattern of activation left at the end of the previ - + +ous time slice are computed . + +It is important to remember that the input is applied , one slice at a time , proceeding from left to right as though it were an ongoing stream of speech " writing on " the successive time slices of the Trace . The interactive activation process is occurring throughout the Trace on each time slice , even though the external input is only coming in to the feature units one slice at a time . Processing interactions can continue even after the left to right sweep through the input reaches the end of the Trace . Once this happens , there are simply no new input specifica tions applied to the Trace ~ the continuing interactions are based on what has already been presented . This interaction process is assumed to continue indefinitely , though for practical purposes it is always ter minated after some predetermined number of time cycles has elapsed . + +Activations and overt responses . Activations of units in the Trace rise and fall as the input sweeps across the feature level . At any time , a decision can be made based on the pattern of activation as it stands at that moment . The decision mechanism can , we assume , be directed to consider the set of units located within a small window of adjacent slices within any level . The units in this set then constitute the set of response alternatives , designated by the identity of the item for which the unit stands ( note that with several adjacent slices included in the set , several units in the alternative set may correspond to the same overt response ) . Word - identification responses are assumed to be based on readout from the word level , and phoneme - identification responses are assumed to be based on readout from the phoneme level . + +15, THE TRACE MODEL 75 + +As far as phoneme identification is concerned, then, a homogeneous mechanism is assumed to be used with both word and nonword stimuli . The decision mechanism can be asked to make a response either (a) at a critical time during processing, or (b) when a unit in the alternative set reaches a critical strength relative to the activation of other alternative units. Once a decision has been made to make a response, one of the alternatives is chosen from the members of the set. The probability of choosing a particular alternative i is then given by the Luce (1959) + +choice rule: + +Si + +P (Ri) = -::r;s; J + +Parameters. At the expense of considerable realism, we have tried to keep both TRACE I and TRACE II simple by using homogeneous parameters wherever possible. The strength of the total excitation coming into a particular phoneme unit from the feature units is normalized to the same value for all phonemes, thus making each phoneme equally excitable by its own canonical pattern. Other simplifying assumptions should be noted as well. For example, there are no differences in connections or resting levels for words of different frequency. It would have been a simple matter to incorporate frequency as McClelland and Rumelhart (1981) did, and a complete model would, of course, include some account for the ubiquitous effects of word frequency. We left it out here to facilitate an examination of the many other factors that appear to influence the process of word recognition in speech + +perception. + +Even with all the simplifications described above, TRACE II still has 10 free parameters~ these are listed in Table 2. There was some trial and error in finding the set of parameters used in the reported simulations, but, in general, the qualitative behavior of the model is remarkably robust under parameter variations, and no systematic search of the + +space of parameters is necessary. + +In all the reported simulations using TRACE II , the parameters were held at the values given in Table 2. The only exception to this occurred in the simulations of categorical perception and trading relations. Since we were not explicitly concerned with the effects of feedback to the feature level in any of the other simulations, we set the + +where j indexes the members of the alternative set , and Si = ekai . The exponential transformation ensures that all activations are positive and gives great weight to stronger activations ~ the Luce rule ensures that the sum of all of the response probabilities adds up to 1.0 . Substan tially the same assumptions were used by McClelland and Rumelhart + +( 1981 ) . + +76 PSYCHOLOGICAL PROCESSES + +TABLE 2 + +feedback from the phoneme level to the feature level to zero to speed up the simulations in all other cases. In the categorical perception and trading relations simulations this parameter was set at 0.05. Phonemeto-feature feedback tended to slow the effective rate of decay at the feature level and to increase the effective distinctiveness of different feature patterns. Rate of decay of feature level activations and strength of phoneme-to-phoneme competition were set to 0.03 and 0.05 to compensate for these effects. No lexicon was used in the categorical perception and trading relations simulations, which is equivalent to setting the phoneme-to-word excitation parameter to zero. In TRACE I, the parameters were tuned separately to compensate for the finer time scale + +of that version of the model. + +FACTORS INFLUENCING PHONEME IDENTIFICATION + +We are ready to examine the performance of TRACE , to see how well it can account for psychological data on the process of speech perception and, to determine how well it can cope with the computational challenges posed by speech. In this section we consider the process of phoneme identification . In the next section we examine several aspects of word recognition . The sections may be read independently, in either + +order. + +In the introduction , we motivated the approach taken in the TRACE model in general terms. In this section, we will see that the simple concepts that lead to TRACE provide the basis for a coherent and synthetic account of a large number of different kinds of findings on the + +PARAMETERS OF TRACE II + +Parameter Value + +Feature - Phoneme Excitation .02 Phoneme - Word Excitation .05 Word - Phoneme Excitation .03 Phoneme - Feature Excitation .00 Feature - Level Inhibition .04 Phoneme - Level Inhibition \* .04 Word - Level Inhibition \* .03 Feature - Level Decay .01 Phoneme - Level Decay .03 Word - Level Decay .05 + +\* Per 3 time slices of overlap . + +15. THE TRACE MODEL 77 + +perception of phonemes . Previous models have been able to provide fairly accurate accounts of a number of these phenomena . For exam ple , Massaro and aden 's feature integration model (Massaro , 1981~ Massaro & aden , 1980a, 1980b ~ aden & Massaro , 1978) accounts in detail for a large body of data on the influences of multiple cues to phoneme identity , and the Pisoni / Fujisaki -Kawashima model of categorical perception (Fujisaki & Kawashima , 1968 ~ Pisoni , 1973, 1975) accounts for a large body of data on the conditions under which subjects can discriminate sounds within the same phonetic category . Marslen - Wilson 's COHORT model (Marslen - Wilson & Welsh , 1978) can account for the time course of certain aspects of lexical influences on phoneme identification . Recently Fowler ( 1984) has proposed an interesting account of the way listeners cope with coarticulatory influ ences on the acoustic parameters of speech sounds . Here we will show that TRACE brings these phenomena , and several others not con sidered by any of these other models , together into a coherent picture + +of the process of phoneme perception as it unfolds in time . + +This section consists of four main parts . The first focuses on lexical effects on phoneme identification and the conditions under which these effects are obtained . The second part of this section focuses on the question of the role of phonotactic rules - that is, rules specifying which phonemes can occur together in English - in phoneme identification . Here , we see how TRACE mimics the apparently rule -governed behavior of human subjects , in terms of a "conspiracy " of the lexical items that instantiate the rule . The third part focuses on two aspects of phoneme identification often considered quite separately from lexical effects - namely , the contrasting phenomena of cue tradeoffs in phoneme perception and categorical perception . The simulations in the first three parts were all done using TRACE II . The fourth part describes our simulations with TRACE I , illustrating how the connection -modulation mechanisms embedded in that version of the model account for the fact that listeners appear to alter the cues they + +use to identify phonemes in different contexts . + +Lexical Effects + +You can tell a phoneme by the company that it keeps. 1 In this section , we describe a simple simulation of the basic lexical effect on + +1 This title is adapted from the title of a talk by David E. Rumelhart on related phenomena in letter perception . These findings are described in Rumelhart and McC ]el - + +78 PSYCHOLOGICAL PROCESSES + +phoneme identification reported by Ganong (1980) . We start with this phenomenon because it , and the related phonemic restoration effect, were among the primary reasons why we felt that the interactive activation mechanisms provided by POP models would be appropriate for speech perception, as well as visual word recognition and reading. + +For the first simulation , the input to the model consisted of a feature specification which activated Ibl and Ipl equally, followed by (and partially overlapping with ) the feature specifications for I 11, then I A I , then I gl . Figure 5 shows phoneme- and word-level activations at several points in the unfolding of this input specification. Each panel of the figure represents a different point in time during the presentation and concomitant processing of the input . The upper portion of each panel is used to display activations at the word level~ the lower panel is used for activations at the phoneme level. Each unit is represented by a rectangle labeled with the identity of the item the unit stands for . The horizontal extension of the rectangle indicates the portion of the input spanned by the unit . The vertical position of the rectangle indicates the degree of activation of the unit . In this and subsequent figures, activations of the phoneme units located between the peaks of the input specifications of the phonemes (at Slices 3, 9, 15, etc.) have been deleted from the display for clarity . The input itself is indicated below each panel, with the successive phonemes positioned at the temporal positions of the centers of their input specifications. The " A" along the x-axis represents the point in the presentation of the input stream at + +which the snapshot was taken. + +The figure illustrates the gradual build-up of activation of the two interpretations of the first phoneme, followed by gradual build -ups in activation for subsequent phonemes. As these processes unfold , they begin to produce word-level activations. It is difficult to resolve any word-level activations in the first few frames, however, since in these frames, the information at the phoneme level simply has not evolved to the point where it provides enough constraint to select anyone particular word. It is only after the Igl has come in that the model has infor mation telling it whether the input is closer to plug, plus, blush, or blood (TRACE 's lexicon contains no other words beginning with / pIA I or IblA I ) . After that point , as illustrated in the fourth panel, plug wins the competition at the word level, and through feedback support to Ip / , causes / p/ to dominate Ib / at the phoneme level. The model, then, provides an explicit account for the way in which lexical information + +can influence phoneme identification . + +Factors influencing the lexical effect. There is now a reasonable body of literature on lexical effects on phoneme identification . One important property of this literature is the fact that the lexical effect is + +15. THE TRACE MODEL 79 + +laD + + b b b - I "" g - - ) "" g - - l "" g - P P P + +\_bl ""g-P + +"'\_11=:'1 8:" + +FIGURE 5. Phoneme - and word -level activations at sev~ral points in the unfolding of a segment ambiguous between / b/ and / p/ , followed by / 1/ , / A/ , and / g/ . See text for a + +full explanation . + +often somewhat difficult to obtain . For example , Fox ( 1982, 1984) found that the lexical effect can be eliminated by time pressure . Ganong reported that the lexical effect only shows up with segments that are ambiguous ~ we know that in running speech , people often perceived as co: rectly pronounced words with deliberate errors (Marslen - Wilson & Welsh , 1978) , but at the beginnings of isolated words lexical influences appear to lead to misperceptions of unambiguous tokens of phonemes . In reaction time studies , it has been observed by Foss and Blank ( 1980) that there is no lexical effect on the reaction time to + +detect word -initial phonemes . + +Many of these findings have been taken as evidence against the view that top -down influences really playa role in normal perceptual processing (Foss & Gernsbacher , 1983) , and only come into play in a post perceptual stage of processing (Fox , 1982) . However , we observe the same results in simulations with TRACE , where top -down influences are always at work . The reason why lexical effects do not emerge until late in processing for word -initial targets is simply that the contextual information is not available until then . The reason why lexical effects do not emerge with word -initial targets that are not ambiguous is simply that the bottom -up information is there to identify the target , long before the contextual information would be available . Simulations demonstrating the absence of lexical effects for word -initial segments + +12 1 -- g~ + +B B B 12 l "" g~ + +- B + +~!1!1i!I!I~~:iJ:~)- ~ :1!;t~IJ:~J} + +- . . . . - + +1 g + +1 .... gl g g p r r - b + +P .... k r k + +- ~ - ? - a + +r d - a - + +80 PSYCHOLOGICAL PROCESSES + +under speeded conditions or when the segment is unambiguous are + +described in McClelland and Elman (in press) . + +The crucial observations concern what happens with lexical effects on word -final segments . It is well known that lexical effects are larger later in words than they are at the beginnings of words (Marslen - Wilson & Welsh , 1978) and can be obtained in reaction time studies + +even with unambiguous segments (Marslen - Wilson , 1980) . + +TRACE produces stronger lexical effects when the target comes late in the word , simply because the context is already providing top -down support for the target when it starts to come in under these cir cumstances . We illustrate by comparing response strength for the phoneme It I in Isikrtl (the word secret) and in the nonword IgAldAtl ( guldut) in Figure 6. The figure shows the strength of the It I response as a function of processing cycles , relative to all other responses based on activations of phoneme units centered at Cycle 42, the peak of the input specification for the I t/ . Clearly , response strength grows faster for the I tl in I sikr tl than for the I tl in IgA IdA tl ~ picking an arbitrary threshold of 0.9 for response initiation , we find that the It I in Isikr tl reaches criterion about 3 cycles or 75 msec sooner than the It I in I gA IdA t/ . The size of the effect Marslen- Wilson (1980) obtains is quite + +comparable to the effect observed in Figure 6. + +t + +1 . 00 + +0 .80 S kr - t g - ld - t + +0 .60 + +0 .40 + +0 . 20 + +0 . 00 + +0 6 12 18 24 30 36 42 48 54 60 66 72 Processing Cycles + +41~UdJ1S dsuodsdH + +FIGURE 6. Probability of the It I response as a function of processing cycles, based on activation of phoneme units at Cycle 42, for the stream I sikr" tl (secret) and I g" ld" tl (guldut). Vertical lines indicate the peaks of the input patterns corresponding to the succes- + +15. THE TRACE MODEL 81 + +Are Phonotactic Rule Effects the Result of a Conspiracy ? + +Recently , Massaro and M . M . Cohen ( 1983) have reported evidence they take as support for the use of phonotactic rules in phoneme iden tification . In one experiment , Massaro and Cohen ' s stimuli consisted of phonological segments ambiguous between Irl and III in different con texts . In one context (/ t\_ i/ ) , Irl is. permissible in English , but III is not . In another context (/ s\_ i/ ) , III is permissible in English but Irl is not . In a third context (/ f\_ i/ ) , both are permissible , and in a fourth (I v\_i I ) , neither is permissible . Massaro and Cohen found a bias to perceive ambiguous segments as I r I when I r I was permissible , or as III when III was permissible . No bias appeared in either of the other + +two conditions . + +With most of these stimuli , phonotactic acceptability is confounded with the actual lexical status of the item ~ thus Iflil and Ifril (flee and free ) are both words , as is Itril but not Itli / . In the Is \_ if context , however , neither / slil or / sri / are words , yet Massaro and Cohen found a bias to hear the ambiguous segment as Ill , in accordance with + +phonotactic rules . + +It turns out that TRACE produces the same effect , even though it lacks phonotactic rules . The reason is that the ambiguous stimulus pro duces partial activations of a number of words (sleep and sleet in the model ' s lexicon ~ it would also activate sleeve , sleek , and others in a model with a fuller lexicon ) . None of these word units gets as active as it would if the entire word had been presented . However , all of them (in the simulation , there are only two , but the principle still applies ) are partially activated , and all conspire together and contribute to the activation of I II . This feedback support for the I II allows it to dom inate the I r I , just as it would if I sli I were an actual word , as shown in + +Figure 7. + +The hypothesis that phonotactic rule effects are really based on word activations leads to a prediction : We should be able to reverse these effects if we present items that are supported strongly by one or more lexical items even if they violate phonotactic rules . A recent experi ment by Elman ( 1983) confirms this prediction . In this experiment , ambiguous phonemes (for example , halfway between Ihl and Id / ) were presented in three different types of contexts . In all three types , one of the two (in this case, the I d/ ) was phonotactically acceptable , while the other (the Ib / ) was not . However , the contexts differed in their relation to words . In one case, the legal item actually occurred in a word (bwindleldwindle ) . In a second case, neither item made a word , but the illegal item was very close to a word (bwacelef Idwacelet ) . In a third case, neither item was particularly close to a word (bwif/le Idwif /le) . 82 PSYCHOLOGICAL PROCESSES + +- S 1 - + +I . - S 1 - + +I - S 1 - + +- - S 1 - + +TABLE 3 + +PERCENT CHOICE OF PHONOT ACTICALL Y IRREGULAR CONSONANT + +Percentage of Identifications + +Stimulus Type Example as 'f Illegal ,. Phoneme (/ b/ ) \* + +Legal word/ illegal nonword dwindle/ bwindle 37 /r) Legal nonword/ illegal non word dwiffle/ bwiffle 46% + +FIGURE 7 . State of the Trace at several points in processing a segment ambiguous between / 1 / and / r / in the context / s \_ i / . The units for sleep ( / slip / ) and sleet ( / slit / ) + +are boxed together since they take on identical activation values . + +Results of the experiment are shown in Table 3 . The existence of a word identical to one of the two alternatives or differing from one of the alternatives by a single phonetic feature of one phoneme strongly influenced the subjects ' choices between the two alternatives . Indeed , in the case where the phonotactically irregular alternative ( bwacelet ) was one feature away from a particular lexical item ( bracelet ) , subjects tended to hear the ambiguous item in accord with the similar lexical item ( that is , as a I hi ) even though it was phonotactically incorrect . + +B- G- . As 1 i P 1 + +B - rs 1 ~ pL IS 1 i II + +ls 1 i lj ~ ~~ ~=r1- + +~~II ~j~} -{:~j:;i!:I!i!!~~!~!f i-::-sl- - {!::] : I } {:::2 + +- - s + +- s + +i - - s 1 + +1 - 1 1 + +S t + +- - ua - - r - + +84 PSYCHOLOGICAL PROCESSES + +Trading Relations and Categorical Perception + +In the simulations considered thus far, phoneme identification is influenced by two different kinds of factors: featural and lexical. When one sort of information is lacking, the other can compensate for it . The image that emerges from these kinds of findings is of a system that exhibits great flexibility by being able to base identification decisions on different sources of information . It is, of course, well established that within the featural domain each phoneme is generally signaled by a number of different cues and that human subjects can trade these cues off against each other. The TRACE model exhibits this same flexibil - + +ity , as we shall detail shortly. + +But there is something of a paradox. While the perceptual mechanisms exhibit great flexibility in the cues that they rely on for phoneme identification , they also appear to be quite "categorical" in nature. That is, they produce much sharper boundaries between phonetic categories than we might expect based on their sensitivity to multiple cues~ and they appear to treat acoustically distinct feature patterns as perceptually equivalent, as long as they are identified as instances of the same + +phoneme. + +In this section, we illustrate that in TRACE , just as in human speech perception, flexibility in feature interpretation coexists with a strong + +tendency toward categorical perception. + +For these simulations, the model was stripped down to the essential minimum necessary so that the basic mechanisms producing cue tradeoffs and categorical perception could be brought to the fore. The word level was eliminated altogether, and at the phoneme level there were only three phonemes, I ai , I g/ , and I k/ , plus silence (I -I ) . From these four items, inputs and percepts of the form I -ga-1 and I -ka-1 could be constructed. The following additional constraints were imposed on the feature specifications of each of the phonemes: (a) the lal and I -I had no featural overlap with either Igl or Ikl so that neither lal nor I -I would bias the activations of the Igl and / kl phoneme units where they overlapped with the consonant in time ~ (b) Igl and I kl were identical on five of the seven dimensions and differed only on + +the remaining two dimensions. + +The two dimensions which differentiated Igl and I k/ were voice onset time (VOT) and the onset frequency of the first formant (FIOF ) . These dimensions replaced the voicing and burst amplitude dimensions used in all of the other simulations. Figure 9 illustrates how FIOF + +tends to increase as voice onset time is delayed. + +15. THE TRACE MODEL 85 + +.. + +]~~r.I.~tZ ~. + +/ + +2000 + +1500 + +1000 + +500 + +FIGURE 9. Schematic diagram of a syllable that will be heard as / ga/ or / ka/ , depending on the point is the syllable at which voicing begins. Before the start of voicing, F2 (top curve) and F3 are energized by aperiodic noise sources, and FI is "cut back" (the noise source has little or no energy in this range) . Because of the fact that Fl rises over time after syllable onset (as the vocal tract moves from a shape consistent with the consonant into a shape consistent with the vowel), its frequency at the onset of voicing is higher for later values of VaT . Parameters used in constructing this schematic syllable + +are derived from Kewley-Port (1982). + +excitatory inputs to determine how strongly the input will activate a particular phoneme unit . All else being equal, the phoneme unit receiving the largest sum bottom-up excitation will be more strongly activated than any other and will therefore be the most likely response when a choice must be made between one phoneme and another. Since the net bottom -up input is just the sum of all of the inputs, no + +one input is necessarily decisive in this regard. + +Generally, experiments demonstrating trading relations between two or more cues manipulate each of the cues over a number of values ranging between a value more typical of one of two phonemes and a value more typical of the other. Summerfield and Haggard (1977) did this for VaT and F1OF and found the typical result, namely, that the val ue of one cue that gives rise to 50% choices of / k/ was affected by the value of the other cue: The higher the value of F1OF, the shorter the value of VaT needed for 50% choices of / k/ . Unfortunately , they did not present full curves relating phoneme identification to the values used on each of the two dimensions. In lieu of this, we present curves in Figure 10 from a classic trading relations experiment by Denes (1955) . Similar patterns of results have been reported in other studies, using other cues (e.g., Massaro, 1981) , though the transitions are often + +0 50 100 150 300 TIME + +100 ' + +( / ) 0 + +~ . + +~ 19 80 0 : ) + +J . + +< n + +( / ) . . . + +w 60 ~ w U 0 > LJ... 4 0 + +0 VOWEL W DURATION 19 . 50 MSEC ~ 20 0 100 MSEC Z . 150 MSEC ~ .6. 200 MSEC + +rr UJ 0 + +a.. 100 150 200 250 + +FRICATION DURATION ( MSEC ) + +86 PSYCHOLOGICAL PROCESSES + +FIGURE 10. Results of an experiment demonstrating the trade-off between two cues to the identity of I sl and I z/ . Data from Denes, 1955, reprinted and fitted by the model of Massaro and Cohen. (From "The Contribution of Voice-Onset Time and Fundamental Frequency as Cues to the Izi / -/ sil Distinction" by D. W. Massaro and M. M. Cohen, 1977, Perception &Psychoph)'sics, 22, p. 374. Copyright 1977 by the Psychonomic Society. + +Reprinted by permission.) + +To demonstrate that TRACE would simulate the basic tradeoff effect, we generated a set of 25 intermediate phonetic segments made up by pairing each of five different intermediate patterns on the VaT dimension with each of five different intermediate patterns on the FI0F dimension. The different feature patterns used on each dimension are shown in Figure 11, along with the canonical feature patterns for Igl and Ikl on each of the two dimensions. On the remaining five dimensions, the intermediate segments all had the common canonical + +feature values for I gl and I kl . + +The model was tested with each of the 25 stimuli , preceded by silence (I -I ) and followed by la -I . The peak on the intermediate phonetic segment occurred at Slice 12, the peak of the following vowel occurred at Slice 18, and the peak of the final silence occurred at Slice 24. For each input presented, the interactive activation process was allowed to continue through a total of 60 time .slices, well past the end of the input . At the end of the 60th time slice, we recorded the activation of the units for I g/ and / k/ in Time -Slice 12 and the probability of choosing Igl based on these activations. It makes no difference to the + +88 PSYCHOLOGICAL PROCESSES + +j + +')f/ .a'u~soo4J Jo Al~I~qeqo.1d + +FIGURE 12. Simulated probability of choosing / k/ at Time-Slice 60, for each of the 25 stimuli used in the trading relations simulation experiment . Numbers next to each curve refer to the intermediate pattern on the F10F continuum used in the 5 stimuli contribut - + +ing to each curve. Higher numbers correspond to higher values of F10F . + +/ k/ , we can see that the VaT needed increases as the FIOF decreases, + +Categorical perception. In spite of the fact that TRACE is quite flexible in the way it combines information from different features to determine the identity of a phoneme, the model is Quite categorical in its overt responses. This is illustrated in two ways: First, the model shows a much sharper transition in its choices of responses as we move from / g/ to / k/ along the VaT and FIOF dimensions than we would expect from the slight changes in the relative excitation of the / g/ and / k/ units. Second, the model tends to obliterate differences between different inputs which it identifies as the same phoneme, while sharpening differences between inputs assigned to different categories. We will consider each of these two points in turn , after we describe the + +stimuli used in the simulations. + +Eleven different consonant feature patterns were used, embedded in the same simulated / -\_a-/ context as in the trading relations simulation . The stimuli varied from very low values of both VaT and FIOF , more extreme than the canonical / g/ , through very high values on both dimensions, more extreme than the canonical / k/ . All the stimuli were spaced equal distances apart on the VaT and FIOF dimensions. The locations of the peak activation values on each of these two continua + +just as these investigators found . + +Figure 14 indicates the relative initial bottom -up activation of the / g/ and / k/ phoneme units for each of the 11 stimuli used in the simulation . The first thing to note is that the relative bottom -up excitations of the two phoneme units differ only slightly . For example, the canonical feature pattern for / g/ sends 75% as much excitation to / g/ .as it sends to / k/ . The feature pattern two steps toward / g/ from / k/ (stimulus number 5) , sends 88% as much activation to / g/ as to / k/ . The figure also indicates, in the second panel, the resulting activations of the units for / g/ and / k/ at the end of 60 cycles of processing. The slight differences in net input have been greatly amplified , and the activation curves exhibit a much steeper transition than the relative + +bottom -up excitation curves. + +There are two reasons why the activation curves are so much sharper than the initial bottom -up excitation functions . The primary reason is competitive inhibition. The effect of the competitive inhibition at the phoneme level is to greatly magnify the slight difference in the excitatory inputs to the two phonemes. It is easy to see why this happens. + +15. THE TRACE MODEL 89 + +/ g/ / k/ + +1 2 3 4 5 678 91011 + +/ g/ / k/ + +1 2 3 4 5 6 7 8 91011 + +FIGURE 13. Locations of peak activations along the VaT and FI0F dimensions, for + +each of the 11 stimuli used in the categorical perception simulation. + +- + +0 2 3 4 5 6 7 + +Voice Onset Time + +8 9 + +0 2 + +Fl + +3 4 Onset + +5 6 Frequency 7 + +FIGURE 15. Simulated identification functions and forced-choice accuracy in the ABX + +15. THE TRACE MODEL91 + +task. + +will be discussed later . The identification functions are even sharper than the activation curves ~ there is only a 4 % chance that the model will choose / k / instead of / g / for Stimulus 5 , for which / k / receives 88 % as much bottom - up support as / g / . The increased sharpness is due to the properties of the response strength assumptions . These assumptions essentially implement the notion that the sensitivity of the decision mechanism , in terms of d ' for choosing the most strongly activated of two units , is a linear function of the difference in activation of the two units . When the activations are far enough apart , d ' will be sufficient to ensure near - IOO % correct performance , even though both + +units have greater than zero activation . 2 + +In TRACE , the categorical output of the model comes about only after an interactive competition process that greatly sharpens the differ ences in the activation of the detectors for the relevant units . This interactive process takes time . In the simulation results reported here , we assumed that subjects waited a fixed time before responding . But , if we assume that subjects are able to respond as soon as the response strength ratio reaches some critical level , we would find that subjects + +2 Many readers will note that the apparent sharpness of the identification functions shown in Figure 15 contrasts with the much shallower functions shown previously in the trading relations simulations . The reason for this is simply that the stimuli are spaced more closely together in the trading relations simulation than in the categorical perception case. This follows the standard experimental practice of emphasizing gradualness in trade -off experiments and sharpness in categorical perception experiments (Lane , 1965) . + +92 PSYCHOLOGICAL PROCESSES + +would be able to respond more quickly to stimuli near the prototype of each category than they can to stimuli near the boundary . This is + +exactly what was found by Pisoni and Tash ( 1974 ) . + +There is another aspect to categorical perception as exhibited by TRACE . This is the fact that feedback from the phoneme to the feature level tends to cause the model to obliterate the differences between input feature patterns that result in the identification of the same phoneme . This allows the model to account for poor within category discrimination and good between -category discrimination - the second hallmark of categorical perception . 3 The way it works is this . When a feature pattern comes in , it sends more excitation to some phoneme units than others ~ as they become active , they begin to com pete , and one gradually comes to dominate the others . This much we have already observed . But as this competition process is going on , there is also feedback from the phoneme level to the feature level . Thus , as a particular phoneme becomes active , it tends to impose its canonical pattern of activation on the feature level . The effect of the feedback becomes particularly strong as time goes on since the feature input only excites the feature units very briefly ~ the original pattern of activation produced by the phoneme units is , therefore , gradually replaced by the canonical pattern imposed by the feedback from the phoneme level . The result is that the pattern of activation remaining at the feature level after 60 cycles of processing has become assimilated to the prototype . In this way , feature patterns for different inputs assigned to the same category are rendered nearly indistinguishable . This effect is illustrated in Figure 16 , which shows how different pairs of patterns of activation at the feature level are at the end of 60 cycles of processing . The measure of difference is simply 1 - r ab , where r ab stands for the correlation of the patterns produced by stimuli a and b . Only the two dimensions which actually differ between the + +canonical / g / and / k / are considered in the difference measure . + +3 Strictly speaking , at least as defined by Liberman , Cooper , Shankweiler , and Studdert -Kennedy ( 1967) , true categorical perception is only exhibited when the ability to discriminate different sounds is no better than could be expected based on the assump tion that the only basis a listener has for discrimination is the categorical assignment of the stimulus to a particular phonetic category . However , it is conceded that " true " categorical perception in this sense is never in fact observed (Studdert -Kennedy , Liber man , Harris , & Cooper , 1970) . While it is true that the discrimination of sounds is much better for sounds that perceivers assign to different categories than for sounds they assign to the same category , there is also at least a tendency for discrimination to be somewhat better ' than predicted by the identification function , even between stimuli that are always assigned to the same category . TRACE II produces this kind of approximate categorical + +0 . 40 + +0 . 30 + +0 . 20 + +0 . 10 + +0 . 00 + +0 2 3 4 5 6 7 8 9 10 11 12 Stimulus Number + +15. THE TRACE MODEL93 + +- - ~ + +~ " - " + +--- + +III.. + +FIGURE 16. Differences between patterns of activation at the feature level at Cycle 60, for pairs of stimuli one step apart along the / g/ - / k/ continuum used for producing the + +identification functions shown previously in Figure 15. + +To relate the difference between two stimuli to probability correct choice performance in the ABX task generally used in categorical perception experiments, we once again use the Luce (1959) choice model. The probability of identifying stimulus x with alternative a is given by + +Sax p (Rx=a) = Sax + Sbx' + +This is + +Sax = ekr'ax, + +and similarly for Sbx. Here, k, is the parameter that scales the relation between correlations and strengths. The resulting response probabilities + +are shown in Figure 15. + +Basically, the figures show that the effect of feedback is to make the feature patterns for inputs well within each category more similar than those for inputs near the boundary between categories. Differences between stimuli near the prototype of the same phoneme are almost obliterated. When two stimuli straddle the boundary, the feature level patterns are much more distinct . As a result, the probability of correctly discriminating stimuli within a phoneme category is much lower than the probability of discriminating stimuli in different + +where Sax is the " strength " of the similarity between a and x . given simply by the exponential of the correlation of a and x , + +94 PSYCHOLOGICAL PROCESSES + +Like the completion process considered earlier , the process of "canonicalization " of the representation of a speech sound via the feed back mechanism takes time . During this time , two things are happen ing : One is that the activations initially produced by the speech input are decaying ~ another is that the feedback , which drives the representa tion toward the prototype , is building up . In the simulations , we allowed a considerable amount of time for these processes before com puting similarities of different activation patterns to each other . Obvi ously , if we had left less time , there would not have been as much of an opportunity for these forces to operate . Thus , TRACE is in agreement with the finding that there tends to be an increase in within category discrimination when a task is used that allows subjects to base their responses on judgments of the similarity of stimuli spaced closely + +together in time (Pisoni & Lazarus , 1974) . + +It should be noted that it would be possible to account for categorical perception in TRACE without invoking feedback from the phoneme level to the feature level . All we would need to do is assume that the feature information that gives rise to phoneme identification is inaccessible , as proposed by the motor theory of speech perception (Liberman , Cooper , Shankweiler , & Studdert -Kennedy , 1967) , or is rapidly lost as proposed by the dual code model (Fujisaki & Kawashima , 1968~ Mas saro, 1975, 1981 ~ Pisoni , 1973, 1975) . The dual code model has had considerable success accounting for categorical perception data and accounts for all the aspects of categorical perception discussed thus far . Both feedback models and dual code models can also accommodate the fact that vowels show less of a tendency toward categorical percep tion than consonants (Fry , Abramson , Eimas , & Liberman , 1962~ Pisoni , 1973) . It is simply necessary to assume that vowel features are more persistent than consonant features (Crowder , 1978, 1981 ~ Fujisaki & Kawashima , 1968~ Pisoni , 1973, 1975) . However , the two classes of interpretations do differ in their predictions of performance in discrim inating two stimuli , both away from the center of a category , but still within it . Here , TRACE tends to show greater discrimination than it shows between stimuli squarely in the middle of a category . Standard interpretations of categorical perception can account for increases in discriminability near the boundary between two categories (where iden tification may in fact be somewhat variable ) by assuming that marginal stimuli are more likely to give rise to different category labels . But TRACE can account for increases in discriminability at extreme values of feature continua which would not give rise to different category labels . In TRACE , the reason for this increase in discriminability is that the activation of the appropriate item at the phoneme level is weaker , and therefore the feedback signal is weaker than it is when the input occurs near the center of the category . This results in less + +15. THE TRACE MODEL 95 + +canonicalization of the extreme stimuli and produces a W -shaped discrimination function , as shown in Figure 16. Few studies of categorical perception use stimuli that extend far enough into the extreme ranges of each phonetic category to observe reliable W -shaped curves~ however, Samuel (1977) did carry out such a study and obtained just + +such W -shaped discrimination curves. + +In summary, TRACE appears to provide a fairly accurate account of the phenomena of cue trade-offs and categorical perception of speech sounds. It accounts for categorical perception without relying on the notion that the phenomenon depends on read-out from an abstract level of processing; it assumes instead that the feature level, like other levels of the system, is subject to feedback from higher levels which actually changes the representation as it is being retained in memory, pushing it toward a canonical representation of the phoneme most + +strongly activated by the input . + +Retuning of Phoneme Detectors by Con text + +In our simulations of trading relations, we have shown that the boundary between phonetic categories on one dimension can be affected by inputs on other dimensions. Other factors also influence the phoneme perceived as a result of particular featural input . The identity of phonemes surrounding a target phoneme, the rate of speech of a syllable in which a particular feature value occurs, as well as characteristics of the speaker and the language being spoken all influence the interpretations of features. See Repp and Liberman (1984) for a review of + +these effects. + +In TRACE , we account for local, coarticulatory influences on phoneme identification by assuming that activations of phoneme units can modulate the feature to phoneme connections among units in adjacent time slices. This idea provides one way of implementing what Fowler (1984) has called a factoring of coarticulatory influences out of the pattern of activation produced by a feature pattern at the phoneme level. The modulation of connections can also account for the fact that phoneme boundaries shift as a function of local phonetic context (Mann & Repp, 1980) . In simulations using TRACE I, we were able to improve the performance of the model in identifying the correct consonant at the beginning of a CV syllable from 79% correct without using connection modulation to 90% correct with connection modulation in place. Interestingly , the model is capable of generalizing from the connection strengths appropriate for the vowels it has been trained + +96 PSYCHOLOGICAL PROCESSES + +on to other vowels, such as lei , which fall between those on which it was trained. Figure 17 shows phoneme-level activations produced by the same token of the syllable Idel with connection modulation turned on, in the upper panel, and off , in the lower panel. Though other units are activated in both cases, units for / d/ tend to dominate in the + +former case, but not the latter. + +It has been suggested by J. L . Miller , Green, and Schermer (1984) that lexical effects and semantic and syntactic influences on phoneme identification may be due to a different mechanism than influences of such variables as speech rate and coarticulatory influences due to local phonetic context. The assumptions we have incorporated into TRACE + +d + +d ~ d t Cl + +d g d t i i + +t t + +P . i P t 1 - i P i I i P - 1 P - - P i i + +d d d d d d d d d d e e e e e e e e e e + +UO~t + +~A~t + +;)U dPOU dWdUOqd + +- + +P h k I + +t si ad ~ t - - - + +[J k~ k kd i p t + +P d k + +P t d - . + +dddddddddde e e e e e e e e e + +FIGURE 17. Activation of phoneme units resulting from the input I del , with variable connection strengths enabled, in the upper panel, and disabled, in the lower panel. The + +15. THE TRACE MODEL 97 + +make a similar distinction . Lexical effects are due to the additional source of input to the phoneme level provided by units at the word level. This is quite different from the connection modulation mechanism we have used to account for coarticulatory influences. In the discussion, we will consider ways of extending the connection modulation idea to accommodate effects of variations in rate and speaker + +parameters. + +Summary of Phoneme Identification Simulations + +We have considered a number of phenomena concerning the identifi cation and perception of phonemes. These include lexical influences on phoneme identification and the lack thereof under certain circumstances~ phonotactic rule effects on phoneme identification and the role of specific lexical items in influencing these effects~ the integration of multiple cues to phoneme identity ~ and the categorical nature of the percept that results from this integration . We have also seen how connection modulation can be used to implement context-sensitive phoneme detectors, thereby allowing the model to improve its performance in identifying real speech and to account for effects of phonetic context on boundaries between phonemes. TRACE integrates all of these phenomena into a single account that incorporates aspects of the accounts offered for particular aspects of these results by other models. In the next section, we show how TRACE can also encompass a number of phenomena concerning the recognition of spoken words. + +THE TIME COURSE OF SPOKEN WORD RECOGNITION + +The study of spoken word recognition has a long history , and many models have been proposed . Morton ' s now -classic logogen model (Morton , 1969) was the first to provide an explicit account of the integration of contextual and sensory information in word recognition . Other models of this period (e.g., Broadbent , 1967) concentrated pri marily on effects of word frequency . Until the midseventies , however , there was little explicit consideration of the time course of spoken word recognition . Several studies by Marslen - Wilson and his collaborators (Marslen - Wilson , 1973~ Marslen - Wilson & Tyler , 1975) , and by R . A . Cole and his collaborators (Cole , 1973~ Cole & Jakimik , 1978, + +98 PSYCHOLOGICAL PROCESSES + +Marslen - Wilson ' s COHORT model ( Marslen - Wilson & Tyler , 1980 ~ Marslen - Wilson & Welsh , 1978 ) of speech perception was based on this early work on the time course of spoken word recognition . The COHORT model was one of the sources of inspiration for TRACE for two main reasons . First , it provided an explicit account of the way top - down and bottom - up information could be combined to produce a word recognition mechanism that actually worked in real time . Second , it accounted for the findings of a number of important experiments demonstrating the on - line character of the speech recognition process . However , several deficiencies of the COHORT model have been + +pointed out , as we shall see . + +Because TRACE was motivated in large part by a desire to keep what is good about COHORT and improve upon its weaknesses , we begin this section by considering the COHORT model in some detail . First we review the basic assumptions of the model , then consider its + +strengths and weaknesses . + +There appear to be four basic assumptions of the COHORT model : + +1 . The model uses the first sound ( in Marslen - Wilson & Tyler , 1980 , the initial consonant - cluster - plus - vowel ) of the word to determine which words will be in an initial cohort or candidate + +set . + +2 . Once the candidate set is established , the model eliminates words from the cohort immediately , as each successive phoneme arrives , if the new phoneme fails to match the next phoneme in the word . Words can also be eliminated on the basis of semantic constraints , although the initial cohort is + +assumed to be determined by acoustic input alone . + +3 . Word recognition occurs immediately , as soon as the cohort has been reduced to a single member ~ in an auditory lexical deci sion task , the decision that an item is a nonword can be made as soon as there are no remaining members in the cohort . + +4 . Word recognition can influence the identification of phonemes in a word only after the word has been recognized . + +There is a considerable body of data that supports various predictions of the COHORT model . It has been observed in a variety of paradigms that lexical influences on phoneme identification responses are much greater later in words than at their beginnings ( Bagley , 1900 ~ R . A . Cole & Jakimik , 1978 , 1980 ~ Marslen - Wilson , 1980 ~ Marslen - Wilson + +15. THE TRACE MODEL 99 + +& Welsh , 1978 ) . We considered some of this evidence in earlier sec tions . Another important finding supporting COHORT is the fact that the reaction time to decide that an item is a nonword is constant when measured from the occurrence of the first phoneme that rules out the + +last remaining word in the cohort (Marslen - Wilson , 1980 ) . + +Perhaps the most direct support for the basic word -recognition assumptions of COHORT comes from the gating paradigm , introduced first by Grosjean ( 1980 ) . In this paradigm , subjects are required to guess the identity of a word after hearing successive presentations of the word . The first presentation is cut off so that the subject hears only the first N msec (N = 30 to 50 in different studies ) . Later presenta tions are successively lengthened in N msec increments until eventually the whole word is presented . The duration at which half the subjects correctly identify the word is called the isolation point . Considerably more input is required before subjects are reasonably sure of the iden tity of the word ~ that point is termed the acceptance point . Grosjean ' s initial study confirmed many basic predictions of COHORT , though it also raised a few difficulties for it (see below ) . In a more recent study using the same method , Tyler and Wessels ( 1983 ) carried out a very close analysis of the relation between the empirically determined isola tion point and the point at which the input the subject has received is consistent with one and only one remaining item - the point at which " recognition would be expected to occur in the COHORT model . They report that the isolation point falls very close to this theoretically derived recognition point , strongly supporting the basic immediacy + +assumptions of the COHORT model . + +It should be noted that the gating task is not a timed task , and so it does not provide a direct measure of what the subject knows as the speech input is unfolding . However , it is now in fairly wide use , and Cotton and Grosjean ( 1984 ) have established that the basic patterns of results obtained in Grosjean ' s ( 1980 ) pioneering gating experiment do not depend on the presentation of successively longer and longer + +presentations of the same stimulus . + +A dilemma for COHOR T. Though the COHORT model accounts for a large body of data , there are several difficulties with it . We con sider first the one that seems the most serious : as stated , COHORT requires accurate , undistorted information about the identity of the phonemes in a word up to the isolation point . Words cannot enter into consideration unless the initial consonant -cluster -plus -vowel is heard , and they are discarded from it as soon as a phoneme comes along that they fail to match . No explicit procedure is described for recovering words into the cohort once they have been excluded from it or when + +100 PSYCHOLOGICAL PROCESSES + +the beginning of the word is not accurately perceived due to noise or + +elision . + +These aspects of COHORT make it very difficult for the model to explain recognition of words with distorted beginnings , such as dwibble ( Norris , 1982 ) , or words whose beginnings have been replaced by noise ( Salasoo & Pisoni , 1985 ) . From a computational point of view , this makes the model an extremely brittle one ~ in particular , it fails to deal with the problem of noise and underspecification which is so crucial for + +recognition of real speech ( Thompson , 1984 ) . + +The recognizability of distorted items like dwibble might be taken as suggesting that all we need to do is liberalize the criterion for entering and retaining words in the cohort . Thus , the cohort could be defined as the set of words consistent with what has been heard or mild devia tions ( e .g ., one or two features ) from what has been heard . This would allow mild distortions like replacing / r / with / w / not to disqualify a word from the cohort . It would also allow the model to cope with cases where the beginning of the word is underspecified ~ in these cases , the initial cohort would simply be larger than in the case where the input + +clearly specified the initial phonemes . + +However , there is still a problem . Sometimes we need to be able to rule out items that mismatch the input on one or two dimensions and sometimes we do not . Consider the items pleasant and blacelet . In the first case , we need to exclude present from the cohort , so the slight difference between / 1/ and / r / must be sufficient to rule it out ~ in the second case , we do not want to lose the word bracelet , since it provides the best fit overall to the input . Thus , in this case , the difference between / 1/ and / r / must not be allowed to rule a word candidate out . Thus the dilemma : On the one hand , we want a mechanism that will be able to select the correct word as soon as an undistorted input speci fies it uniquely , to account for the Tyler and Wessels results . On the other hand , we do not want the model to completely eliminate possibili ties that might later turn out to be correct . We shall shortly see that + +TRACE provides a way out of this dilemma . + +Another problem for COHOR T. Grosjean ( 1985 ) has recently pointed out another problem for COHORT , namely , the possibility that the subject may be uncertain about the location of the beginning of each successive word . A tacit assumption of the model is that the sub ject goes into the beginning of each word knowing that it is the begin ning . In the related model of R . A . Cole and lakimik ( 1980 ) , this assumption is made explicit . Unfortunately , it is not always possible to know in advance where one word starts and the next word ends . As we discussed in the introduction , acoustic cues to juncture are not always reliable , and in the absence of acoustic cues , even an optimally efficient + +Competition vs. bottom-up inhibition . TRACE deals with COHORT 's dilemma by using competition rather than phoneme-toword inhibition . The essence of the idea is simply this: Phoneme units have excitatory connections to all the word units they are consistent with . Thus, whenever a phoneme becomes active in a particular slice of the Trace, it sends excitation to all the word units consistent with that phoneme in that slice. The word units then compete with each other~ items that contain each successive phoneme in a sequence dominate all others, but, if no word matches perfectly, a word that provides a close fit to the phoneme sequence can eventually win out over words + +that provide less adequate matches. + +Consider, from this point of view, our two items pleasant and blacelet again. In the first instance, pleasant will receive more bottom-up excitation than present and so will win out in the competition . We have already seen, in our analysis of categorical perception at the phoneme level, how even slight differences in initial bottom -up excitation can be magnified by the joint effects of competition and feedback~ but the real beauty of the competition mechanism is that this action is contingent on the activation of other word candidates. Thus, in the case of blacelet, since there is no word blacelet, bracelet will not be suppressed. Initially , it is true, words like blame and blatant will tend to dominate + +15. THE TRACE MODEL 101 + +mechanism cannot always know that it has heard the end of one word until it hears enough of the next to rule out the possible continuations + +of the first word. + +What is needed, then, is a model that can account for COHORT's successes and overcome these two important deficiencies. The next two sections show that TRACE does quite well on both counts. The first of these sections examines TRACE 's behavior in processing words whose beginnings and endings are clearly delineated for it by the presence of silence. The second considers the processing of multiword + +inputs, which the model must parse for itself . + +One Word at a Time + +In this section, we see how TRACE resolves the dilemma facing COHORT, in that it is immediately sensitive to new information but is still able to cope with underspecified or distorted word beginnings. We also consider how the model accounts for the preference for short-word responses early in processing a long word. The section concludes with a discussion of ways the model could be extended to account for ' word + +frequency and contextual influences. + +102 PSYCHOLOGICAL PROCESSES + +bracelet, but , since the input matches bracelet better than any other word, bracelet will eventually come to dominate the other possibilities. This behavior of the model is illustrated using examples from its restricted lexicon in Figure 18. In one case, the input is legal, and the word regal is completely dominated by legal. In the other case, the input is lugged, and the word rugged eventually dominates because there is no word lugged (pronounced to rhyme with rugged- the word lug is not in the model's lexicon) . Here, rugged must compete with other partial matches of lugged, of course, and it is less effective in this regard than it would be if the input exactly matched it , but it does win out in + +the end. + +It should be noted that the details of what word will be most strongly activated in such cases depend on a number of factors, including , in particular, the distinctiveness of mismatching phonemes. Also, it is possible to find cases in which a word that correctly spans a part of a longer string dominates a longer word that spans the whole string but misses out on a phoneme in one place or another. An item like vigorette mayor may not be a case in point . In such cases, though, the most important thing might not turn out to be winning or losing, but rather the fact that both tend to stay in the game. Such neologisms can suggest a poetic conjunction of meanings, if used just right : "He walked + +briskly down the street, puffing his vigorette." + +Time course of word recognition in TRA CEo So far we have shown how TRACE overcomes a difficulty with the COHORT model in cases where the beginning of a word has been distorted. In earlier sections on phoneme processing, some of the simulations illustrate that the model is capable of recognizing words with underspecified (i.e., ambiguous) initial phonemes. In this section, we examine how well TRACE emulates the COHORT model in cases where the input is an undistorted representation of some particular word. In particular, we wanted to see how close TRACE would come to behaving in accord with COHORT's assumption that incorrect words are dropped from the cohort of active candidates as soon as the input diverges from them. To examine this process, we considered the processing of the word product (/ pradA ct/ ) . Figure 19 shows the state of the Trace at various points in processing this word, and Figure 20 shows the response strengths of several units relative to the strength of the word product itself , as a function of time relative to the arrival of the successive phonemes in the input . In the latter figure , the response strength of product is simply given as 1.0 at each time slice and the response strengths of units for other words are given relative to the strength of product. The curves shown are for the words trot, possible, priest, progress, and produce~ these words differ from the word product (according + +1P r a d ~ k tr + +G 1 ~~ ~ g ~ tl ~j tr B + +~ \_ad ~ ~ ~ + +~~Iil ~~iln E~~lllla t , ~ ~ a Q ~, + +I ~ ~ &- I~ I.r\_~~ I ' I ' ! 1 , ~ - ~ b + 1 ~ ' I' a d 'u Sr + +1~ . ~ ~ rMr' rll I m ~- + +- - p - p p + +- ad + +ra r ~ k + +p r d + +a ~ t + +k - + +r d + +bi 1 b g t ub g - - b t b H g - Iu flB - P + +- prad ~kt - - prad --- kt - - prad ~ kt - - prad ~ kt -- + +FIGURE 19. State of the Trace at various. points in processing the word product + +(/ pradA kt/). + +to the simulation program 's stressless encoding of them !) in the first , second , third , fourth , and fifth phonemes , respectively . Figure 20 shows that these items begin to drop out just after each successive phoneme comes in . Of course , there is nothing hard and fast or absolute about dropping a candidate in TRACE . What we see instead is that mismatching candidates simply begin to fade as the input diverges from them in favor of some other candidate . This is just the kind of behavior the COHORT model would produce in this case, though , of course , the drop -off would be assumed to be an abrupt , discrete event .4 There is one aspect of TRACE ' s behavior which differs from COHORT : Among those words that are consistent with the input up to a particular point in time , TRACE shows a bias in favor of shorter words over longer words . Thus , priest has a slight advantage before the / a/ comes in , and produce is well ahead of product until the / A / comes + +in (in phonemes , produce is one shorter than product ) . + +4 The data reported by Tyler and Wessels actually appears to indicate an even more immediate drop -off than is seen in this simulation . However , it should be remembered that the curves shown in Figure 20 are on -line response strength curves , and thus reflect the lags inherent in the percolation of input from the feature to the word level . The gating task , on the other hand , does not require subjects to respond on -line . If the input is simply turned off at the peak of each phoneme 's input specification and then allowed to + +This advantage for shorter words is due to the competition mechanism. Recall that word units compete with each other in proportion to the overlap of the sets of time slices spanned by each of the words. Overlap is, of course, symmetrical, so long and short words inhibit each other to an equal extent~ but longer words suffer more inhibition from other long words than short words do. For example, progress and probable inhibit product more than they inhibit priest and produce. Thus, units for longer words are generally subjected to extra inhibition , particularly early on in processing when many candidates are active, and so + +they tend to suffer in comparison to short words as a result. + +We were at first somewhat disturbed by this aspect of the model's behavior, but it turns out to correspond quite closely with results obtained in experiments by Grosjean (1980) and Cotton and Grosjean (1984) using the gating paradigm. Both papers found that subjects hearing the beginnings of words like captain tended to report shorter words consistent with what they had heard (e.g., cap) . However, we should observe that in the gating paradigm, when the word captain is truncated just after the / p/ , it will sound quite a bit like cap followed by silence. In TRACE , this silence would activate silence units at the phoneme and word levels, and the word-level silence units would compete with units for words that extend into the silence. The silence will reinforce the preference of the model for short-word interpretations + +15. THE TRACE MODEL 105 + +pad k t + +2.00 T ! 1.80 I i 1.60 i I ! + +> 0 6 12 18 24 30 36 42 48 54 60 66 72 Processing Cycles + +8JI + +Ea1IWEJ + +~ . + +FIGURE 20. Response strengths of the units for several words relative to the response strength of the unit for product (/ pradAkt/ ) , as a function of time relative to the peak of the first phoneme that fails to match the word. The successive curves coming off of the horizontal line representing the normalized response strength of product are for the words trot, possible, priest, progress, and produce, respectively. In our lexicon they are rendered + +as / trat/ , / pasAbAI/ , / prist/ , / pragrAs/ , and / pradus/ , respectively. + +106 PSYCHOLOGICAL PROCESSES + +Lexical Basis of Word Segmentation + +How do we know when one word ends and the next word begins? This is by no means an easy task, as we noted in the introduction . To + +because the detection of the silence will inhibit the detector for the longer word. Thus, there are actually two reasons why TRACE might favor short-word interpretations over long-word interpretations in a gating experiment . Whether human subjects show a residual preference for shorter interpretations over longer ones in the absence of a follow ing silence during the course of processing is not yet clear from avail- + +able data. + +We should point out that the experimental literature indicates that the advantage of shorter words over longer ones holds only under the special circumstances of gated presentation and then only with early gates, when shorter words are relatively more complete than longer ones would be. It has been known for a long time that longer words are generally more readily recognized than shorter ones when the whole word is presented for identification against a background of noise (Lick lider & Miller , 1951) . Presumably, the reason for this is simply that longer words generally provide a larger number of cues than shorter + +words do, and hence are simply less confusable. + +Frequency and context effects. There are, of course, other factors that influence when word recognition will occur, beyond those we have considered thus far. Two very important ones are word frequency and contextual predictability . The literature on these two factors goes back to the turn of the century (Bagley, 1900) . Morton 's (1969) logogen model effectively deals with several important aspects of this huge + +literature , though not with the time course of these effects. + +We have not yet included either word frequency or higher-level contextual influences in TRACE , though, of course, we believe they are important . Word frequency effects could be accommodated, as they were in the interactive activation model of word recognition, in terms of variation in the resting activation level of word units or in terms of variation in the strength of phoneme-to-word connections. Contextual influences can be thought of as supplying activation to word units from even higher levels of processing than the word level. In this way, basic aspects of these two kinds of influences can be captured. We leave it to future research, however, to determine to what extent these elaborations of TRACE would provide a detailed account of the data on the roles of these factors. For now, we turn to the problem of determining + +where one word ends and the next one begins. + +recap our earlier argument, there are some cues in the speech stream, but as several investigators have pointed out (R. A . Cole & lakimik , 1980~ Grosjean & Gee, 1984~ Thompson, 1984) , they are not always sufficient , particularly in fluent speech. It would appear that there is an important role for lexical knowledge to play in determining where one word ends and the next word begins, as well as in identifying the objects that result from the process of segmentation. Indeed, as Reddy (1976) has suggested, segmentation and identification may simply be + +joint results of the mechanisms of word recognition . + +R. A . Cole and lakimik (1980) discuss these points and present evidence that semantic and syntactic context can guide segmentation in cases where the lexicon is consistent with two readings (car go vs. cargo) . Our present model lacks syntactic and semantic levels, so it cannot make use of these higher-level constraints~ but it can make use of its knowledge about words, not only to identify individual words in isolation, but to pick out a sequence of words in continuous streams of phonemes. Word identification and segmentation emerge together from the interactive activation process as part and parcel of the process + +of word activation. + +This section considers several aspects of the way in which word segmentation emerges from the interactive activation process, as observed in simulations with TRACE II . Before we consider these, it is worth recalling the details of some of the assumptions made about the bottom -up activation of word units and about competitive inhibition between word units. First, the extent to which a particular phoneme excites a particular word unit is independent of the length of the word. Second, the extent to which a particular word unit will inhibit another word unit is proportional to the temporal overlap of the two word units. This means that words which do not overlap in time will not inhibit each other but will gang up on other words that partially overlap each of them. These two assumptions form most of the basis of the effects + +we will observe in the simulations. + +15. THE TRACE MODEL 107 + +The boundary is in the ear of the "behearer." First , we consider the basic fact that the number of words we will hear in a sequence of phonemes can depend on our knowledge of the number of words the sequence makes. Consider the two utterances she can't and secant. Though we can say either item in a way that makes it sound like a single word or like two words, there is an intermediate way of saying them so that the first seems to be two words and the second seems like only + +one. + +To see what TRACE II would do with single and multiple word inputs, we ran simulation experiments with each individual word in the main 21 I -word lexicon preceded and followed by silence, and then with + +PROCESSES + +1P art i ~ + +1P art i ~ + +G {=fu~~L] } - R + +G- 1H a ~~. , 1P a r tr if) a to' tr -{ ~ + +ip art i ~ + +:fi:iik !:-,--, 1 par k ~ 1 i ~ ill a r ffi!:r ~ {2~ {IJ} -E~111~5~- t {i~~ij ~h {IJIll 1~rnn . . + +- - p - p P t - P art - ar i r . t 1 + +r . + +b 1 ulP p + +- a - d t ~ ~ - ul u - - P + +108 PSYCHOLOGICAL + +211 pairs of words , with a silence at the beginning and at the end of the entire stream . The pairs were made by simply permuting the lexicon twice and \ then abutting the two permutations so that each word occurred once as the first word and once as the second word in the entire set of 211 pairs . We stress, of course , that real speech would tend to contain cues that would mark word boundaries in many cases ; the experiment is simply designed to show what TRACE can do in + +cases where these cues are lacking . + +With the individual words , TRACE made no mistakes - that is, by a few slices after the end of the word , the word that spanned the entire input was more strongly activated than any other word . An example of this is shown using the item / parti / in Figure 21. The stream / parti / might be either one word (party ) or two (par tea, or par tee- the model knows of only one word pronounced / ti / ) . At early points in processing the word , par dominates over party and other longer words for reasons discussed in the previous section . By the time the model has had a chance to process the end of the word , however , party comes to dom - + +inate . + +Why does a single longer word eventually win out over two shorter ones in TRACE ? There are two main reasons . First of all , a longer word eventually receives more bottom -up support than either shorter word , simply because there are more phonemes activating the longer word than the shorter word . The second reason has to do with the + +{2~ ~1~ ~ ~LJ {-~--?:=I} ~ rk ~ + +E G -[ f ] J { [ } } G B + +~ J} -{Q~=It~J} + +~ - ~ I =rJ } + +w ~=r =u 112 a r t ~ 1P art i ~ + +{~ ~ ;~~ I:fl =H ~ 1 bar k ~ {~Im- + +~ Q -[[I} {Q~~ ~ t ~ ~ t J -@=:r} {[ I } { [ I } L - L . - , - k , - -- ct P ~ r 1 Par - 1 b rt1 Par 1 - - - a - + +- - + +~ - P - + +.. .. ... .. .. ... - . . - . . + +15. THE TRACE MODEL 109 + +~) art 1 - + 3 - par - t i - +3 -- bar t i ~ +3 - parki - +3 + +sequential nature of the input . In the case of / parti/ , by the time the / ti / is coming in, the word party is well enough established that it keeps / ti / from getting as strongly activated as it would otherwise. This behavior of the model leads to the prediction that short words imbedded in the ends of longer words should not get as strongly activated as shorter words coming earlier in the longer word. This prediction could be tested using the gating paradigm or a cross-modal priming paradigm + +such as the one used by Swinney (1982) . + +However, it should be noted that this aspect of the behavior of the model can be overridden if there is bottom -up information favoring the two-word interpretation . Currently , this can only happen in TRACE through the insertion of a brief silence between the par and the tea. As shown in Figure 22, this results in par and tea dominating all other + +word candidates. + +What happens when there is no long word that spans the entire stream, as in / barti/ ? In this case, the model settles on the two word interpretation bar tea, as shown in Figure 22. Note that other words, such as art, that span a portion of the input , are less successful than either bar or tea. The reason is that the interpretations bar and art overlap with each other, and art and tea overlap with each other, but bar and tea do not overlap. Thus, art receives inhibition from both bar and tea, while bar and tea each receive inhibition only from art . Thus , two words that do not overlap with each other can gang up on a third + +word that each overlaps with partly and drive it out . + +These remarkably simple mechanisms of activation and competition do a very good job of word segmentation without the aid of any sylla bification , stress , phonetic word -boundary cues, or semantic and syntac tic constraints . In 189 of the 211 word pairs tested in the simulation experiment , the model came up with the correct parse, in the sense that no other word was more active than either of the two words that had been presented . Some of the failures of the model occurred in cases where the input was actually consistent with two parses, either a longer spanning word rather than a single word (as in party ) or a dif ferent parse into two words , as in part rust for par trust . In such cases TRACE tends to prefer parses in which the longer word comes first . There were , however , some cases in which the model did not come up with a valid parse, that is, a pattern than represents complete coverage of the input by a set of nonoverlapping words . For example , consider the input / parki / . Though this makes the two words par and key, the word park has a stronger activation than either par or key, as illustrated + +in Figure 22. + +This aspect of TRACE II ' s behavior indicates that the present ver sion of the model is far from the final word on word segmentation . A complete model would also exploit syllabification , stress, and other cues to word identity to help eliminate some , of the possible interpretations of TRACE II 's simple phoneme streams . The activation and competi tion mechanisms in TRACE II are sufficient to do quite a bit of the word segmentation work , but we do not expect them to do this per- + +fectly in all cases without the aid of other cues. + +Some readers may be troubled by a mechanism that does not insist upon a parse in which each phoneme is covered by one and only one word . Actually , though , this characteristic of the model is often a vir tue , since in many cases, the last phoneme of a word must do double duty as the first phoneme of the next , as in hound dog or brush shop. While speakers tend to signal the doubling in careful speech, the cues to single vs. double consonants are not always sufficient for disambi guation , as is clear when strings with multiple interpretations are used as stimuli . For example , an utterance intended as no notion will some times be heard as kno 'n notion (Nakatani & Dukes , 1977) . The model is not inclined to suppress activations of partially overlapping words , even when a nonoverlapping parse is available . This behavior of TRACE is illustrated with / bA stapf (bus top or bus stop) in Figure 23. In this case, higher levels could provide an additional source of inf or mation that would help the model choose between overlapping and + +110 PSYCHOLOGICAL PROCESSES + +{b ~ - + +--- r - s- l a ~ ~ l {~ ~ B G {~~ + +{I =~=:Q} + +~ ~ + +b st P- b S P- - """ a - r ..... + +- - + +Thus far in this section, we have considered the general properties of the way in which TRACE uses lexical information to segment a speech stream into words, but we have not considered much in the way of empirical data that these aspects of the model shed light on. However, there are two findings in the literature which can be interpreted in accordance with TRACE 's handling of multiword speech streams. + +15. THE TRACE MODEL 111 + +- b -- stap - - br ""'- Sap - + +FIGURE 23. State of the Trace at the end of the streams / bustap/ (bus stop or bus top) + +and / bruSap/ (bmsh shop). + +Where does a nonword end? A number of investigators (e.g., R. A . Cole & Jakimik , 1980) have suggested that when one word is identi fied , its identity can be used to determine where it ends and, therefore , where the next word begins. In TRACE , the interactive activation process can often establish where a word will end even before it actually does end, particularly in the case of longer words or when activations at the word level are aided by syntactic and semantic constraints. However, it is much harder to establish the end of a nonword since the fact that it is a nonword means that we cannot exploit any knowledge of + +where it should end to do so. + +This fact may account for the finding of Foss and Blank (1980) that subjects are much slower to respond to target phonemes at the beginning of a word preceded by a nonword than at the beginning of a word 112 PSYCHOLOGICAL PROCESSES + +preceded by a word. For example, responses to detect word-initial / d/ + +The long and short of word identification . One problematic feature of speech is the fact that it is not always possible to identify a word unambiguously until one has heard the word after it . Consider, for example, the word tar. If we are listening to an utterance and have gotten just to the / r / in The man saw the tar box, though tar will tend to be + +were faster in stimuli such as the following : + +At the end of last year, the government decided . . . + +than they were when the word preceding the target phoneme (in this case, government) was replaced by a nonword such as gatabont. It should be noted that the targets were specified as word-initial segments. Therefore , the subjects had not only to identify the target phoneme~ they had to determine that it fell at the beginning of a word as well. The fact that reaction times were faster when the target was preceded by a word suggests that subjects were able to use their knowledge of where the word government ends to help them determine where the + +next word begins. + +An example of how TRACE allows one word to help establish where its successor begins is illustrated in Figure 24. In the example, the model receives the stream possible target or pagusle target, and we imagine that the target is word-initial j tj . In the first case, the word .possible is clearly established, and competitors underneath it have been completely crushed by the time the initial j tj in target becomes active at the phoneme level (second panel in the upper part of the figure) , so there is no ambiguity about the fact that this j tj is at the beginning of the next word. (The decision mechanism would, of course, be required to note that the model had established the location of the end of the preceding word. We have not yet incorporated explicit assumptions about how this would be done.) In the second case, words beginning and ending at a number of different places, including some that overlap with the location of the / tj , are partly activated. Thus, a listener would have to wait until the input is well into the word target before it becomes clear that the first j t/ in target is in fact a word-initial j t/ . In reality, the situation is probably not as bleak for the perceiver as it appears in this example because in many cases there will be cues in the manner of pronunciation and the syllabification of the input that will help to indicate the location of the word boundary. However, given the imprecision and frequent absence of such cues, it is not surprising that the lexical status of one part of a speech stream plays an important role in helping listeners determine where the beginning of the next word + +must be. + +{f)\_a s ~ b ~ I ~ 1P a ~ b ~ I ~ 1P a s ~ b ~ I ~ + +~ A=~ ~ B- G + +~ u ~ { fn : g ~ + +1P\_~~ fg ~l 8 ~ e:~ t~ m ~-':l - - ' ~ t ' -Jt , ~ M ~ -~ --"' + +- P ~ P ~ b ~ b ~ t a - as Pas I s b ~ - . + +I a + +~ t r I g + +> a u 1 r .,. k + +ru r b - PfiI - ki ~ a d P P + +1~:~ ~~~~] } -{32 a k ~ t ~ + +1P a p "'~ 1P a P ~~ f : ij ~En + +~l-.:: JiJJ ;~~~III!~~~!:!]} + +a 1 ~ . 1 ~ d ~ I t~ + +1~~~~Bi !Fr-u--f} a ~ . S t ~~t;lil~~~ - ~ fl + +tilt : ~. a ::s~ tilt ~ st + +- P + +a ~ p ~ + +g - a s ~ P ~ ~ s g \_ a s t ~ I g I a + +t r + +k a g - S, r k rBlil pu k a a - k ~ r b - k di P + +the preferred hypothesis at this point , we do not have enough informa tion to say unequivocally that the tar will not turn out to be target or tarnished or one of several other possibilities. It is only after more time has passed, and we have perceived either a silence or enough of the next word to rule out any of the continuations of / tar / , that we can decide we have heard the word tar. This situation, as it arises in TRACE with the simple utterance / tarbaks/ (tar box) , is illustrated in Figure 25. Though tar is somewhat more active than the longer word target when the / r / is coming in , it is only when the word box emerges as the interpretation of the phonemes following tar that the rival target + +15. THE TRACE MODEL 113 + +- pas ~ b ~ I targ ~ t - - pas ~b ~ l targ ~ t - - pas ~ b ~ I t ;1 r g - t - + +- pag ~s~ ltarg ~t - - pag ~s~ lta ~g~ t - - pag ~s~ ltarg ~t - FIGURE 24. State of the Trace at several points during the processing of possible target + +and pagusle target. + +OCESSES + +li ~ ,iI ~ ~ + +{~ q B - @~ ::::-1 tar g ~ t ~ + +G + +{ La r g ~ tr + +~a r~ l 1 l ' "1 ~~~ ::!} - ~el~~Ff~ . I ~1~ h1=JJ ~ ~ @} s la rr {I~~~ - {s\f~~g===lJ -, + +- t. \_ t r \_ tarb k + +- a b a . S - + +- a r + +r pugS ug Pa p + +u ul u + +~ t S - p . l - gi - ul ~pk - - 1 + +-r.g:~ ~ ~ ~ [ i =. : l ~ i ~ \_1<~s} + +~ ~ fl + +B - G - G - G + +1ba k sr + +~ ~} {~ + +~ ~ t } ~lli ;f J} ~~ d 1 {Qll:r ~ @j -B {arUm :IE 1 r { ~ - b b g - g ~ t - g ~ t r g t r k ~ a - ~ a a t ar s b ak + +a s k u ulPu pug g aH 1 uS - . - k P d --:- - ul S P + +1a d gl tk - - + +114 PSYCHOLOGICAL PR + +- larbaks - - tarbaks - - tarbaks - -- tar b a k s - + +~ + +- g ~ tarbaks - - g ~ tarbaks - - g ~ tarbaks -- - g ~ tarbaks - + +FIGURE 25. State of the Trace at several points in processing tar box and guitar box . + +With longer words the situation is different . As we have already seen in another example , by the time the end of a longer word is reached it is much more likely that only one word candidate will remain . Indeed , with longer words it is often possible to have enough information to identify the word unambiguously well before the end of the word . An illustration of this situation is provided by a simulation using the utterance guitar box / gA tarbaksj . By the time the / r / has registered , guitar is clearly dominant at the word level and can be + +15. THE TRACE MODEL 115 + +short words followed by a second word and measured how much of the word and its successor the subject needed to hear to identify the target . With longer words , subjects could usually guess the word correctly well before the end of the word ~ and by the end of the word , they were quite sure of the word 's identity . With monosyllabic words , on the other hand , many of the words could not be identified correctly until well into the next word . On average , subjects were not sure of the word ' s identity until about the end of the next word or the beginning of the one after . As Grosjean ( 1985) points out , a major reason for this is simply that the spoken input often does not uniquely specify the iden tity of a short word . In such cases, the perceptual system is often forced to process the short word and its successor at the same time . + +Recognizing the words in a short sentence. One last example of TRACE II 's performance in segmenting words is illustrated in Figure 26. The figure shows the state of the Trace at several points during the processing of the stream j SiSA tA baksj . By the end , the words of the phrase she shut a box, which fits the input perfectly with no overlap , + +dominate all others . + +This example illustrates how far it is sometimes possible to go in parsing a stream of phonemes into words without even considering syntactic and semantic constraints , or stress, syllabification , and juncture cues to word identification . The example also illustrates the difficulty the model has in perceiving short , unstressed words like a. This is, of course , just an extreme version of the difficulty the model has in pro cessing monosyllabic words like tar and is consistent with Grosjean ' s data on the difficulty subjects have with identifying short words . In fact , Grosjean and Gee ( 1984) report pilot data indicating that these difficulties are even more severe with function words like a and of It should be noted that TRACE makes no special distinction between con tent and function words per se, and neither do Grosjean and Gee . However , function words are usually unstressed and considerably shorter than content words . Thus , it is not necessary to point to any special mechanisms for closed versus open class morphemes to account + +for Grosjean and Gee 's results . + +Summary of Word Identification Simulations + +While phoneme identification has been studied for many years , data from on -line studies of word recognition is just beginning to accumu late . There is an older literature on accuracy of word identification in noise , but it has only been quite recently that useful techniques have + +PROCESSES + +- + +l ~ 3 1 ~ {~ J~ ~ + +~ + +rc -~ ~ - '-' 1 ~ t " + +! ~ . , ~ ==: I } ~::1~ ; :=ill + +! . . , 1S ~ t ~ l ~ + +0 ' = = ~ } ~~i ~' I ~I ~ {E ~ \_~ - s - [~J. ~~ s + +. 1 + +1 S ~ - Si ~ S S t t ~ ~ b + +S U + +- s a + +a t } a L - a P + +a U SU U ~ S Pad I d i g + +{')~ ",,--~= n 1b a k s~ - ~ U 1b a k s~ + +@J } ~ ~ lJ - + +G G - B + +- B + +: : 2. + +~ art -E=:P} k s -B + +- @J~ a ~ ~ td ~~ bb . ~ + +' t t ~ ltltl .~ ~a rt ~ + +- ~ ~ t ~ b ~ t ~ b k t b ks - ~ IS -.. ~ a ~ a - ~ 1 ::; , ~ a s - - SiS + +PuaS + +to g + +Pu S g + +- P ~ d D - - P ~ P - u + +116 PSYCHOLOGICAL + +- SI5 ~ t ~ bClks ~ S 1 S~ t - baks - - SiS ~ t ~ baks - + +SIS ~ t ~ baks - - SIS ~ t ~ baks - - SiS ~ t ~baks - + +FIGURE 26. The state of the Trace at several points during the processing of the stream + +/ SiSA.tA.baks/ (she shut a box). + +What evidence there is, though, indicates the complexity of the word identification process. While the word identification mechanism is sensitive to each new incoming phoneme as it arrives, it is nevertheless robust enough to recover from underspecification or distortion of word beginnings. And , it appears to be capable of some simultaneous processing of successive words in the input stream. TRACE appears to capture these aspects of the time course of word recognition . In these respects, it improves upon the COHORT model, the only previously extant model that provides an explicit account of the on-line process of + +15. THE TRACE MODEL 117 + +4. The model augments information from the speech stream with feedback from the lexical level in reaching decisions about the identity of phonemes. These lexical influences on phoneme identification occur in conditions similar to those in which lexi- + +phonemes, as do human subjects. The model's tendency toward categorical perception is affected by many of the same parameters that affect the degree of categorical perception shown by human subjects; in particular, the extent to which perception will be categorical increases with time between + +stimuli that must be compared. + +GENERAL DISCUSSION + +Summary of TRACE's Successes + +word recognition . And , the mechanisms it uses to accomplish this are the same ones that it used for the simulations of the process of + +phoneme identification described in the preceding section. + +3 . The model combines feature information from a number of dif ferent dimensions and exhibits cue trade - offs in phoneme iden - + +tification . + +In this chapter, we have seen that TRACE can account for a number of different aspects of human speech perception. We begin by listing the major correspondences between TRACE and what we know about + +the human speech understanding process. + +1. TRACE , like humans, uses information from overlapping portions of the speech wave to identify successive phonemes. + +2. The model shows a tendency toward categorical perception of + +cal effects have been reported, but do not occur in conditions + +in which these effects have not been obtained. + +5. Like human subjects, the model exhibits apparent phonotactic rule effects on phoneme identification , though it has no explicit representation of the phonotactic rules. The tendency to prefer phonotactically regular interpretations of ambiguous phonemes can be overridden by particular lexical items, just as + +118 PSYCHOLOGICAL PROCESSES + +7 . In processing unambiguous phoneme sequences preceded by silence, the model exhibits immediate sensitivity to information favoring one word interpretation over another. It shows an initial preference for shorter words relative to longer words, but eventually a sequence of phonemes that matches a long word perfectly will be identified as that word, overturning the initial preference for the short-word interpretation . These aspects of the model are consistent with human data from gating experi- + +ments. + +11. The model does not demand a parse of a phoneme sequence that includes each phoneme in one and only one word. This allows it to cope gracefully with elision of phonemes at word boundaries. It will often permit several alternative parses to remain available for higher-level influences to choose among. + +beginning. + +6. Our simulations with TRACE I show that the model is able to use activations of phoneme units in one part of the Trace to adjust the connection strengths determining which features will activate which phonemes in adjacent parts of the Trace. In this way the model can adjust as human subjects do to coarticulatory influences on the acoustic properties of phonemes (Fowler, + +1984~ Mann & Repp, 1980) . + +8. Though the model is heavily influenced by word beginnings, it can recover from undersoecification or distortion of a word's + +9. The model can use its knowledge of the lexicon to parse sequences of phonemes into words and to establish where one word ends and the next one begins when cues to word bound- + +aries are lacking. + +10. Like human subjects, the model sometimes cannot identify a word until it has heard part of the next word. Also like human subjects, it can better determine where a word will begin when + +it is preceded by a word rather than a nonword. + +15. THE TRACE MODEL 119 + +Reasons for TRACE's Successes + +We think there are two main reasons why TRACE has worked so well . The first is its use of massively parallel , interactive processing . The second is the Trace architecture . We do not believe that the model would have worked without both of these characteristics . The Trace provides a processing structure that lays out the hypotheses about the contents of an utterance in a way that captures directly the task to be performed - to find an interpretation of the utterance consisting of a + +sequence of units on each of several processing levels . Appropriate competition within levels and mutual facilitation between levels is quite naturally arranged in such a situation . This is important , but it would not work without the parallel , interactive processing that is provided by + +the PDP framework . + +There is evidence to support both parts of this point . One source comes from our early attempts to model speech perception without adopting the Trace architecture . Our early model ( described in Elman & McClelland , 1984 ) failed to provide a straightforward representation + +of the temporal structure of the speech stream . + +It is a commonplace observation in the field of artificial intelligence that success in modeling depends on having the right representation , and Marr ( 1982 ) made very much of this point . But it is also true that one must have the right kind of processing system to exploit the archi tecture . The fact that the HEARSAY speech understanding system was not terribly successful attests to this . HEARSAY had the right architecture - a better one , in fact , in some ways , than we have in the current version of TRACE ( see Chapter 16 ) . But HEARSAY lacked the massively parallel , interactive capabilities of PDP models . + +Some Deficiencies of TRACE + +Although TRACE has had a number of important successes , it also has a number of equally important deficiencies . One fundamental defi ciency is the fact that the model requires reduplication of units and connections , copying over and over again the connection patterns that determine which features activate which phonemes and which phonemes activate which words . One reason why this is a problem has to do with learning . Learning in PDP models involves tuning connec tions between pairs of units based on both of their states . This kind of learning is inherently local to the specific connections between the specific units involved . Given TRACE ' s architecture , such learning would not generalize from one part of the Trace to another and so + +would not be accessible for inputs arising at different locations in the Trace. A second problem is that the model, as is, is insensitive to variation in global parameters such as speaking rate, speaker characteristics and accent, and ambient acoustic characteristics. A third deficiency is that it fails to account for the fact that one presentation of a word has an effect on the perception of it a very short time later (Nusbaum & Slowiaczek, 1982) . These two presentations, in the current version of the model, simply excite separate tokens for the same word + +in different parts of the Trace. + +All these deficiencies reflect the fact that the Trace consists of a large set of independent tokens of each feature, phoneme, and word unit . What appears to be called for instead is a model in which there is a single stored representation of each phoneme and each word in some central representational structure. If this structure is accessed every time the word is presented, then we could account for repetition priming effects. Likewise, if there were a single central structure, learning could occur in just one set of units, as could dynamic retuning of feature-phoneme and phoneme-word connections to take account of + +changes in global parameters or speaker characteristics. + +However, it remains necessary to keep straight the relative temporal location of different feature, phoneme, and word activations as we argued just above. Thus, it will not do to simply abandon the Trace in favor of a single set of units consisting of just one copy of each + +phoneme and one copy of each word. + +It seems that we need to have things both ways: We need a central representation that plays a role in processing every phoneme and every word and that is subject to learning, retuning , and priming . We also need to keep a dynamic trace of the unfolding representation of the speech stream so that we can continue to accommodate both left and right contextual effects. The next chapter describes a model of reading that has some of these characteristics. It uses connection information stored in a central PDP network to set connections in a processing structure much like the Trace, thereby effectively prqgramming this structure in the course of processing. The next step in the development of TRACE is to apply these ideas to speech perception. Some comments about how this might be done are included at the end of the + +next chapter. + +120 PSYCHOLOGICAL PROCESSES + +CONCLUSION + +Our aim in this chapter has been to show that parallel distributed processing mechanisms provide a natural framework for developing models capable of meeting the computational challenges posed by + +speech and of accounting for the data on human speech perception. The TRACE model does quite well on both counts. Though the architecture of the model is partially responsible for its successes, we have argued that the successes of the model depend at least as much on the parallel distributed processing operations that take place within the architecture. TRACE does have some limitations , but it successes so far have been quite encouraging. Just how easy it will be to overcome the + +limitations is a matter for future research. + +MENTS + +15. THE TRACE MODEL 121 + +ACKNOWLEDG + +The work reported here was supported in part by a contract from the Office of Naval Research (N-00014-82-C-0374, NR 667-483) , in part by a grant from the National Science Foundation (BNS- 79-24062) , and in part by a Research Scientist Career Development Award to the first author from the National Institute of Mental Health (5-KOl - + +MHOO385) . + +CHAPTER 16 + +The Programmable Blackboard Model of Reading + +J. L. McCLELLAND + +In 1975, Rumelhart outlined a model of reading called the interactive model. That model , inspired by the HEARSAY model of speech under standing (Reddy , Erman , Fennell , & Neely , 1973) , supposed that reading involved simultaneous processing at a large number of levels , including visual feature , letter , word , syntactic , and semantic levels . Hypotheses at each level were activated when active hypotheses on adjacent levels suggested them and competed with alternative hypotheses at the same level . This model , of course , was a precursor of the interactive activation model of word recognition and of the + +approach that underlies this whole book . + +In the interactive model of reading , the activation of hypotheses was guided by a set of structures called " knowledge sources ," each of which had expertise with respect to a particular aspect of reading . For exam ple , a lexical knowledge source that contained knowledge of the letter sequences that made up each word was proposed , along with a syntactic knowledge source , a semantic knowledge source , and an orthographic knowledge source containing knowledge of the appearance of the + +letters . + +An important aspect of the interactive model of reading was parallel processing . Processing was supposed to occur in parallel both within and between levels , so that hypotheses could influence and be influ enced by other hypotheses spanning large stretches of the input . How ever , no specific implementation of the mechanism was proposed . In HEARSAY , although the conception was parallel , the reality was quite + +124 PSYCHOLOGICAL PROCESSES + +The figure brings out the fact that the model achieves parallel processing of all of the letters in a four -letter display by having four separate copies of the feature and letter units, and four separate copies of the connections between them. Parallel processing of more than one word at a time would require creating another copy of the entire network . In the TRACE model Elman and I did just this, creating a large number of + +copies of the entire connection network . + +Now, the parallel processing permitted in models like the word perception model and the TRACE model are important to the functioning of these models, since parallel processing permits exploitation of mutual constraints, and to a large extent it is the exploitation of mutual constraints that parallel distributed processing is all about. But the massive reduplication of hardwired connection information leaves something to be desired as a way of providing a mechanism to exploit these mutual constraints. For one thing , it dedicates a lot of hardware to a single task. Also, even if we were willing to give up all the hardware, there would still be a serious problem with learning. In models of this sort, learning amounts to changing the strengths of the connections among units, based on their simultaneous activation. This kind of learning is, as was stressed in Chapter 1, local to the particular connections in which it occurred. Thus, any learning that occurred in one letter-processing channel of the word perception model would not be + +available for processing letters in other channels. + +I was not pleased with this state of affairs. It seemed to me that if parallel distributed processing was going to prove viable, some way would have to be found to have a central knowledge representation, such as in HEARSAY , that could be made available for processing items occurring at different places in a visual display or at different + +points in time . + +One obvious solution is just to 'I go sequential," and put the knowledge in a central location and map inputs into it one at a time . We have already reviewed a way that this can be done within the POP framework in the introduction to this section of the book. The trouble with this solution is that it eliminates parallel processing, and thus the benefits thereof. Obviously, at some point we will have to go sequential- and I will start to do so at a later point in this chapter. But I was not happy with the possibility that the only way we could achieve parallel processing was through the reduplication of connection information . I sought, in short, a mechanism for achieving parallel processing without reduplication of connection information . This chapter reports on the results of my explorations in search of such a + +This section describes a simple system for programming parallel processing structures in response to ongoing task demands and applies it to the processing of words in one- and two-word displays. The system consists of a set of programmable modules. Each module is a network of processing units very similar to those in other POP models, such as the interactive activation model of word perception. The difference is that these units are not dedicated permanently to stand for particular hypotheses, and the knowledge that determines the pattern of excitatory and inhibitory interactions is not hardwired into the connections between them. Rather, the connections in the network are programmable by inputs from a central network in which the knowledge that + +guides processing is stored. + +The first part of this section describes an individual programmable network . Later parts describe the structures needed to program such + +networks in response to ongoing processing demands. + +16. PROGRAMMABLE BLACKBOARD MODEL 125 + +central representation of the knowledge of the letter patterns that make up words. The model is applied to some recent data collected by Mozer (1983) on the processing of two-word displays. The second section extends the ideas developed in the first part to a more complex processing structure called the programmable blackboard, a structure analogous to the Blackboard in HEARSAY . That model is applied to a number of phenomena in word recognition not covered by the original interactive activation model. It also gives an account of several important aspects of reading a line of print , including the integration of information over successive fixations in reading. The final section discusses the proposed mechanisms in more general terms, and describes how they might be extended to the processing of the syntactic and semantic con- + +tent of sentences. + +CONNECTION INFO RMA TI ON D IS TRIBUTI ON + +A Programmable Network + +Figure 2 presents a very simple hardwired network. The task of this section is to see how we could replace this hardwired network with one that could be programmed to do the same work. The network shown in the figure is a very simple interactive activation system, consisting only of a letter and a word level. The figure is laid out differently from the previous figure to highlight the excitatory connections between the + +I I I + +. r-= l + +IN + +NO ON SO l .~~ J + +[~ N/1 @ ~1/2 ~J Second Position + +Letter Units + +126 PSYCHOLOGICAL PROCESSES + +.-..U) :)c "C0..~ + +FIGURE 2. An extremely simple connectionist mechanism, capable of processing one two-letter string made up of the letters I , N, 0 , and S. The model knows only the five words that can be made of two of these letters~ namely IN ~ IS~ NO~ OJ\r~ and SO. No top-down connections are included in this simple model. Units bracketed together are mutually inhibitory . (From " Putting Knowledge in its Place: A Scheme for Programming Parallel Processing Structures on the Fly " by J. L. McClelland , 1985, Cognitive Science, 9, + +p. 118. Copyright 1985 by Ablex Publishing. Reprinted by permission.) + +units and lay them out in a way which will be convenient as we + +proceed. + +In this simple network , there are detectors only for the letters I , N, 0 , and S in each of two letter positions. At the word level, there is a detector for each of the English words that can be made out of two of these letters. For simplicity , this model contains only letter-to-word connections~ another matrix would be needed to capture word-to-letter feedback. Units that are in mutual competition are included in the same square brackets. This is just a shorthand for the bidirectional inhibitory connections, which could also be represented in another con- + +nection matrix . + +In this diagram, letter units are shown having output lines that ascend from them. Word units are shown having input lines that run from left to right . Where the output line of each letter unit crosses the input line of each word unit , there is the possibility of a connection + +between them. + +The knowledge built into the system, which lets it act as a processor for the words IN , IS, NO, ON, and SO, is contained in the excitatory connections between the letter and word units. These are represented + +First Position Letter Units + +16. PROGRAMMABLE BLACKBOARD MODEL 127 + +FIGURE 3. A programmable version of the simplified activation model shown in Figure 2. Each triangle represents a programmable connection that can be turned on by a signal coming from the central knowledge store,! shown here as lying outside the figure to the upper right. If the triangular connections pass the product of the two signals arriving at their base along to the receiving unit'! the lines coming into the matrix from above can be thought of as programming the network. (From II Putting Knowledge in its Place: A Scheme for Programming Parallel Processing Structures on the Fly'l by J. L. McClelland,! 1985'! Cognitive Science, 9'! p. 119. Copyright 1985 by Ablex Publishing. Reprinted by + +Now we are ready to see how we could build a programmable net work , one that we could instruct to behave like the hardwired network shown in Figure 2 . Suppose that instead of fixed connections from specific letter units to particular word units , there is a potential connec tion at the junction between the output line from each letter unit and the input line to each word unit . Then all we would need to do to " pro gram " the network to process the words IN , IS , NO , ON , and SO correctly would be to send in signals from outside turning on the con nections that are hardwired in Figure 2 . This proposal is illustrated in + +Figure 3 . + +Multiplicative interactions yield programmable connections . At first glance , the notion of sending instructions to connections may seem to be adding a new kind of complexity to the basic processing elements out of which connectionist mechanisms are built . Actually , though , all we really need to do is to let each connection multiply two signals + +before passing along the result . + +This point may be appreciated by considering the following equation . For the standard connections used in most connectionist models , the + +~ + +128 PSYCHOLOGICAL PROCESSES + +time-varying signal to some unit i from some unit j is multiplied by the fixed weight or connection strength Wi) to determine the value of + +the input to i from j : + +inputi} (t ) = signal} (t ) x Wi} . + +All we are assuming now is that the signal from unit j is multiplied by a second time - varying signal , for example , the signal arising from some + +other unit k instead of the fixed connection strength Wij : + +inputi } ( t ) = signal } ( t ) x signalk ( t ) . + +We can think of the signal from unit k as setting the strength of the connection to i from j . When the value of the second signal is greater + +than 0 , we will say that the connection to i from j is active . + +Function and implementation of programmable connections . Multi plicative connections of the kind proposed here were introduced in Chapter 2 , and the increase in computational capability that their intro duction affords is considered in Chapter 10 . The specific idea of using a second signal to modulate connections has been used in other connec tionist models . Hinton ( 1981b ) used such a scheme to map inputs from local ( retinocentric ) feature detectors onto central ( object centered ) feature detectors in a viewpoint - dependent way . My use of multiplicative connections here was inspired by Hinton ' s . J . A . Feld man and Ballard ( 1982 ) have also suggested the idea of making connec tions contingent on the activation of particular units . The general notion of using one set of signals to structure the way a network processes another set of signals has previously been proposed by + +Sejnowski ( 1981 ) and Hinton ( 1981a ) . + +Let us briefly consider the functional significance of programmable + +connections . In essence , what connections do in POP models of per ceptual processing is specify contingencies between hypotheses . 1 A posi tive weight on the connection to unit i from unit j is like the condi tional rule , " if j is active , excite i . " Fixed connections establish such contingencies in a fixed , permanent way . Programmable connections allow us to specify what contingencies should be in force , in a way + +which is itself contingent on other signals . By using multiplicative + +interactions between signals , in place of fixed connections , we now have a way of setting from outside a network the functional connec tions or contingencies between the units inside the network . This means that we can dynamically program processing modules in response + +to expectations, task demands, etc. The little module shown in Figure 3 could be used for a variety of different processing tasks, if different connection patterns were sent into it at different times. For example, if we sent in different signals from outside, we could reprogram the module so that the word units would now respond to the two-letter words in some other language. In conjunction with reprogramming the connections from feature level units to the letter units, we could even assign the network the task of processing words in a language with a different alphabet or of processing completely different kinds of + +patterns. + +At a neurophysiological level, multiplicative or quasi-multiplicative interactions between signals can be implemented in various ways. Neurons can implement multiplication -like interactions by allowing one signal to bring the unit 's activation near threshold, thereby strongly increasing the extent to which another signal can make the unit fire (Sejnowski, 1981) . There are other possibilities as well. A number of authors (e.g., Poggio & Torre , 1978) have suggested ways in which multiplication -like interactions could take place in subneuronal structures. Such interactions could also take place at individual synapses, though there is little evidence of this kind of interaction in cortex. For + +a fuller discussion of these issues, see Chapters 20 and 21. + +16. PROGRAMMABLE BLACKBOARD MODEL 129 + +The Connection Information Distribution Mechanism + +We are now ready to move up to a complete Connection Information Distribution (CID ) mechanism containing a number of programmable modules along with the structures required to program them. The basic parts of the mechanism are shown and labeled in Figure 4~ they are + +shown again, with some of the interconnections, in Figure 5. + +The CID mechanism consists of a central knowledge store, a set of programmable modules, and connections between them. The structure is set up in such a way that all of the connection information that is specific to recognition of words is stored in the central knowledge store. Incoming lines from the programmable modules allow information in each module to access the central knowledge, and output lines from the central knowledge store to the programmable modules allow connection activation information to be distributed back to the programmable + +modules. + +The two programmable modules are just copies of the module shown in Figure 3. It is assumed that lower-level mechanisms, outside of the model itself , are responsible for aligning inputs with the two modules, so that when two words are presented, the left word activates + +[6 + +PL Units I PW Units + +I I ' { ? ! I + +[0 \ Q ~ ~ OJ t PL Units I PW Units + +130 PSYCHOLOGICAL PROCESSES + +Central Module Connection Activation System + +Programmable Modules ~ + +FIGURE 4. A simplified example of a connection information distribution (CID ) mechanism, sufficient for simultaneous bottom -up processing of two two-letter words. The programmable modules consist of the programmable letter (PL) units, programmable word (PW) units, and programmable connections between them (open trjangles). The central module consists of a set of central letter (CL) units, a set of central word (CW) units, and hardwjred connections between them (filled trjangles). The connection activation system includes the central word units, a set of connection activation (CA ) units, and hardwired connections between them. Connections between the central knowledge system (central module plus connection activation system) and the programmable modules are shown in the next figure. (From " Putting Knowledge in its Place: A Scheme for Programming Parallel Processing Structures on the Fly" by J. L. McClelland, 1985, Cognitive Science, 9, p. 122. Copyright 1985 by Ablex Publishing. Adapted by per- + +mission.) + +appropriate programmable letter units in the left module, and the right one activates appropriate programmable letter units in the right module. + +The central knowledge store. The knowledge store in the CID mechanism is shown at the top of Figure 4. This is the part of the mechanism that contains the word-level knowledge needed to program + +0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 + +0 0 0 0 0 + +\ I + +\ I CW CL Units Units CA Units + +'01' + +[ + +16. PROGRAMMABLE BLACKBOARD MODEL 131 + +FIGURE 5. Each CA unit projects to the corresponding connection in both programmable modules, and each central letter unit receives projections from the corresponding programmable letter unit in both programmable modules. The inputs to two central letter units and the outputs from two CA units are shown. (From " Putting Knowledge in its Place: A Scheme for Programming Parallel Processing Structures on the Fly" by J. L. McClelland, 1985, Cognitive Science, 9, p. 124. Copyright 1985 by Ablex Publishing. + +Reprinted by permission.) + +the programmable modules. It consists of two parts. One part is called the central module, and the other part is called the connection activation + +system. + +The central module consists of central letter units, central word units, and connections between the central letter units and the central word units. The letter units in the local modules project to the letter units in the central module, so that whenever a particular letter unit is active in either programmable module, the corresponding central letter unit is also (Figure 5) . Note that the correspondence of local and central letter units is quite independent of what letters these units stand + +for . + +The central letter units are connected to the central word units via connections of the standard, hardwired type. These connections allow patterns of activation at the letter level to produce corresponding activations at the word level, just as in the original interactive activation + +model. However, it should be noted that the central word unit activations are based on a superposition of the inputs to each of the two programmable modules. Thus, the activations in the central letter units do not specify which module the letters came from , though relative position within each module is preserved. Thus, activations in the central module do not distinguish between the input IN SO and the input SO IN or even SN 10. In short, the central module cannot correctly deter- + +mine which aspects of its inputs belong together. + +The second part of the central knowledge system, the connection activation system, also consists of two sets of units and their interconnections. One of these sets of units is the set of central word unitsthey belong both to the central module and to the connection activation system. The other set is the set of connection activation (CA) units. The purpose of the connection activation system is to translate activations of central word units into activations of connections appropriate for processing the corresponding words in the local modules. The CA units serve as a central map of the connections in each of the programmable modules, and provide a way to distribute connection information to all of the programmable modules at the same time . (The CA units are not strictly necessary computationally , but they serve to maintain the conceptual distinction between that part of the mechanism that contains the knowledge about words and the parts that simply distribute that knowledge to the local modules) . There is one CA unit corresponding to the connection between a particular programmable letter unit and a particular programmable word unit . I have arranged the CA units in Figure 4 to bring out this correspondence. Each CA unit projects to the corresponding connection in both programmable modules. I have illustrated the projections of two of the CA units in Figure 5. For example, the top-left CA unit corresponds to the connection between the left -most programmable letter unit and the top-most programmable word unit . This CA unit projects to its corresponding connection in each of the programmable modules and provides one of that connection's two inputs. So, when a particular CA unit is active, it activates the corresponding connection in all of the programmable + +modules. In this way it acts as a master switch. + +At a functional level, we can see each CA unit as standing for a contingency between two activations. Thus, if we index the programmable letter units by subscript i , and the programmable word units by j , the ij th CA unit stands for the contingency, "if letter unit i is active, excite word unit j ." Thus, we can think of the CA units as contingency activation units, as much as connection activation units. When we activate a CA unit (to a certain degree) we are implementing the contingency it represents (with a corresponding strength) in both of the + +132 PSYCHOLOGICAL PROCESSES + +The central word units, of course, are responsible for activating the CA units. There are excitatory connections from each word unit to each of the CA units for the connections needed to process the word. For example, the central word unit for IN activates two CA units. One is the CA unit for the connection between the left -most programmable letter unit and the top-most programmable word unit . The other is the CA unit for the connection from the sixth programmable letter unit from the left to the same programmable word unit . These connections effectively assign the top programmable word unit to be the detector for IN (assuming, of course, that lower levels of processing have been arranged so that I in the first position and N in the second position + +activate the appropriate programmable letter units) . + +In summary, the CID mechanism consists of (a) the programmable modules~ (b) the central knowledge store, including the central module and the connection activation system~ (c) converging inputs to the central knowledge store from the programmable modules~ and (d) diverging outputs from the central knowledge store back to the pro- + +grammable modules. + +We can now see how this mechanism allows the programmable modules to be programmed dynamically in response to current inputs. When an input causes activations in some of the programmable letter units in one of the programmable modules (say, the programmable letter units for I in the first position and N in the second position of the left programmable module) , these activations are passed to the corresponding central letter units. From the central letter units they activate the central word unit for IN . Central word units for patterns that overlap partially with the input (such as IS and ON ) also receive excitation, but only in proportion to their overlap with the input . The central word units pass activation to the CA units, and these in turn pass activation back to the connections in both programmable modules. Connections are only turned on to the extent that they are consistent with the input . When different patterns are presented to each programmable module, connections appropriate for both patterns are turned on, thereby programming both programmable modules to process either pattern. Central word units - and therefore connections- are also turned on for any words that appear in the superimposed input from the two programmable modules. However, the results of processing in each programmable module still depend on the activations of the programmable letter units. Thus the appropriate programmable word unit will tend to be the most active in each local module. Although the output of the central module does not specify which word was presented to which local module, this information is represented (though with some tendencies to error , as we shall see) in the outputs of the local + +16. PROGRAMMABLE BLACKBOARD MODEL 133 + +134 PSYCHOLOGICAL PROCESSES + +The correspondence between programmable and central units in the CID mechanism illustrated in Figures 4 and 5 may lead some readers to feel that the local units are really dedicated to process the particular word I have said that the mechanism programs it to process. This is an artifact of the use of one unit to represent each word. If distributed representations are used instead, each local output unit unit can be programmed in different ways on different occasions, depending on which of a large number of different distributed patterns the local modules are programmed to produce. The discussion that follows is generally applicable to both local and distributed CID mechanisms~ I chose to use the local case because I thought it was generally easier to grasp intuitively . The main difference between local and distributed CID mechanisms is that the latter make much more efficient use of the units in the pro- + +grammable modules, as discussed in Chapter 12. + +Computer Simulation of Word Recognition Using the + +CID Mechanism + +To examine the behavior of CID mechanisms in more detail , I implemented a CID version of the interactive activation model of word perception . The model , which I just call CID (" Sid " ) , is scaled-up from the example we have been considering so that it can process two strings of four letters each. Only three or four different letter alternatives were allowed in each position within each string . These were B , L , P, and S in the first position ~ A , E, I , and 0 in the second position ~ N , R , and V in the third position ~ and D , E, and T in the fourth position . The lexicon used in the simulation consisted of the 32 words shown in + +Table 1 . + +Like the smaller -scale version shown in the figures , the model con sisted of two programmable modules , one for each of the two -letter strings , and a central knowledge store consisting of the central module and the connection activation system . Each programmable module had 16 programmable letter units and 32 programmable word units . The programmable letter units were grouped into four groups of four , with each group to be used for letters in one display location . The members of each group had mutual , hardwired , inhibitory connections . Simi larly , all of the programmable word units in each module were mutually inhibitory . Each programmable module contained 16 x 32 = 512 pro grammable connections , and there were 512 CA units , one for each each programmable connection . The central module contained 16 letter and 32 word units , like the programmable modules . There were no inhibitory connections either between the central word units or between the central letter units . The connections between the central letter + +16. PROGRAMMABLE BLACKBOARD MODEL 135 + +BAND BIRD LAND LINE LORD PART PORE SAVE + +BIND BORE LEND LONE PANT POND SANE SORT + +-- - + +BARE BEND BOND BONE LANE LARD LINT LIVE LOVE PANE PINE PINT PORT SAND SEND SORE + +Note: From " Putting Knowledge in its Place: A Scheme for Programming Parallel Processing Structures on the Fly" by J. L. McClelland, 1985, Cogniti~'e Science, 9, p. 126. Copyright 1985 by Ablex Publishing. + +Reprinted by permission. + +units and the central word units and the connections from the central word units to the appropriate CA units were hardwired with the connection information needed to make the central letter units activate the right central word units and to make the central word units activate the + +right CA units. + +Inputs to the simulation model were simply specifications of bottomup activations to the programmable letter units in either or both programmable modules. Inputs were presented when all the units in the model were at their resting activation values and turned off after some + +fixed number of time cycles. + +The only substantive difference between CID and the original interactive activation model is in the strengths of the excitatory connections between units. In CID , these strengths vary as a function of the current input , while in the original model they were fixed . Highly simplified activation rules are used to capture the essence of the connection activation process via the central letter units, central word units, and CA units. The activation of a particular central letter unit is simply the number of input units projecting to it that have activations greater than O. Thus, the activation of a particular central letter unit just gives a count of the corresponding programmable letter units that are active. The activation of a central word unit is just the sum of the active central letter units that have hardwired connections to the central letter unit . The activation of a CA unit is just the activation of the central word unit that projects to it , and this value is transmitted unaltered to the corresponding programmable connection in each programmable + +module. + +RESULTS OF THE SIMULATIONS + +The net effect of these assumptions is to make the activation of the connections coming into a particular programmable word unit proportional to the number of active units for the letters of the word, summed over both modules. Active letter units count only if they stand for letters in appropriate positions within the programmable + +module of origin. + +Output. So far we have said nothing about how the activations that arise in the programmable modules might give rise to overt responses. Following the original interactive activation model, I assume there is a readout mechanism of unspecified implementation which translates activations at either the letter or the word level into overt responses. 2 The readout mechanism can be directed to the word or the letter level of either module, and at the letter level it can be directed to a particular letter position within a module. In cases where more than one stimulus is to be identified on the same trial , the readout of each of the items is + +independent. + +The probability of choosing a particular response depends on the strength of the unit corresponding to that response divided by the sum of the strengths of all the relevant alternatives (e.g., units for words in the same position) following the formulas introduced in Chapter 15. The main import of these assumptions for present purposes is that the probability of a particular response is solely a function of the activations of units relevant to the response. All interactions between display items are thus attributed to the unit and connection activation mechan- + +isms, and not to the readout mechanisms themselves. + +Two principle findings emerged from working with the simulation model . First , when processing a single word , the CID mechanism causes the model to behave as though it were sharply tuned to its inputs , thereby mimicking the benefits of the bottom - up inhibition used in the original word perception model without actually incurring anyl of its deficiencies . Second , when processing two words at a time , the connection activation scheme causes the model to make errors simi lar to those made by human subjects viewing two - word displays . These + +2 There must be coordination between the readout mechanism and the CID mechan ism . For example , it would not do for the system to program the top - most letter unit to represent the word BAND , say , if the readout mechanism took this unit to correspond to some other word . The problem is a general one and is no different in programmable net - + +16. PROGRAMMABLE BLACKBOARD MODEL 137 + +errors arise as a result of the essential characteristics of the CID + +mechanism . + +One Word at a Time : The Poor Get Poorer + +In the original word perception model , bottom -up inhibition from the letter level to the word level was used to sharpen the net bottom -up input to word units . For example , consider a display containing the word SAND . Due to bottom -up inhibition , units for words matching only three of the four letters shown (e.g., LAND ) would receive less than 3/ 4 as much net bottom -up excitation as the unit for the word + +SAND itself . + +The CID version of the model closely emulates this feature of the original , even though it lacks these bottom -up inhibitory connections . In CID , the activation of the connections coming into a word unit varies with the number of letters of the word that are present in the input . At the same time , the number of inputs to these same connections from the programmable letter units also varies with the number of letters in the input that match the word . The result is that in the CID version of the model , the amount of bottom -up activation a programmable word unit receives varies as the square of the number of letters in common + +with the input . Poorer matches get penalized twice . + +In working with the original model , Rumelhart and I picked values for the bottom -up excitation and inhibition parameters by trial and error as we searched for a set of parameters that allowed the model to fit the results of a large number of experiments . The values we hit upon put the strength of bottom -up inhibition at 4/ 7 the strength of bottom -up excitation . For words that share two , three , or all four letters in common with the input , this ratio produces almost exactly the same relative amounts of net bottom -up activation as is produced by the CID mechanism (Table 2) . Words with less than two letters in common received net bottom -up inhibition in the old version , whereas in the CID version they receive little or no excitation . In both cases their activation stays below zero due to competition , and thus they have + +no effect on the behavior of the model . + +This analysis shows that the CID version of the model can mimic the original , and even provides an unexpected explanation for the particular value of bottom - up inhibition that turned out to work best in our ear lier simulations . As long as the bottom -up input to the letter level was unambiguous , the correspondence of the CID version and a no- + +16. PROGRAMMABLE BLACKBOARD MODEL 139 + +will show how CID captures important aspects of the data obtained in experiments in which subjects are shown two words at a time . Here the CID architecture becomes essential , since simultaneous processing of two patterns introduces considerations that do not arise in the process - + +ing of one pattern at a time . + +When letters are presented to both modules , all of the letters are combined to turn on connections that are distributed to both of the pro grammable modules . The result is that the. connections appropriate for the word presented in one module are turned on in the other module as well . This biases the resulting activations in each module . The pro grammable word unit for the word presented to a particular module will generally receive the most activation . However , the activation of pro grammable word units for words containing letters presented to the other module is enhanced . This increases the probability that incorrect responses to one of the words will contain letters presented in the + +other . + +At first this aspect of the model disturbed me , for I had hoped to build a parallel processor that was less subject to crosstalk between simultaneously presented items . However , it turns out that human subjects make the same kinds of errors that CID makes . Thus , though CID may not be immune to crosstalk , its limitations in this regard seem to be shared by human subjects . I ' ll first consider some data on human performance , and then examine in detail why CID behaves the same + +way . + +The data come from a recent experiment by Mozer ( 1983) . In his paradigm , a pair of words (e.g, SAND LANE ) is displayed , one to the left and one to the right of fixation . The display is followed by a patterned mask which occupies the same locations as the letters in the words that were presented . In addition , the mask display contains a row of underbars to indicate which of the two words the subject is to report . Subjects were told to say the word they thought they saw in the + +cued location or to say " blank " in case they had no idea . + +In his first experiment , Mozer presented pairs of words that shared two letters in common . The pairs of words had the further property that either letter which differed between the two words could be trans posed to the corresponding location in the other word and the result would still be a word . In our example SAND -LANE , SAND and LANE have two letters in common , and either the L or the E from LANE can be moved into the corresponding position in SAND , and the result would still be a word (LAND and SANE ) . Of course , it was also always true with these stimuli that the result would be a word if both letters " migrated ." The duration of the two -word display was adjusted after each counterbalanced block of trials in an attempt to home in on a duration at which the subject would get approximately 70% of the + +MOZER + +140 PSYCHOLOGICAL PROCESSES + +TABLE 3 + +METHOD AND RESULTS OF (1983), EXPERIMENT 1 + +Example Display SAND LANE + +Results: + +Response Type Example % of Total + +Total + +Pseudo-migration \* + +Method: + +Target Cue + +IIIII + +! + +I- + +. - -. - + +~ - + +(SAND) (SANE or LAND) (LANE) + +Correct response Single migration Double migration + +Other + +\*Pseudo-migration rate is the percentage of reports of the given single migration responses (SANE, LAND) when a context word which does not contain these letters is presented. In this example, the context string might have been BANK. From" Putting Knowledge in its Place: A Scheme for Programming Parallel Processing Structures on the Fly" by J. L. McClelland, 1985, Cognitive Science, 9, p. 131. Copyright 1985 by + +whole-word responses correct. Thus, the overall error rate was fixed by + +design, though the pattern of errors was not. + +The principal results of Mozer's experiment are shown in Table 3. Of the trials when subjects made errors, nearly half involved what Mozer called " migration errors" - errors in which a letter in the context word showed up in the report of the target. To demonstrate that these errors were truly due to the presentation of these letters in the context, Mozer showed that these same error responses occurred much less frequently when the context stimulus did not contain these letters. Such "control " errors are referred to in the table as pseudo-migration errors. As I already suggested, migration errors of the type Mozer reported are a natural consequence of the CID mechanism. Since the letters from both words are superimposed as they project onto the central module, the connections for words whose letters are present (in the correct letter position) in either of the two input strings are strongly activated in both programmable modules. The result is that programmable units for words containing letters from the context are more easily activated than they would be in the absence of the input + +presented to the other module. + +Table 4 compares relative programmable word unit activations for various words, for two different cases: In one case, the word SAND is 16. PROGRAMMABLE BLACKBOA.RD MODEL 141 + +presented alone~ in the other, it is presented in the context of the word LANE . When SAND is presented alone, all words that share three letters with it receive (3/ 4)2 or 9/ 16 as much bottom -up activation as the unit for SAND itself - we already explored this property of the CID model in the previous section. When SAND is presented with LANE , however, words fitting the pattern (L or S)-A-N-(D or E) all have their connections activated to an equal degree because of the pooling of the input to the connection activation apparatus from both modules. These words are, of course, SAND and LANE themselves and the single migration error words LAND and SANE. Indeed, over both letter strings, there are 6 occurrences of the letters of each of these words (the A and the N each occur twice) . The result is that the excitatory input to the programmable word units in the left module for LAND and SANE is 3/ 4 of that for SAND, as opposed to 9/ 16. Other words having three letters in common with the target have their connections less activated. Their bottom -up activation is either 5/ 8 or 1/ 2 that of SAND, depending on whether two of the letters they have in common with the target are shared with the context (as in BAND) or not (as in SEND) . Thus, we expect LAND and SANE to be reported more often + +than other words sharing three letters in common with SAND. + +The reader might imagine that the effect would be rather weak. The difference between 3/ 4 and 5/ 8 or 1/ 2 does not seem strikingly large. However, a raw comparison of the relative bottom -up activation does not take into account the effects of within -level inhibition . Within -level inhibition greatly amplifies small differences in bottom -up activation. + +TABLE4 + +TWO WORDS AT A TIME: CROSSTALK. + +alone + +activation ratio + +with LANE + +-- + +activation ratio + +SAND LAND BAND SEND LANE + +4x4 3x3 3x3 3x3 2x2 + +Note: Ratio refers to the bottom-up activation of the unit, divided by bottom-up activation of SAND. From" Putting Knowledge in its Place: A Scheme for Programming Parallel Processing Structures on the Fly" by J. L. McClelland, 1985, Cognitive Science, 9, p. 132. Copyright 1985 by Ablex Publishing. Reprinted by permission. + +RELATIVE BOTTOM-UP ACTIVATIONS PRODUCED BY SAND PRESENTEDITHER ALONE OR WITH LANE AS CONTEXT + +> 4x6 3x6 3x5 3x4 2x6 + +- .56 .56 .56 .16 + +- .75 .62 .50 .50 + +0 .9 + +0 .7 sand + +0 .5 + +03 . + +land sane + +0 . 1 + +- 0 .1 band + +- 0 .3 + +0 5 10 15 20 25 30 35 Time + +142 PSYCHOLOGICAL PROCESSES + +This is especially true when two or more units are working together at the same level of activation. In this case, the units for LAND and SANE act together. Neither can beat out the other, and both "gang up" on those receiving slightly less bottom -up activation, thereby pushing these other alternatives out. This "gang effect " was also observed in the original version of the word perception model. The results of this feature of the model are illustrated in Figure 6. Through the mutual inhibition mechanism, SAND and LANE come to dominate other words that share three letters in common with the target. Some of these, in turn , dominate words that have only two letters in common with the target, including , for example, LANE , even though the connections for LANE are strongly activated. This result of the simulation agrees with the experimental result that double or "whole-word" migrations are + +quite rare in Mozer's experiment , as shown in Table 3. + +Mozer (1983) reported several additional findings in his study of the processing of two-word displays. A full discussion of these effects can be found in McClelland (1985) . Suffice it to say here that the major findings of Mozer's experiments are consistent with what we would + +expect from CID . + +8!W! + +mr. + +FIGURE 6. Activation curves for various programmable word units in the module to which SAND is shown when the input to the other module is LANE . The horizontal axis represents time cycles from the onset of the two-word display. (From " Putting Knowledge in its Place: A Scheme for Programming Parallel Processing Structures on the Fly" by J. L. McClelland, 1985, Co..f:nifive Science, 9, p. 133. Copyright 1985 by Ablex + +16. PROGRAMMABLE BLACKBOARD MODEL 143 + +THE PROGRAMMABLE BLACKBOARD MODEL + +The model described in the previous section provides an illustrative example of the way in which knowledge in a central processing structure can be used to program local processing structures in response to ongoing processing demands, but it is a long way from a fully adequate model of the reading process, even excluding syntactic and semantic processing levels above the word. This section describes a more sophisticated model. The model is incomplete, but I believe it takes us several steps further toward a complete model of the reading process. + +Overlapping the Programmable Processing Structures + +In the preceding section , as in the original word perception model , we considered words of a fixed length , and we assumed that some mechanism not included in the model would solve the problem of aligning the inputs appropriately with the programmable letter units in + +each of the local modules . + +Obviously , any plausible model of reading must be capable of accom modating arbitrary strings of text , including words of different lengths , without requiring prealignment of each word with a specific location in + +a module . + +In the TRACE model described in the previous chapter , Elman and I dealt with this problem by allowing units in adjacent slots to have over lapping "receptive fields ." The ideas from that model can be applied to reading as follows . Suppose we have several sets of letter units , one for each of a reasonably large number of letter positions in a string of text . Each of these sets of units will be the top end of a position -specific letter -processing channel , like the ones in the original word perception model . Let 's suppose we can present letter strings so that the left letter projects to anyone of the letter channels and adjacent letters in the string activate letter units in adjacent slots . Then the model would be able to process words starting in any slot if there were a number of overlapping word processing channels , one starting in every slot . If a string like BINK / 4 was shown (BINK starting in the fourth letter posi tion ) , units for BLINK / 3, INK / 5, BIN / 4, and SLINKY / 3 would all be activated , along with units for BIND / 4, SINK / 4 and others than would have been activated in the original model . These units would all pro duce feedback to the units for the letters they contain in the appropriate positions . This would allow conspiracies of partial activations of words of various lengths . The word units could also compete with each other + +16. PROGRAMMABLE BLACKBOARD MOEL 145 + +lexical knowledge source , or central knowledge system , consisting of two sets of letter units , one for the first letter of the word and one for the second letter , and a set of word units . In addition , we would need a set of connection activation units , one for each programmable con nection in each overlapping word -processing channel . Finally , we would need converging input lines coming into the central knowledge structure and diverging output lines from the CA units to the program - + +mable connections . + +A problem arises with the converging input lines . Since each letter slot can contain letters in either role within the word , the letter units in each letter slot would have to send outputs to the central letter units in each central letter channel . The problem with thi ~ would be that every occurrence of a particular letter , regardless of what role it turned out to play within a word , would turn on the connections for words which have that letter in them anywhere . Consider , for example , the display - ON - (dashes indicate blanks in the display ) . This will turn on the connections for all words having 0 in them anywhere , since the 0 will be treated as a potential first letter of a word beginning in the second position and as a potential second letter of a word beginning in the first position . Similarly , the N will turn on the weights for all words having N in them anywhere , since it will be treated as a potential first letter of a word beginning in the third position and a potential second letter of a word beginning in the second position . For this example , then , the connections for NO will be turned on just as much as the connections for ON . When multiple words are presented , this would tend to cause the model to make migration errors for nonhomologous positions . For example , in a version of the model with a forth overlapping module , the display IS-NO would activate the connections for the word IN just as much as the display IS -ON . We would therefore expect subjects to report IN as an incorrect report of the contents of the first two letter positions equally often in these two cases. More generally , migration errors would not be expected to honor relative position within the word . Analyses reported in Shallice and McGill ( 1978) reveal that + +nonhomologous migration errors are quite rare indeed . + +Role -specific letter units . It appears that we need to have some way of treating letters differently depending on their role within the word . One poor way to do this would be to imagine that there is a separate detector in each letter channel for each letter in every role it might play . For our two -letter word case, letters can occur in either of two roles - as the first letter in a two -letter string , or as the last . So, if we went with role -specific letter detectors , each letter slot would contain eight letter units , one for each letter as the first letter in a word , and + +146 PSYCHOLOGICAL PROCESSES + +Obviously this solution has serious weaknesses . For one thing , it duplicates units ad nauseam . If we wished to process longer words , we would need very large numbers of role -specific units in each letter slot . + +Coarse coding . There is a better way . Suppose that each letter is represented , not as an activation of a single unit , but as a pattern of activation involving several active units . With such an encoding , we would imagine that a given letter - say, the letter I - produces a slightly different pattern when it occurs in different roles . All these different patterns will represent different versions of the letter I , and to the degree that they are similar they will have similar effects , but their differences can be used to produce a sufficient degree of differentiation of letters in different contexts to allow our model to work and to reduce the incidence of nonhomologous migration errors . This idea is an instance of the idea of coarse coding , which is described more fully + +in Chapter 3. + +In the present application of the coarse coding idea , there are four detectors for each letter . Each detector serves as a partial specification of a letter / role combination . One of the detectors is activated when the letter is preceded by a blank ~ one when it is preceded by any other letter ~ one when it is followed by a blank ~ and one when it is followed by any other letter . With this scheme , the pattern of active letter / role units can indicate whether a particular letter is a s~parate string unto itself (blanks on both sides) ~ the first letter in a string (blank on left , letter on right ) ~ the last letter in a string (letter on left , blank on right ) ~ + +or an internal letter in a string (letters on both sides) . + +Notationally , I will designate particular units by the letter they stand for in upper case, preceded or followed by an underbar to indicate a blank or by an x to indicate any letter . The code for a letter in a partic ular role would be given by two such specifications in the same parentheses , with a space between them . The code for an entire word is given by a series of letter codes in square brackets . For example , the + +word EVE would be coded [ ( E Ex) (xV Vx) (xE E ) ] . + +One property of this coding scheme is that similar letter roles pro duce overlapping patterns of activation . For example , the code for the letter I at the beginning of a word, l I Ix) , overlaps with the code for the same letter in medial position , (xl Ix ) . It also overlaps with the code for the same letter in isolation, II I\_) . Similarly , the code for a letter in final position , (xl I\_ ) , overlaps with the code for the same letter in medial position , (xl Ix ) , and with the code for the letter in isolation . However , there is no overlap of the codes for initial and final letters - disjoint subsets of units are activated in the two cases. Simi larly , there is no overlap of codes for isolated letters and medial letters + +16. PROGRAMMABLE BLACKBOARD MODEL 147 + +Obviously this particular code could be improved upon to make all occurrences of a particular letter have something in common and to make nonterminal letters in different positions differ from each other . However , this scheme captures the essence of the coarse coding idea and works surprisingly well for words up to four letters long , so we will + +stick with it for now . + +For our two - letter word example , this coding scheme does not buy us much . The advantages of the scheme only begin to emerge with longer words . However , for visualization , I represent a version sufficient for the two letter I - N - O - S words in Figure 8 ~ some of the connections from the CA units to two of the programmable modules are shown in Figure 9 . For two - letter words , we don ' t need all four different role specifica tions , so I ' ve only included the \_ x and x - units where x stands for I , N , + +0 , or S . + +With these coarse - coded letter Irole units in each letter channel , the units in each programmable letter channel project to a single central letter channel . Different role specifications are still preserved , so that the word ON will activate no central units in common with the + +word NO . + +Other Enhancements in the Programmable Blackboard Model + +Feedback . In describing CID , I did not discuss word - to - letter level feedback , although a version of that model has been implemented that incorporates this . For the programmable blackboard model , I wished to incorporate feedback to illustrate how the overlapping modules in CID allow feedback from activations of words of different lengths appropri ately aligned with the input . I assume feedback is implemented by another set of programmable connections running from the program mable word units back down to the programmable letter units . ( It is important to distinguish the connection activation process from word to - letter level feedback . They are different things serving very dif ferent roles in the model ) . Because of the symmetry of the bottom up and top - down activations , the very same set of CA units can be used to program both the bottom - up and the top - down connections . That is , the same CA unit that turns on the bottom - up connection from a par ticular letter unit to a particular word unit can also turn on the connec - + +tion from that same word unit to the same letter unit . + +Shifting the focus of attention . While there is some reason to believe we process more than one word at a time , it is clear that we do not process whole pages or even whole lines of text at a time . In read ing , the eyes make saccadic jumps from word to word , stopping for + +148 PSYCHOLOGICAL PROCESSES + +Central Knowledge System + +Central Module + +Programmable Blackboard + +FIGURE 8. A simplified programmable blackboard sufficient for processing the twoletter I-N-O-S words, using coarse coded representations at the letter level. The hardwired connections between the central letter and word units are illustrated as are the , connections from the central word units to the CA units for the connections needed to process two of these words. The programmable letter units in each letter channel project to the central letter units, and the CA units project back to the programmable connections between the letter units and the word units. Some of these projections are shown + +in the next figure . + +200-500 msec about once a word. Shorter words may be skipped and + +16. PROGRAMMABLE BLACKBOARD MOEL 149 + +FIGURE 9. A replica of Figure 8, with the outgoing connections from the central word unit for IN to two of the programmable modules via the CA units. Also shown are the units for \_I and N- in the third , fourth , and fifth letter slots, and the unit for IN in the fourth programmable word slot. The programmable letter units in each letter channel project to the central letter units, and the CA units project back to the programmable connections between the letter and the word units, but these connections are not actually + +shown. + +purposes, as an approximation, it may not be unreasonable to treat it so. But there is evidence that we can process more than one word per fixation , though there is some degradation of performance with an increase in the contents of the display. Of course, this finding is compatible with sequential processing within fixations , but I will assume that within a fixation , all processing activity is taking place in parallel. However, I will assume that the higher resolution of the fovea and the + +150 PSYCHOLOGICAL PROCESSES + +focusing of attention to the right of fixation causes some parts of the contents of the fixation to be processed more successfully and more + +completely than others. + +A sketch that may help visualize these assumptions is shown in Figure 10. Several sets of programmable word and letter units are illustrated, with schematic illustrations of the connections between and within slots. Along the bottom , a fragment of a possible line of text is displayed with the letters lined up below the letter slots. The assumption is that the letters lying within the foveal region and the right penumbra are mapped into successive slots in the programmable blackboard. Converging inputs from these slots, and only these slots, are sent to the central letter units, and connection activations from the connection activation structures are projected back to the programmable + +connections in these slots only. + +Connection activations are assumed to be "sticky": That is, it is assumed that once a connection has been programmed by the central knowledge structures, it stays that way. This allows interactive activation processes to continue in older parts of the programmable + +> I .eft Righ l fJenumbra Penumbra + +> > focus of attention + +. + +I s 0 n l h c + +x IJojnl of fixation + +~'ovca + +FIGURE 10. Schematic illustrations of the programmable blackboard, with illustrations of the fovea, the left and right penumbras, and the span of the focus of attention during + +16. PROGRAMMABLE BLACKBOARD MODEL 151 + +blackboard while they are being set up in newer parts as the eye moves along from left to right . So , what has already been processed in earlier fixations can continue to influence the processing of the contents of the current fixation , and , in case of unresolved ambiguities , can be influ - + +enced by the new information coming in . + +To make this model work , we would need to imagine that when the + +eye moves , we change the mapping from a low - level , retinocentric + +representation of the contents of the current fixation into the program mable blackboard . The mapping mechanism proposed by Hinton ( 1981b ) would be appropriate for doing this , assuming the activations of the " mapping units " could be updated in tandem with the commands to move the eyes . Hinton ' s scheme can also be used to map from the programmable letter units into the central letter units and from the connection activation units to the appropriate programmable + +connections . + +Details of the Simulation Model + +The simulation model developed to embody these assumptions is called PABLO , an approximate acronym for Programmable Blackboard . PABLO uses an alphabet of 9 letters , including blank ( written as " - " ) and the letters A , C , D , E , H , I , N , and T . Its lexicon consists of all the words of one to four letters made up pnly of those letters that were found in a large computerized dictionary . Archaic forms , past tenses , plurals , proper nouns and abbreviations were deleted , leaving a lexicon of 92 words , as shown in Table 5 . Also , blank was treated as a ( spe cial ) one - letter word . As in TRACE ( Chapter 15 ) , blanks served to provide competition against words that would otherwise tend to in vade + +the spaces between words . + +PABLO contained a sufficient programmable blackboard to read lines of text 20 characters long . To accomplish this , it contained 20 overlap ping programmable modules , each capable of being programmed for processing all of the words in the lexicon . Each module consisted of a set of programmable word units , four sets of programmable letter units shared with adjacent modules , and two sets of programmable connec tions between the letter units and the word units . One set of connec tions was used for bottom - up connections from the letter to the word level , the other for top - down connections from the word to the letter + +There were 93 word units in each module , one for each of the 93 words ( including blank ) . Each letter slot consisted of a complete set of letter Irote specifjc ~ ~ tion units . Each set contained four units for each of 152 PSYCHOLOGICAL PROCESSES + +TABLES + +THE WORDS USED IN PABLO + +A AD ANT CANT CHIN DEAD DIE EAT HATE HI ICE ITCH NIT TEEN THE TINE + +ACT AND CANE CHIC DATE DICE EACH HAT HEN I IT NINE TEE THAT TIN + +ACE ACHE ACID ACNE ADD AID AIDE AN ANTE AT CAD CAN CAT CEDE CENT CHAT CHIT CITE DAD DATA DEAN DEED DEN DENT DIET DIN DINE DINT EDIT END ETCH HAND HE HEAD HEAT HEED HIDE HIND HINT HIT IDEA IN INCH INN NEAT NEED NET NICE TACT TAD TAN TEA TEN TEND TENT THAN THEN THIN TIDE TIE + +TINT + +the nine letters , one for each partial role specification described above . + +Thus , there were 36 letter I role units in each letter slot . + +Each complete programmable module included four letter slots . + +Thus , module i included letter slots i , i + 1 , i + 2 , and i + 3 . + +As in TRACE , competition between word units depends upon the extent of the overlap of the words the units represent . That is , each word unit inhibits every other word unit once for every letter position in which they overlap . Thus CA TI 1 and HA TI 1 , which overlap in all three letter positions , inhibit each other three times . CA TI 1 and A TEl 2 , which overlap in two letter positions , inhibit each other twice . Again , for simplicity , these inhibitory connections are hardwired . 3 + +In addition to these programmable processing structures , there is a central knowledge structure consisting of a central module and a con nection activation system . The central module consists of one set of central letter units , one set of 93 central word units , and one hard wi red + +3 For these connections to be hardwired , knowledge of the length of the word the local word units will be allocated to must be built into the local modules . This state of affairs would obviously be unacceptable in the ultimate version of the model . These inhibitory interactions could , of course , be programmed , as suggested earlier . An alternative scheme , in which patterns of activation are coarse -coded at the word as well as the letter level , would get around the problem by using a kind of " natural competition " that occurs + +16. PROGRAMMABLE BLACKBOARD MOEL 153 + +connection matrix linking the central letter units to the central word units. The central unit for each word also has hardwired connections to the CA units appropriate for activating both bottom -up and top-down connections between the programmable letter units and the program- + +mable word unit for this word. + +An input to be presented to the model for processing could be a sequence of letters up to twenty letters long. The sequence could include blanks (represented by 11- II) . The blanks were treated as characters just as the letters were. The sequence of blanks and letters were used to specify which letter / role units should receive external excitatory input in each letter slot. The 1'\_" character always activated the same two letter/ role units no matter what preceded or followed it . So, for example, the input-specification \_CA T- caused external input to the letter / role units for \_C and Cx in the second slot, xA and Ax in the third letter slot, xT and T- in the fourth letter slot, and to the two + +letter / role units for " " in the first and fifth slots. + +Single and Multiple Fixations + +The simulation model was studied in two modes: One involved short displays- one or at most two short words- which were presented for processing within a single fixation . The second mode involved whole lines of text . For the latter~ I assumed that PABLO " read" them from left to right with one fixation per word. Fixation durations were fixed ~ for simplicity ~ though we l~now that they can be influenced by visual + +and linguistic factors (Just & Carpenter~ 1980) . + +First I will describe the assumptions made for the multiple fixation case. It was assumed that~ on each fixation , the spotlight of attention consisted of two regions: a center and a penumbra. The center of the spotlight consisted of several letter positions in the input centered around the point of fixation . The penumbra of the spotlight consisted of several more letter positions further to the right . Note that the parafoveal region to the left of the point of fixation is not included in the spotlight of attention . Evidence from a number of sources (e.g.~ Rayner~ 1975) suggests that information in this region is not utilized . Letters in both the center and the penumbra of the spotlight of attention are projected to the corresponding letter units. To keep things simple~ I assume for present purposes that the letters in the penumbra simply produce weaker bottom -up activations than those in the center of the spotlight. A more realistic assumption would be that letters in the penumbra produce less precise activations (i.e. ~ activations that encompass all the letters in the same shape-class) but I have foregone this assumption for now to keep things simple and as clear as possible. + +154 PSYCHOLOGICAL PROCESSES + +The spotlight of attention falls on a particular place in the input text, and its contents are projected to the corresponding region in the programmable blackboard. This region is called the illuminated region. The programmable letter units in this part of the blackboard project to the central module, and the connection activation units project back to the + +programmable connections in the illuminated region.4 + +In single fixation mode, I assumed that both the display and the spotlight of attention were centered on the fovea. For simplicity , the entire display was assumed to fall within the center of the spotlight so + +that each letter in the display was given equal weight. + +Details of activation dynamics . The rules for updating program mable letter and word unit activations were the same as in CID . How ever , the introduction of coarse coding and overlapping slots necessi tated a number of changes in the quantitative parameters . The values I used were chosen so that PABLO would produce approximately the + +same behavior with single four -letter words as CID . + +The activation assumptions for units in the connection programming loop (the central letter and word units , and the connection activator units ) , and for the programmable connections themselves , were kept simple as before . Two modifications were introduced , however . First , letter -level activations in the penumbra of attention were treated as weaker inputs to the central letter units than letter -level activations in the center : They only turned on the corresponding central letter units half as much as those in the center of attention . Second , activations of central word units were normalized by the length of the word . This was done so that that the connections for a word would be turned on to the same extent , regardless of word length , whenever all the letters of the word were present in the center of attention . For example , the activa tion of the central word unit for the word CA T is just a count of the active letter Irole units for CA T C\_ C , Cx , xA , Ax , xT , and T\_ ) in the center of the illuminated zone , plus .5 times a count of the active letter I role units in the penumbra , divided by 6 . With the display \_ CA T\_ , centered in the fovea , this number would therefore be 1.0 . + +As before , each CA unit simply multiplies the activation value it receives from its CW unit by the appropriate global excitatory constant , + +4 An alternative conception would be to imagine that the contents of the fixation are always projected directly to the central module and to the illuminated region of the programmable blackboard. There are reasons for preferring this view, one of which is that it opens up the possibility that the information projected into the central module might be of higher grain than that projected to the programmable blackboard. This is desirable because higher fidelity is needed in the connection activation process than in the programmable blackboard once the correct connections have been activated. (See Chapter + +16. PROGRAMMABLE BLACKBOARD MODEL 155 + +depending on whether the connection is letter - to - word or word - to - + +letter , and passes the result on as the activation of the programmable + +connections it projects to in each local matrix . Projections into the + +penumbra were assumed to be half strength . + +Finally , as noted above , the model assumes that programmable con nection activations are " sticky " - they tend to retain the values pro grammed into them when the spotlight of attention moves on . For simplicity , I adopted the most radical version of this assumption . Input from the central module can increase the activation of a programmable connection , and , once activated to a level , it stays at that level while the rest of the line of text is processed . At the beginning of a new line , + +of course , the slate is wiped clean . + +One Fixation at a Time + +Simultaneous resolution of two tokens of the same ambiguous char acter . Consider the ambiguous character in T . LolE CJ4T . Let us see what happens when this display is presented to PABLO . We assume that the whole display , with blanks on both sides , fits inside the center of attention , with the first T lined up with the second input position , so that each letter activates all of the appropriate letter / role units in the appropriate positions . For the two slots to which the ~ character is presented , we assume that xH and Hx and xA and Ax are all activated to equal degrees . PABLO will end up selecting xH and Hx for the first + +~ and xA and Ax for the second J - I , in parallel . + +Once the letter / role units have been activated in the appropriate letter level slots , they will activate the central word units for various words to various degrees . For example , the central word unit for the word THE will receive eight excitatory inputs : from the \_ T and Tx at the beginning of THE , from the xH and Hx in Tf4E , from the E - and xE at the end of TJ - lE , and from the xH and Hx in the middle of CI - 1T . + +The central word unit for the word CA T will receive eight excitatory inputs as well : two from the initial C of C .JJ . T , two from the final T of C ~ T , and two from each ( possible ) medial A . Normalizing for length , the central word units for both words end up getting an activation value + +of 8 / 6 or 1 . 33 . + +The central word units for other words will also be turned on to some extent . For example , the unit for the word HA T will receive eight excitatory inputs as well . The two Hx units activated by the f1 figures will each contribute one input , the two xA and the two Ax activated by the two Ii figures will each contribute one input , and the xT and T - occurring at the end of CHT will each contribute one input . 156 PSYCHOLOGICAL PROCESSES + +THE CHT + +FIGURE 11. Word - and letter-level activations in PABLO in response to TJ1E CJ4T At the word level (upper panel), each rectangle represents a word unit . The vertical position of the rectangle indicates the activation of the unit , and the horizontal placement relative to the input shown at bottom indjcates the portion of the jnput that the unit spans. At the letter level (lower panel), the height of each square represents the average activation of the two active letter/ role unjts representing the letter inscribed in the square. + +Note that the medial H turns on the weights for HA T half as much as an initial H would because it only has one letter-form feature in common with the initial H pattern of the word HA T. In any case, when we normalize again for length, the CW unit for HA T ends up getting an + +activation value of 8/ 6 or 1.33 as well. + +The CW units for THA T and CHA T will be set at activation values of 1.25. The display contains a total of 10 tokens of the eight letter/ role elements of each of these two words, and the denominator for each is 8. It is important to remember that the activation of central word units do not directly determine what is seen~ they simply turn on connections in the programmable blackboard and thereby permit local letter units to interact with local word units. We now examine the activations that + +result from these interactions. + +Letter and word activations resulting from TJ-J,E CI-J.T after 10 cycles of processing are shown in Figure 11. The model has successfully completed the first word as THE and the second as CA T by the end of 10 + +- { t~ ~ + +t + +t c a - - h - + +a h + +16. PROGRAMMABLE BLACKBOARD MOEL 157 + +cycles and is in the process of reinforcing the correct interpretation of the J1 figure in each position through feedback. Words such as HA T whose weights are strongly activated playa stronger role in the competition than words such as CAN, which contain letters that do not occur anywhere in the input string, but even HA T, as well as THA T and CHA T, are eventually driven out. After 30 cycles (not shown) THE/ 2 and CA T / 6 are the only word units left active, and, at the letter level, + +the H has beaten A in T~ E while A has beaten H in CJ4T. + +Conspiracies of Words of Different Lengths + +So far what we have illustrated could have been done in a three-letter word version of CID , though the details about what words got activated would have been somewhat different . Now, however, we can present the words starting in any letter position- as long as they do not falloff either end of our series of overlapped modules- and they can be of any length up to the maximum length allowed by the structural parameters of the model. An even more important advantage of PABLO is that, when nonwords are shown, they can profit from conspiracy effects arising from words of different lengths. The mechanism causes the activations of the conspirators to be aligned appropriately with the input . + +PABLO has been tested with each of the words that it knows and with pseudowords made from each word by replacing either a vowel with a vowel or a consonant with a consonant. In all cases, the letter string was presented alone, surrounded by blanks. The model works well with either words or pseudowords. When a word of any length is shown surrounded appropriately by blanks, the appropriate word unit always wins the competition . When an nonword is shown, both shorter and longer strings can participate, as shown in Figure 12. In the figure , several representative conspiracies are shown for nonwords of four , three, and two letters in length. Though in some cases one word the model knows is a much better match than all the others, and therefore dominates the competition , in other cases there is a much more homogeneous conspiracy. Generally speaking, words both longer and shorter than the item shown get into the act- though of course no words longer than four letters are activated, because they have not been + +included in the model. + +Within - word crosstalk. One idiosyncrasy of PABLO needs to be mentioned. It has a tendency to activate words that have repetitions of the same letter more strongly than words that do not, even when only one copy of the letter is shown. For example, DA T activated DA T A + +16. PROGRAMMABLE BLACKBOARD MODEL 159 + +more strongly than it activated DA TE. The reason is that the xA unit activated by DA T turns on the weights for DA TA two times- that is, there is a double excitatory link from this letter / role unit to the CW unit for DA T A . At the present , I know of no data tv indicate whether + +this characteristic is consistent with human behavior or not . + +There is another kind of within - word crosstalk that occurs in PABLO for which there is evidence . Connections for words that are anagrams of the display are strongly activated , particularly if they involve switches of the two internal letters . For example , the display CLAM activates the connections for CALM as much as the connections for CLAM , and the display BCAK activates the weights for BACK as much as BACK itself does. These connection activations make CALM a reasonably likely error response when CLAM is shown and make BA CK a very likely error response when BCAK is shown . Johnston , Hale , and van Santen ( 1983) have reported evidence of such " transposition " errors in word perception . Generally , such errors are attributed to imprecise positional specificity , so that letters in one position activate detectors for words having these same letters in adjacent positions . In PABLO , such effects occur for a slightly different reason : It is not that the model does not keep straight which letter occurred where , it is just that the description of a letter that is projected into the central module is very similar to the description that would be projected by the same letter in a similar role . The results of simulations illustrating these effects are shown in Figure 13. One feature of these data was originally puzzling when Johnston et ale first reported them . On the one hand , it seemed that subjects had very accurate letter position information , since they only rarely rear ranged letters in real words to make other real words . On the other hand , they acted as though they had poor letter position information when the rearrangement of the string formed a word but the display itself did not . In PABLO , the reason for the difference is simply that in the first case, there is a word that matches the input better than the transposition word ~ due to competitive inhibition , the correct word dominates the transposition word . When there is no correct word , the transposition word is not dominated , so it may become quite strongly activated . This effect is clearly illustrated in the simulation shown in + +Figure 13. + +Effects of Display Length on Amount of Feedback + +One additional feature of PABLO is that shorter displays receive less benefit from feedback than longer displays . This is true , even though I have normalized the activation of central word units , and therefore of + +160 PSYCHOLOGICAL PROCESSES + +DRAT PTAH + +connection strengths, for word length. The reason for this is simply that shorter displays activate fewer letter / role units than longer ones, and therefore provide less excitatory input to the word level than longer displays. Word units are less strongly activated than they are by longer displays. Consequently, less feedback is generated. This occurs both for word and for pronounceable nonword displays. The activations shown in Figure 12 illustrate this aspect of the model in the case of + +pronounceable nonword displays. + +At first I found this characteristic of the model undesirable. However, recent evidence collected by Samuel, van Santen, and Johnston (1982) is consistent with the model as it is. Samuel et al. examined accuracy of letter identification for letters in one-, two-, three-, and four -letter words and random letter strings and found that letter identi fication accuracy increased as a function of word-length for letters in words but not for letters in random strings. The advantage for letters in words over letters in random strings was either very small or nonexistent for one-letter words and grew as the words grew longer, up to about four or five letters. Thus, the data appear to support this aspect of the model's behavior. It should be noted that this aspect of the + +FIGURE 13. Word-level activations produced by two displays which can be made into + +words by rearranging the central two letters. + +-1path ~ -{~ - -{=:=J- + +-1pithl - + +-1peatt - + +-1dratl - I + +-EJ- -1~ - + +-1rat ~ + +-1dart }- + +16. PROGRAMMABLE BLACKBOARD MODEL 161 + +model does not depend on the connection activation aspects of PABLO but would occur in a hardwired version of the original model, as long as the net excitatory input to the word unit from a complete specification + +of the word varied linearly with the length of the word. + +Sequences of Fixations + +Up to now I have examined the behavior of PABLO within single fixations . Now, we will examine the model as it reads along a line of text . The present version of the model is fairly rudimentary , and there are a lot of important properties of human reading that it does not capture. However, it does read in a limited sense: It makes a series of fix ations, and builds up a representation of the letters and words in its programmable blackboard as it moves along, as illustrated in Figure 14. PABLO 's reading in this simulation is not affected by semantic and syntactic constraints since it lacks these higher levels. Furthermore , as it presently stands, PABLO does not even monitor its own perform ance. Instead, each fixation lasts a fixed number of cycles. PABLO does adjust the point of its fixation for the word it is viewing, however: It fixates on the center of words containing an odd number of letters, or the middle of the letter before the center for words containing an + +even number of letters. 5 + +Although it lacks many of the features of Thibadeau, Just, and Carpenter's (1982) READER model, PABLO does show one property that READER does not: It integrates information over successive fixations. That is, while it is looking at one word in a particular fixation , it is also gathering some information about the next word. This is, of course, something that human readers do also (Rayner, 1975~ for a dissenting view, see McConkie , lola , Blanchard, & Wolverton , 1982) . We can see that PABLO is picking up information from peripheral vision in Figure 14, but it is hard to tell from the figure how much difference this makes. To get a handle on this matter, I repeated with PABLO the same experiment Rayner (1975) did to demonstrate the pickup of peripheral information in human readers. That is, I adjusted the display during PABLO 's saccade, so that what the model saw in the periphery and what it saw when it later fixated the previously peripheral location was not necessarily the same. Rayner showed that when the + +5 The reader should be clear about the fact that P ABLO's fixation shifting apparatus i not simulated using interactive activation processes, though Ithink it could be. A saccade for PABLO simply amounts to moving a pointer into the array of input letters and + +\_{~~~~I ~J- -{:=J- + +-1~ ~ JJ - + +-EJ - + +-{J ~h : iJ- ~ l h all - - @~~] J~ + +- did - + +that + +- cat + +the + +162 PSYCHOLOGICAL PROCESSES + +-{~~~~~~~~~~ -{~ - + +-{!I ~ - + +-{:=J- + +- C8l - + +did - + +\_ the + +THE CAT DID THAT THE CAT DID THAT + +THE CAT DID THAT THE CAT DID THAT + +FIGURE 14. Pattern of activation at the letter and word level in PABLO, at the end of each fixation, as the model reads along a line of text. Location of the fovea and penum- + +1=~=h~ - + +-{=::]- -E }- + +-1~t -~ ~ It: h a :![EJ - + +- the - + +at - + +-{~j~1!~~I }- + +-I\_d i d ~ + +-EJ - + +-{~ ~ : JJ- -{h ~ 1J- + +-{:=J- + +- that + +- did + +cst + +164 PSYCHOLOGICAL PROCESSES + +and target. For intermediate cases, it can show either a facilitation or an interference, depending on the target and the exact distortion of it . On the average, the intermediate condition shows a slight interference effect when two letters are changed, as in the example shown in the + +figure . + +To relate these results to Rayner's, we would begin by assuming that human readers, unlike PABLO , move on to the next fixation when their certainty of the contents of one fixation reaches a satisfactory level. In the simulation , PABLO has a fixed duration for each fixation , but if the fixation was terminated when the activation of one of the words reached some criterion , then the duration of the fixation on the target would have been shortest in the case where the preview matches the target and longest in the case where the two differ the most, just as + +Rayner found . + +Thus, PABLO integrates information over successive fixations , and conforms to the main result of Rayner's experiment . Though PABLO does not capture all the details, I would expect it to capture more of them if some of the simplifying assumptions were replaced with more realistic ones. For example, end letters appear to be more critical to human readers than to PABLO , and people are sensitive to the similarity of shape between original and replacement letters. A more elaborate version of PABLO , including a real feature level, would surely + +show these effects. + +D ISCUSSI 0 N + +I have described two models that rely on the same basic principles of connection information distribution from a central knowledge source to local, programmable modules. CID , the first model, illustrated some basic properties of the connection information distribution scheme, but it had serious limitations because of its fixed -length, nonoverlapping programmable modules. PABLO overcame this deficiency of CID and provided a framework for beginning to think about the problem of reading by a series of fixations and integrating information from one + +fixation to the next. + +Benefits of Connection Information Distribution + +At this point , it is appropriate to step back from these particular models and take a look at the more general implications of the idea of connection information distribution . I believe this is quite a powerful + +idea. Connection information distribution allows us to instruct parallel processing structures from outside the network , making their behavior contingent on instructions originating elsewhere in the network . This means, for example, that the way a network responds to a particular input can be made contingent on the state of some other network in the system, thereby greatly increasing the flexibility of parallel process- + +ing mechanisms. + +Perhaps the most general way of stating the benefit of connection information distribution is to note that it is analogous, in a way, to the invention of the stored program. 6 Before programs were invented, special-purpose logic circuits were built to carry out particular tasks~ the invention of the computer program made it possible for a single, general-purpose machine to carry out anyone of a huge number of tasks. The use of centrally stored connection information to program local processing structures is analogous. This allows the very same processing structures to be programmed to perform a very wide range of + +different tasks. + +More specifically, there are two computational problems facing POP models to which connection information distribution can be beneficially addressed. Connection iIiformation distribution allows multiple tokens of the same type to be active at once. PABLO , for example, would have no difficulty processing the same word twice if it occurred in two different locations in the programmable blackboard, and higher levels would be able to make different choices from alternative word activations in different places, just as the word level in PABLO was able to make different choices between A and H for the two instances of the H character in THE GJJ.T. The ability to treat different tokens of the same type separately is, of course, very important in such domains as sentence processing, in which several tokens of the same kind of object (e.g., noun phrase, sentence, etc.) must be kept straight and assigned + +to appropriate roles in larger structures. + +Connection information distribution also carries out a form of what is known in production systems as "resolution ," binding the right tokens in the blackboard together into higher-order structural patterns. In PABLO , we have the following situation: Activations from everywhere in the programmable blackboard (analogous for present purposes to the working memory in production system models) are projected into the central knowledge system (analogous to the production memory) . Central word units (analogous to productions) are activated to the extent the input from anywhere in the programmable blackboard activates them. The problem faced in production systems is to avoid spuriously + +16. PROGRAMMABLE BLACKBOARD MODEL 165 + +166 PSYCHOLOGICAL PROCESSES + +firing productions when the activations in working memory lack the proper overall organization and to bind the correct pieces together, so that each production has the correct set of arguments rather than a melange of arguments coming from different places. If spurious activations occur and the bindings are done improperly , the consequence will be that the wrong things will be added to the working memory. The ultimate problem faced in PABLO is analogous. We need to avoid allowing the wrong word units to get activated in the programmable blackboard by spurious conjunctions of letters. PABLO solves this problem, not by explicitly binding productions to particular elements and checking that they occur in the right conjunctions, but by distribut ing connection information so that when and if the right combination of elements occurs, the appropriate word unit will be activated. This allows different elements to be bound to different higher-order structures in parallel, as we saw in the case of THE Cf-iT~ one of the Ii 's was "bound" to an appropriate "instantiation " of THE, and the other to an appropriate instantiation of CA T. This scheme does involve some crosstalk, as we saw, but the crosstalk is of about the same kind and magnitude as the crosstalk shown by human subjects when they have to process more than one pattern in parallel. In short, it looks as though the CID model captured pretty well some of the features of the way + +elements are bound together in human information processing. + +Costs of Connection Information Distribution + +At first glance, it may seem that the ability to program parallel processing structures is being purchased at a very high price. For it appears that, wherever we had a connection in a hardwired POP model, we now need a lot of extra circuitry to program that connection. The cost appears particularly high in terms of connection activation units and programmable connections. If there are n x n units in a programmable module, it appears that we need n 2 programmable connections and the same number of CA units to activate the programmable connections. This can get very expensive very quickly as processing struc- + +tures get to realistic sizes. + +Actually , however, the situation is not as bleak as this observation seems to suggest. It turns out that with programmable modules, it is possible to process patterns with far fewer units than we would need in a hardwired parallel processing structure. The reason is that the size of a module required to process a pattern without error depends on the number of patterns the module must be prepared to process at one time . To see this, consider a module which must either be hardwired 16. PROGRAMMABLE BLACKBOARD .MOEL 167 + +to process three different languages or which can be programmed to process anyone of them. Clearly, we can get by with a smaller module in the latter case. More generally, if we use distributed representations, simple mathematical analyses show that the more patterns a module is set up to process, the larger it must be to avoid errors in processing any one pattern that might be presented on a particular occasion. The reason why this fact is relevant is that in conventional , hardwired POP mechanisms, the model is programmed to process all of the patterns that it knows, all of the time . With programmable modules, on the other hand, the module only gets loaded with the connection informa tion relevant to processing the patterns whose central representations are active. Since this number is vastly smaller than the number of total patterns a person might know, the size of the programmable processing structure can be very much smaller than a hardwired processing structure would have to be to do the same work . A full discussion of these issues is presented in Chapter 12 on the resource requirements of POP + +models. + +One interesting result of the analysis of the resource requirements of connection information distribution is the fact that the required number of units and connections varies with the number of different patterns the network is being programmed to process at a particular time. This fact means that for a CID mechanism of a given size, there is a limit of the amount of parallelism it can handle (quite independently of the number of programmable modules) . But the limit is in programming the modules, not in their actual parallel operation once they have been set up. Thus if we can program each module separately, we can let them run in parallel~ though we are forced to go sequential at the level of programming the modules, they can still be allowed to process simultaneously and to mutually constrain each other though interactions with higher-level processing structures. We therefore get the main benefit we wanted parallel distributed processing for - simultaneous, mutual constraint- without reduplicating hardwired knowledge or paying an undue price in terms of programmable connections and connec- + +tion activation units. + +Extensions of Connection Information Distribution + +A programmable version of TRA CEo In PABLO, we programmed the programmable blackboard sequentially, in fixation-sized blocks. In extending the basic ideas inherent in PABLO to speech, we notice immediately that the speech signal forces seriality on us by its very sequential nature. We argued, though, in Chapter 15, for a dynamic + +168 PSYCHOLOGICAL PROCESSES + +parallel processing structure in which we could exploit both forward and backward interactions, simply allowing new constraints to be added from the input at the right edge of the Trace, as the speech input unfolded in time . Now, to make the Trace into a programmable parallel processing structure, we can use the seriality of speech to program the Trace sequentially, as the speech comes in, thereby minimizing the resource requirements of the connection information distribution + +apparatus. + +There would be several advantages to implementing a programmable version of TRACE . One is that retuning, priming , and learning effects could be accounted for by adjustment of the strengths of connections in the central knowledge source. Another is that the rather high cost of the connection modulation scheme for tuning feature-phoneme connections based on phoneme activations in the context could be born just once in the central knowledge structures. A third is that the central knowledge source could be retuned by global variables such as rate, etc., thereby allowing it to create in the Trace just the right pattern of interconnections to fit the expected form different possible utterances might take in the given situation . Such a model might be seen as performing an analysis of the speech signal by synthesis of the appropriate connection information , capturing some of the flexibility and context sensitivity which Halle and Stevens (1964) noted that speech perception + +calls for in their seminal article on "Analysis by Synthesis." + +Processing syntactic structures. Introducing programmable connections into the TRACE model of speech perception will be a challenging task. Equally challenging will be the problem of extending the approach described here to higher levels of language structure. At higher levels, we must come to grips with the recursive structure of sentences, and the unbounded dependencies among elements of sentences. Some ideas about how this might be done are described in + +Chapter 19. + +CONCLUSION + +In this chapter, I have tried to argue that connection information distribution provides a way of overcoming some apparent limitations of parallel distributed processing mechanisms. Using connection informa tion distribution , we can create local copies of relevant portions of the contents of a central knowledge store. These local copies then serve as the basis for interactive processing among the conceptual entities they program local hardware units to represent. With this mechanism, PDP + +16. PROGRAMMABLE BLACKBOARD MODEL 169 + +models can now be said to be able to create multiple instantiations of the same schema , bound appropriately to the correct local variables , though subject to just the kinds of binding errors human subjects seem + +to make . + +Perhaps the main lesson is that some of the limitations of POP mechanisms that connection information distribution has been proposed to overcome are more apparent than real . For I have not really done anything more than show how existing tools in the arsenal of parallel distributed processing mechanisms can be used to create local copies of networks . This is not to say that all the challenges facing PDP models have suddenly vanished . Obviously there is a long way still to go in the development of computationally adequate models of reading , speech perception , and higher levels of language processing . I hope this chapter helps to indicate that POP mechanisms will help us get there in a way that captures the flexibility and interactive character of human + +processing capabilities . + +ACKNOWLEDGMENTS + +This work was supported by ONR Contract NOOO14 - 82 - C - O374 , NR 667 - 483 , by a grant from the System Development Foundation , by a grant from the National Science Foundation ( BNS - 79 - 24062 ) , and by a NIMH Research Scientist Career Development Award . Special thanks for useful ideas and suggestions are due to Gary Cottrell , Geoff Hin - + +ton , Dave Rumelhart , and David Zipser . + +CHAPTER 17 + +J. L. McCLELLAND and D. E. RUMELHART + +The view that human memory is distributed has come and gone several times over the years. Hughlings-Jackson, the 19th century neurologist~ Kurt Goldstein, the Gestalt neurologist of the early 20th century ~ and Karl Lashley, the physiological psychologist of the same era, all held to variants of a distributed model of the physiology of learning + +and memory. + +While Lashley's and Goldstein 's more radical views have not been borne out, the notion that memory is physiologically distributed within circumscribed regions of the brain seems to be Quite a reasonable and plausible assumption (see Chapters 20 and 21) . But given the rather loose coupling between a psychological or cognitive theory and a theory of physiological implementation , we can ask, does the notion of distrib uted memory have anything to offer us in terms of an understanding of + +human cognition ? + +In Chapter 3, several of the attractive properties of distributed models are described, primarily from a computational point of view. This chapter addresses the relevance of distributed models from the point of view of the psychology of memory and learning. We begin by + +A Distributed Model of + +Human Learning and Memory + +This chapter is a modified version of the article " Distributed Memory and the Representation of General and Specific Information'! by J. L. McClelland and D. E. Rumelhart, which appeared in Journal Qf Experimental Psychology: General, 1985, 114, 159-188. Copyright 1985 by the American Psychological Association, Inc. Adapted with + +17. A DISTRIBUTED MOEL OF MEMORY 171 + +considering a dilemma that faces cognitive theories of learning and memory, concerning the representations of general and specific infor mation . Then we show how a simple version of a distributed model circumvents the dilemma. We go on to show how this model can account for a number of recent findings about the learning and representation of general and specific information . We end by considering some other phenomena that can be accounted for using a distrib uted model, and we consider a limitation of the model and ways this + +limitation might be overcome. + +The Dilemma + +One central dilemma for theories of memory has to do with the choice to represent general or specific information . On the one hand, human memory and human learning seem to rely on the formation of summary representations that generalize from the details of the specific experiences that gave rise to them. A large number of experiments, going back to the seminal findings of Posner and Keele (1968) indicate that we appear to extract what is common to a set of experiences. On the basis of this sort of evidence, a number of theorists have proposed that memory is largely a matter of generalized representations, either abstracted representations of concepts discarding irrelevant features, or prototypes- representations of typical exemplars (Rosch, 1975) . On the other hand, specific events and experiences playa prominent role in memory . Experimental demonstrations of the importance of specific stimulus events even in tasks which have been thought to involve abstraction of a concept or rule are now legion. Responses in categorization tasks (Brooks, 1978~ Brooks, Jacoby, & Whittlesea, 1985~ Medin & Schaffer, 1978), perceptual identification tasks (Jacoby, 1983a, 1983b~ Whittlesea, 1983) , and pronunciation tasks (Glushko , 1979) all seem to be quite sensitive to the congruity between particular training stimuli and particular test stimuli , in ways which most abstraction or prototype + +formation models would not expect. + +One response to this dual situation has been to propo~e models in which apparent rule-based or concept-based behavior is attributed to a process that makes use of stored traces of specific events or specific exemplars of the concepts or rules. According to this class of models, the apparently rule-based or concept-based behavior emerges from what might be called a conspiracy of individual memory traces or from a sampling of one from the set of such traces. Models of this class include the Medin and Schaffer (1978) context model, the Hintzman (1983) multiple trace model, and the Whittlesea (1983) episode model. + +This trend is also exemplified by our interactive activation model of word perception and an extension of the interactive activation model to generalization from exemplars (McClelland , 1981) . Both of these + +models were described in Chapter 1. + +One feature of some of these exemplar models is very troublesome . Many of them are internally inconsistent with respect to the issue of abstraction . Thus , though our word perception model assumes that linguistic rules emerge from a conspiracy of partial activations of detec tors for particular words , thereby eliminating the need for abstraction of rules , the assumption that there is a single detector for each word implicitly assumes that there is an abstraction process that lumps each occurrence of the same word into the same single detector unit . Thus , the model has its abstraction and creates it too , though at somewhat + +different levels . + +One logically coherent response to this inconsistency is to simply say that each word or other representational object is itself the result of a conspiracy of the entire ensemble of memory traces of the different individual experiences we have had with the object . We will call this view the enumeration of specific experiences view . It is exemplified most clearly by Jacoby ( 1983a, 1983b) , Hintzman ( 1983) , and Whittlesea + +( 1983) . + +As the papers just mentioned demonstrate , enumeration models can work quite well as an account of quite a number of empirical findings . However , there still seems to be a drawback . Enumeration models seem to require an unlimited amount of storage capacity , as well as mechanisms for searching an almost unlimited mass of data . This is especially true when we consider that the primitives out of which we normally assume each experience is built are themselves based on generalizations . For example , a word is a sequence of letters , and a sentence is a sequence of words . Are we to believe that all these units are mere notational conveniences for the theorist , and that every event is stored separately as an extremely rich (obviously structured ) represen - + +tation of the event , with no condensation of details ? + +Thus , the dilemma remains . It would appear that enumeration models cannot completely eliminate the need for some kind of abstrac tive representation in memory . Yet the evidence that the characteris tics of particular events influence memory performance cannot be + +disposed of completely . + +One response to this dilemma is to propose the explicit storage of both general and specific information . For example , Elio and J. R. Anderson ( 1981) have proposed just such a model . In this model , memory traces are stored in the form of productions , and mechanisms of production generalization and differentiation form summary + +172 PSYCHOLOGICAL PROCESSES + +17. A DISTRIBUTED MODEL OF MEMORY 173 + +Distributed models suggest another alternative . As we shall demon strate in this chapter , a very simple distributed model , relying on a very simple learning rule - the delta rule - is capable of accounting for empirical data that has been taken as suggesting that we store summary representations ( e . g . , prototypes ) as well as data that has been taken as suggesting that memory consists of an enumeration of specific experi - + +ences . + +The specific model we consider does have a limitation that it shares with enumeration models : It relies on a fixed set of representational primitives . However , we shall argue that natural extensions of the model which overcome this limitation are now possible . Though we do not explore these extensions in detail , we do consider some issues that + +will arise if these extensions are incorporated . + +A DISTRIBUTED MODEL OF MEMORY + +The model we shall describe is a member of the class of models dis cussed in Chapter 3 . In developing the ideas presented here , we were strongly influenced by the work of J . A . Anderson ( e . g . , 1977 , 1983 ~ Anderson , Silverstein , Ritz , & Jones , 1977 ~ Knapp & Anderson , 1984 ) and Hinton ( 1981a ) . We have adopted and synthesized what we found to be the most useful aspects of their distinct but related models , + +preserving ( we hope ) the basic spirit of both . + +In keeping with the overall enterprise of the book , our distributed model is a model of the microstructure of memory . It specifies the internal workings of some of the components of information processing and memory , in particular those concerned with the retrieval and use of prior experience . The model does not specify in and of itself how these acts of retrieval and use are planned , sequenced , and organized into coherent patterns of behavior . Some thoughts about ways this might be + +done may be found in Chapters 8 and 14 . + +General Properties + +Our model shares a number of basic assumptions about the nature of the processing and memory system with most other distributed models . In particular , the processing system is assumed to consist of a highly interconnected network of units that take on activation values and com municate with other units by sending signals modulated by weights associated with the connections between the units , according to the principles laid out in Chapter 2 . Sometimes we may think of the units + +OCESSES + +Modular structure. We assume that the units are organized into modules. Each module receives inputs from other modules; the units within the module are richly interconnected with each other~ and they send outputs to other modules. Figure 1 illustrates the internal structure of a very simple module, and Figure 2 illustrates some hypotheti cal interconnections between a number of modules. Both figures grossly under-represent our view of the numbers of units per module and the number of modules. We would imagine that there would be thousands to millions of units per module and many hundred or perhaps many thousand partially redundant modules in anything close + +to a complete memory system. + +The state of each module represents a synthesis of the states of all of the modules it receives inputs from . Some of the inputs will be from relatively more sensory modules, closer to the sensory end-organs of + +174 PSYCHOLOGICAL PR + +as corresponding to particular representational primitives , but they need not. For example, even what we might consider to be a primitive feature of something, like having a particular color, might be a pattern + +of activation over a collection of units. + +. . . . . . . . + +FIGURE 1. A simple information processing module, consisting of a small ensemble of eight processing units. Each unit receives inputs from other modules (indicated by the single input impinging on the input line of the unit from the left~ this can stand for a number of converging input signals from several units outside the module) and sends outputs to other modules (indicated by the rightward output line from each unit). Each unit also has a modifiable connection to all the other units in the module, as indicated by the branches of the output lines that loop back onto the input lines leading into each unit. + +17. A DISTRIBUTED MODEL OF MEMORY + +one modality or another. Others will come from relatively more abstract modules, which themselves receive inputs from and send outputs to other modules placed at the abstract end of several diff eren t modalities. Thus, each module combines a number of different sources + +of information . + +175 + +Units play specific roles within patterns. A pattern of activation only counts as the same as another if the same units are involved . The reason for this is that the knowledge built into the system for re-creating the patterns is built into the set of interconnections among the units, as we will explain below. For a pattern to access the right knowledge, it must arise on the appropriate units. In this sense the units play specific + +roles in the patterns. + +Obviously, a system of this sort is useless without sophisticated perceptual processing mechanisms at the interface between memory and the outside world , so that input patterns arising at different locations in the world can be mapped into the same set of units internally . The scheme proposed by Hinton (1981b~ see Chapter 4) is one such mechanism. Chapter 16 describes mechanisms that allow several dif ferent patterns to access the same set of units at the same time ~ in the present chapter, we restrict attention to the processing of one pattern + +FIGURE 2. An illustrative diagram showing several modules and interconnections among them . Arrows between modules simply indicate that some of the units in one module send inputs to some of the units in the other . The exact number and organiza tion of modules is, of course , unknown ~ the figure is simply intended to be suggestive . + +176 PSYCHOLOGICAL PROCESSES + +Relation to Basic Concepts in Memory + +Several standard concepts in the memory literature map easily onto corresponding aspects of distributed memory models . Here we consider three key concepts in memory and their relation to our distributed + +memory model . + +Mental state as pattern of activation . In a distributed memory system , a mental state is a pattern of activation over the units in some subset of the modules . The patterns in the different modules capture different aspects of the content of the mental states in a kind of a partially overlapping fashion . Alternative mental states are simply alterna tive patterns of activation over the modules . Information processing is + +the process of evolution in time of mental states. + +Memory traces as changes in the weights . Patterns of activation come and go, leaving traces behind when they have passed. What are the traces ? They are changes in the strengths or weights of the connec tions between the units in the modules . 1 As we already said, each memory trace is distributed o\'er many different connections , and each connection participates in many different memory traces . The traces of different mental states are therefore superimposed in the same set of + +weights . + +Retrieval as reinstatement of prior pattern of activation . Retrieval amounts to partial reinstatement of a mental state , using a cue which is a fragment of the original state . For any given module , we can see the cues as originating from outside of it . Some cues could arise ultimately from sensory input . Others would arise from the results of previous retrieval operations , fed back to the memory system under the control of a search or retrieval plan . It would be premature to speculate on how such schemes would be implemented in this kind of a model , but + +it is clear that they must exist . + +Detailed Assumptions + +In the rest of our presentation , we will be focusing on operations that take place within a single module . This obviously oversimplifies the behavior of a complete memory system since the modules are assumed + +MODEL + +Continuous activation values. The units used in the present model are fairly standard units, taking on continuous activation values in the range from - 1 to + 1. Zero is in this case a neutral resting value, + +toward which the activations of the units tend to decay. + +Unlike the models described in some of the previous chapters in this section, there is no threshold activation value. This means that both + +positive and negative activations influence other units. + +Inputs, outputs, and internal connections. Each unit receives input from other modules and sends output to other modules. For simplicity , we assume that the inputs from other modules occur at connections whose weights are fixed . In the simulations , we also treat the input from outside the module as a static pattern that comes on suddenly, ignoring for simplicity the fact that the input pattern evolves in time and might be affected by feedback from the module under study. While the input to each unit might arise from a combination of sources in other modules, we can lump the external input to each unit into a single real valued number representing the combined effects of all components of the external input . In addition to extramodular connections, each unit is connected to all other units in the module via a weighted connection. The weights on these connections are modifiable , as described below. The weights can take on any real values: positive, negative, or zero. There is no connection from a unit onto itself . + +An input pattern is presented at some point in time over some or all of the input lines to the module and is then left on for several ticks, until the pattern of activation it produces settles down and stops + +changing. + +17. A DISTRIBUTED OF MEMORY177 + +to be in continuous interaction . The simplification is justified , however, in that it allows us to examine some of the basic properties of distributed memory systems which are visible even without these interac- + +tions with other modules. + +Let us look , therefore, at the internal structure of one very simple module, as shown in Figure 1. Again, our image is that in a system sufficient for real memories, there would be much larger numbers of units. We have restricted our analysis to small numbers simply to illustrate basic principles as clearly as possible~ this also helps to keep the + +running time of simulations in bounds. + +The processing cycle. The model is a synchronous model, like all of the other models in this section. On each processing cycle, each unit determines its net input , based on the external input to the unit and the activations of all of the units at the end of the preceding cycle modulated by the weight coefficients which determine the strength and + +178 PSYCHOLOGICAL PROCESSES + +direction of each unit 's effect on every other unit . Then the activations + +of all of the units are updated simultaneously. + +The net input to a unit consists of two parts, the external input , arising from outside the module, and the internal input , arising from the other units in the module. The internal input to unit i , ii , is then just the sum of all of these separate inputs, each weighted by the appropri- + +ate connection strength: + +i. = La . w.. I . J IJ . J + +Here, j ranges over all units in the module other than i , a} is the activation of unit j at the end of the previous cycle, and Wi} is the weight of the connection to unit i from unit j . This sum is then added to the external input to the unit , arising from outside the module, to + +obtain the net input to unit i , neti: + +net. = i. + e. I I I + +where e; is just the lumped external input to unit i . + +Activations are updated according to a simple nonlinear "squashing" function like the one we have used in several other chapters. If the net input is positive, the activation of the unit is incremented by an amount proportional to the distance left to the ceiling activation level of + 1.0. If the net input is negative, the activation is decremented by an amount proportional to the distance left to the floor activation level of - 1.0. There is also a decay factor which tends to pull the activation of the + +unit back toward the resting level of O. For unit i , if net; > 0, + +Llai = Eneti (1 - ai ) - Dai ' (1) + +If neti ~ 0, + +~ ai = Eneti (ai - (- 1)) - Dai . (2) + +In these equations, E and D are global parameters that apply to all units and set the rates of excitation and decay, respectively. The term ai is the activation of unit i at the end of the previous cycle, and dai is the change in ai ~ that is, it is the amount added to (or, if negative, subtracted from ) the old value ai to determine its new value for the next + +cycle. + +The details of these assumptions are quite unimportant to the behavior of the model. Many of the same results have been obtained using other sigmoid squashing functions . The fact that activations range from - 1 to + 1 is, likewise, not very relevant, though if activations ranged from 0 to 1 instead, it would be necessary to incorporate threshold terms in addition to the connection strengths to get the + +17. A DISTRIBUTED MODEL OF MEMORY 179 + +Given a fixed set of inputs to a particular unit , its activation level will be driven up or down in response until the activation reaches the point where the incremental effects of the input are balanced by the decay. In practice, of course, the situation is complicated by the fact that as each unit 's activation is changing it alters the input to the others. Thus, it is necessary to run the simulation to see how the system will behave for any given set of inputs and any given set of weights. In all the simulations reported here, the model is allowed to run for 50 cycles, which is considerably more than enough for it to + +achieve a stable pattern of activation over all the units. + +Memory traces. The memory trace of a particular pattern of activation is a set of changes in the entire set of weights in the module. We call the whole set of changes an increment to the weights. After a stable pattern of activation is achieved, weight adjustment takes place. This is thought of as occurring simultaneously for all of the connections in the + +module. + +We use the delta rule to determine the size and direction of the change at each connection. This learning rule is explored extensively in Chapters 2, 8, and 11. Here, we consider it from the point of view of indicating how it implements, in a direct and simple way, the storage of the connection information that will allow a module to re-create complete patterns of activation originally produced by external input when + +only a part of the pattern is presented as a II retrieval " cue. + +To achieve pattern completion , we want to set up the internal connections among the units in the module so that when part of the pattern is presented, the internal connections will tend to reproduce the rest. Consider, in this light , a particular pattern of activation, and assume for the moment that in this pattern the external input to a particular unit j is excitatory. Then we will want the internal input from other units in the module to tend to excite unit j when they take on the activation values appropriate for this particular pattern. In general, what we need to do for each unit is to adjust the weights so that the internal connections in the module will tend to reproduce the external input to that unit , given that the rest of the units have the activation + +values appropriate for this particular pattern. + +The first step in weight adjustment is to see how well we are already doing. If the network is already doing what it should, the weights do not need to be changed. Therefore , for each unit i , we compute the difference 8i between the external input to the unit and the net internal + +180 PSYCHOLOGICAL PROCESSES + +In determining the activation value of the unit , we added the external input together with the internal input . Now, in adjusting the weights, we are taking the difference between these two terms. This implies that the unit must be able to aggregate all inputs for purposes of determining its activation, but it must be able to distinguish between exter- + +nal and internal inputs for purposes of adjusting its weights. + +Let us consider the term 8i for a moment . If it is positive, the internal input is not activating the unit enough. If negative, it is activating the unit too much. If it is zero, everything is fine and we do not want to change anything. Thus, 8i determines the magnitude and direction of the overall change that needs to be made in the internal input to unit i . To achieve this overall effect, the individual weights are then + +adjusted according to the following formula : + +What the delta rule can and cannot do. Several important points about the delta rule have been discussed in Chapters 2, 8, and 11. Here we consider just those that are most relevant to our present purposes. Basically, the most important result is that, for a set of patterns that we present repeatedly to a module, if there is a set of weights that will allow the system to reduce a to 0 for each unit in each pattern, this rule will find it through repeated exposure to all of the members of the set of patterns. However, it is important to note that the existence of a set of weights that will allow 8 to be reduced to 0 is not guaranteed, but depends on the structure inherent in the set of patterns that the model + +~ w..= 'Y}8.a. (3) IJ . , I J' + +The parameter 1] is just a global strength parameter which regulates the overall magnitude of the adjustments of the weights~ Il Wi} is the change + +in the weight to i from j . + +The delta rule, given by Equation 3, has all the intended consequences. That is, it tends to drive the weights to the right values to make the internal inputs to a unit match the external inputs. For example, consider the case in which Di is positive and aj is positive. In this case, the value of D i tells us that unit i is not receiving enough excitatory input , and the value of a} tells us that unit j has positive activation. In this case, the delta rule will increase the weight from j to i . The result will be that the next time unit j has a positive activation, its excitatory effect on unit i will be increased, thereby reducing Di. Similar reasoning applies to cases where Di is negative, aj is negative, or both are negative. Of course, when either a i or a} is zero, Wi} is not changed. In the first case, there is no error to compensate for ~ in the second case, a change in the weight will have no effect the next time + +unit j has the same activation value. + +17. A DISTRIBUTED MODEL OF MEMORY 181 + +is given to learn . To be perfectly learnable by our model , the patterns + +must conform to the following linear predictability constraint : + +Over the entire set of patterns , the external input to each unit must be predictable from a linear combination of the activa - + +tions of every other unit . + +While this limitation is severe , it is important to realize that the extent to which a set of patterns satisfy the linear predictability constraint depends on the way the set of patterns is represented . From this point of view , we must distinguish clearly between the theoretical description of a set of stimuli presented to a human subject for processing and the patterns of activation produced in some module deeply embedded in the cognitive system . As a rule of thumb , an encoding which treats each dimension or aspect of a stimulus separately is unlikely to be suffi cient ~ what is required is a context sensitive or conjunctive encoding , such that the representation of each aspect is colored by other aspects . A fuller discussion of this issue is presented in Chapter 3 ~ we also return to it below in considering some recent evidence obtained by + +Medin and Schwanenflugel ( 1981 ) . + +No hidden units . As explained in Chapters 7 and 8 , the linear pred ictability constraint arises from the fact that the present model contains no hidden units . If hidden units were incorporated ~ the generalized delta rule described in Chapter 8 could be used to train the connections into these units , thereby allowing the model to form new representa tional primitives to overcome the linear predictability constraint when it arises . At the end of the chapter , we consider the introduction of hid den units and the effects that this would have on the behavior of the + +model . + +Decay in the increments to the weights . We assume that each trace or increment undergoes a decay process , though the rate of decay of the increments is assumed to be much slower than the rate of decay of patterns of activation . Following a number of theorists ( e . g . , Wickel gren , 1979 ) , we imagine that traces at first decay rapidly , but then the remaining portion becomes more and more resistant to further decay . Whether it ever reaches a point where it is no longer decaying at all , we do not know . The basic effect of this assumption is that individual inputs exert large short - term effects on the weights , but , after they decay , the residual effect is considerably smaller . The fact that each increment has its own temporal history increases the complexity of computer simulations enormously . In many of the simulations , there fore , we will specify simpler assumptions to keep the simulations + +182 PSYCHOLOGICAL PROCESSES + +Parameters and details. In simulations using the model, it is important to keep the net input to each unit on each processing cycle relatively small, so that activations do not jump too suddenly and go out of range. For this purpose we set the parameters E and D equal to .15. It is also important to reduce 'YJ in proportion to the number of internal inputs to each unit . The number of internal inputs to each unit is just 1 minus the number of units, since each unit receives an input from every other unit . Thus, if we define 'YJ = SI (n - 1) , where n is the number of units, then the rate of learning, in terms of the reduction in 8, will be about the same for all values of n . Instability can result if S is set greater than 1.0. Generally a value of .85 was used in the follow - + +ing simulations. + +Illustrative Examples + +In this section, we describe a number of simulations to illustrate several key aspects of the model's behavior. We wish to demonstrate + +several points: + +Learning a prototype from exemplars. To illustrate the first point, we consider the following hypothetical situation . A little boy sees many different dogs, each only once and each with a different name. All the dogs are a little different from each other, but in general there is a pattern which represents the typical dog- each one is just a different distortion of this prototype. (We are not claiming that the dogs in the world have no more structure than this~ we make this assumption for + +keep them straight . + +4. Representations of specific , repeated exemplars can coexist in the same set of connections with knowledge of the prototype . + +1. The model can extract what appears to be the prototype or central tendency of a set of patterns, if the patterns are in fact ran- + +dom distortions of the same base or prototype pattern. + +2. The model can do this for several different patterns, using the same set of connections to store its knowledge of all the proto- + +types. + +3. This ability does not depend on the exemplars being presented with labels so that the model is given the where-with -all to + +17. A DISTRIBUTED MODEL OF MEMORY 183 + +purposes of illustration only ) . For now we will assume that the names of the dogs are all completely different . We would expect , given this experience , that the boy would learn the prototype of the category , even without ever seeing any particular dog that matches the prototype directly (Posner & Keele , 1968, 1970~ J. A . Anderson , 1977, applies an earlier version of a distributed model to this case) . That is, the proto type will seem as familiar as any of the exemplars , and the boy will be able to complete the pattern corresponding to the prototype from any part of it . He will not , however , be very likely to remember the names of each of the individual dogs , though he may remember the most + +recen t on es . + +We model this situation with a module consisting of 24 units . We assume that the presentation of a dog produces a visual pattern of activation over 16 of the units in the hypothetical module (the 9th through 24th , counting from left to right ) . The name of the dog pro duces a pattern of activation over the other 8 units (Units 1 to 8, + +counting from left to right ) . + +Each visual pattern , by assumption , is a distortion of a single proto type . The prototype used for the simulation simply had a random series of + 1 and - 1 values . Each distortion of the prototype was made by probabilistically flipping the sign of randomly selected elements of the prototype pattern . For each new distorted pattern , each element has an independent chance of being flipped , with probability .2. Each name pattern was simply a random sequence of + Is and - Is for the eight name units . Each encounter with a new dog is modeled as a presentation of a new name pattern with a new distortion of the proto type visual pattern . Fifty different trials were run , each with a new + +name -pattern / visual -pattern pair . + +For each presentation , the pattern of activation is allowed to stabilize , and then the weights are adjusted as described above . The increment to the weights is then allowed to decay considerably before the next input is presented . For simplicity , we assume that before the next pattern is presented , the last increment decays to a fixed small proportion (5%) of its initial value and thereafter undergoes no further decay. What does the model learn ? The module acquires a set of weights which is continually buffeted about by the latest dog exemplar , but which captures the prototype dog quite well . Waiting for the last incre ment to decay to the fixed residual yields the weights shown in + +Figure 3. + +These weights capture the correlations among the values in the pro totype dog pattern quite well . The lack of exact uniformity is due to the more recent distortions presented , whose effects have not been corrected by subsequent distortions . This is one way in which the model gives priority to specific exemplars , especially recent ones . The + +finding the central tendency of a set of related patterns. In and of itself this is an important property of the model, but the importance of this property increases when we realize that the model can average several different patterns in the same composite memory trace. Thus, several different prototypes can be stored in the same set of weights. This property is important because it means that the model does not fall into the trap of needing to decide which category to put a pattern into before knowing which prototype to average it with . The acquisition of the different prototypes proceeds without any sort of explicit categorization . If the patterns are sufficiently dissimilar (i.e., orthogonal) , there is no interference among them at all. Increasing similarity leads to increased confusability during learning, but eventually the delta rule finds a set of connection strengths that minimizes the confusability of similar patterns. These points are discussed mathematically in Chapter 11 ~ here we illustrate this through a simulation of the following + +hypothetical situation . + +Let us suppose that our little boy sees different dogs, different cats, and different bagels in the course of his day-to-day experience. First, let's consider the case in which each experience with a dog, a cat, or a bagel is accompanied by someone saying "dog," "cat," or "bagel," as + +appropriate. + +The simulation analog of this situation involved forming three "visual" prototype patterns of 16 elements: two of them (the one for dog and the one for cat) somewhat similar to each other (r = .5) and the third (for the bagel) orthogonal to both of the other two. Paired with each visual pattern was a name pattern of eight elements. Each name pattern was orthogonal to both of the others. Thus, the prototype visual pattern for cat and the prototype visual pattern for dog were + +similar to each other, but their names were not related. + +Stimulus presentations involved presentations of distorted exemplars of the name/ visual pattern pairs to a module like the one used in the previous simulation . This time , both the name pattern and the visual pattern were distorted, with each element having its sign flipped with an independent probability of .1 on each presentation. Fifty different distortions of each name/ visual pattern pair were presented in groups of three, consisting of one distortion of the dog pair, one distortion of the cat pair, and one distortion of the bagel pair. Weight adjustment occurred after each presentation, with decay to a fixed residual before + +each new presentation. + +At the end of training , the module was tested by presenting each name pattern and observing the resulting pattern of activation over the visual units, and by presenting each visual pattern and observing the pattern of activation over the name units. The results are shown in Table 1. In each case, the model reproduces the correct completion for + +17. A DISTRIBUTED MODEL OF MEMORY 185 + +the probe, and there is no apparent contamination of the "cat" pattern by the "dog" pattern, even though the visual patterns are both similar . In general, pattern completion is a matter of degree. Below, in simulating particular experimental results, we will introduce an explicit measure of the degree to which a particular pattern is active in the units of a module. For now, it is sufficient simply to note that the sign of all of the elements is correct~ given this, the average magnitude of the elements gives an approximate measure of the "degree" of pattern + +reinstatement. + +In a case like the present one, in which the patterns known to the model are not all orthogonal, the values of the connection strengths that the model produces do not necessarily have a simple interpretation . Though their sign always corresponds to the sign of the correlation between the activations of the two patterns, their magnitude is not a simple reflection of the magnitude of their correlation , but is influ enced by the degree to which the model is relying on this particular correlation to predict the activation of one unit from the others. Thus, in a case where two units (call them i and j ) are perfectly correlated, the strength of the connection from i to j will depend on the number of other units whose activations are correlated with j . If i is the only unit correlated with j , it will have to do all the work of " predicting" j , so the weight will be very strong~ on the other hand, if many units besides i are correlated with j , then the work of exciting j will be spread around, and the weight between i and j will be considerably smaller. The situation is exactly the same as the one that arises in linear regression: if several variables predict another, they share the weight. The weight matrix acquired as a result of learning the dog, cat, and bagel patterns (Figure 4) reflects these effects. For example, across the set of three prototypes, Units 1 and 5 are perfectly correlated, as are Units 2 and 6. Yet the connection from Unit 2 to Unit 6 is stronger than the connection from Unit 1 to Unit 5 (these connections are \*d in the figure) . The reason for the difference is that Unit 2 is one of only three units which correlate perfectly with Unit 6, while Unit 1 is one of seven units which correlate perfectly with Unit 5.2 + +Thus far we have seen that several prototypes, not necessarily orthogonal, can be stored in the same module without difficulty . It is true, though we do not illustrate it , that the model has more trouble with the cat and dog visual patterns earlier on in training , before learning has essentially reached asymptotic levels, as it has by the end of 50 + +17. A DISTRIBUTED MODEL OF MEMORY 187 + +2 In Figure 4, the weights do not reflect these contrasts perfectly in every case because the noise introduced into the learning happens, by chance, to alter some of the correlations present in the prototype patterns. Averaged over time , though, the weights will + +188 PSYCHOLOGICAL PROCESSES + +Prototypes + ++ + + + + + + + + + - - - - - - - - - - + ++ + + + + + - - - - - - - - + ++ + + + + + + + - - - - + +Weights + ++2\*- 1 - 1+4\* +5- 2- 1 - 3+2- 1 + 2 - 1 + +- 3 - 1 - 3 + 3 + 1 - 5 + +- 1 - 1 - 2 - 1 - 2 - 1 + 3 - 1 - 1 - 1 + 5 - 3 - 1 + ++3 + +- 1 - 1 + 1 - 1 - 1 + ++ 5 - 1 + 2 + 1 - 2 + ++ 1 + 1 - 1 - 1 + 2 + 3 - 1 - 1 + +- 1 + 3 - 3 - 1 - 1 - 1 + 1 - 1 + 3 - 2 - 1 + +- 2+2 + ++ 3 - 1 - 1 - 2 +1 - 1 - 1 - 1 + 2 +3+3 + +> - 3 + 2 - 1 + 3 + 3 + 1 - 1 - 2 - 2 + 1 - 1 + 2 - 1 - 3 - 3 + 1 + 3 - 1 - 1 - 2 + 2 + +- 2 - 1 - 2 + 2 - 1 + 1 + 2 - 3 + 1 + 2 + 1 - 1 - 3 - 1 + 3 + 1 - 3 - 1 + +-- 2 + 1 - 1 - 1 - 3 - 1 + 1 + +- 3 - 1 + 1 - 3 + 1 + 1 + ++ 3 +3 + 1 + +- 1 - 1 - 1 +3 + 1 + 1 + 1 - 3 +2- 1 - 1 - 1 +3 - 2 + 1 + 1 - 1 + 2 - 1 - 1 - 1 - 1 + 2 - 2 + 1 + 1 + 1 - 3 + 3 - 1 + 2 + +- 1 - 1 +2 - 1 - 1 + 1 + +- 1 - 3 - 1 + 1 - 3 + 3 - 1 + 1 - 3 - 1 + 2 - 2 + 2 - 3 + ++2 +1 - 1 - 1 - 2 - 1 +1 +2 +3 + +- 2 + 1 + 1 + 1 - 3 + 2 - 1 - 1 + 2 + 1 + 1 + +- 1 + 3 + 1 - 1 - 1 + ++ 5 - 1 - 1 - 1 + 4 - 1 - 1 - 5 - 1 - 1 + 1 - 2 + 1 + 1 - 3 + 1 - 2 + 2 + 1 - 1 - 3 - 3 - 1 + 1 - 2 - 3 + 1 + 1 - 5 + 2 + 1 + 1 - 5 + 3 - 2 + 1 - 1 + 1 + 1 + 1 - 2 + 1 - 2 + 1 - 3 + ++ 2 - 1 - 1 + 3 - 1 + 2 + 1 + 2 - 2 - 3 + 2 + 1 + ++ 3 - 4 + 1 + 3 - 4 + 1 + 1 - 1 + 1 + 1 + 1 - 5 - 1 - 3 + 1 + 2 + 2 - 1 - 1 - 1 + 2 - 3 + 2 + 2 - 1 - 3 + 1 - 1 + 3 - 2 - 1 - 1 + 5 - 3 - 1 + 3 + 1 - 1 - 1 + 1 - 2 + 3 - 1 FIGURE 4 . Weights acquired in learning the three prototype patterns shown . ( Blanks in the matrix of weights correspond to weights with absolute values less than or equal to + 5 stands for a weight of + . 25 . The gap in the horizontal and vertical dimensions is + +used to separate the name field from the visual pattern field . ) + +cycles through the full set of patterns . And , of course , even at the end of learning , if we present as a probe a part of the visual pattern that does not differentiate between the dog and the cat , the model will pro duce a blended response . Both of these aspects of the model seem gen erally consistent with what we should expect from human subjects . + ++ 1 + +Dog : + - Cat : + + Bagel : + + ++ + ++ + + + +- - + ++ + +- 1 + ++ + + ++ 1 - 1 + ++ 3 - 3 - 1 - 1 - 1 + ++ 3 - 2 + +- 1 + +- 1 + ++3 - 2 + +> - 2 +1 - 1 - 3 +3 +2 +3- 3 + ++ + ++ + +17. A DISTRIBUTED MODEL OF MEMORY + +ticular, repeated exemplars + +189 + +TABLE 2 + ++ + + + +- - - - + + +- - - + ++ 3- 3+ 3+ 3- 3- 4 - 3- 3+ 6+ 5+ 6+ 5+ 3- 2- 3- 2 + ++ + + + + + + + +- - - - - Cat visual pattern: + +Probe: Response: + ++ + +- - + ++ + + + + + + + + +- + +Probe: Response: + +Dog visual pattern: + +Bagel visual pattern: + +RESULTS OF TESTS AFTER LEARNING THE DOG, CAT, AND BAGEL PATTERNS WITHOUT NAMES + +> + + + + + +Probe: + + +Response: + +- + +Category learning without labels . An important further fact about the model is that it can learn several different visual patterns , even without the benefit of distinct identifying name patterns during learn ing . To demonstrate this we repeated the previous simulation , simply replacing the name patterns with Os . The model still learns about the internal structure of the visual patterns so that , after 50 cycles through the stimuli , any unique subpart of anyone of the patterns is sufficient to reinstate the rest of the corresponding pattern correctly . This aspect of the model ' s behavior is illustrated in Table 2 . Thus , we have a model that can , in effect , acquire a number of distinct categories , sim ply through a process of incrementing connection strengths in response to each new stimulus presentation . Noise , in the form of distortions in the patterns , is filtered out . The model does not require a name or other guide to distinguish the patterns belonging to different categories . + +Coexistence of the prototype and repeated exemplars . One aspect of our discussion up to this point may have been slightly misleading . We may have given the impression that the model is simply a prototype extraction device . It is more than this , however ~ it is a device that cap tures whatever structure is present in a set of patterns ( subject ~ of course ~ to the linear predictability constraint ) . When the set of patterns has a prototype structure , the model will act as though it is extracting prototypes ~ but when it has a different structure , the model will do its best to accommodate this as well . For example , the model permits the coexistence of representations of prototypes with representations of par - 190 PSYCHOLOGICAL PROCESSES + +As an illustration of this point , consider the following situation . Let us say that our little boy knows a dog next door named Rover and a dog at his grandma's house named Fido. And let's say that the little boy goes to the park from time to time and sees dogs, each of which + +his father tells him is a dog. + +The simulation analog of this involved three different eight-element name patterns, one for Rover, one for Fido, and one for dog. The visual pattern for Rover was a particular randomly generated distortion of the dog prototype pattern, as was the visual pattern for Fido. For the dogs seen in the park, each one was simply a new random distortion of the prototype. The probability of flipping the sign of each element was again .2. The learning regime was otherwise the same as in the + +dog- cat- bagel example. + +At the end of 50 learning cycles, the model was able to retrieve the visual pattern corresponding to either repeated exemplar (see Table 3) given the associated name as input . When given the dog name pattern as input , it retrieves the prototype visual pattern for dog. It can also retrieve the appropriate name from each of the three visual patterns. This is true, even though the visual pattern for Rover differs from the visual pattern for dog by only a single element. Because of the special importance of this particular element, the weights from this element to the units that distinguish Rover's name pattern from the the prototype name pattern are quite strong. Given part of a visual pattern, the model will complete it~ if the part corresponds to the prototype, then that is what is completed, but if it corresponds to one of the repeated exemplars, then that exemplar is completed. The model, then, knows both the prototype and the repeated exemplars quite well. Several other sets of prototypes and their repeated exemplars could also be stored in the same module, as long as its capacity is not exceeded~ given large numbers of units per module, a lot of different patterns can + +be stored. + +Let us summarize the observations we have made in these several illustrative simulations. First , our distributed model is capable of storing not just one but a number of different patterns. It can pull the ,t central tendency" of a number of different patterns out of the noisy inputs~ it can create the functional equivalent of perceptual categories with or without the benefit of labels~ and it can allow representations of repeated exemplars to coexist with the representation of the prototype of the categories they exemplify in the same composite memory trace. The model is not simply a categorizer or ,t prototyping 't device~ rather, it captures the structure inherent in a set of patterns, whether it be characterizable by description in terms of prototypes or not, as long as the ensemble of patterns adheres to the linear predictability constraint. + +SIMULATIONS OF EXPERIMENTAL RESULTS + +Up to this point , we have discussed our distributed model in general terms and have outlined how it can accommodate both generalization and representation of specific information in the same network . We now consider, in the next two sections, how well the model does in accounting for some recent evidence about the details of the influence of specific experiences on performance and the conditions under which functional equivalents of summary representations such as logogens and + +prototypes emerge. + +Repetition and Familiarity Effects + +When we perceive an item - say a word, for example- this experience has effects on our later performance. If the word is presented again within a reasonable interval of time , the prior presentation makes it possible for us to recognize the word more quickly or from a briefer + +presentation. + +Traditionally , this effect has been interpreted in terms of units that represent the presented items in memory. In the case of word perception , these units are called word detectors or logogens and a model of repetition effects for words has been constructed around the logogen concept (Morton , 1979) . The idea is that the threshold for the logogen is reduced every time it "fires " (that is, every time the word is recognized) , thereby making it easier to fire the logogen at a later time . There is supposed to be a decay of this priming effect, with time , so + +that eventually the effect of the first presentation wears off . + +This traditional interpretation has come under serious question of late, for a number of reasons. Perhaps paramount among the reasons is the fact that the exact relation between the specific context in which the priming event occurs and the context in which the test event occurs makes a huge difference (Jacoby, 1983a, 1983b) . Generally speaking, nearly any change in the stimulus - from spoken to printed , from male speaker to female speaker, etc. - tends to reduce the magnitude of the + +The ability to retrieve accurate completions of similar patterns is a property of the model that depends on the use of the delta learning rule . This allows both the storage of different prototypes that are not orthogonal and the coexistence of prototype representations and + +repeated exemplars. + +These facts might easily be taken to support the enumeration of specific experiences view, in which the logogen is replaced by the entire ensemble of experiences with the word, with each experience capturing aspects of the specific context in which it occurred. Such a view has + +been championed most strongly by Jacoby (1983a, 1983b) . + +Our distributed model offers an alternative interpretation . We see the traces laid down by the processing of each input as contributing to the composite, superimposed memory representation. Each time a stimulus is processed, it gives rise to a slightly different memory trace- either because the item itself is different or because it occurs in a different context that conditions its representation. The logogen is replaced by the set of specific traces, but the traces are not kept separate. Each trace contributes to the composite, but the characteristics of particular experiences tend nevertheless to be preserved, at least until they are overridden by canceling characteristics of other traces. Also, the traces of one stimulus pattern can coexist with the traces of other + +stimuli , within the same composite memory trace. + +It should be noted that we are not faulting either the logogen model or models based on the enumeration of specific experiences for their physiological implausibility here, since these models are generally not stated in physiological terms, and their authors might reasonably argue that nothing in their models precludes distributed storage at a physiological level. What we are suggesting is that a model which proposes explicitly distributed , superpositional storage can account for the kinds of findings that logogen models have been proposed to account for , as well as other findings which strain the utility of the concept of the logo- + +gen as a psychological construct. + +To illustrate the distributed model's account of repetition priming effects, we carried out the following simulation experiment . We made up a set of eight random vectors, each 24 elements long, each one to be thought of as the prototype of a different recurring stimulus pattern. Through a series of 10 training cycles using the set of eight vectors, we constructed a composite memory trace. During training , the model did not actually see the prototypes, however. On each training presentation it saw a new random distortion of one of the eight prototypes. In each of the distortions , each of the 24 elements had its value flipped with a probability of .1. Weights were adjusted after every presentation and were then allowed to decay to a fixed residual before the presentation + +of the next pattern. + +The composite memory trace formed as a result of this experience plays the same role in our model that the set of logogens or detectors play in a model like Morton 's or, indeed, the interactive activation model of word perception. That is, the trace contains information which allows the model to enhance perception of familiar patterns, + +17. A DISTRIBUTED MODEL OF MEMORY193 + +0 .5 + +0 .4 familiar + +unfamiliar + +o .s + +0 .2 + +0 . 1 + +0 .0 + +0 5 10 15 30 35 + +Processing + +194 PSYCHOLOGICAL PROCESSES + +Pattern activation and response strength. The measure of activation shown in the figure is the dot product of the pattern of activation over the units of the module with the stimulus pattern itself , normalized for the number n of elements in the pattern: For the pattern p we call this + +expression ap ' In mathematical notation it is just + +1 ctp = - Laiepi(t ) n i + +where i indexes the units in the module, and epi indexes the external input to unit i in pattern p . Essentially, a represents the degree to which the actual pattern of activation on the units captures the input pattern. It is an approximate analog of the activation of an individual + +unit in models that allocate a single unit to each whole pattern. + +To relate these pattern activations to response probabilities, we must assume that mechanisms exist for translating patterns of activation into + +('l n po + +.rd 'lOp) uoJ'l "9AnOY + +20 25 Cycles + +FIGURE 5. Growth of the pattern of activation for new distortions of familiar and unfamiliar patterns. The measure of the strength of the pattern of activation is the dot product of the response pattern with the input vector. See text for an explanation. + +relative to unfamiliar ones . We demonstrate this by comparing the activations resulting from the processing of subsequent presentations of new distortions of our eight familiar patterns , compared to other random patterns with which the model is not familiar . The pattern of activation that is the model 's response to the input is stronger and grows to a particular level more quickly if the stimulus is a new distor tion of an old pattern than if it is a new pattern . This effect is illus - + +trated in Figure 5. + +17. A DISTRIBUTED MODEL OF MEMORY 195 + +overt responses measurable by an experimenter. We will assume that these mechanisms obey the same principles discussed in Chapter 15 for relating activations to response probabilities, simply replacing the activations of particular units with the a measure of pattern activation.3 These assumptions finesse an important issue, namely, the mechanism by which a pattern of activation gives rise to a particular response. A specific mechanism for response generation is described in Chapter 18. For now, we wish only to capture basic properties any actual response selection mechanism must have: It must be sensitive to the input pattern, and it must approximate other basic aspects of response + +selection behavior captured by the Luce (1963) choice model. + +F; ffects of experimental variables on time -accuracy curves . Apply ing the assumptions described above , we can calculate probability of correct response as a function of processing cycles for familiar and unfamiliar patterns . The result for a particular choice of scaling param eters is shown in Figure 6 . If we assume that performance in a percep tual identification task is based on the height of the curve at the point where processing is cut off by masking ( McClelland & Rumelhart , 1981 ) , then familiarity would lead to greater accuracy of perceptual identification at a given exposure duration . In a reaction time task , if the response is emitted when its probability reaches a particular thresh old activation value , familiarity would lead to speeded responses . Thus , the model is consistent with -the ubiquitous influence of familiarity both on response accuracy and speed , in spite of the fact that it has no detec - + +tors for familiar stimuli . + +But what about priming and the role of congruity between the prime event and the test event ? To examine this issue , we carried out a second experiment . Following learning of eight patterns as in the pre vious experiment , new distortions of half of the random vectors previ ously learned by the model were presented as primes . For each of these primes , the pattern of activation was allowed to stabilize , and changes in the strengths of the connections in the model were then made . We then tested the model ' s response to (a) the same four dis tortions , (b) four new distortions of the same patterns , and (c) distor tions of the four previously learned patterns that had not been + +3 One complication arises due to the fact that it is not, in general, possible to specify exactly what the set of alternative responses might be for the denominator of the Luce choice rule used in the word perception model. For this reason, the strengths of other responses are represented by a constant C (which stands for the competition ). Thus, the expression for probability of choosing the response appropriate to pattern p is just ( ka ka p r p) = (e P)/ (C + e P) ~'here a p represents the ti me average of a p' and k is a scal- + +ing constant. + +196 PSYCHOLOGICAL PROCESSES + +'l e.I.IO~ A 'lIIIQ "9Q O.Id + +FIGURE 6. Simulated growth of response accuracy over the units in a 24-unit module, as a function of processing cycles, for new distortions of previously learned patterns com- + +pared to new distortions of patterns not previously learned. + +presented as primes. There was no decay in the weights over the course of the priming experiment~ if decay had been included, its main effect would have been to reduce the magnitude of the priming effects. The results of the experiment are shown in Figure 7. The response of the model is greatest for the patterns preceded by identical primes, intermediate for patterns preceded by similar primes, and weakest for + +patterns not preceded by any related prime. + +Our model, then, appears to provide an account, not only for the basic existence of priming effects, but also for the graded nature of priming effects as a function of congruity between prime event and test event. It avoids the problem of multiplication of context-specific detectors which logogen theories fall prey to, while at the same time avoiding enumeration of specific experiences. Congruity effects are captured + +in the composite memory trace. + +The model also has another advantage over the logogen view. It accounts for repetition priming effects for unfamiliar as well as familiar stimuli . When a pattern is presented for the first time , a trace is produced just as it would be for stimuli that had previously been presented. The result is that, on a second presentation of the same pattern or a new distortion of it , processing is facilitated. The functional equivalent of a logogen begins to be established from the very first + +1 .0 + +familiar + +0.8 un a. J1JIJJar f ~ - ':1~ + +0 . 6 + +0 .4 + +0 .2 + +0 . 0 + +0 5 10 15 20 25 30 35 Processing Cycles + +1 .0 + +identical I?rime simila .r prime + +0.8 no prIme + +0 .6 + +0 .4 + +0 .2 + +0 .0 + +0 5 10 15 20 25 30 35 40 45 Processing Cycles + +17. A DISTRIBUTED MOEL OF MEMORY 197 + +1~a.I.I J A1JIJq"9qO.ld + +FIGURE 7. Response probability as a function of exposure time , for patterns preceded + +by identical primes, similar primes, or no related prime. + +observed for familiar patterns, we carried out a third experiment. This time , after learning eight patterns as before, a priming session was run, in which new distortions of four of the familiar patterns and distortions of four new patterns were presented. Then, in the test phase, 16 stimuli were presented: New distortions of the primed, familiar patterns~ new distortions of the unprimed , familiar patterns~ new distortions of the primed, previously unfamiliar patterns~ and finally , new distortions of four patterns that were neither primed nor familiar . The results are shown in Figure 8. What we find is that long-term familiar ity and recent priming have approximately additive effects on the asymptotes of the time-accuracy curves. The time to reach any given activation level shows a mild interaction , with priming having slightly + +more of an effect for unfamiliar than for familiar stimuli . + +These results are consistent with the bulk of the findings concerning the effects of pre-experimental familiarity and repetition in a recent series of experiments by Feustel, Shiffrin , and Salasoo (1983) and Salasoo, Shiffrin , and Feustel (1985) . They found that preexperimental familiarity of an item (word vs. nonword) and prior exposure had this very kind of interactive effect on exposure time required for accurate identification of all the letters of a string, at least when words and nonwords were mixed together in the same lists of materials. A further aspect of the results reported by Salasoo, Shiffrin , and Feustel is also consistent with our approach. In one of their experiments, they examined the threshold for accurate identification as a function of number of prior presentations, for both words and + +In the previous section, we cast our distributed model as an alternative to the view that familiar patterns are represented in memory either by separate detectors or by an enumeration of specific experiences. In this section, we show that the model provides alternatives to both abstraction and enumeration models of learning from exemplars of + +17. A DISTRIBUTED MODEL OF MEMORY 199 + +PIoqse + +.r'tIJ, 1 seI + +:J,AJ + +FIGURE 9. Time to reach a fixed accuracy criterion (60% correct) for previously familiar + +and unfamiliar patterns, as a function of repetitions. + +connection strengths are formed for these stimuli during training , and thus the strength of the association between the item and the learning + +context would be less. + +If our interpretation is correct, we would expect to see a disadvantage for pseudowords relative to words if the testing were carried out in a situation which did not reinstate the mental state associated with the original learning experience since for these stimuli much of what was learned would be tied to the specific learning contex~. Such a prediction would appear to differentiate our account from any view that postulated the formation of an abstract, context-independent logogen as + +the basis for the absence of a pseudoword decrement effect. + +Representation of General and Specific Information + +prototype of a set of distorted exemplars than the specific exemplars they experienced during learning (Posner & Keele, 1968) . However, pure abstraction models have never fared very well since there is nearly always evidence of some superiority of the particular training stimuli over other stimuli equally far removed from the prototype. A favored model, then, is one in which there is both abstraction and memory for + +particular training stimuli . + +Recently, proponents of models involving only enumeration of specific experiences have noted that such models can account for the basic fact that abstraction models are primarily designed to account for - enhanced response to the prototype, relative to particular previously seen exemplars, under some conditions - as well as failures to obtain such effects under other conditions (Hintzman , 1983~ Medin & Schaffer, 1978) . In evaluating distributed models, then, it is important to see if they can do as well. J. A. Anderson (1977) has made impor tant steps in this direction , and Knapp and J. A . Anderson (1984) have shown how their distributed model can account for many of the details of the Posner-Keele experiments. Recently, however, two sets of find ings have been put forward that appear to strongly favor the enumeration of specific experiences view, at least relative to pure abstraction models. It is important , therefore, to see how well our distributed + +model can do in accounting for these effects. + +The first set of findings comes from a set of studies by Whittlesea (1983) . In a large number of studies, Whittlesea demonstrated a role for specific exemplars in guiding performance on a perceptual identifi cation task. We wanted to see whether our model would demonstrate a similar sensitivity to specific exemplars. We also wanted to see whether our model would account for the conditions under which such effects + +are not obtained. + +Whittlesea used letter strings as stimuli . The learning experiences subjects received involved simply looking at the stimuli one at a time on a visual display and writing down the sequence of letters presented. Subjects were subsequently tested for the effect of this training on their ability to identify letter strings bearing various relationships to the training stimuli and to the prototypes from which the training stimuli were derived. The test was a perceptual identification task~ the subject was + +simply required to try to identify the letters from a brief flash. + +The stimuli Whittlesea used were all distortions of one of two prototype letter strings. Table 4 illustrates the essential properties of the sets of training and test stimuli he used. The stimuli in Set la were each one step away from the prototype. The Ib items were also one step from the prototype and one step from one of the la distortions . The Set IIa stimuli were each two steps from the prototype and one step from a particular Ia distortion . The Set lIb items were also two steps + +200 PSYCHOLOGICAL PROCESSES + +17. A DISTRIBUTED MODEL OF MEMORY201 + +TABLE 4 + +SCHEMATIC DESCRIPTION OF STIMULUS SETS USED IN SIMULATIONS OF WHITTLESEA ' S EXPERIMENTS + +Prototype la Ib Ila lIb Ilc III V PPPPP APPPP BPPPP ABPPP ACPPP APCPP ABCPP CCCCC + +> PAPPP PBPPP PABPP PACPP PAPCP PABCP CBCBC PPAPP PPBPP PPABP PPACP PPAPC PPABC BCACB PPPAP PPPBP PPPAB PPPAC CPPAP CPPAB AB~ BA PPPPA PPPPB BPPPA CPPPA PCPPA BCPPA CACAC + +Note : The actual stimuli used can be tilled in by replacing P with + - + - ~ A with + + - - ~ B with + - - + ~ and C with + + + + . The model is not sensitive to the fact the same + +subpattern was used in each of the 5 slots . + +from the prototype , and each was one step from one of the IIa distor tions . The Set IIc distortions were two steps from the prototype also , and each was two steps from the closest IIa distortion . Over the set of five IIc distortions , the A and B subpatterns each occurred once in each position , as they did in the case of the IIa distortions . The distortions in Set III were three steps from the prototype and one step from the closest member of Set IIa . The distortions in Set V were each five + +steps from the prototype . + +Whittlesea ran seven experiments using different combinations of training and test stimuli . We carried out simulation analogs of all of these experiments plus one additional experiment that Whittlesea did not run . The main difference between the simulation experiments and Whittlesea ' s actual experiments was that he used two different proto - + +types in each experiment , while we only used one . + +The simulation employed a simple 20 - unit module . The set of 20 units was divided into five submodules , one for each letter in Whittlesea ' s letter strings . The prototype pattern and the different dis tortions used can be derived from the information provided in Table 4 . Each simulation experiment began with null connections between the units . The training phase involved presenting the set or sets of training stimuli analogous to those Whittlesea used , for the same number of presentations . To avoid idiosyncratic effects of particular orders of training stimuli , each experiment was run six times , each with a dif ferent random order of training stimuli . On each trial , activations were allowed to settle down through 50 processing cycles , and then connec tion strengths were adjusted . There was no decay of the increments to + +202 PSYCHOLOGICAL PROCESSES + +Ia + +IIa + +IIa + +IIa + +Ia + +IIa,b,c + +.16 .16 .19 + +III + +.24 .13 .17 + +IIa + +of prior test items on performance , we simply turned off the adjust - + +ment of weights during the test phase . + +A summary of the training and test stimuli used in each of the experiments , of Whittlesea ' s findings , and of the simulation results are shown in Table 5 . The numbers represent relative amounts of enhancement in performance as a result of the training experience , + +TABLES + +SUMMARY OF PERCEPTUAL IDENTIFICATION EXPERIMENTS WITH EXPERIMENTAL AND SIMULATION RESULTS + +Whittlesea ~s Trajning Test Experimental Simulatjon Experiment Stimulus Stimulus Results Results + +Number Set ( s) Sets + +. 15 + +. 21 . 16 . 10 + +> . 19 . 23 . 15 + +> > . 16 . 16 . 10 + +. 29 . 12 - .08 + +> . 29 . 14 . 12 + +. 24 . 21 . 29 . 15 + +. 28 . 24 . 12 + +. 25 . 21 . 18 .09 + +. 14 . 19 . 30 . 29 . 12 . 15 + +3 + +4 + +4 ' + +5 + +6 + +7 + +relative to a pretest baseline. For Whittlesea's data, this is the perletter increase in letter identification probability between a pre- and posttest. For the simulation , it is the increase in the size of the dot product for a pretest with null weights and a posttest after training . For comparability to the data, the dot-product difference scores have been doubled. This is simply a scaling operation to facilitate qualitative com- + +parison of experimental and simulation results. + +A comparison of the experimental and simulation results shows that wherever there is a within -experiment difference in Whittlesea's data, the simulation produced a difference in the same direction . (Betweenexperiment comparisons are not considered because of subject and material differences which render such differences unreliable) . The next several paragraphs review some of the major findings in detail. Some of the comparisons bring out the importance of congruity between particular test and training experiences. Experiments 1, 2, and 3 show that when distance of test stimuli from the prototype is controlled , similarity to particular training exemplars makes a difference both for the human subject and in the model. In Experiment 1, the relevant contrast was between Ia and Ib items. In Experiment 2, it was between IIa and IIc items. Experiment 3 shows that the subjects and the model both show a gradient in performance with increasing distance + +of the test items from the nearest old exemplar. + +Experiments 4, 4', and 5 explore the status of the prototype and other test stimuli closer to the prototype than any stimuli actually shown during training . In Experiment 4, the training stimuli were fairly far away from the prototype, and there were only five different training stimuli (the members of the IIa set) . In this case, controlling for distance from the nearest training stimuli , test stimuli closer to the prototype showed more enhancement than those farther away. (Ia vs. III comparison) . However, the actual training stimuli nevertheless had an advantage over both other sets of test stimuli , including those that were closer to the prototype than the training stimuli themselves (IIa + +vs. Ia comparison) . + +In experiment 4' (not run by Whittlesea) , the same number of training stimuli were used as in Experiment 4, but these were closer to the prototype. The result is that the simulation shows an advantage for the prototype over the old exemplars. The specific training stimuli used, even in this experiment , do influence performance, however, as Whittlesea's first experiment (which used the same training set) shows (Ia-Ib contrast) . This effect holds both for the subjects and for the simulation . The pattern of results is similar to the findings of Posner and Keele (1968) , in the condition where subjects learned six exemplars which were rather close to the prototype. In this condition , their subjects' categorization performance was most accurate for the + +17. A DISTRIBUTED MODEL OF MEMOR Y 203 + +prototype, but more accurate for old than for new distortions , just as in + +this simulation experiment . + +In Experiment 5, Whittlesea demonstrated that a slight advantage for stimuli closer to the prototype than the training stimuli would emerge, even with high-level distortions , when a large number of different distortions were used once each in training , instead of a smaller number of distortions presented three times each. The effect was rather small in Whittlesea's case (falling in the third decimal place in the per-letter enhancement effect measure) but other experiments have produced similar results, and so does the simulation . In fact, since the prototype was tested in the simulation , we were able to demonstrate a monotonic drop in performance with distance from the prototype in this + +experiment . + +Experiments 6 and 7, which used small numbers of training exemplars rather far from the prototype, both explore in different ways the relative influence of similarity to the prototype and similarity to the set of training exemplars. Both in the data and in the model, similarity to particular training stimuli is more important than similarity to the prototype, given the sets of training stimuli used in these experiments. Taken together with other findings , Whittlesea's results show clearly that similarity of test items to particular stored exemplars is of paramount importance in predicting perceptual performance. Other experiments show the relevance of these same factors in other tasks, such as recognition memory, classification learning, etc. It is interesting to note, though, that performance does not honor the specific exemplars so strongly when the training items are closer to the prototype. Under such conditions, performance is superior on the prototype or stimuli closer to the prototype than the training stimuli . Even when the training stimuli are rather distant from the prototype, they produce a benefit for stimuli closer to the prototype if there are a large number of distinct training stimuli each shown only once. Thus, the dominance of specific training experiences is honored only when the training experiences are few and far between. Otherwise, an apparent advantage for the prototype, though with some residual benefit for particular + +training stimuli , is the result. + +The congruity of the results of these simulations with experimental findings underscores the applicability of distributed models to the question of the nature of the representation of general and specific informa tion . In fact, we were somewhat surprised by the ability of the model to account for Whittlesea's results, given the fact that we did not rely on context-sensitive encoding of the letter-string stimuli . That is, the distributed representation we assigned to each letter was independent of the other letters in the string. A context-sensitive encoding would, however, prove necessary to capture a larger ensemble of stimuli . + +204 PSYCHOLOGICAL PROCESSES + +17. A DISTRIBUTED MODEL OF MEMORY 205 + +Whether a context-sensitive encoding would produce the same or slightly different results depends on the exact encoding. The exact degree of overlap of the patterns of activation produced by different distortions of the same prototype determines the extent to which the model will tend to favor the prototype relative to particular old exemplars. The degree of overlap, in turn , depends upon the specific assumptions made about the encoding of the stimuli . However, the general form of the results of the simulation would be unchanged: When all the distortions are close to the prototype, or when there is a very large number of different distortions , the central tendency will produce the strongest response~ but when the distortions are fewer and farther from the prototype, the training exemplars themselves will produce the strongest activations. What the encoding would effect is the + +similarity metric . + +In this regard, it is worth mentioning another finding that may appear to challenge our distributed account of what is learned through repeated experiences with exemplars. This is the finding of Medin and Schwanenflugel (1981) . Their experiment compared learning of two different sets of stimuli in a categorization task. One set of stimuli could be categorized by a linear combination of weights assigned to particular values on each of four dimensions considered independently. The other set of stimuli could not be categorized in this way. The experiment demonstrated clearly that linear separability was not necessary for categorization learning. Linearly separable stimuli were less easily learned than a set of stimuli that were not linearly separable but had a higher degree of similarity between exemplars within + +categories. + +At first glance, it may seem that Medin and Schwanenflugel's experiment is devastating to our distributed approach since our distributed model can only learn linear combinations of weights. However, whether a linear combination of weights can suffice in the Medin and Schwanenflugel experiments depends on how patterns of activation are assigned to stimuli . If each stimulus dimension is encoded separately in the representation of the stimulus , then the Medin and Schwanenflugel stimuli cannot be learned by our model. But if each stimulus dimension is encoded in a context sensitive way, then the patterns of activation associated with the different stimuli become linearly separable . + +agaIn. + +One way of achieving context sensitivity is via separate enumeration of traces. But it is well known that there are other ways as well. Several different kinds of context-sensitive encodings which do not require separate enumeration of traces or the allocation of separate units to individual experiences are considered in Chapter 3 and in + +206 PSYCHOLOGICAL PROCESSES + +It should be noted that the motivation for context-sensitive encoding in the use of distributed representations is captured by, but by no means limited to, the kinds of observations reported in the experiment by Medin and Schwanenflugel. Context-sensitive encoding is required if distributed models are to be able to overcome the linear predictability constraint, and this constraint pervades both computational and psycho- + +logical applications of the idea of distributed representations. + +EXTENSIONS OF THE MODEL + +There are a number of phenomena in the learning and memory literature that lend themselves to accounts in terms of distributed models of memory. Here we will give a brief list. In some cases, the phenomena are addressed in other chapters, and we merely give pointers. In other cases, we have not yet had an opportunity to carry out detailed simulations~ in these cases we describe briefly how we might envision encompassing the phenomena in terms of distributed + +models. + +The Emergence of Semantic Memory From Episodic Traces + +A distributed model leads naturally to the suggestion that semantic memory may be just the residue of the superposition of episodic traces. Consider, for example, representation of a proposition encountered in several different contexts, and assume for the moment that the context and content are represented in separate parts of the same module. Over repeated experience with the same proposition in different contexts, the proposition will remain in the interconnections of the units in the proposition submodule, but the particular associations to particular contexts will wash out. However, material that is only encountered in one particular context will tend to be somewhat contextually bound. So we may not be able to retrieve what we learn in one context when we need it in other situations. Other authors (e.g., J. R. Anderson & Ross, 1980) have recently argued against a separation between episodic and semantic memory, pointing out interactions between traditionally episodic and semantic memory tasks. Such findings are generally con- + +Distributed models also provide a natural way of accounting for spared learning by amnesics- persons who have diminished ability to learn new information after some traumatic event. There are generally two types of spared learning effects observed. First , in domains where amnesics show deficits, they nevertheless show a residual ability to learn gradually from repeated experiences. Indeed, they generally appear to be relatively more spared in their ability to extract what is common about an ensemble of experiences than in their ability to remember the details of individual events. Second, there are some domains in which most amnesics show no deficits at all. These phenomena are taken up from the point of view of a distributed model of learning and memory in Chapter 25. Here, we briefly consider the + +main points of the arguments made in that chapter. + +First, distributed models provide a natural way of explaining why there should be residual ability to learn gradually from repeated experience even within those domains where amnesics are grossly deficient in their memory for specific episodic experiences. For if we simply imagine that the effective size of the increments to the connections is reduced in amnesia, then the general properties of distributed + +17. A DISTRIBUTED MODEL OF MEMORY 207 + +Emergence of Regularities in Behavior and Their Coexistence + +With Exceptions + +Distributed models also influence our thinking about how human behavior might come to exhibit the kind of regularity that often leads linguists to postulate systems of rules. In Chapter 18 we describe a distributed model of a system that can learn the past-tense system of English, given as inputs pairs of patterns corresponding to the phonological structure of the present and past tense forms of actual English verbs. The model accounts for several interesting phenomena which have been taken as evidence for the acquisition of " linguistic rules," such as the fact that children at a certain stage overregularize the pronunciation of irregular forms . It also accounts for the coexistence of irregular pronunciations with productive use of the regular past tense in + +the mature language user. + +In general, then, distributed models appear to provide alternatives to a variety of models that postulate abstract, summary representations such as prototypes, logogens, semantic memory representations, or + +even linguistic rules. + +Spared Learning in Amnesia + +208 PSYCHOLOGICAL PROCESSES + +Interference and Fan Effects + +models - the fact that they extract the central tendency from a set of similar experiences and build up a trace of the prototype from a series of repeated exemplars - automatically provide an account of the gradual accumulation of reoeated information in the face of a profound deficit in remembering any specific episode in which the information was presented . Indeed , in some cases reduced increments in the sizes of connections can actually be an advantage for pulling out the central ten dency of a set of experiences since reduction in the size of the incre ments means that the idiosyncratic properties of recent experiences will + +not unduly dominate the composite memory trace . + +The fact that large changes in connection strengths are not univer sally beneficial in distributed models may also provide a basis for explaining why certain aspects of learning and memory are completely unaffected in amnesia . The domains in which learning is almost com pletely spared are just the ones in which learning is very gradual in nor mals and is independent of awareness of having learned . These kinds of learning , we suggest , are acquired gradually by normals because large changes in the strengths of connections do not facilitate learning in + +such cases . + +Memory Blends + +Loftus ( 1977 ) has observed that subjects often combine information from two episodes when they attempt to describe some aspect of just one of these events . Many observations of this kind of effect have been observed in the context of legal testimony , but Loftus has now begun to explore the same effects in more basic experimental para digms . The general result is that subjects do not simply report the correct property from one or the other memory trace ~ rather , they report a property that results from averaging or blending the properties of the individual traces . In one study , for example , many subjects reported that the color of a vehicle was green . However , no subject had actually seen a green truck ~ instead , they had seen a yellow truck in the original scene and a blue one in a distorted version of it . Such blend errors , obviously , are the beginnings of the formation of a sum - + +mary representation and fall naturally out of distributed models . + +17. A DISTRIBUTED MOEL OF MEMORY 209 + +interfere with each other was a central topic in memory research for years ( see Crowder , 1976 , for a review ) . Recently , this sort of interfer ence effect has been explored by John Anderson , under the name of the fan effect ( see J . R . Anderson , 1983 , for a review ) . The fan effect refers to the fact that reaction times to indicate recognition of proposi tions goes up with the number of propositions studied that share argu ments with the proposition under test . For example , The boy kissed the girl is harder to recognize if the subject has studied other sentences + +involving the boy or the girl than if he has not . + +Distributed models like the one we have described here exhibit interference of just this kind . Singley ( personal communication , 1985 ) has in fact simulated a simple fan - effect experiment . He trained a module of 48 units on " propositions " consisting of four parts . The parts correspond to a subject , a verb , an object , and a fourth part that served as a conjunctive representation of the three other constituents ( following Hinton , 1981a ) . Some of the propositions shared arguments ( subpatterns ) with others . After several exposures to the set of pat terns , Singley tested the module ' s response to each of the learned pat terns and found that the response was generally weaker and took longer to reach a strength criterion for those patterns which shared arguments with other patterns . Obviously there is a lot more to fan effects than this ~ how well distributed models will be able to do in accounting for the details of the fan effect literature and other aspects of interference + +is a matter for further research . + +AU GM ENTIN G THE MODEL WITH HIDDEN UNITS + +For all its successes , it must be said that our model does suffer from the fact that it can only learn to respond appropriately to sets of pat terns that obey the linear predictability constraint . While this constraint can be overcome in specific cases by providing a conjunctive coding capable of serving as a basis for learning any prespecified set of pat terns , it cannot be overcome , in general , without great cost in terms of units to cover the space of possibly necessary conjunctive representa tions . To overcome this limitation , it is necessary to have a model that can create the right conjunctive representation to solve the problems it faces in a way that is efficient in terms of units and connections . Both the Boltzmann learning rule ( Chapter 7 ) and the generalized delta rule ( Chapter 8 ) provide ways of constructing just the required set of representations . Here we briefly sketch the application of the gen eralized delta rule to the case of an auto - associator with hidden units . The basic idea is simple . A module consists of a large network of units . Some units are designated as input / output or simply input units + +210 PSYCHOLOGICAL PROCESSES + +and the remaining are designated as hidden units. As in the case without hidden units, the goal of the system is to have the net input from internal sources impinging on a particular input / output unit equal the external input to that unit . In this case, however, input from the hidden units is added as part of the total input from internal sources. The basic difference between a hidden unit and an input / output unit is that hidden units receive no inputs from outside the module, nor do they send outputs outside of the module. Rather, they receive inputs from other hidden units or from the input / output units. The generalized delta rule allows the system to develop a set of connections to and among the hidden units which, in principle, allows the system to retrieve the correct input pattern from any unique subportion of the + +input pattern- provided there are enough hidden units. + +The 'I classical II example of a set of vectors for which hidden units are required is due to Hinton (1981a) . This is the one- same- one problem. Suppose that the input vectors are divided into three portions. The first portion represents a number (either one or zero) ~ the second portion represents a relation (either same or different ) ~ and the final portion represents a number (again either one or zero) . Further , suppose that we want to store four vectors in the system representing the four propositions, one- same- one, one- different- zero, zero- same- zero, and zero- different- one. Now, we probe the system with two of the three sections of a stored input vector and hope that the memory system reconstructs the missing portion . For example, we present the system with one- same- ? or zero- ?- one and see what values get filled in for the + +unspecified portion of the vector. + +For this example, learning done with the standard delta rule will not succeed. These vectors violate the linear predictability constraint. For example, suppose we present the system with one- same- ? In this case, the pattern associated with one in the first position are as often associated with zero in the third position as they are with one in that position. Thus, this pattern will try to establish a blend of zero and one in the unspecified portion of the input vector. Similarly , the pattern representing same in the middle portion are as often associated with the zero as with one in both other slots. Each portion will singly try to produce a blend of the two possibilities in the missing portion and both together will simply produce the same blend. The same argument can be made for each slot. However, with hidden units , the problem can be solved. A given hidden unit can relate bits from two or more slots together, and in that way it can fill in the appropriate pattern when it is + +missing from the input . + +We have tested a network on a very simple version of this problem, using the generalized delta rule (Chapter 8) to learn the appropriate weights to and from the hidden units. In this case there were only + +17. A DISTRIBUTED MODEL OF MEMORY 211 + +three input / output units, one for each of the three components of the one- some- one propositions. The number one and the predicate same were represented by 1 s in the appropriate positions, and the number zero and the predicate different were represented by Os in the appropriate positions. Thus, the proposition one- same- one was represented by the input pattern 111 and the proposition zero- different- one was represented by pattern 001. The other two propositions were analo- + +gously represented as 010 and 100. + +The basic auto-associative memory paradigm was modified slightly from the ones presented earlier in this chapter to accommodate the requirements of hidden units. Most of the modifications are not substantive, but were made to accommodate the technical requirements of the generalized delta rule. In particular, a logistic sigmoid "squashing" function was substituted for the one described in Equations 1 and 2. This was done because our original squashing function was not dif ferentiable as required by the generalized delta rule (see Chapter 8 for details) . This is a minor difference and has little effect on the performance of the system. Similarly , output values of units were allowed to range between [0,1] rather than [- 1,1] . This change again is minor . It essentially involves a scale change and the addition of a bias or threshold term (again, see Chapter 8 for details) . In this case 0.5 is the resting level rather than 0.0. One other somewhat more significant change of paradigm was also required. In the standard auto-associator we did not allow units to connect to themselves. The technical reason for this is that they can "learn" the input (i.e., they can make the internal input equal to the external input) simply by learning to "predict" themselves. However, this does not facilitate reconstruction of the whole pattern from a part. If the strongest connections are from a unit to itself , when that unit is not present in the probe pattern, the missing element will not be well predicted. We wished to impose the same restriction to the model with hidden units, but in this case the restriction becomes harder to enforce. That is, the system can learn to get around a constraint on direct connections by using hidden units to I'shadow" each of the input units. When a particular input unit is turned on, it turns on its "shadow" hidden unit which in turn feeds activation back to the input unit . Thus we again have a unit predicting itself . Since we are most interested in the case of pattern completion , we want to avoid this situation. One way to avoid this is to require that the input from all units except the unit in question match the external input . To accomplish this, we used the following procedure: For each pattern to be learned, for example, 111, we actually trained the module to associate + +212 PSYCHOLOGICAL PROCESSES + +or to any hidden unit . Hidden units were allowed to connect to any input unit and any hidden unit - including themselves. The model was repeatedly presented with each of the three training inputs of each of the four patterns as indicated above, and the network was allowed to learn until it became stable and correctly filled in the missing parts of the patterns. The system was taught to fill in the missing portion of the pattern in three cycles and then to hold this completed pattern. Table 6 shows the state achieved by the three hidden units for each of the four input patterns. We see a distributed pattern over the hidden units in which the first unit signals that the predicate was either dif ferent or the proposition was one- same- one. The second hidden unit indicates that the predicate was either same or the proposition was onedifferent- zero, and the final hidden unit indicates that the predicate was either different or the proposition was one- same- one. This provides a unique~ linearly independent basis from which to reconstruct the + +required input patterns. + +The final network is shown in Figure 10 and the weight matrix is shown in Table 7. A number of interesting features of the network should be observed. First, since none of the input units can predict any other of the input units, the potential connections among input units have all gone to zero. Second, the hidden units all connect positively to themselves and negatively to each other. This allows a unit once turned on to stay on and shut down any noise feeding into those units that were not turned on. Finally , the connections between the input units and the hidden units are roughly symmetric. That is, whenever a particular hidden unit is turned on by a given input unit ~ that hidden unit tries, in turn , to turn on that input unit . It is interesting that this general kind of architecture in which units are connected roughly symmetrically and in which there are pools of mutually inhibitory units which evolved following the presentation of these very difficult patterns is very much like the architecture we have assumed in a number of our + +TABLE 6 + +Hidden Unit + +one - sa me - one one - different - zero zero - same - zero zero - different - one + +Propositions Input + +Patterns Patterns + +11111-- - + +HIDDEN UNIT REPRESENTATIONS FOR THE ONE-SA ME-ONE PROBLEM + +17. A DISTRIBUTED MOEL OF MEMORY 213 + +INPUT + +INPUT ~ . ; + +/ \ / \ I / \ I I \ I , / \ / ' \ / " - / " / ' - ........ + +........ """ ...... - - .- hidden units - + +t INPUT + +FIGURE 10. The network used in solving the one- same- one problem. See text for + +models, including the interactive activation model of word perception + +and the models described in Chapters 15 and 16. + +Finally , before leaving this section, it should be noted that the hidden-units version of an auto-associator will behave very much like the system we have described throughout this chapter if the situation does not require hidden units. In this case, the connections among the + +TABLE 7 + +WEIGHTS ACQUIRED IN LEARNING THE ONE-SAME-ONE PROBLEM + +FROM Input Units Hidden Units + +Input Units + +TO + +explanation. + +0 0 0 -6 4 4 0 0 0 4 4 -6 0 0 0 4 -6 4 + +- 5 6 6 6 -3 - 3 6 6 - 5 - 3 6 - 3 6 - 5 6 -3 -3 6 214 PSYCHOLOGICAL PROCESSES + +input units can capture the structure of the problem, and the connections to and from the hidden units will tend not to play an important role. This is because direct connections are learned more quickly than those which propagate information through hidden units. These will lag behind, and if they are not required, their strength will stay relatively + +small. + +It should also be emphasized that the use of hidden units overcomes a problem that our present model shares with enumeration models: the problem of having a fixed set of representational primitives . Hidden units really are new representational primitives that grow and develop to meet the representational needs of the particular set of patterns that have been encountered. They allow the model to change its representation and thereby to change the pattern of similarity among the input patterns. We have only begun our exploration of the generalized delta rule and its application to the case of the auto-associator. We are very optimistic that it can serve as a mechanism for building the kinds of internal representations required by allowing distributed memories the + +flexibility of adapting to arbitrary sets of stimulus patterns. + +CONCLUSION + +In this chapter, we have argued that a distributed model of memory provides a natural way of accounting for the fact that memory appears to extract the central tendencies of a set of experiences and for the fact that memory is sensitive to the details of specific events and experiences. We have seen how a simple distributed model, using the delta rule, provides a fairly direct and homogeneous account for a large body of evidence relevant to the representation of general and specific infor mation. The delta rule - and now the generalized delta rule- provide very simple mechanisms for extracting regularities from an ensemble of inputs without the aid of sophisticated generalization or ruleformulating mechanisms that oversee the performance of the processing system. These learning rules are completely local, in the sense that they change the connection between one unit and another on the basis of information that is locally available to the connection rather than on the basis of global information about overall performance. The model thus stands as an alternative to the view that learning in cognitive systems involves the explicit formulation of rules and abstractions under the guidance of some explicit overseer. We do not wish to suggest that explicit rule formation has no place in a cognitive theory of learning and memory~ we only wish to suggest that such mechanisms need not + +17. A DISTRIBUTED MODEL OF MEMORY 215 + +be invoked whenever behavior is observed that appears to be describ - + +able by some generalization or rule . + +We emphasize that the basic properties of distributed models are largely independent of specific detailed assumptions about implementa tion , such as the dynamic range of the units involved or the exact form of the activation update rule . This points are underscored by the models considered in Chapters 18 and 19 , in which some of the same general properties arise from models making use of somewhat different + +detailed assumptions . + +ACKNOWLEDGMENTS + +The work reported was supported in part by a grant from the System Development Foundation , in part by a contract from the Office of Naval Research ( NOOO14 - 79 - C - O323 , NR667 - 437 ) , and in part by a NIMH Career Development Award ( MHOO385 ) to the first author . Many of the ideas described here were developed and elaborated in the context of a conference organized by Lee Brooks and Larry Jacoby entitled " The Priority of the Specific , " June , 1983 , Elora , Ontario . The chapter owes a great deal to this conference and to stimulating discus - + +sions with the organizers and participants . + +CHAPTER 18 + +- + +Past Tenses of English Verbs + +On Learning the + +D. E. RUMELHART and J. L. McCLELLAND + +THE ISSUE + +Scholars of language and psycholinguistics have been among the first to stress the importance of rules in describing human behavior . The reason for this is obvious . Many aspects of language can be character ized by rules , and the speakers of natural languages speak the language correctly . Therefore , systems of rules are useful in characterizing what they will and will not say. Though we all make mistakes when we speak , we have a pretty good ear for what is right and what is wrong and our judgments of correctness - or grammaticality - are generally + +even easier to characterize by rules than actual utterances . + +On the evidence that what we will and won 't say and what we will and won 't accept can be characterized by rules , it has been argued that , in some sense, we " know " the rules of our language . The sense in which we know them is not the same as the sense in which we know such " rules " as "i before e except after c ," however , since we need not necessarily be able to state the rules explicitly . We know them in a way that allows us to use them to make judgments of grammaticality , it is often said, or to speak and understand , but this knowledge is not in a form or location that permits it to be encoded into a communicable ver bal statement . Because of this , this knowledge is said to be implicit . + +18. LEARNING THE PAST TENSE 217 + +So far there is considerable agreement . However , the exact charac terization of implicit knowledge is a matter of great controversy . One view , which is perhaps extreme but is nevertheless quite clear , holds that the rules of language are stored in explicit form as propositions , and are used by language production , comprehension , and judgment mechanisms . These propositions cannot be described verbally only because they are sequestered in a specialized subsystem which is used in language processing , or because they are written in a special code that only the language processing system can understand . This view we + +will call the explicit inaccessible rule view . + +On the explicit inaccessible rule view , language acquisition is thought of as the process of inducing rules . The language mechanisms are thought to include a subsystem - often called the language acquisition device ( LAD ) - whose business it is to discover the rules . A consider able amount of effort has been expended on the attempt to describe how the LAD might operate , and there are a number of different pro posals which have been laid out . Generally , though , they share three + +assumptions : + +. The mechanism hypothesizes explicit inaccessible rules . + +. Hypotheses are rejected and replaced as they prove inadequate + +to account for the utterances the learner hears . + +. The LAD is presumed to have innate knowledge of the possible + +range of human languages and , therefore , is presumed to con sider only hypotheses within the constraints imposed by a set of + +linguistic universals . + +The recent book by Pinker ( 1984 ) contains a state - of - the - art example + +of a model based on this approach . + +We propose an alternative to explicit inaccessible rules . We suggest that lawful behavior and judgments may be produced by a mechanism in which there is no explicit representation of the rule . Instead , we suggest that the mechanisms that process language and make judgments of grammaticality are constructed in such a way that their performance is characterizable by rules , but that the rules themselves are not written in explicit form anywhere in the mechanism . An illustration of this view , which we owe to Bates ( 1979 ) , is provided by the honeycomb . The regular structure of the honeycomb arises from the interaction of forces that wax balls exert on each other when compressed . The honeycomb can be described by a rule , but the mechanism which pro - + +218 PSYCHOLOGICAL PROCESSES + +1981, 1982) , we noted that lawful behavior emerged from the interactions of a set of word and letter units. Each word unit stood for a particular word and had connections to units for the letters of the word. There were no separate units for common letter clusters and no explicit provision for dealing differently with orthographically regular letter sequences- strings that accorded with the rules of English- as opposed to irregular sequences. Yet the model did behave differently with orthographically regular nonwords than it behaved with words. In fact, the model simulated rather closely a number of results in the word perception literature relating to the finding that subjects perceive letters in orthographically regular letter strings more accurately than they perceive letters in irregular, random letter strings. Thus, the behavior of + +the model was lawful even though it contained no explicit rules. + +It should be said that the pattern of perceptual facilitation shown by the model did not correspond exactly to any system of orthographic rules that we know of. The model produced as much facilitation , for example, for special nonwords like SLNT , which are clearly irregular, as it did for matched regular nonwords like SLET. Thus, it is not correct to say that the model exactly mimicked the behavior we would expect to emerge from a system which makes use of explicit orthographic rules. However, neither do human subjects. Just like the model, they showed equal facilitation for vowelless strings like SLNT as for regular nonwords like SLET. Thus, human perceptual performance seems, in this case at least, to be characterized only approximately by rules. + +Some people have been tempted to argue that the behavior of the model shows that we can do without linguistic rules. We prefer, however, to put the matter in a slightly different light . There is no denying that rules still provide a fairly close characterization of the performance of our subjects. And we have no doubt that rules are even more useful in characterizations of sentence production , comprehension, and grammaticality judgments. We would only suggest that parallel distributed processing models may provide a mechanism sufficient to capture lawful behavior, without requiring the postulation of explicit but inaccessible rules. Put succinctly, our claim is that POP models provide an alternative to the explicit but inaccessible rules account of implicit + +knowledge of rules. + +We can anticipate two kinds of arguments against this kind of claim. The first kind would claim that although certain types of rule-guided behavior might emerge from PDP models, the models simply lack the computational power needed to carry out certain types of operations which can be easily handled by a system using explicit rules. We believe that this argument is simply mistaken. We discuss the issue of computational power of POP models in Chapter 4. Some applications of POP models to sentence processing are described in Chapter 19. + +18. LEARNING THE PAST TENSE 219 + +. The child can now generate a past tense for an invented word. For example, Berko (1958) has shown that if children can be convinced to use rick to describe an action, they will tend to say ricked when the occasion arises to use the word in the past + +The second kind of argument would be that the details of language behavior , and , indeed , the details of the language acquisition process , would provide unequivocal evidence in favor of a system of explicit + +rules . + +It is this latter kind of argument we wish to address in the present chapter . We have selected a phenomenon that is often thought of as demonstrating the acquisition of a linguistic rule . And we have developed a parallel distributed processing model that learns in a natural way to behave in accordance with the rule , mimicking the gen - + +eral trends seen in the acquisition data . + +THE PHENOMENON + +The phenomenon we wish to account for is actually a sequence of three stages in the acquisition of the use of past tense by children learn ing English as their native tongue . Descriptions of development of the use of the past tense may be found in Brown ( 1973 ) , Ervin ( 1964 ) , and + +Kuczaj ( 1977 ) . + +In Stage 1 , children use only a small number of verbs in the past tense . Such verbs tend to be very high - frequency words , and the majority of these are irregular . At this stage , children tend to get the past tenses of these words correct if they use the past tense at all . For example , a child ' s lexicon of past - tense words at this stage might con sist of came , got , gave , looked , needed , took , and went . Of these seven verbs , only two are regular - the other five are generally idiosyncratic + +examples of irregular verbs . In this stage , there is no evidence of the use of the rule - it appears that children simply know a small number of + +separate items . + +In Stage 2 , evidence of implicit knowledge of a linguistic rule emerges . At this stage , children use a much larger number of verbs in the past tense . These verbs include a few more irregular items , but it turns out that the majority of the words at this stage are examples of the regular past tense in English . Some examples are wiped and pulled . The evidence that the Stage 2 child actually has a linguistic rule comes not from the mere fact that he or she knows a number of regu - + +lar forms . There are two additional and crucial facts : + +220 PSYCHOLOGICAL PROCESSES + +. Children now incorrectly supply regular past-tense endings for words which they used correctly in Stage 1. These errors may involve either adding ed to the root as in corned I kA md/ , or adding ed to the irregular past tense form as in camed / kAmd/ l + +(Ervin , 1964~ Kuczaj, 1977) . + +Such findings have been taken as fairly strong support for the assertion that the child at this stage has acquired the past-tense "rule." To + +quote Berko (1958) : + +If a child knows that the plural of witch is witches, he may simply have memorized the plural form . If , however, he tells us that the plural of gutch is gulches, we have evidence that he actually knows, albeit unconsciously, one of those rules which the descriptive linguist , too, would set forth in his grammar. + +(p. 151) + +In Stage 3, the regular and irregular forms coexist. That is, children have regained the use of the correct irregular forms of the past tense, while they continue to apply the regular form to new words they learn. Regularizations persist into adulthood- in fact, there is a class of words for which either a regular or an irregular version are both considered acceptable- but for the commonest irregulars such as those the child acquired first , they tend to be rather rare. At this stage there are some clusters of exceptions to the basic, regular past-tense pattern of English. Each cluster includes a number of words that undergo identical changes from the present to the past tense. For example, there is a inglang cluster, an ing I ung cluster, an eet I it cluster, etc. There is also a group of words ending in Idl or It I for which the present and past are + +iden tical. + +Table 1 summarizes the major characteristics of the three stages. + +Variability and Gradualness + +The characterization of past-tense acquisition as a sequence of three stages is somewhat misleading. It may suggest that the stages are clearly demarcated and that performance in each stage is sharply dis- + +tinguished from performance in other stages. + +1 The notation of phonemes used in this chapter is somewhat nonstandard. It is derived from the computer-readable dictionary containing phonetic transcriptions ofthe + +18. LEARNING THE PAST TENSE 221 + +Correct Regularized Correct Regularized Regularized + +- + +- + +In fact, the acquisition process is quite gradual. Little detailed data exists on the transition from Stage 1 to Stage 2, but the transition from Stage 2 to Stage 3 is quite protracted and extends over several years (Kuczaj, 1977) . Further , performance in Stage 2 is extremely variable. Correct use of irregular forms is never completely absent, and the same child may be observed to use the correct past of an irregular, the base+ ed form , and the past+ ed form , within the same conversation. + +Other Facts About Past-Tense Acquisition + +Beyond these points, there is now considerable data on the detailed types of errors children make throughout the acquisition process, both from Kuczaj (1977) and more recently from Bybee and Slobin (1982) . We will consider aspects of these findings in more detail below. For now, we mention one intriguing fact: According to Kuczaj (1977) , there is an interesting difference in the errors children make to irregular verbs at different points in Stage 2. Early on, regularizations are typically of the base+ ed form , like goed~ later on, there is a large + +increase in the frequency of past + ed errors, such as wented. + +THE MODEL + +The goal of our simulation of the acquisition of past tense was to simulate the three-stage performance summarized in Table 1, and to see whether we could capture other aspects of acquisition. In particular, we wanted to show that the kind of gradual change characteristic of normal acquisition was also a characteristic of our distributed model, and we wanted to see whether the model would capture detailed aspects + +Verb Type Stage 1 Stage 2 Stage 3 + +Early Verbs Regular Other Irregular Novel + +Correct Correct Correct or Regularized Regularized + +TABLE 1 + +CHARACTERISTICS OF THE THREE STAGES OF PAST TENSE ACQUISITION + +form , and (b) a decoding network that converts a featural representation of the past-tense form into a phonological representation. All learning occurs in the pattern associator~ the decoding network is simply a mechanism for converting a featural representation which may be a near miss to any phonological pattern into a legitimate phonological representation. Our primary focus here is on the pattern associator. + +We discuss the details of the decoding network in the Appendix . + +18. LEARNING THE PAST TENSE 223 + +Units. The pattern associator contains two pools of units. One pool, called the input pool, is used to represent the input pattern corresponding to the root form of the verb to be learned. The other pool, called the output pool, is used to represent the output pattern generated by the model as its current guess as to the past tense corresponding to the + +root form represented in the inputs. + +Each unit stands for a particular feature of the input or output string. The particular features we used are important to the behavior of the + +model, so they are described in a separate section below. + +Connections. The pattern associator contains a modifiable connection linking each input unit to each output unit . Initially , these connections are all set to 0 so that there is no influence of the input units on the output units. Learning, as in other PDP models described in this book, involves modification of the strengths of these interconnections, + +as described below. + +Operation of the Model + +On test trials, the simulation is given a phoneme string corresponding to the root of a word. It then performs the following actions. First , it encodes the root string as a pattern of activation over the input units. The encoding scheme used is described below. Node activations are discrete in this model, so the activation values of all the units that should be on to represent this word are set to 1, and all the others are set to O. Then, for each output unit , the model computes the net input to it from all of the weighted connections from the input units. The net input is simply the sum over all input units of the input unit activation times the corresponding weight. Thus, algebraically, the net input + +to output unit i is + +net. = :La}. Wi} I .} + +1 . 0 + +0 . 5 + +- 4 - 3 - 2 - 1 0 1 2 3 4 5 (net; - 9; IT) + +224 PSYCHOLOGICAL PROCESSES + +Each unit has a threshold, (J, which is adjusted by the learning procedure that we will describe in a moment. The probability that the unit is turned on depends on the amount the net input exceeds the threshold. The logistic probability function is used here as in the Boltzmann machine (Chapter 7) and in harmony theory (Chapter 6) to determine whether the unit should be turned on. The probability is given by 1 + +p (a; = 1) = - (net l +e I. - (Jj)/ T (1) + +where T represents the temperature of the system. The logistic function is shown in Figure 2. The use of this probabilistic response rule allows the system to produce different responses on different occasions with the same network . It also causes the system to learn more slowly so the effect of regular verbs on the irregulars continues over a much longer period of time . As discussed in Chapter 2, the temperature, T , can be manipulated so that at very high temperatures the response of the units is highly variable~ with lower values of T , the units behave + +more like linear threshold units. + +Since the pattern associator built into the model is a one-layer net with no feedback connections and no connections from one input unit to another or from one output unit to another, iterative computation is of no benefit . Therefore , the processing of an input pattern is a simple matter of first calculating the net input to each output unit and then + +> 0.0 - 5 + +FIGURE 2. The logistic function used to calculate probability of activation. The x-axis shows val ues of (nefi - H i/ T), and the y-axis indicates the corresponding probability that + +setting its activation probabilistically on the basis of the logistic equation given above. The temperature T only enters in setting the variability of the output units~ a fixed value of T was used throughout the + +simulations. + +To determine how well the model did at producing the correct output, we simply compare the pattern of output Wickelphone activations to the pattern that the correct response would have generated. To do this, we first translate the correct response into a target pattern of activation for the output units, based on the same encoding scheme used for the input units. We then compare the obtained pattern with the target pattern on a unit -by-unit basis. If the output perfectly reproduces the target, then there should be a 1 in the output pattern wherever there is a 1 in the target. Such cases are called hits, following the conventions of signal detection theory (Green & Swets, 1966) . There should also be a 0 in the output whenever there is a 0 in the target. Such cases are called correct rejections. Cases in which there are Is in the output but not in the target are called false a/arms, and cases in which there are Os in the output that should be present in the input are called misses. A variety of measures of performance can be computed. We can measure the percentage of output units that match the correct past tense, or we can compare the output to the pattern for any other response alternative we might care to evaluate. This allows us to look at the output of the system independently of the decoding network. We can also employ the decoding network and have the system synthesize a phonological string. We can measure the performance of the system either at the f eatural level or at the level of strings of phonemes. We shall employ both of these mechanisms in the evalua- + +tion of different aspects of the overall model. + +On a learning trial , the model is presented with both the root form of the verb and the target. As on a test trial , the pattern associator network computes the output it would generate from the input . Then, for each output unit , the model compares its answer with the target. Connection strengths are adjusted using the classic perceptron convergence procedure (Rosenblatt, 1962) . The perceptron convergence procedure is simply a discrete variant of the delta rule presented in Chapter 2 and discussed in many places in this book. The exact procedure is as f 01 lows: We can think of the target as supplying a teaching input to each output unit , telling it what value it ought to have. When the actual output matches the target output , the model is doing the right thing + +18. LEARNING THE PAST TENSE 225 + +Learning + +226 PSYCHOLOGICAL PROCESSES + +and so none of the weights on the lines coming into the unit are adjusted. When the computed output is 0 and the target says it should be 1, we want to increase the probability that the unit will be active the next time the same input pattern is presented. To do this, we increase the weights from all of the input units that are active by a small amount 1] . At the same time , the threshold is also reduced by 1] . When the computed output is 1 and the target says it should be 0, we want to decrease the probability that the unit will be active the next time the same input pattern is presented. To do this, the weights from all of the input units that are active are reduced by 1] , and the threshold is increased by 1] . In all of our simulations, the value of 11 is simply set to 1. Thus, each change in a weight is a unit change, either up or down. For nonstochastic units, it is well known that the perceptron con vergence procedure will find a set of weights that will allow the model to get each output unit correct, provided that such a set of weights exists. For the stochastic case, it is possible for the learning procedure to find a set of weights that will make the probability of error as low as desired. Such a set of weights exists if a set of weights exists + +that will always get the right answer for nonstochastic units. + +Learning Regular and Exceptional Patterns in a + +In this section, we present an illustration of the behavior of a simple pattern associator model. The model is a scaled-down version of the main simulation described in the next section. We describe the scaleddown version first because in this model it is possible to actually examine the matrix of connection weights, and from this to see clearly how the model works and why it produces the basic three-stage learning phenomenon characteristic of acquisition of the past tense. Various aspects of pattern associator networks are described in a number of places in this book (Chapters 1, 2, 8, 9, 11, and 12, in particular) and elsewhere (J. A . Anderson, 1973, 1977~ J. A . Anderson, Silverstein, Ritz , & Jones, 1977~ Kohonen , 1977, 1984) . Here we focus our attention on their application to the representation of rules for mapping one + +set of patterns into another. + +For the illustration model, we use a simple network of eight input and eight output units and a set of connections from each input unit to each output unit . The network is illustrated in Figure 3. The network is shown with a set of connections sufficient for associating the pattern of activation illustrated on the input units with the pattern of activation illustrated on the output units. (Active units are darkened~ positive + +Pattern Associator + +18. LEARNING THE PAST TENSE 227 + ++15 - 15 +15 - 15 - 15 +15 - 15 - 15 +15 - 15 +15 - 15 - 15 +15 - 15 - 15 + ++15 - 15 +15 - 15 - 15 +15 - 15 - 15 + +FIGURE 3. Simple network used in illustrating basic properties of pattern associator networks~ excitatory and inhibitory connections needed to allow the active input pattern to produce the illustrated output pattern are indicated with + and - . Next to the network , the matrix of weights indicating the strengths of the connections from each input unit to each output unit . Input units are indexed by the column they appear in~ output units are + +indexed by row. + +and negative connections are indicated by numbers written on each connection ) . Next to the network is the matrix of connections abstracted from the actual network itself , with numerical values assigned to the positive and negative connections . Note that each weight is located in the matrix at the point where it occurred in the actual network diagram . Thus , the entry in the ith row of the jth column indicates the connection Wij from the j th input unit to the i th + +output unit . + +Using this diagram , it is easy to compute the net inputs that will arise on the output units when an input pattern is presented . For each out put unit , one simply scans across its rows and adds up all the weights found in columns associated with active input units . (This is exactly what the simulation program does !) The reader can verify that when the input pattern illustrated in the left -hand panel is presented , each output unit that should be on in the output pattern receives a net input of + 45 ~ each output unit that should be off receives a net input of - 45 . 2 Plugging these values into Equation 1, using a temperature + +2 In the examples we will be considering in this section, the thresholds of the units are fixed at O. Threshold terms add an extra degree of freedom for each output unit and allow the unit to come on in the absence of input , but they are otherwise inessential to the operation of the model. Computationally , they are equivalent to an adjustable weight + +~ + +iTllIIII + +228 PSYCHOLOGICAL PROCESSES + +of 15 ,3 we can compute that each output unit will take on the correct value about 95 % of the time . The reader can check this in Figure 2~ when the net input is + 45 , the exponent in the denominator of the logistic function is 3 , and when the net input is - 45 , the exponent is - 3 . These correspond to activation probabilities of about .95 and + +.05 , respectively . + +One of the basic properties of the pattern associator is that it can store the connections appropriate for mapping a number of different input patterns to a number of different output patterns . The perceptron convergence procedure can accommodate a number of arbitrary associa tions between input patterns and output patterns , as long as the input patterns form a linearly independent set (see Chapters 9 and 11) . Table 2 illustrates this aspect of the model . The first two cells of the table show the connections that the model learns when it is trained on each of the two indicated associations separately . The third cell shows connections learned by the model when it is trained on both patterns in alternation , first seeing one and then seeing the other of the two . Again , the reader can verify that if either input pattern is presented to a network with this set of connections , the correct corresponding output pattern is reconstructed with high probability ~ each output unit that should be on gets a net input of at least + 45 , and each output unit that + +should be off gets a net input below - 45 . + +The restriction of networks such as this to linearly independent sets of patterns is a severe one since there are only N linearly independent patterns of length N . That means that we could store at most eight unrelated associations in the network and maintain accurate perform ance . However , if the patterns all conform to a general rule , the capac ity of the network can be greatly enhanced . For example , the set of connections shown in Table 20 is capable of processing all of the pat terns defined by what we call the rule of 78. The rule is described in Table 3 . There are 18 different input / output pattern pairs correspond ing to this rule , but they present no difficulty to the network . Through repeated presentations of examples of the rule , the perceptron con ver gence procedure learned the set of weights shown in cell D of Table 2 . Again , the reader can verify that it works for any legal association fit ting the rule of 78 . (Note that for this example , the " regular " pairing + +3 For the actual simulations of verb learning, we used a value of T equal to 200. This means that for a fixed value of the weight on an input line, the effect of that line being active on the unit 's probability of firing is much lower than it is in these illustrations . This is balanced by the fact that in the verb learning simulations , a much larger number of inputs contribute to the activation of each output unit . Responsibility for turning a + +of (1 4 7) with (1 4 8) was used rather than the exceptional mapping + +illustrated in Table 3) . + +We have, then, observed an important property of the pattern associator: If there is some structure to a set of patterns, the network may be able to learn to respond appropriately to all of the members of the set. This is true, even though the input vectors most certainly do not form a linearly independent set. The model works anyway because the response that the model should make to some of the patterns can be predicted from the responses that it should make to others of the pat- + +terns. + +Now let's consider a case more like the situation a young child faces in learning the past tenses of English verbs. Here, there is a regular pattern, similar to the rule of 78. In addition., however., there are exceptions. Among the first words the child learns are many exceptions, but as the child learns more and more verbs, the proportion that are regular increases steadily. For an adult, the vast majority of verbs + +are regular. + +To examine what would happen in a pattern associator in this kind of a situation, we first presented the illustrative 8-unit model with two pattern pairs. One of these was a regular example of the 78 rule [(2 5 8) --+ (2 5 7)] . The other was an exception to the rule [(1 4 7) --+ (1 4 7)] . The simulation saw both pairs 20 times., and connection strengths were adjusted after each presentation. The resulting set of connections is shown in cell A of Table 4. This number of learning trials is not enough to lead to perfect performance~ but after this much experience., the model tends to get the right answer for each output unit close to 90 percent of the time. At this point ., the fact that one of the patterns is an example of a general rule and the other is an exception to that rule is irrelevant to the model. It learns a set of connections that can accommodate these two patterns., but it cannot gen- + +eralize to new instances of the rule. + +This situation, we suggest., characterizes the situation that the language learner faces early on in learning the past tense. The child knows, at this point., only a few high-frequency verbs, and these tend, by and large, to be irregular , as we shall see below. Thus each is treated by the network as a separate association, and very little generali- + +zation is possible. + +But as the child learns more and more verbs, the proportion of regular verbs increases. This changes the situation for the learning model. Now the model is faced with a number of examples, all of which follow the rule, as well as a smattering of irregular forms . This new situation changes the experience of the network, and thus the pattern of interconnections it contains. Because of the predominance of the regular REPRESENTING EXCEPTIONS : WEIGHTS IN THE 8-UNIT NETWORK + +18. LEARNING THE PAST TENSE 231 + +TABLE 4 + +-12 13 -11 -12 11 -12 11 -13 + +-12 13 -11 -12 11 -12 11 -13 + +- 10 2 - 5 -34 44 - 28 - 2 + +After 30 more exposures to all 18 associations + +D. After a total of 500 exposures + +-6 - 6 - 5 62 -38 - 38 22 - 18 + +64 - 39 - 39 - 5 - 5 - 5 71 - 70 + +-39 63 -40 -5 -5 -5 -28 27 + +- 39 - 39 64 - 5 - 5 - 5 - 29 28 + +- 5 - 5 - 5 64 - 39 -39 70 - 70 + +- 7 - 7 - 8 - 8 - 7 - 8 - 92 91 + +B. After 10 more exposures to all 18 associations + +to all 18 associations + +A. After 20 exposures to + +(1 4 7)- (1 4 7), ( 2 5 8)- (2 5 7) + +C . + +- 4 - 8 - 8 - 4 - 9 - 4 - 1 - 2 - 9 - 26 - 4 - 11 - 27 - 7 - 7 42 - 7 - 10 - 6 - 35 38 6 36 - 42 + +> - 7 - 8 - 7 - 7 - 8 - 7 106 - 106 + +form in the input , the network learns the regular pattern, temporarily "overregularizing" exceptions that it may have previously learned. + +Our illustration takes this situation to an extreme, perhaps, to illustrate the point . For the second stage of learning, we present the model with the entire set of eighteen input patterns consisting of one active unit from (1 2 3) , one from (4 5 6) , and one from (7 8) . All of these patterns are regular except the one exception already used in the first + +stage of training . + +At the end of 10 exposures to the full set of 18 patterns, the model has learned a set of connection strengths that predominantly captures the "regular pattern." At this point, its response to the exceptional pattern is worse than it was before the beginning of Phase 2~ rather than getting the right output for Units 7 and 8, the network is now regulariz- + +ing it . + +The reason for this behavior is very simple. All that is happening is that the model is continually being bombarded with learning experiences directing it to learn the rule of 78. On only one learning trial out + +- 2 - 11 - 5 45 -31 - 31 11 - 13 232 PSYCHOLOGICAL PROCESSES + +In this example, the deck has been stacked very strongly against the exception. For several learning cycles, it is in fact quite difficult to tell from the connections that the model is being exposed to an exception mixed in with the regular pattern. At the end of 10 cycles, we can see that the model is building up extra excitatory connections from input Units 1 and 4 to output Unit 7 and extra inhibitory strength from Units 1 and 4 to Unit 8, but these are not strong enough to make the model get the right answer for output Units 7 and 8 when the (1 4 7) input pattern is shown. Even after 40 trials (panel C of Table 4) , the model still gets the wrong answer on Units 7 and 8 for the (1 4 7) pattern more than half the time . (The reader can still be checking these assertions by computing the net input to each output unit that would result + +from presenting the (1 4 7) pattern.) + +It is only after the model has reached the stage where it is making very few mistakes on the 17 regular patterns that it begins to accommodate to the exception. This amounts to making the connection from Units 1 and 4 to output Unit 7 strongly excitatory and making the connections from these units to output Unit 8 strongly inhibitory . The model must also make several adjustments to other connections so that the adjustments just mentioned do not cause errors on regular patterns similar to the exceptions, such as (1 5 7) , (2 4 7) , etc. Finally , in panel D, after a total of 500 cycles through the full set of 18 patterns, the weights are sufficient to get the right answer nearly all of the time . Further improvement would be very gradual since the network makes errors so infrequently at this stage that there is very little opportunity + +for change. + +It is interesting to consider for a moment how an association is represented in a model like this. We might be tempted to think of the representation of an association as the difference between the set of connection strengths needed to represent a set of associations that includes the association and the set of strengths needed to represent the same set excluding the association of interest. Using this definition , we see that the representation of a particular association is far from invari ant. What this means is that learning that occurs in one situation (e.g., in which there is a small set of unrelated associations) does not necessarily transfer to a new situation (e.g., in which there are a number of regular associations) . This is essentially why the early learning our illustrative model exhibits of the (1 4 7) --.. (1 4 7) association in the context of just one other association can no longer support correct perf ormance when the larger ensemble of regular patterns is introduced. Obviously, the example we have considered in this section is highly simplified . However, it illustrates several basic facts about pattern associators. One is that they tend to exploit regularity that exists in the mapping from one set of patterns to another. Indeed, this is one of the + +18. LEARNING THE PASTTENSE 233 + +main advantages of the use of distributed representations . Second , they allow exceptions and regular patterns to coexist in the same network . Third , if there is a predominant regularity in a set of patterns , this can swamp exceptional patterns until the set of connections has been acquired that captures the predominant regularity . Then further , grad ual tuning can occur that adjusts these connections to accommodate both the regular patterns and the exception . These basic properties of the pattern associator model lie at the heart of the three - stage acquisi tion process , and account for the gradualness of the transition from + +Stage 2 to Stage 3 . + +Featural Representations of Phonological Patterns + +The preceding section describes basic aspects of the behavior of the pattern associator model and captures fairly well what happens when a pattern associator is applied to the processing of English verbs , follow ing a training schedule similar to the one we have just considered for the acquisition of the rule of 78 . There is one caveat , however : The input and target patterns - the base forms of the verbs and the correct past tenses of these verbs - must be represented in the model in such a way that the features provide a convenient basis for capturing the regu larities embodied in the past - tense forms of English verbs . Basically , + +there were two considerations : + +. We needed a representation that permitted a differentiation of + +all of the root forms of English and their past tenses . + +. We wanted a representation that would provide a natural basis for generalizations to emerge about what aspects of a present + +tense correspond to what aspects of the past tense . + +A scheme which meets the first criterion , but not the second , is the scheme proposed by Wickelgren ( 1969 ) . He suggested that words should be represented as sequences of context - sensitive phoneme units , which represent each phone in a word as a triple , consisting of the phone itself , its predecessor , and its successor . We call these tripJes Wicke /phones . Notationally , we write each Wickelphone as a tripJe of phonemes , consisting of the central phoneme , subscripted on the left by its predecessor and on the right by its successor . A phoneme occur ring at the beginning of a word is preceded by a special symbol ( # ) standing for the word boundary ~ likewise , a phoneme occurring at the + +234 PSYCHOLOGICAL PROCESSES + +end of a word is followed by # . The word I kat/ , for example, would be represented as ~ a' kat, and at# . Though the Wickelphones in a word are not strictly position specific, it turns out that (a) few words contain more than one occurrence of any given Wickelphone, and (b) there are no two words we know of that consist of the same sequence of Wickelphones. For example, I slitl and I siltl contain no Wickelphones in + +common. + +One nice property of Wickelphones is that they capture enough of the context in which a phoneme occurs to provide a sufficient basis for differentiating between the different cases of the past-tense rule and for characterizing the contextual variables that determine the subregularities among the irregular past-tense verbs. For example, the word-final phoneme that determines whether we should add I d/ , I tl or 1 A d/ in forming the regular past. And it is the sequence iN # which is transformed to aN# in the ing --+- ang pattern found in words like sing. The trouble with the Wickelphone solution is that there are too many of them, and they are too specific. Assuming that we distinguish 35 different phonemes, the number of Wickelphones would be 353, or 42,875, not even counting the Wickelphones containing word boundaries. And , if we postulate one input unit and one output unit in our model for each Wickelphone, we require rather a large connection matrix (4.3 x 104 squared, or about 2 x 109) to represent all their possi- + +ble connections. + +Obviously, a more compact representation is required. This can be obtained by representing each Wickelphone as a distributed pattern of activation over a set of feature detectors. The basic idea is that we represent each phoneme, not by a single Wickelphone , but by a pattern of what we call Wickelfeatures. Each Wickelfeature is a conjunctive , or context-sensitive, feature, capturing a feature of the central phoneme, a + +feature of the predecessor, and a feature of the successor. + +Details of the Wickelfeature representation. For concreteness, we will now describe the details of the feature coding scheme we used. It contains several arbitrary properties, but it also captures the basic principles of coarse, conjunctive coding described in Chapter 3. First , we will describe the simple feature representation scheme we used for coding a single phoneme as a pattern of features without regard to its predecessor and successor. Then we describe how this scheme can be extended to code whole Wickelphones. Finall~, we show how we + +"blur " this representation, to promote generalization further . + +To characterize each phoneme, we devised the highly simplified feature set illustrated in Table 5. The purpose of the scheme was (a) to give as many of the phonemes as possible a distinctive code, (b) to allow code similarity to reflect the similarity structure of the phonemes + +18. LEARNING THE PAST TENSE 235 + +T .I:\BLE 5 + +CATEGORIZATION OF PHONEMES ON FOUR SIMPLE DIMENSIONS + +V/ L u / s \'/ L u / s V / L U / S + +Interrupted Stop k + +Nasa! + +b m d n + +p t g + +N + +Cant. Consonant Fric. v/ D + +w/ l + +fiT s + +- + +E A 0 I + +Vowel + +e a/ a + +in a way that seemed sufficient for our present purposes, and (c) to + +keep the number of different features as small as possible. + +The coding scheme can be thought of as categorizing each phoneme on each of four dimensions. The first dimension divides the phonemes into three major types: interrupted consonants (stops and nasals) , continuous consonants (fricatives, liquids , and semivowels) , and vowels. The second dimension further subdivides these major classes. The interrupted consonants are divided into plain stops and nasals; the continuous consonants into fricatives and sonorants (liquids and semi vowels are lumped together) ~ and the vowels into high and low. The third dimension classifies the phonemes into three rough places of articulation - front , middle, and back. The fourth subcategorizes the consonants into voiced vs. voiceless categories and subcategorizes the vowels into long and short. As it stands, the coding scheme gives identical codes to six pairs of phonemes, as indicated by the duplicate entries in the cells of the table. A more adequate scheme could easily be constructed by increasing the number of dimensions and/ or values + +on the dimensions. + +Using the above code, each phoneme can be characterized by one value on each dimension. If we assigned a unit for each value on each dimension, we would need 10 units to represent the features of a single phoneme since two dimensions have three values and two have two + +Place + +Key: N = ng in sing~ 0 = th in fhe~ T = th in wifh~ Z = z in azure~ S = sh in ship~ C = ch in chip~ E = ee in beef~ i = i in bif~ 0 = oa in boaf~ A = u in but or schwa~ U = 00 in boot~ u = 00 in book~ A = ai in bait~ e = e in bef~ I = i\_e in bife~ a = a in baf~ a = a in ,rafher~ W = ow in cow~ \* = aw in saw~ a = a in hot, + +z r + +Front Middle Back + +Z / j + +u + +SIC h + +\*/ 0 + +LiqjSV + +High Low + +236 PSYCHOLOGICAL PROCESSES + +values. We could then indicate the pattern of these features that corresponds to a particular phoneme as a pattern of activation over the + +10 units. + +Now, one way to represent each Wickelphone would simply be to use three sets of feature patterns: one for the phoneme itself , one for its predecessor, and one for its successor. To capture the word-boundary marker, we would need to introduce a special eleventh feature. Thus, + +the Wickelphone ~ a can be represented by + +(000) (00) (000) (00) 1 (100) (10) (001) (01) 0 (001) (01) (010) (01) 0 + +Using this scheme, a Wickelphone could be represented as a pattern of + +activation over a set of 33 units. + +However, there is one drawback with this. The representation is not sufficient to capture more than one Wickelphone at a time. If we add another Wickelphone , the representation gives us no way of knowing + +which features belong together. + +We need a representation, then, that provides us with a way of determining which features go together. This is just the job that can be done with detectors for Wickelfeatures- triples of features, one from the central phoneme, one from the predecessor phoneme, and one + +from the successor phoneme. + +Using this scheme, each detector would be activated when the word contained a Wickelphone containing its particular combination of three features. Since each phoneme of a Wickelphone can be characterized by 11 features (including the word-boundary feature) and each Wickelphone contains three phonemes, there are 11 x 11 x 11 possible Wickelfeature detectors. Actually , we are not interested in representing phonemes that cross word boundaries, so we only need 10 features for + +the center phoneme. + +Though this leaves us with a fairly reasonable number of units (11 x 10 x 11 or 1,210) , it is still large by the standards of what will easily fit in available computers. However, it is possible to cut the number down still further without much loss of representational capacity since a representation using aliI ,210 units would be highly redundant~ it would represent each feature of each of the three phonemes 16 different times, one for each of the conjunctions of that feature with one of the four features of one of the other phonemes and one of the + +four features of the other. + +To cut down on this redundancy and on the number of units required, we simply eliminated all those Wickelfeatures specifying values on two different dimensions of the predecessor and the + +18. LEARNING THE PAST TENSE 237 + +TABLE 6 + +THE SIXTEEN WICKELFEA TL' RES FOR THE WICKELPHONE kAm + +Interrupted Back Stop Unvoiced + +Vowel Front Nasal Voiced Interrupted Front Nasal Voiced Vowel Front Nasal Voiced + +Feature Preceding Context Central Phoneme Following Context + +Interrupted Front Nasal Voiced + +successor phonemes. We kept all the Wickelfeature detectors for all combinations of different values on the same dimension for the predecessor and successor phonemes. It turns out that there are 260 of these (ignoring the word-boundary feature) , and each feature of each member of each phoneme triple is still represented four different times. In addition , we kept the 100 possible Wickelfeatures combining a preceding word-boundary feature with any feature of the main phoneme and any feature of the successor~ and the 100 Wickelfeatures combining a following word boundary feature with any feature of the main phoneme and any feature of the successor. All in all then, we + +used only 460 of the 1,210 possible Wickelfeatures. + +Using this representation, a verb is represented by a pattern of activation over a set of 460 Wickelfeature units. Each Wickelphone activates 16 Wickelfeature units. Table 6 shows the 16 Wickelfeature units activated by the Wickelphone kAm ' the central Wickelphone in the word came. The first Wickelfeature is turned on whenever we have a Wickelphone in which the preceding contextual phoneme is an interrupted consonant, the central phoneme is a vowel, and the following phoneme is an interrupted consonant. This Wickelfeature is turned on for the Wickelphone kAm since I k/ and / m/ , the context phonemes, are both interrupted consonants and / AI , the central phoneme, is a vowel. This same Wickelfeature would be turned on in the + +> Interrupted Back Stop Unvoiced + +Vowel Vowel Vowel \ rowel + +Front Front Front Front Low Low Low Low Long Long Long Long + +Interrupted Back Stop Unvoiced Interrupted Back Stop Unvoiced + +238 PSYCHOLOGICAL PROCESSES + +representation of ~ d ' pAt , map , and many other Wickelfeatures . Simi larly , the sixth Wickelfeature listed in the table will be turned on when ever the preceding phoneme is made in the back , and the central and following phonemes are both made in the front . Again , this is turned on because I kl is made in the back and I AI and I ml are both made in the front . In addition to kAm this feature would be turned on for the Wickelphones giV ' gAp , kAp , and others . Similarly , each of the sixteen Wickelfeatures stands for a conjunction of three phonetic features and occurs in the representation of a large number of Wickelphones . + +Now , words are simply lists of Wickelphones . Thus , words can be represented by simply turning on all of the Wickelfeatures in any Wick elphone of a word . Thus , a word with three Wickelphones ( such as came , which has the Wickelphones ~ A ' kAm ' and am # ) will have at most 48 Wickelfeatures turned on . Since the various Wickelphones may have some Wickelfeatures in common , typically there will be less than 16 times the number of Wickelfeatures turned on for most words . It is important to note the temporal order is entirely implicit in this representation . All words , no matter how many phonemes in the word , + +will be represented by a subset of the 460 Wickelfeatures . + +Blurring the Wickelfeature representation . The representational scheme just outlined constitutes what we call the primary representation of a Wickelphone . In order to promote faster generalization , we further blurred the representation . This is accomplished by turning on , in addition to the 16 primary Wickelfeatures , a randomly selected sub set of the similar Wickelfeatures , specifically , those having the same value for the central feature and one of the two context phonemes . That is , whenever the Wickelfeature for the conjunction of phonemic features 11 , 12 , and 13 is turned on , each Wickelfeature of the form < ? ~f2 13 > and < / lh ? > may be turned on as well . Here " ? " stands for " any feature ." This causes each word to activate a larger set of Wickelfeatures , allowing what is learned about one sequence of phonemes to generalize more readily to other similar but not identical + +sequences . + +To avoid having too much randomness in the representation of a par ticular Wickelphone , we turned on the same subset of additional Wick elfeatures each time a particular Wickelphone was to be represented . Based on subsequent experience with related models ( see Chapter 19 ) , + +we do not believe this makes very much difference . + +There is a kind of trade - off between the discriminability among the base forms of verbs that the representation provides and the amount of generalization . We need a representation which allows for rapid gen eralization while at the same time maintains adequate discriminability . We can manipulate this factor by manipulating the probability p that + +18. LEARNING THE PAST TENSE 239 + +anyone of these similar Wickelfeatures will be turned on. In our simulations we found that turning on the additional features with fairly high probability (.9) led to adequate discriminability while also producing + +relatively rapid generalization. + +Although the model is not completely immune to the possibility that two different words will be represented by the same pattern, we have encountered no difficulty decoding any of the verbs we have studied. However, we do not claim that Wickelfeatures necessarily capture all the information needed to support the generalizations we might need to make for this or other morphological processes. Some morphological processes might require the use of units that were further differentiated according to vowel stress or other potential distinguishing characteristics. All we claim for the present coding scheme is its sufficiency for the task of representing the past tenses of the 500 most frequent verbs in English and the importance of the basic principles of distributed , coarse (what we are calling blurred) , conjunctive coding that it + +embodies (see Chapter 3) . + +Summary of the Structure of the Model + +In summary, our model contained two sets of 460 Wickelfeature units, one set (the input units) to represent the base form of each verb and one set (the output units) to represent the past-tense form of each + +verb. + +The model is tested by typing in an input phoneme string, which is translated by the fixed encoding network into a pattern of activation over the set of input units. Each active input unit contributes to the net input of each output unit , by an amount and direction (positive or negative) determined by the weight on the connection between the input unit and the output unit . The output units are then turned on or off probabilistically , with the probability increasing with the difference between the net input and the threshold, according to the logistic activation function . The output pattern generated in this way can be compared with various alternative possible output patterns, such as the correct past-tense form or some other possible response of interest, or can be used to drive the decoder network described in the Appendix . The model is trained by providing it with pairs of patterns, consisting of the base pattern and the target, or correct, output . Thus, in accordance with common assumptions about the nature of the learning situation that faces the young child , the model receives only correct input from the outside world. However, it compares what it generates internally to the target output , and when it gets the wrong answer for a + +THE SIMULATIONS + +The simulations described in this section are concerned with demon - + +That the model captures the basic three-stage pattern of acquisi- . + +That the model is capable of responding appropriately to verbs it has never seen before, as well as to regular and irregular + +verbs actually experienced during training . + +. + +The Three-Stage Learning Curve + +The results described in this and the following sections were obtained from a single (long) simulation run. The run was intended to capture + +strating three main points : + +tion. + +particular output unit , it adjusts the strength of the connection between the input and the output units so as to reduce the probability that it will make the same mistake the next time the same input pattern is presented. The adjustment of connections is an extremely simple and local procedure, but it appears to be sufficient to capture what we know about the acquisition of the past tense, as we shall see in the next + +section. + +. That the model captures most aspects of differences in performance on different types of regular and irregular verbs. + +In the sections that follow we will consider these three aspects of the + +model's performance in turn . + +The corpus of verbs used in the simulations consisted of a set of 506 verbs. All verbs were chosen from the Kucera and Francis (1967) word list and were ordered according to frequency of their gerund form . We divided the verbs into three classes: 10 high-frequency verbs, 410 medium-frequency verbs, and 86 low-frequency verbs. The ten highest frequency verbs were: come (/ kAm/ ) , get (/ get/ ) , give (/ giv/ ) , look (/ luk / ) , take (/ tAk/ ) , go (/ go/ ) , have (/ hav/ ) , live (/ liv / ) , and feel (/ fEI/ ) . There is a total of 8 irregular and 2 regular verbs among the top 10. Of the medium-frequency verbs, 334 were regular and 76 were irregular. Of the low-frequency verbs, 72 were regular and 14 were + +irregular. + +18. LEARNING THE PAST TENSE241 + +approximately the experience with past tenses of a young child picking up English from everyday conversation. Our conception of the nature of this experience is simply that the child learns first about the present and past tenses of the highest frequency verbs~ later on, learning occurs for a much larger ensemble of verbs, including a much larger proportion of regular forms . Although the child would be hearing present and past tenses of all kinds of verbs throughout development~ we assume that he is only able to learn past tenses for verbs that he has already + +mastered fairly well in the present tense. + +To simulate the earliest phase of past-tense learning, the model was first trained on the 10 high-frequency verbs, receiving 10 cycles of training presentations through the set of 10 verbs. This was enough to produce quite good performance on these verbs. We take the perform ance of the model at this point to correspond to the performance of a child in Phase 1 of acquisition. To simulate later phases of learning, the 410 medium -frequency verbs were added to the first 10 verbs, and the system was given 190 more learning trials, with each trial consisting of one presentation of each of the 420 verbs. The responses of the model early on in this phase of training correspond to Phase 2 of the acquisition process~ its ultimate performance at the end of 190 exposures to each of the 420 verbs corresponds to Phase 3. At this point , the model exhibits almost errorless performance on the basic 420 verbs. Finally , the set of 86 lower-frequency verbs were presented to the system and the transfer responses to these were recorded. During this phase, connection strengths were not adjusted. Performance of the + +model on these transfer verbs is considered in a later section. + +We do not claim, of course, that this training experience exactly captures the learning experience of the young child . It should be perfectly clear that this training experience exaggerates the difference between early phases of learning and later phases, as we]l as the abruptness of the transition to a larger corpus of verbs. However, it is generally observed that the early, rather limited vocabulary of young children undergoes an explosive growth at some point in development (Brown, 1973) . Thus, the actual transition in a child's vocabulary of verbs would appear quite abrupt on a time-scale of years so that our assump- + +tions about abruptness of onset may not be too far off the mark. + +Figure 4 shows the basic results for the high frequency verbs. What we see is that during the first 10 trials there is no difference between regular and irregular verbs. However, beginning on Trial 11 when the 410 midfrequency verbs were introduced, the regular verbs show better performance. It is important to notice that there is no interfering effect on the regular verbs as the midfrequency verbs are being learned. There is, however, substantial interference on the irregular verbs. This interference leads to a dip in performance on the irregular verbs. + +242 PSYCHOLOGICAL PROCESSES + +1~~~~OJ s + +~~n1~a~ 1u + +~~~ad 1 . 0 + +0 . 9 + +0.8 Irregular + +0 . 7 + +0 . 6 + +0 . 5 + +0 40 80 120 160 200 Trials + +Equality of performance between regular and irregular verbs is never again attained during the training period. This is the so-called Ushaped learning curve for the learning of the irregular past tense. Performance is high when only a few high-frequency, largely irregular verbs are learned, but then drops as the bulk of lower-frequency regular + +verbs are being learned. + +We have thus far only shown that performance on high-frequency irregular verbs drops~ we have not said anything about the nature of the errors. To examine this question, the response strength of various possible response alternatives must be compared. To do this, we compared the strength of response for several different response alternatives. We compared strengths for the correct past tense, the present, the base+ ed and the past+ ed. Thus, for example with the verb give we compared the response strength of / gA v / , / giv / , / givd/ , and / gA vd/ . We determined the response strengths by assuming that these response alternatives were competing to account for the features that were actually turned on in the output . The details of the competition mechanism, called a binding network, are described in the Appendix . For present purposes, suffice it to say that each alternative gets a score that represents the percentage of the total features that it accounts for . If two alternatives both account for a given feature, they divide the score for that feature in proportion to the number of features each accounts for uniquely . We take these response strengths to correspond roughly + +FIGURE 4. The percentage of correct features for regular and irregular high-frequency + +verbs as a function of trials. + +to relative response probabilities, though we imagine that the actual generation of overt responses is accomplished by a different version of the binding network , described below. In any case, the total strength of all the alternatives cannot be greater than 1, and if a number of features are accounted for by none of the alternatives, the total will be + +less than 1. + +Figure 5 compares the response strengths for the correct alternative to the combined strength of the regularized alternatives. 4 Note in the figure that during the first 10 trials the response strength of the correct alternative grows rapidly to over .5 while that of the regularized alternative drops from about .2 to .1. After the midfrequency verbs are intro duced, the response strength for the correct alternative drops rapidly while the strengths of regularized alternatives jump up. From about Trials 11 through 30, the regularized alternatives together are stronger than the correct response. After about Trial 30, the strength of the correct response again exceeds the regularized alternatives and continues to grow throughout the 200-trial learning phase. By the end, the correct response is much the strongest with all other alternatives + +below .1. + +18. LEARNING THE PAST TENSE 243 + +1 . 0 + +0 . 8 + +0 . 6 + +0 . 4 + +0 . 2 + +Regularized + +0 . 0 + +0 40 80 120 160 200 Trials + +q1~tIa + +.I1S astIodsaCI + +FIGURE 5. Response strengths for the high-frequency irregular verbs. The response strengths for the correct responses are compared with those for the regularized alterna- + +tives as a function of trials. + +alternatives are considered the base + ed the paper we shall discuss the pattern of ;t cases the base+ ed alternative is much + +4 Unless otherwise indicated , the regularized and past + ed alternatives . In a later section of differences between these alternatives . In mo5 + +244 PSYCHOLOGICAL PROCESSES + +The rapidity of the growth of the regularized alternatives is due to the sudden influx of the medium -frequency verbs . In real life we would expect the medium -frequency verbs to come in somewhat more slowly so that the period of maximal regularization would have a some - + +what slower onset . + +Figure 6 shows the same data in a slightly different way . In this case, we have plotted the ratio of the correct response to the sum of the correct and regularized response strengths . Points on the curve below the . 5 line are in the region where the regularized response is greater that the correct response . Here we see clearly the three stages. In the first stage, the first 10 trials of learning , performance on these high -frequency verbs is quite good . Virtually no regularization takes place. During the next 20 trials , the system regularizes and systemati cally makes errors on the verbs that it previously responded to correctly . Finally , during the remaining trials the model slowly elim inates the regularization responses as it approaches adult performance . In summary , then , the model captures the three phases of learning quite well , as well as the gradual transition from Phase 2 to Phase 3. It does so without any explicit learning of rules . The regularization is the product of the gradual tuning of connection strengths in response + +(~aa.I.IoJ + +paZJ.I"BIn~aH)/ + +~aa.I.IoJ + +1 . 0 + +0 . 8 + +0 . 6 + +0 . 4 + +0 . 2 + +0 . 0 + +0 40 80 120 160 200 Trials + +FIGURE 6. The ratio of the correct response to the sum of the correct and regularized response. Points on the curve below the .5 line are in the region where the regularized + +Learning the medium-frequency verbs. Figure 7A compares the learning curves for the regular verbs of high and medium frequency, and Figure 7B compares the learning curves for the corresponding groups of irregular verbs. Within only two or three trials the mediumfrequency verbs catch up with their high-frequency counterparts. Indeed, in the case of the irregular verbs, the medium-frequency verbs seem to surpass the high-frequency ones. As we shall see in the fol lowing section, this results from the fact that the high-frequency verbs include some of the most difficult pairs to learn, including , for example, the go/ went pair which is the most difficult to learn (aside from the verb be, this is the only verb in English in which the past and root form are completely unrelated) . It should also be noted that even at this early stage of learning there is substantial generalization. Already, on Trial 11, the very first exposure to the medium-frequency verbs, between 65 and 75 percent of the features are produced correctly. Chance responding is only 50 percent. Moreover , on their first presentation , 10 percent more of the features of regular verbs are correctly responded to than irregular ones. Eventually , after 200 trials of learning, nearly all of the features are being correctly generated and the system is near asymptotic performance on this verb set. As we shall see below, during most of the learning period the difference between highand medium-frequency verbs is not important . Rather, the differences between different classes of verbs is the primary determiner of per- + +formance. We now turn to a discussion of these different types. + +18. LEARNING THE PAST TENSE 245 + +to the predominantly regular correspondence exhibited by the medium -frequency words. It is not quite right to say that individual pairs are being stored in the network in any simple sense. The connection strengths the model builds up to handle the irregular forms do not represent these items in any separable way~ they represent them in the way they must be represented to be stored along with the other verbs in + +the same set of connections. + +Before discussing the implications of these kinds of results further , it is useful to look more closely at the kinds of errors made and at the learning rates of the medium-frequency regular and irregular verbs. + +Types of Regular and Irregular Verbs + +18. LEARNING THE PAST TENSE 247 + +Bybee and Slobindivided the irregular verbs into nine classes, + +defined as follows: 5 + +I. Verbs that do not change at all to form the past tense, e.g., + +II . Verbs that change a final / d/ to / t/ to form the past tense , e.g., + +VIII . All verbs that undergo a vowel change and that end in a dip - + +A complete listing by type of all of the irregular verbs used in our study + +is given in Table 7. + +In addition to these types of irregular verbs, we distinguished three categories of regular verbs: (a) those ending in a vowel or voiced consonant, which take a Idl to form the past tense~ (b) those ending in a voiceless consonant, which take a It / ~ and (c) those ending in It I or + +5 Criteria from Bybee and Slobin (1982, pp. 268-269). + +6 Following Bybee and Slobin, we included buy/ bought in this class even though no + +beat, cut, hit. + +send/ sent, build / built . + +drink / drank . + +give/ gave, break/ broke. + +thongal sequence , e.g., blow/ blew, fly /flew . + +III . Verbs that undergo an internal vowel change and also add a final / t/ or / d/ , e.gijeel /felt , lose/ lost, say/ said, tell/ told. + +IV . Verbs that undergo an internal vowel change, delete a final consonant, and add a final / t/ or / d/ , e.g., bring/ brought, + +catch/ caught. 6 + +v . Verbs that undergo an internal vowel change whose stems end + +in a dental, e.g., bite/ bit, find /found, ride/ rode. + +VIa. Verbs that undergo a vowel change of / if to / a/ e.g., sing/ sang, + +VIb. Verbs that undergo an internal vowel change of / i/ or / a/ to + +/ A/ e.g., sting/ stung, hang/ hung. 7 + +VII . All other verbs that undergo an internal vowel change, e.g., + +248 PSYCHOLOGICAL PROCESSES + +TABLE 7 + +IRREGULAR VERBS + +Type High Low + +bend lend + +III feel creep + +weep + +IV have make catch + +v get breed + +wind grind + +drink ring sing swim + +drag hang swing djg cling + +stick + +give take come tear + +VIII go + +Frequency + +Medium + +thrust bid + +I + +II + +shake arise rise run become bear wear speak brake drive strike fall freeze choose throw blow grow draw fly know see + +/ d/ , which take a final / A d/ to form the past tense. The number of regular verbs in each category, for each of the three frequency levels, is + +given in Table 8. + +Type 1.0 No -change verbs. A small set of English verbs require no change between their present- and past-tense forms . One factor common to all such verbs is that they already end in It I or Id / . Thus, they superficially have the regular past-tense form - even in the present tense. Sternberger (1981) points out that it is common in inflectional languages not to add an additional inflection to base forms that already appear to have the inflection . Not all verbs ending in / t/ or / d/ show no change between present and past (in fact the majority of such verbs + +beat fit set spread hit cut put + +build send spend deal do flee tell sell hear keep leave sleep lose mean say sweep think buy bring seek teach + +meet shoot write lead understand sit mislead bleed feed stand light find fight read meet hide hold ride + +18. LEARNING THE PAST TENSE 249 + +TABLE 8 + +NUMBER OF REGULAR VERBS OF EACH TYPE + +start look + +0 1 + +move + +End in dental End in voice!ess consonant End in voiced consonant or vowel + +Regular walk smoke melt pat smile climb + +Vowel change drink break run swim throw meet shoot ride Vowel change + t / d do buy lose sell sleep help teach catch + +Frequency + +Type Suffix Example High Medium Low + +13 30 + +29 + +I ~dl Itl + +/d/ + +94 64 + +176 + +in English do show a change between present and past tense ) , but there is a reasonably large group - the Type I verbs of Bybee and Slobin - that do show this trend . Bybee and Slobin ( 1982) suggest that children learn relatively early on that past-tense verbs in English tend to end in / t/ or / d/ and thus are able to correctly respond to the no -change verbs rather early . Early in learning , they suggest , children also incorrectly generalize this " no -change rule " to verbs whose present and past tenses + +differ . + +The pattern of performance just described shows up very clearly in data Bybee and Slobin ( 1982) report from an elicitation task with preschool children . In this task , preschoolers were given the present tense form of each of several verbs and were asked to produce the corresponding past-tense form . They used the set of 33 verbs shown in + +Table 9 . + +The results were very interesting . Bybee and Slobin found that verbs not ending in l / d were predominately regularized and verbs ending in l / d were predominately used as no -change verbs . The number of occurrences of each kind is shown in Table 10. These preschool + +TABLE 9 + +VERBS USED BY BYBEE & SLOBIN + +Type of Verb Verb List + +250 PSYCHOLOGICAL PROCESSES + +TABLE 10 + +REGULAR AND NO CHANGE RESPONSES TO t/ d AND OTHER VERBS (Data from Bybee & Siobin, 1982) + +No Change + +Not t / d lid + +children have, at this stage, both learned to regularize verbs not ending in t Id and, largely, to leave verbs ending in t / d without an additional + +ending. + +Interestingly , our simulations show the same pattern of results. The system learns both to regularize and has a propensity not to add an additional ending to verbs already ending in t Id . In order to compare the simulation results to the human data we looked at the performance of the same verbs used by Bybee and Slobin in our simulations . Of the 33 verbs, 27 were in the high- and medium-frequency lists and thus were included in the training set used in the simulation . The other six verbs (smoke, catch, lend, pat, hurt and shut) were either in the lowfrequency sample or did not appear in our sample at all. Therefore , we will report on 27 out of the 33 verbs that Bybee and Slobin tested. + +It is not clear what span of learning trials in our simulation corresponds best to the level of the preschoolers in Bybee and Slobin's experiment . Presumably the period during which regularization is occurring is best. The combined strength of the regularized alternatives exceeds correct response strength for irregulars from about Trial 11 through Trials 20 to 30 depending on which particular irregular verbs we look at. We therefore have tabulated our results over three dif ferent time ranges- Trials 11 through 15, Trials 16 through 20, and Trials 21 through 30. In each case we calculated the average strength of the regularized response alternatives and of the no-change response alternatives. Table 11 gives these strengths for each of the different + +time periods. + +The simulation results show clearly the same patterns evident in the Bybee and Slobin data. Verbs ending in tld always show a stronger no-change response and a weaker regularized response than those not ending in lid . During the very early stages of learning, however, the regularized response is stronger than the no-change response- even if the verb does end with lid . This suggests that the generalization that the past tense of tld verbs is formed by adding I Adl is stronger than the generalization that verbs ending in lid should not have an ending + +Verb Ending Regular Suffix + +34 157 + +203 42 + +18. LEARNING THE PAST TENSE 251 + +TABLE 11 + +AVERAGE SIMULATED STRENGTHS OF REGULARIZED AND NO-CHANGE RESPONSES + +Verb Ending No Change + +0 . 10 0 .27 0 .12 0 .35 0 .11 0 .41 + +11-15 + +16-20 + +21-30 + +added . However , as learning proceeds , this secondary generalization is made (though for only a subset of the t/ d verbs , as we shall see) , and the simulation shows the same interaction that Bybee and Slobin ( 1982) + +found in their preschoolers . + +The data and the simulations results just described conflate two aspects of performance , namely , the tendency to make no -change errors with t/ d verbs that are not no -change verbs and the tendency to make correct no -change responses to the t/ d verbs that are no -change verbs . Though Bybee and Slobin did not report their data broken down by this factor , we can examine the results of the simulation to see whether in fact the model is making more no -change errors with t/ d verbs for which this response is incorrect . To examine this issue , we return to the full corpus of verbs and consider the tendency to make no-change errors separately for irregular verbs other than Type I verbs and for reg- + +ular verbs . + +Erroneous no -change responses are clearly stronger for both regular and irregular t / d verbs . Figure 8A compares the strength of the erroneous no -change responses for irregular verbs ending in t / d (Types II and V ) versus those not ending in t / d (Types III , IV , VI , VII , and VIII ) . The no -change response is erroneous in all of these cases. Note , however , that the erroneous no -change responses are stronger for the t/ d verbs than for the other types of irregular verbs . Figure 8B shows the strength of erroneous no -change responses for regular verbs ending in t / d versus those not ending in t / d. Again , the response strength for the no -change response is clearly greater when the regular + +verb ends in a dental . + +We also compared the regularization responses for irregular verbs whose stems end in t / d with irregulars not ending in t / d. The results are shown in Figure 8C. In this case, the regularization responses are initially stronger for verbs that do not end in t/ d than for those that do . + +Time Period Regularized + +not t /d t/d not lid lid not t / d t/d + +0.44 0.35 0.32 0.25 0.52 0.32 + +0 . 5 + +Irreg not ending in t/ d + +0 . 4 + +0 . 3 + +0 .2 + +0 . 1 + +Irreg ending in t / d + +0 . 0 + +0 40 80 120 160 200 Trials + +252 PSYCHOLOGICAL PROCESSES + +Irreg ending in t / d + +0 . 2 + +0 . 1 + +0 . 0 + +0 40 80 120 160 200 Trials + +ql-~ua + +.Il-S asuodsal + +{ ql-~ua + +.Il-S asuodsal + +{ + +A + +0.2 Reg ending in t / d + +0 . 1 + +Reg not ending in t / d + +0 . 0 + +0 . 0 80 120 160 200 Trials + +B + +q1~Ua.I1S asuodsail + +c + +FIGURE 8. A: The strength of erroneous no-change responses for irregular verbs ending in a dental versus those not ending in a dental. B: The strength of erroneous no-change responses for regular verbs ending in a dental versus those not ending in a dental. C: The strength of erroneous regularization responses for irregular verbs ending in a dental + +18. LEARNING THE PAST TENSE 253 + +Thus, we see that even when focusing only on erroneous responses, the system shows a greater propensity to respond with no change to t Id verbs, whether or not the verb is regular, and a somewhat greater ten- + +dency to regularize irregulars not ending in tide + +There is some evidence in the literature on language acquisition that performance on Type I verbs is better sooner than for irregular verbs involving vowel changes- Types III through VIII . Kuczaj (1978) reports an experiment in which children were to judge the grammaticality of sentences involving past tenses. The children were given sentences involving words like hit or hilled or ate or eated and asked whether the sentences sounded "silly." The results, averaged over three age groups from 3~4 to 9~0 years, showed that 70 percent of the responses to the no-change verbs were correct whereas only 31 percent of the responses to vowel-change irregular verbs were correct. Most of the errors involved incorrect acceptance of a regularized form . Thus, the results show a clear difference between the verb types, with perf ormance on the Type I verbs superior to that on Type III through VIII + +verbs. + +The simulation model too shows better performance on Type I verbs than on any of the other types. These verbs show fewer errors than any of the other irregular verbs. Indeed the error rate on Type I verbs is equal to that on the most difficult of the regular verbs. Table 12 gives the average number of Wickelfeatures incorrectly generated (out of 460) at different periods during the learning processes for no-change (i.e., Type I) irregular verbs, vowel-change (i.e., Type III -VIII ) irregular verbs, regular verbs ending in lid , regular verbs not ending in lid , and regular verbs ending in lid whose stem is a CVC (consonantvowel-consonant) monosyllable. The table clearly shows that throughout learning, fewer incorrect Wickelfeatures are generated for no-change verbs than for vowel-change verbs. Interestingly , the table + +TABLE 12 + +A VERAGE NUMBER OF WICKELFEA TURES INCORRECTLY GENERATED + +Trial Number + +11 - 15 89 .8 123 .9 74 .1 82 .8 87 .3 16 -20 57 .6 93 .7 45 .3 51 .2 60 .5 21 -30 45 .5 78 .2 32 .9 37 .4 47 .9 31 - 50 34 .4 61 .3 22 .9 26 .0 37 .3 51 - 100 18 .8 39 .0 11 .4 12 .9 21 .5 101 - 200 11 .8 21 .5 6 .4 7 .4 12 .7 + +Irregular Verbs Regular Verbs + +Type I Types III-VIII Ending in lid Not Ending in lid CVlld + +254 PSYCHOLOGICAL PROCESSES + +also shows that one subset of regulars are no easier than the Type I irregulars. These are the regular verbs which look on the surface most like Type I verbs, namely, the monosyllabic CVC regular verbs ending in t / d. These include such verbs as bat, wait, shout, head, etc. Although we know of no data indicating that people make more nochange errors on these verbs than on multisyllabic verbs ending in t / d, this is a clear prediction of our model. Essentially what is happening is that the model is learning that monosyllables ending in t/ d sometimes take no additional inflection .8 This leads to quicker learning of the nochange verbs relative to other irregular verbs and slower learning of regular verbs which otherwise look like no-change verbs. It should be noted that the two regular verbs employed by Bybee and Slobin which behaved like no-change verbs were both monosyllables. It would be interesting to see if whether no-change errors actually occur with verbs + +like decide or devote. + +Types 111- VIII .. Vowel-change verbs. To look at error patterns on vowel-change verbs (Types III -VIII ) , Bybee and Slobin (1982) analyzed data from the spontaneous speech of preschoolers ranging from 11/2 to 5 years of age. The data came from independent sets of data collected by Susan Ervin -Tripp and Wick Miller , by Dan Slobin, and by Zell Greenberg. In all, speech from 31 children involving the use of 69 irregular verbs was studied. Bybee and Slobin recorded the percentages of regularizations for each of the various types of vowel-change verbs. Table 13 gives the percentages of regularization by preschoolers, ranked from most to fewest erroneous regularizations. The results show that the two verb types which involve adding a lid plus a vowel change (Types III and IV ) show the least regularizations, whereas the verb type in which the present tense ends in a diphthong (Type VIII ) shows by far + +the most regularization. + +It is not entirely clear what statistic in our model best corresponds to the percentage of regularizations. It will be recalled that we collected response strength measures for four different response types for irregular verbs. These were the correct response, the no-change response, the base + ed regularization response, and the past + ed regularization response. If we imagine that no-change responses are, in general, diffi cult to observe in spontaneous speech, perhaps the measure that would be most closely related to the percentage of regularizations would be the ratio of the sum of the strengths of the regularization responses to + +8 Though the model does not explicitly encode number of syllables, monosyllabic words are distinguished from multisyllabic words by the fact that the former contain no Wickelphones of the form C . There are no no-change verbs in English containing such . v v Wlckelphones. + +18. LEARNING THE PAST TENSE 255 + +TABLE 13 + +the sum of the strengths of regularization responses and the correct + +(base + ed + past + ed ) (base+ ed + past + ed + correct ) . + +As with our previous simulation , it is not entirely clear what portion of the learning curve corresponds to the developmental level of the children in this group. We therefore calculated this ratio for several different time periods around the period of maximal overgeneralization. + +Table 14 shows the results of these simulations. + +The spread between different verb classes is not as great in the simulation as in the children 's data, but the simulated rank orders show a + +TABLE 14 + +Average Trials 11 -30 + +Trials 21-30 + +Trials 11-15 + +Trials 16-20 + +> .76 .74 .60 .59 .57 .52 + +VIII VII IV V III VI + +VIII VI V VII III IV + +VIII VI V VII + +IV + +blew sang bit broke felt caught + +response - that is, + +VIII .86 VII .80 VI .76 V .72 IV .69 III .67 + +VIII .71 VII .69 V .56 IV .56 III .53 VI .52 + +STRENGTH OF REGULARIZATION RESPONSES RELATIVE TO CORRECT RESPONSES + +> VIII VII V IV III VI + +PERCENTAGE OF REGULARIZATION BY PRESCHOOLERS (Data from Bybee & Slobin , 1982) + +Percentage + +Verb Type Example Regularizations + +Data + +Rank + +Order Type Percent Type Ratio Type Ratio Type Ratio Type Ratio + +- + +remarkable similarity to the results from the spontaneous speech of the preschoolers, especially in the earliest time period. Type VIII verbs show uniformly strong patterns of regularization whereas Type III and Type IV verbs, those whose past tense involves adding a lid at the end, show relatively weak regularization responses. Type VI and Type VII verbs produce somewhat disparate results. For Type VI verbs, the simulation conforms fairly closely to the children 's speech data in the earliest time period, but it shows rather less strength for regularizations of these verbs in the later time periods and in the average over Trials 11-30. For Type VII verbs, the model errs in the opposite direction : Here it tends to show rather greater strength for regularizations of these verbs than we see in the children 's speech. One possible reason for these discrepancies may be the model's insensitivity to word frequency. Type VI verbs are, in fact, relatively low-frequency verbs, and thus, in the children 's speech these verbs may actually be at a relatively earlier stage in acquisition than some of the more frequent irregular verbs. Type VII verbs are, in general, much more frequent - in fact, on the average they occur more than twice as often (in the gerund form ) in the Kucera-Francis count than the Type VI verbs. In our simulations, all medium-frequency verbs were presented equally often and the distinction was not made. A higher-fidelity simulation including finer gradations of frequency variations among the verb types might lead to a closer correspondence with the empirical results. In any case, these verbs aside, the simulation seems to capture the major features of the + +data very nicely. + +Bybee and Slobin attribute the pattern of results they found to factors that would not be relevant to our model. They proposed, for example, that Type III and IV verbs were more easily learned because the final lid signaled to the child that they were in fact past tenses so the child would not have to rely on context as much in order to determine that these were past-tense forms. In our simulations , we found these verbs to be easy to learn, but it must have been for a different reason since the learning system was always informed as to what the correct past tense really was. Similarly , Bybee and Slobin argued that Type VIII verbs were the most difficult because the past and present tenses were so phonologically different that the child could not easily determine that the past and present tenses of these verbs actually go together. Again, our simulation showed Type VIII verbs to be the most difficult , but this had nothing to do with putting the past and present tense together since the model was always given the present and past tenses + +together. + +Our model, then, must offer a different interpretation of Bybee and Slobin's findings . The main factor appears to be the degree to which the relation between the present and past tense of the verb is + +256 PSYCHOLOGICAL PROCESSES + +Types of regularization . We have mentioned that there are two distinct ways in which a child can regularize an irregular verb: The child can use the base+ ed form or the past+ ed form . Kuczaj (1977) has provided evidence that the proportion of past + ed forms increases, relative to the number of base+ ed forms , as the child gets older. He found , for example, that the nine youngest children he studied had more base + ed regularizations than past + ed regularizations whereas four out of the five oldest children showed more past + ed than base + ed regularizations. In this section, we consider whether our model exhibits this same general pattern. Since the base form and the past-tense form are identical for Type I verbs, we restrict our analysis + +18. LEARNING THE PAST TENSE 257 + +idiosyncratic. Type VIII verbs are most difficult because the relationship between base form and past tense is most idiosyncratic for these verbs. Thus, the natural generalizations implicit in the population of verbs must be overcome for these verbs, and they must be overcome in a different way for each of them. A very basic aspect of the mapping from present to past tense is that most of the word, and in particular everything up to the final vowel, is unchanged. For regular verbs, all of the phonemes present in the base form are preserved in the past tense. Thus, verbs that make changes to the base form are going against the grain more than those that do not~ the larger the changes, the harder they will be to learn. Another factor is that past tenses of + +verbs generally end in j tj or j d/ . + +Verbs that violate the basic past-tense pattern are all at a disadvantage in the model, of course, but some suffer less than others because there are other verbs that deviate from the basic pattern in the same way. Thus, these verbs are less idiosyncratic than verbs such as go/ went, see/ saw, and draw/ drew which represent completely idiosyncratic vowel changes. The difficulty with Type VIII verbs, then, is simply that, as a class, they are simply more idiosyncratic than other verbs. Type III and IV verbs (e.g., feel/felt , catch/ caught) , on the other hand, share with the vast bulk of the verbs in English the feature that the past tense involves the addition of a t/ d. The addition of the t/ d makes these verbs easier than, say, Type VII verbs (e.g., come/ came) because in Type VII verbs the system must not only learn that there is a vowel change, but it must also learn that there is not an addition of t / d to the + +end of the verb. + +Type VI verbs (sing/ sang, drag/ drug) are interesting from this point of view, because they involve fairly common subregularities not found in other classes of verbs such as those in Type V. In the model, the Type VI verbs may be learned relatively quickly because of this + +subregularity. + +258 PSYCHOLOGICAL PROCESSES + +Figure 9 compares the average response strengths for base+ ed and past + ed regularizations as a function of amount of training . The results of this analysis are more or less consistent with Kuczaj's findings . Early in learning, the base + ed response alternative is clearly the stronger of the two. As the system learns, however, the two come together so that by about 100 trials the base+ ed and the past+ ed response alternatives are roughly equally strong. Clearly, the simulations show that the percentage of regularizations that are past + ed increases with experience- just as Kuczaj found in children . In addition , the two curves come together rather late, consistent with the fact, reported by Kuczaj (1977) , that these past+ ed forms predominate for the most part in children who are exhibiting rather few regularization errors of either type. Of the four children exhibiting more past + ed regularizations, three were regularizing less than 12% of the time . + +A closer look at the various types of irregular verbs shows that this curve is the average of two quite different patterns. Table 15 shows the overall percentage of regularization strength due to the base + ed alternative. It is clear from the table that the verbs fall into two general categories, those of Types III , IV , and VIII which have an overall preponderance of base+ ed strength (the percentages are all above .5) and Types II , VII , V, and VI which show an overall preponderance of past + ed strength (the percentages are all well below .5) . The major variable which seems to account for the ordering shown in the table is the amount the ending is changed in going from the base form to the + +0 .3 Base + ed + +0 . 2 + +0 . 1 + +0 . 0 + +0 40 80 120 160 200 Trials + +Q1jua + +.l1S asuodsaH + +18. LEARNING THE PAST TENSE 259 + +TABLE 15 + +PERCENTAGE OFREGULARIZATION STRENGTH DUE TO BASE+ ED + +Verb Type Percent base + ed Examples + +past-tense form . If the ending is changed little , as in sing/ sang or come/ came, the past+ ed response is relatively stronger. If the past tense involves a greater change of the ending, such as see/ saw, or sleep/ slept, then the past+ ed form is much weaker. Roughly, the idea is this: To form the past + ed for these verbs two operations must occur. The normal past tense must be created, and the regular ending must be appended. When these two operations involve very different parts of the verb, they can occur somewhat independently and both can readily occur. When, on the other hand, both changes occur to the same portion of the verb, they conflict with one another and a clear past + ed response is difficult to generate. The Type II verbs, which do show an overall preponderance of past + ed regularization strength, might seem to violate this pattern since it involves some change to the end in its past-tense form . Note, however, that the change is only a one feature change from / d/ to / t/ and thus is closer to the pattern of the verbs involving no change to the final phonemes of the verb. Figure lOA shows the pattern of response strengths to base+ ed and past+ ed regularizations for verb Types II , VII , V, and VI which involve relatively lit tle change of the final phonemes from base to past form . Figure lOB shows the pattern of response strengths to base + ed and past + ed for verb Types III , IV , and VIII . Figure lOA shows very clearly the pattern expected from Kuczaj's results. Early in learning, base+ ed responses are by far the strongest. With experience the past+ ed response becomes stronger and stronger relative to the base + ed regularizations until , at about Trial 40, it begins to exceed it . Figure lOB shows a dif ferent pattern. For these verbs the past + ed form is weak throughout learning and never comes close to the base + ed regularization response. Unfortunately , Kuczaj did not present data on the relative frequency of the two types of regularizations separately for different verb types. + +0.77 0.69 0.68 0.38 + +sleep/ slept catch/ caught see/ saw spend/ spent come/ came bite/ bit sing/ sang + +0.38 0.37 0.26 + +III IV VIII II VII V VI + +Base + ed + +0 . 0 + +0 .40 80 120 160 200 + +260 PSYCHOLOGICAL PROCESSES + +Verb Types II, V, VI and VII + +0 . 3 + +Base + ed + +0 . 2 + +Past + ed + +0 . 1 + +0 . 0 + +0 40 80 120 160 200 Trials + +.l1S astIodsaM + +A + +Verb Types III , IV and VIII + +B + +FIGURE 10. A: The pattern of response strengths to base+ ed and past + ed regularizations for verb Types II, V ~ VI, and VII. B: The pattern of response strengths to + +base+ ed and past + ed for verb Types III, IV, and VIII . + +18. LEARNING THE PASTTENSE 261 + +Transfer to Novel Verbs + +To this point we have only reported on the behavior of the system on verbs that it was actually taught. In this section, we consider the response of the model to the set of 86 low-frequency verbs which it never saw during training. This test allows us to examine how well the behavior of the model generalizes to novel verbs. In this section we also consider responses to different types of regular verbs, and we examine the model's performance in generating unconstrained + +responses. + +Overall degree of transfer. Perhaps the first question to ask is how accurately the model generates the correct features of the new verbs. Table 16 shows the percentage of Wickelfeatures correctly generated, averaged over the regular and irregular verbs. Overall, the performance is quite good. Over 90 percent of the Wickelfeatures are correctly generated without any experience whatsoever with these verbs. Performance is, of course, poorer on the irregular verbs, in which the actual past tense is relatively idiosyncratic. But even there, almost 85 percent + +of the Wickelfeatures are correctly generated. + +Unconstrained responses. Up until this point we have always proceeded by giving the model a set of response alternatives and letting it assign a response strength to each one. This allows us to get relative response strengths among the set of response alternatives we have provided. Of course, we chose as response alternatives those which we had reason to believe were among the strongest. There is the possibility , however, that the output of the model might actually favor some other, untested alternative some of the time . To see how well the output of the model is really doing at specifying correct past tenses or errors of the kind that children actually make, we must allow the model + +to choose among all possible strings of phonemes. + +To do this, we implemented a second version of the binding network . This version is also described in the Appendix . Instead of a + +TABLE 16 + +Regular Irregular Overall + +.92 .84 .91 + +PROPORTION OF WICKELFEA TURES CORRECTLY GENERATED + +262 PSYCHOLOGICAL PROCESSES + +competition among alternative strings , it involves a competition among individual Wickelphone alternatives , coupled with mutual facilitation between mutually compatible Wickelphones such as ~ A and kAm . 9 The results from the free -generation test are quite consistent with our expectations from the constrained alternative phase , though they did uncover a few interesting aspects of the model ' s performance that we had not anticipated . In our analysis of these results we have con sidered only responses with a strength of at least .2 . Of the 86 test verbs , There were 65 cases in which exactly one of the alternatives exceeded .2 . Of these , 55 were simple regularization responses , four were no -change responses , three involved double marking of regular verbs , (e.g., type was responded to with / tIptAd / ) , and there was one case of a vowel change (e .g ., slip / slept ) . There were 14 cases in which two alternatives exceeded threshold and one case in which three exceeded threshold . Finally , in six cases , no response alternative exceeded threshold . This occurred with the regular verbs jump , pump , soak , warm , trail , and glare . In this case there were a number of alterna tives , including the correct past -tense form of each of these verbs , + +competing with a response strength of about .1. + +Table 17 shows the responses generated for the 14 irregular verbs . The responses here are very clear . All of the above -threshold responses made to an irregular verb were either regularization responses , no -change responses (to Type I and V verbs as expected ) or correct vowel -change generalizations . The fact that bid is correctly gen erated as the past for bid , that wept is correctly generated as the past for weep , and that clung is correctly generated as a past tense for cling illus trates that the system is not only sensitive to the major regular past tense pattern , but is sensitive to the subregularities as well . It should also be noted that the no -change responses to the verbs grind and wind occurs on monosyllabic Type V verbs ending in t / d, again showing evi dence of a role for this subregularity in English past -tense formation . Of the 72 regular verbs in our low -frequency sample , the six verbs mentioned above did not have any response alternatives above thresh old . On 48 of the remaining 66 regular verbs , the only response exceeding threshold was the correct one . The threshold responses to + +the remaining 18 verbs are shown in Table 18 . + +9 The major problem with this method of generating responses is that it is tremendously computer intensive. Had we used this method to generate responses throughout the learning phase, we estimate that it would have taken over three years of computer time to complete the learning phase alone! This compares to the 260 hours of computer time the learning phase took with the response alternatives supplied. It took about 28 hours to complete the response generation process in testing just the 86 low-frequency verbs used in this section of the study. Of course, in biological hardware, this would not be a prob- + +18. LEARNING THE PAST TENSE 263 + +TABLE 17 + +THE MODEL'S RESPONSES TO UNFAMILIAR LOW-FREQUENCY IRREGULAR VERBS + +Verb Type Presented Word + +II + +III + +VI + +VII + +Note that for 12 of the 18 verbs listed in the table, the correct response is above threshold. That means that of the 66 regular verbs to which any response at all exceeded threshold, the correct response exceeded threshold in 60 cases. It is interesting to note, also, that the model never chooses the incorrect variant of the regular past tense. As shown in Table 8, verbs ending in a It I or Idl take I "dl in the past tense; verbs ending in unvoiced consonants take Itl , and verbs ending in vowels or voiced consonants take Id / . On no occasion does the model assign a strength greater than .2 an incorrect variant of the past tense. Thus, the model has clearly learned the substructure of the regular correspondence and adds the correct variant to all different types of base forms . These results clearly demonstrate that the model acts in accordance with the regular pattern for English verbs and that it can apply this pattern with a high level of success to novel as well as fami- + +liar verbs. + +In addition to the regular responses, five of the responses were nochange responses. In three cases the no-change response was to a verb ending in tide Four of the responses followed the pattern of Type III verbs, modifying the vowel and adding a final I t/ . Thus, for example, + +English Rendition Response Strength + +Phonetic Input / bid/ /TrA st/ + +0.55 0.57 + +Phonetic Response + +IV V + +/ bid / / Tr" st" d/ / bend " d/ / lend " d / / krEpt / / WEpt/ / wept / / kact / IbrEd ~dl IgrIndl / wInd / / kliNd / / kl " N/ / digd / / stikt / / terd / + +/ dig/ / stik/ / ter/ + +/ bend / / lend / / krEp / / WE P / + +/ kac / / brEd / / grInd / / wInd / / kliN / + +bid thrust bend lend creep weep + +0.28 0.70 0.51 0.34 0.33 0.67 0.48 0.44 0.37 + +( bid ) ( thrusted ) ( bended ) ( tended ) ( creeped ) ( weeped ) ( wept ) ( catched ) ( breeded ) ( grind ) ( wind ) ( clinged ) ( clung ) ( digged ) ( sticked ) ( teared ) + +catch breed grind wind cling + +dig stick tear + +0.28 0.23 0.22 0.53 0.90 + +264 PSYCHOLOGICAL PROCESSES + +TABLE 18 + +SYSTEM RESPONSES TO UNFAMILIAR LOW -FREQUENCY REGULAR VERBS + +guard ,/ gard / / gard / (guard ) + +/ gardA d / (guarded ) + +kid / kid / (kid ) + +(kidded ) + +mate / mAt / + +squat / skw \*t/ + +/ kid / / kid"d/ / mAt " d/ / mAdAd / / skw \*tAd/ / skw \*t / / skw \*kt / + +tour + +we have the past of sip rendered as sept, presumably on the model of sleep/ slept, keep/ kept, sweep/ swept, etc. Interestingly , three of the four cases involved verbs whose base form ended in / p/ just as in the models listed above. Even though these last responses are, strictly + +Verb Presented Phonetic Phonetic English Response Type Word Input Response Rendition Rendition + +End in rid + +End in un voiced consonant + +End in voiced consonant or vowel + +(mated) (maded) (squated) (squat) (squawked) + +carp + +drip + +map + +shape + +SIp + +slip smoke + +snap step type + +/ karp / + +/ drip/ + +/ map/ + +/ SAp/ + +/ sip/ + +/ slip/ / smOk/ + +/ snap/ / step/ / tlp/ + +/ karptl / karptAd / / driptA d/ / dript/ / mapt~ d/ / mapt/ / SApt/ / sipt/ I siptl I sept I / slept/ / smOktA d/ / smOk/ / snaptAd/ / steptAd/ / tIptA d/ + +(carped) (carpted) (dripted) (dripped) (mapted) (mapped) (shaped) (shipped) (sipped) (sepped) (slept) (smokted) (smoke) (snapted) (stepted) (typted) + +0.28 0.21 0.28 0.22 0.24 0.22 0.43 0.27 0.42 0.28 0.40 0.29 0.22 0.40 0.59 0.33 + +/ brwn / + +/ h" g/ / ffiA " l/ + +/ tur / + +/ brwnd / / br \*nd / / hAg/ / mAAld / / membAld / / turd " r/ / turd / + +(browned) (brawned) (hug) (mailed) (membled) (toureder) ( toured) + +brown + +hug mail + +0.46 0.39 0.59 0.38 0.23 0.31 0.25 + +18. LEARNING THE PAST TENSE 265 + +speaking, incorrect, they all indicate a sensitivity to the regular and + +subregular patterns of the English past tense. + +Perhaps the most surprising result evident from the table is the occurrence of a double past marker on the responses to seven of the verbs. Although we know of no references to this phenomenon in the literature , we expect that children (and adults) do occasionally make this kind of error . It is interesting, and possibly significant , that all seven of these responses occurred to verbs whose correct past tense is the addition of a / t/ . It would be interesting to see whether children 's + +errors of this type follow a similar pattern. + +Finally , there were just four responses that involved the addition or modification of consonants. These were maded as a past tense of mate, squawked as a past tense for squat, membled as a past tense for mail, and toureder as a past tense for tour. It is unlikely that humans would make these errors, especially the last two, but these responses are, for the most part, near threshold. Furthermore , it seems likely that many of these responses could be filtered out if the model incorporated an auto-associative network of connections among the output units. Such a network could be used to clean up the output pattern and would probably increase the tendency of the model to avoid bizarre responses. Unfortunately , we have not yet had the chance to implement this + +suggestion. + +Summary . The system has clearly learned the essential characteris tics of the past tense of English . N'ot only can it respond correctly to the 460 verbs that it was taught , but it is able to generalize and transfer rather well to the unfamiliar low -frequency verbs that had never been presented during training . The system has learned about the conditions in which each of the three regular past-tense endings are to be applied , and it has learned not only the dominant , regular form of the past + +tense , but many of the subregularities as well . + +It is true that the model does not act as a perfect rule -applying machine with novel past-tense forms . However , it must be noted that people - or at least children , even in early grade-school years - are not perfect rule -applying machines either . For example , in Berko 's classic ( 1958) study , though her kindergarten and first -grade subjects did often produce the correct past forms of novel verbs like spow, mott , and rick , they did not do so invariably . In fact , the rate of regular past-tense forms given to Berko 's novel verbs was only 51 percent : o Thus , we see + +10 Unfortunately, Berko included only one regular verb to compare to her novel verbs. The verb was melt. Children were 73 percent correct on this verb. The two novel verbs that required the same treatment as melt (mott and bodd) each received only 33 percent + +266 PSYCHOLOGICAL PROCESSES + +CONCLUSIONS + +We have shown that our simple learning model shows, to a remarkable degree, the characteristics of young children learning the morphol ogy of the past tense in English. We have shown how our model generates the so-called U-shaped learning curve for irregular verbs and that it exhibits a tendency to overgeneralize that is quite similar to the pattern exhibited by young children . Both in children and in our model, the verb forms showing the most regularization are pairs such as know/ knew and see/ saw, whereas those showing the least regularization are pairs such as feel/felt and catch/ caught. Early in learning, our model shows the pattern of more no-change responses to verbs ending in t / d whether or not they are regular verbs, just as young children do. The model, like children , can generate the appropriate regular pasttense form to unfamiliar verbs whose base form ends in various consonants or vowels. Thus, the model generates an / Ad/ suffix for verbs ending in t/ d, a / t/ suffix for verbs ending in an unvoiced consonant, and a / d/ suffix for verbs ending in a voiced consonant or vowel. + +In the model, as in children , different past-tense forms for the same word can coexist at the same time . On rule accounts, such transitional behavior is puzzling and difficult explain. Our model, like human children, shows an relati vely larger proportion of past + ed regularizations later in learning. Our model, like learners of English, will sometimes generate past-tense forms to novel verbs which show sensitivities to the subregularities of English as well as the major regularities. Thus, the past of cring can sometimes be rendered crang or crung. In short, our simple learning model accounts for all of the major features of the + +acquisition of the morphology of the English past tense. + +In addition to our ability to account for the major known features of the acquisition process, there are also a number of predictions that the + +model makes which have yet to be reported. These include: + +We expect relatively more past + ed regularizations to irregulars whose correct past form does not involve a modification of the + +final phoneme of the base form . + +. + +little reason to believe that our model's "deficiencies II are significantly + +greater than those of native speakers of comparable experience. + +18. LEARNING THE PAST TENSE 267 + +. We expect that the double inflection responses (/ dript~d/ ) will occasionally be made by native speakers and that they will roccur more f requen tly to verbs whose stem is ends in / p / or + +/ k/ . + +The model is very rich and there are many other more specific predictions which can be derived from it and evaluated by a careful analysis + +of acquisition data. + +We have, we believe, provided a distinct alternative to the view that children learn the rules of English past-tense formation in any explicit sense. We have shown that a reasonable account of the acquisition of past tense can be provided without recourse to the notion of a "rule " as anything more than a description of the language. We have shown that, for this case, there is no induction problem. The child need not figure out what the rules are, nor even that there are rules. The child need not decide whether a verb is regular or irregular. There is no question as to whether the inflected form should be stored directly in the lexicon or derived from more general principles. There isn't even a question (as far as generating the past-tense form is concerned) as to whether a verb form is one encountered many times or one that is being generated for the first time . A uniform procedure is applied for producing the past-tense form in every case. The base form is supplied as input to the past-tense network and the resulting pattern of activation is interpreted as a phonological representation of the past form of that verb. This is the procedure whether the verb is regular or irregular, + +familiar or novel. + +In one sense, every form must be considered as being derived. In this sense, the network can be considered to be one large rule for generating past tenses from base forms . In another sense, it is possible to imagine that the system simply stores a set of rote associations between base and past-tense forms with novel responses generated by "on-line " + +generalizations from the stored exemplars. + +Neither of these descriptions is quite right , we believe. Associations are simply stored in the network , but because we have a superpositional memory, similar patterns blend into one another and reinforce each other. If there were no similar patterns (i.e., if the feat ural representations of the base forms of verbs were orthogonal to one another) there would be no generalization. The system would be unable to generalize and there would be no regularization. It is statistical relationships among the base forms themselves that determine the pattern of responding. The network merely reflects the statistics of the featural + +268 PSYCHOLOGICAL PROCESSES + +the view that children do respond according to general rules of language. Why otherwise, it is sometimes asked, should they generate forms that they have never heard? The answer we offer is that they do so because the past tenses of similar verbs they are learning show such a consistent pattern that the generalization from these similar verbs outweighs the relatively small amount of learning that has occurred on the irregular verb in question. We suspect that essentially similar ideas will prove useful in accounting for other aspects of language acquisition . We view this work on past-tense morphology as a step toward a revised understanding of language knowledge, language acquisition, and + +linguistic information processing in general. + +ACKNOWLEDGMENTS + +This research was supported by ONR Contracts NOOO14-82-C-O374, NR 667-483 and NOOO14-79-C-O323, NR 667-437, by a grant from the System Development Foundation, and by a Research Scientist Career Development Award MHOO385 to the second author from the National + +Institute of Mental Health. + +18. LEARNING THE PAST TENSE 269 + +APPENDIX + +One important aspect of the Wickelfeature representation is that it completely suppressed the temporal dimension. Temporal information is stored implicitly in the feature pattern. This gives us a representational format in which phonological forms of arbitrary length can be represented. It also avoids an a priori decision as to which part of the verb (beginning, end, center, etc.) contains the past-tense inflection . This grows out of the learning process. Unfortunately , it has its negative side as well. Since phonological forms do contain temporal infor mation , we need to have a method of converting from the Wickelfeature representation into the time domain- in short, we need a decoding network which converts from the Wickelfeature representation to either the Wickelphone or a phonological representational for mat. Since we have probabilistic units, this decoding process must be able to work in the face of substantial noise. To do this we devised a special sort of decoding network which we call a binding network. Roughly speaking, a binding network is a scheme whereby a number of units compete for a set of available features- finally attaining a strength that is proportional to the number of features the units account for . We proceed by first describing the idea behind the binding network , then describing its application to produce the set of Wickelphones implicit in the Wickelfeature representation, and finally to produce the + +set of phonological strings implicit in the Wickelfeatures. + +Binding Networks + +The basic idea is simple. Imagine that there are a set of input features and a set of output features. Each output feature is consistent with certain of the input features, inconsistent with certain other of the input features, and neutral about still other of the input features. The idea is to find a set of output features that accounts for as many as possible of the output features while minimizing the number of input features accounted for by more than one output feature. Thus, we want each of the output features to compete for input features. The more input features it captures, the stronger its position in the competition and the more claim it has on the features it accounts for . Thus consider the case in which the input features are Wickelfeatures and the output features are Wickelphones. The Wickelphones compete among one another for the available Wickelfeatures. Every time a particular Wickelphone "captures" a particular Wickelfeature , that input feature no + +270 PSYCHOLOGICAL PROCESSES + +a .1 + +where kj ranges over the set of output units consistent with input units j . The total strength of output unit k at time t is a linear function of + +its inputs at time t - 1 and is thus given by + +" i . ak (t - 1) ~ Jk + +Jk + +ak (t) = LiJk WkJk (t) = La/. (t - 1) Jk / . Jk + +'/ k + +where Jk ranges over the set of input features consistent with output feature k , Ijk ranges over the set of output features consistent with input feature Jk, and ij takes on value 1 if input feature J is present and + +is 0 otherwise. + +We used the binding network described above to find the set of Wickelphones which gave optimal coverage to the Wickelfeatures in the input . The procedure was quite effective . We used as the set of output all of the Wickelphones that occurred anywhere in any of the 500 or so verbs we studied. We found that the actual Wickelphones were always the strongest when we had 80 percent or more of the correct Wickel features. Performance dropped off as the percentage of correct + +w . . = + +IJ Lakj k../ + +longer provides support for other Wickelphones. In this way, the system comes up with a set of more or less nonoverlapping Wickelphones which account for as many as possible of the available Wickelfeatures. This means that if two Wickelphones have many Wickelfeatures in common (e.g., k Am and kAm) but one of them accounts for more features than the other, the one that accounts for the most features will remove nearly all of the support for the very similar output feature which accounts for few if any input features uniquely . The binding network described below has the property that if two output units are competing for a set of input features, each will attain a strength proportional to the number of input features uniquely accounted for by that output feature divided by the total number of input features uniquely + +accounted for by any output feature. + +This is accomplished by a network in which each input unit has a fixed amount of activation (in our case we assumed that it had a total activation value of 1) to be distributed among the output units consistent with that input feature. It distributes its activation in proportion to the strength of the output feature to which it is connected. This is thus a network with a dynamic weight. The weight from input unit j to + +output unit i is thus given by + +18. LEARNING THE PAST TENSE 271 + +Wickelfeatures dropped . Still when as few as 50 percent of the Wickel features were correct , the correct Wickelphones were still the strongest most of the time . Sometimes , however , a Wickelphone not actually in the input would become strong and push out the 'I correct II Wickel phones . If we added the constraint that the Wickelphones must fit together to form an entire string (by having output features activate features that are consistent neighbors ) , we found that more than 60 percent of correct Wickelfeatures lead to the correct output string more + +than 90 percent of the time . + +The binding network described above is designed for a situation in which there is a set of input features that is to be divided up among a set of output features . In this case, features that are present , but not required for a particular output feature play no role in the evaluation of the output feature . Suppose , however , that we have a set of alternative output features , one of which is supposed to account for the entire pattern . In this case, input features that are present , but not consistent , with a given output feature must count against that output feature . One solution to this is to have input units excite consistent output units according the the rule given above and to inhibit inconsistent output units . In the case in which we tried to construct the entire phonological string directly from a set of Wickelfeatures we used the following + +activation rule : + +ak (t ) = LiJk WkJk (t ) - Lilk ,ik lk + +where lk indexes the input features that are inconsistent with output feature k . In this case, we used as output features all of the strings of less than 20 phonemes which could be generated from the set of Wick elphones present in the entire corpus of verbs . This is the procedure employed to produce responses to the lowest frequency verbs as shown + +in Tables 17 and 18. + +CHAPTER + +Mechani.sms of Sentence Processing : + +J. L. McCLELLAND and A. H. KAWAMOTO + +Like many natural cognitive processes, the process of sentence comprehension involves the simultaneous consideration of a large number of different sources of information . In this chapter, we consider one aspect of sentence comprehension: the assignment of the constituents of a sentence to the correct thematic case roles. Case role assignment is not, of course, all there is to comprehension, but it reflects one important aspect of the comprehension process, namely, + +the specification of who did what to whom. + +Case role assignment is not at all a trivial matter either , as we can see by considering some sentences and the case roles we assign to their constituents. We begin with several sentences using the verb break: + +19 + +Assigning Roles to Constituents of Sentences + +MULTIPLE CONSTRAINTS ON ROLE ASSIGNMENT + +(1) (2) (3) (4) (5) + +The boy broke the window. The rock broke the window. + +The window broke. + +We can see that the assignment of case roles here is quite complex . The first noun phrase (NP ) of the sentence can be the Agent (Sen tences 1, 4 , and 5) , the Instrument (Sentence 2) , or the Patient + +The boy broke the window with the rock. The boy broke the window with the curtain . + +(Sentence 3) . The NP in the prepositional phrase (PP) could be the Instrument (Sentence 4) , or it could be a Modifier of the second NP , as it is in at least one reading of Sentence 5. Another example again + +brings out the ambiguity of the role assignment of with -NPs : + +(6) The boy ate the pasta with the sauce. (7) The boy ate the pasta with the fork . + +In (6) the with - NP clearly does not specify an Instrument , but in (7) it + +clearly does. + +Before we go much further , it should be said that there is no univer sally accepted set of case roles , nor universal agreement as to the correct assignment of constituents to roles . We have adopted conven tions close to those originally introduced by Fillmore ( 1968) in "The Case for Case," but we do not think the details are of crucial impor tance to the behavior of our model . Later we will suggest ways in which an extension of our model might circumvent certain of the diffi - + +culties involved in specifying the correct assignment of cases. + +These complications aside, it appears from the examples that the meaning of the words in these sentences influences the assignment of arguments to roles . However , the placement of NPs within the sen- + +tences is also very important . Consider these two cases: + +(8) The vase broke the window . (9) The window broke the vase. + +Here we must rely on word -order constraints . That such constraints are + +very strong in English can be seen from sentences like : + +( 10) The pencil kicked the cow . + +Even though semantic constraints clearly would indicate that the cow is a much more likely Agent and the pencil a much more likely Patient , Sentence 10 simply is not given this interpretation by adult readers who + +are native speakers of English . + +Word -order constraints like those illustrated by ( 10) are very strong in English , but it is important to realize that such heavy reliance on such constraints is not universal . Bates and MacWhinney (in press~ Mac Whinney , Bates, & Kliegl , 1984) have shown that adult speakers of Italian will assign roles to sentences like ( 10) based predominantly on semantic constraints ~ 1 word order plays a very limited role and + +1 We use the phrase "semantic constraints" to refer to the constraints language users impose on the co-occurrence of constituents in particular roles in case-level representations. In the model, as we shall see, these constraints arise from the co-occurrences of + +274 PSYCHOLOGICAL PROCESSES + +determines assignment only when semantics and case-marking inflec- + +tions give no information . + +As the work of Bates and MacWhinney amply demonstrates, case role assignment is influenced by at least three different kinds of factors: word order, semantic constraints, and (when available) inflectional morphology. Reliance on anyone of these constraints is a matter of degree, and varies from language to language. In addition to these factors, there is one more that cannot be ignored, namely, the more global context in which the sentence is presented. Consider, for example, + +Sentence 11: + +(11) The boy saw the girl with the binoculars. + +We get one reading if prior context tells us II A boy was looking out the window, trying to see how much he could see with various optical instruments ." We get quite a different one if it says "Two girls were trying to identify some birds when a boy came along. One girl had a pair of binoculars and the other did not." Crain and Steedman (1985) have experimentally demonstrated contextual influences on parsing + +decisions. + +While the fact that word order and semantic constraints both influ ence role assignment has often been acknowledged (Bever, 1970~ Fodor, Bever, & Garrett , 1974) , there are few existing models that go very far toward proposing a mechanism to account for these effects. However, there are some researchers in language processing who have tried to find ways of bringing semantic considerations into syntactic processing in one way or another. One recent approach has been to rely on the lexicon to influence both syntactic processing and the construction of underlying functional representations (Ford, Bresnan, & Kaplan, 1982~ Kaplan & Bresnan, 1982~ MacWhinney & Sokolov, in press) . + +Ford et al. (1982) considered cases like the following : + +(12) The woman wanted the dress on the rack. (13) The woman positioned the dress on the rack. + +They noted that the preferred reading of the first of these had on the rack as a modifier of the dress, while the preferred reading of the second had on the rack as a locative argument of positioned. To account for this difference in role assignment, they proposed two principles: (a) lexical preference and (b) final arguments. Basically, lexical preference establishes an expected argument structure (e.g., Subject- Verb-Object in the case of want~ Subject- Verb- Object- Prepositional Object in the case of positioned) by consulting an ordered list of possible argument structures associated with each verb. If a constituent is encountered that could fill a slot in the expected argument structure, the constituent is treated as an argument of the verb. However, if a constituent is encountered that appears to satisfy the conditions on the final argument of the expected argument structure, its attachment is delayed to allow for the incorporation into the constituent of subsequent constituents. Thus, with want, the NP the dress is a candidate for final argument and is not attached directly as a constituent of the VP~ rather, a superordinate NP structure containing the dress on the rack is ultimately attached to the VP. With position, however, the dress would not be the final argument, and so is attached directly to the VP and closed. On the rack is then available for attachment as the final argu- + +ment to the VP. + +While this scheme certainly does some of the work that needs to be done in allowing the constraints imposed by the words in a sentence to influence role assignment, we do not think it goes nearly far enough. For as we saw in Sentences 4- 7, the NPs of a sentence also influence syntactic decisions. aden (1978) has verified that all three NPs in sen- + +tences like these influence subjects' role-assignment decisions. + +In the literature on sentence processing, no one disputes that various factors influence the final reading that is assigned to a sentence. However, there are various views of the way in which these factors are taken into account on-line. Kurtzman (1985) argues that the parsing process is directly guided by an ongoing plausibility analysis~ Marslen-Wilson and Tyler (1981) have pioneered this sort of view, and they stress the immediacy with which syntactic, semantic, and pragmatic considerations can all be brought to bear on the course of sentence processing. On the other hand, Frazier and her colleagues (e.g., Frazier & Rayner, 1982~ Rayner, Carlson, & Frazier, 1983) argue that the syntactic parser imposes its preferred structuring on the sentence based only on syntactic considerations, passing the results of this processing on quickly to a thematic interpreter that can reject the syntactic parse in + +favor of a thematically more appropriate reading. + +Whichever view one holds, it is clear that a mechanism is needed in which all the constituents of a sentence can work simultaneously to influence the assignment of roles to constituents. While we ourselves tend to favor a highly interactive view, the model we will describe here takes as its input a partial surface parse (though it is one that leaves certain attachment decisions unspecified) and generates from it a caselevel representation. Intended extensions of the model, which we will describe below, would incorporate feedback to the syntactic structure level~ but most of the model's behavior is not dependent on this feedback, and so readers committed to a less interactive view of the relation between syntactic and thematic analyses may yet find the model to be + +19. SENTENCE PROCESSING275 + +PROCESSES + +The model succeeded in meeting all these goals, as we shall see. + +The model also exhibits an additional property that we had not actually anticipated, even though it is a central characteristic of language understanding: The model exhibits an uncanny tendency to shade its representation of the constituents of a sentence in ways that are contextually appropriate. It does this without any explicit training to do so~ in fact, it does this in spite of the fact that the training inputs it receives are not contextually shaded as they would be in reality. We will examine this aspect of the model's behavior through examples~ and observe + +how it emerges naturally from the model~s structure. + +The model is, of course, very far from a complete or final model of sentence processing or even case role assignment. Perhaps it is best seen as a partial instantiation of one view of what some properties of the interface between syntactic and more conceptual levels of language representation might be like . We offer the model not because it "solves the problem of sentence comprehension." Rather~ we offer it because it suggests new ways of thinking about several aspects of language and language representation. The simulation model that embodies these ideas will undoubtedly require substantial development and elaboration. + +276 PSYCHOLOGICAL + +GOALS + +. + +ate readings of ambiguous words. + +The primary goal of our model is to provide a mechanism that can begin to account for the joint role of word order and semantic constraints on role assignment. We wanted the model to be able to learn to do this based on experience with sentences and their case representations. We wanted the model to be able to generalize what it learned to + +new sentences made up of novel combinations of words. In addition, we had several other goals for the model: + +. We wanted the model to be able to select contextually appropri- + +. We wanted the model to select the appropriate verb frame based on the pattern of arguments and their semantic features. + +. We wanted the model to fill in missing arguments in incom- + +plete sentences with plausible default values. + +We wanted the model to be able to generalize its knowledge of correct role assignment to sentences containing a word it has never seen before, given only a specification of some of the + +semantic properties of the word. + +ARCHITECTURE OF THE MODEL + +The role-assignment model is a distributed model, and has many properties in common with the verb learning model described in Chapter 18. The model consists of two sets of units: one for representing the surface structure of the sentence and one for representing its case structure. The model learns through presentations of correct surface-structurejcase -structure pairs~ during testing, we simply present the surface-structure input and examine the output the + +It is our belief , though , that the basic principles that it embodies will prove extremely valuable as cognitive science continues to try to come + +to grips with the problem of understanding natural language . + +We have limited the model in several ways . Most importantly , we + +have considered only single clause sentences . We have also considered only a limited set of roles and a limited vocabulary . Since we have restricted the analysis to English , case inflectional morphology does not arise . Within these bounds , we will see that we have been able to meet the goals of the model quite successfully , using a very simple POP + +architecture . + +Previous , Related Work + +Both Cottrell ( 1985 ~ Cottrell & Small , 1983 ) and Waltz and Pollack ( 1985 ) have preceded us in noting the appeal of connectionism as a means of exploiting the multiple constraints that appear to influence both case role assignment and the contextual disambiguation of ambi guous noun phrases . Their models differ from ours in several ways , most notably in that both rely primarily on local representations ( one unit - one - concept ) as opposed to distributed representations , although Waltz and Pollack ( 1985 ) do suggest ways that a distributed representa tion could be used to represent global contextual influences on word meaning disambiguation . Within the context of distributed models , ours builds on the work of J . A . Anderson ( 1983 ) and Kawamoto ( 1985 ) : Both models show how context can be used to select the appropriate reading of an ambiguous word . Our work incorporates + +mechanisms quite like theirs to accomplish this and other goals . + +Finally , Hinton ' s ( 1981a ) early discussion of the use of distributed representations to represent propositions played an important role in + +the development of the ideas described here . + +278 PSYCHOLOGICAL PROCESSES + +Sentences. The sentences processed by the model consist of a verb and from one to three NPs. There is always a Subject NP, and optionally there may be an Object NP. If this is present, there may also be a with-NP; that is, a NP in a sentence-final prepositional phrase beginning with the word with. All of the numbered sentences considered in the introduction are examples of sentence types that might be presented to + +the model. + +Input format of sentences . What the model actually sees as input is + +not the raw sentence but a canonical representation of the constituent structure of the sentence , in a form that could be produced by a simple surface parser and a simple lexicon . Such a parser and lexicon are not , + +presented to the model in this canonical format . We discuss ways such a parser could be implemented in a PDP model in the discussion + +section . + +Semantic Microfeatures + +In the canonical input format , words are represented as lists of semantic microfeatures ( Hinton , 1981a ~ see Chapter 3 ~ Waltz & Pol lack , 1985 , also make some use of a microfeature representation ) . For both nouns and verbs , the features are grouped into several dimen sions . Each dimension consists of a set of mutually exclusive values , and , in general , each word is represented by a vector in which one and only one value on each dimension is ON for the word and all of the other values are OFF . Values that are set to be ON are reoresented in + +the feature vectors as Is . Values that are set to be OFF are represented + +as dots ( " . " ) . + +We chose the dimensions and the values on each dimension to cap ture what we felt were important dimensions of semantic variation in the meanings of words that had implications for the role assignments of the words . We should be very clear about one point , though , which is + +that we do not want to suggest that the full range of the phenomena that are described under the rubric of the " meanings " of the words are captured by these semantic microfeatures . Indeed , we do not think of words as actually having some fixed meaning at all . Exactly how we do think of meanings will become clear after we examine the behavior of the model , so we postpone a fuller consideration of this issue until + +HUMAN + +SOFTNESS + +GENDER + +VOLUME + +FORM + +POINTINESS + +BREAKABILITY + +OBJ- TYPE + +different dimensions of the verbs may need some explication. Basically, these dimensions are seen as capturing properties of the scenario specified by the verb. Thus, the DOER dimension indicates whether there is an Agent instigating the event. The CAUSE ,dimension specifies whether the verb is causal. If not, it indicates whether this is because there is no cause specified (as in the case of the window broke) or whether it is 1::~cause there is no change (as in the case of the boy + +human nonhuman + +soft hard + +male female neuter + +small medium large + +compact 1- 0 2- D 3 - D + +pointed rounded + +fragile unbreakable + +food toy tool utensjl furniture + +animate nat - inan + +Verbs + +DOER yes no + +CAUSE yes no -cause no -change + +TOUCH agent jnst both none AisP + +NA T\_ CHNG pieces shreds chemjcal none unused + +AGT \_ MVMT trans part none NA PT - MVMT trans part none N A + +INTENSITY low high + +Note : nat -inan = natural inanimate , AisP = Agent is Patjent , + +N A = not applicable . + +touched the girl ) . The TOUCH dimension indicates whether the Agent , the Instrument , both , or neither touches the Patient ~ the " AisP " value simply indicates that the Agent and the Patient are the same (as in the cat moved) . The N A T\_CHNG dimension specifies the nature of the change that takes place in the Patient . The AGT \_MVMT and PT\_ MVMT specify the movement of the Agent and the Patient , respectively ~ and INTENSITY simply indicates the forcefulness of the action . The labels given to the dimensions are, of course , only for reference ~ they were chosen so that each noun or verb dimension would have a + +unique first letter that could be used to designate the dimension . + +It must be stressed that we are not strongly wedded to this particular choice of features , and that other features would need to be included to extend the model to larger sets of nouns and verbs . On the other hand , the features that we did include were carefully chosen because they seemed highly relevant to determining the case role assignments . For example , the DOER dimension directly specifies whether there is or is not an Agent . Thus , the features of the verb , in particular , often have direct case-structural implications . (We would prefer a model that con structed its own semantic microfeatures using back propagation [Chapter 8] or a related method for learning , but this extension has not + +yet been implemented .) + +Figures 1 and 2 give the vectors that we assigned to each of the words used in the model . It will be immediately noted that some of our encoding decisions were arbitrary , and that sometimes we seem to be forcing words into molds that they do not perfectly fit . Further , each feature has the same weight as all the others , and is as definite as all the others . Reality is not nearly so definite or evenhanded , of course . Balls are round , but may be soft or hard ~ paperweights are generally compact in shape but need not be, etc. The definiteness of the input used in the simulations is a simplification that we have adopted to make the initial coding of the input patterns as straightforward as possible . A more realistic coding would allow some features to be more definite than others . We will see that the model tends to correct this + +deficiency on its own accord . + +One of our goals for the model is to show how it can select the con textually appropriate meaning for an ambiguous word . For ambiguous words (bat, flying or baseball , and chicken , living or cooked ) the input pattern is the average of the feature patterns of each of the two read ings of the word . This means that in cases where the two agree on the value of a particular input dimension , that dimension has the agreed value in the input representation . In cases where the two disagree , the feature has a value of .5 (represented by II? II) in the input representa tion . A goal of the simulations is to see if the model can correctly fill in these unspecified values , effectively retrieving the contextually + +280 PSYCHOLOGICAL PROCESSES + +4 An alternative name for these units would be "surface-structure" units, to indicate that they do not capture the notion of underlying subject, object, etc. However, we have chosen the term "sentence-structure" because, for present purposes, the information they capture is not even a full surface-structure parse of the sentence~ in particular, it does not + +This is indicated in Figure 2 by the pattern of features next to the plain + +verb.3 + +The feature patterns corresponding to the different case frames the model must choose among are indicated on the lines in the table fol lowing its generic pattern. (The labels on these lines are used simply to designate the feature patterns. They indicate the roles the various arguments in the surface structure of the sentence play. Thus, broke A VPI specifies the case frame in which the surface subject is the Agent, the surface object is the Patient, and the with -NP is the Instrument .) Note that the microfeatures of two different readings of the same verb may or may not differ , depending on whether the features of the scenario do + +or do not change in different case frames. + +The feature vectors for the constituents of the sentence The boy broke the window with the hammer are shown just below the corresponding constituents at the top of Figure 3. Note that these are displayed in the order: Verb, Subject NP, Object NP, and With -NP. The row of letters below the feature vectors indicates the first letter of the name of the dimension on which each feature represents a value. For example, the first two elements of the verb feature vector are labeled d for the DOER dimension~ the first two values of each of the three noun + +feature vectors are labeled h for the HUMAN dimension. + +Sentence - structure units . The sentence - structure level representation of an input sentence is not actually the set of constituent feature vec tors ~ rather , it is the pattern of activation these vectors produce over units that correspond to pairs of features . These units are called + +sentence - structure ( SS ) units . 4 + +3 The different handling of nouns and verbs is not a principled distinction , but an exploration of two endpoints on a continuum ranging from underspecification of the input for ambiguous words to complete specification of an input representation , regard less of the fact that the features used in the case role representation will differ as a func tion of context . Perhaps the idea that the features will be altered as a function of context is the best way of putting things in this case . We imagine that the true state of affairs is intermediate between these two extremes , for both nouns and verbs . In any case , the model does not have any prior commitment to the idea that the features in the input representation should be preserved in the output representation ~ the full prespecification simply gives the model a fuller description to work from , thereby allowing greater dif - + +ferentiation of the different verbs . + +HUMAN = yes / GENDER = male + +SOLIDITY = hard / BREAKABILITY = fragile + +among many others ~ for the verb , one of the units corresponds to + +DOER = yes / TOUCH = instrument + +(i .e., there is a doer - the Instrument touches the Patient ) . + +The sentence -structure units are displayed in Figure 3 in four roughly triangular arrays . The verb array is separated from the arrays for the three NPs to indicate that different features are conjoined in the verb + +and NP representations . + +Each array contains the conjunctive units for the constituent immedi ately above it . There is a unit wherever there is aI , a " ? " , or a " ." . Within each array , the units are laid out in such a way that the column a unit is in indicates one of the microfeatures that it stands for , and the row it is in indicates the other microfeature . Rows and columns are both ordered in the same way as the microfeature vectors at the top of the figure . The dimensions are indicated by the row of letters across the top of each array and along the left (for the verb units ) or right (for the three sets of NP units ) . Note that the set of units in each array fills less than half of each block for two reasons . First , there are only [n (n - 1) ] / 2 distinct pairs of n features ~ second , pairs of values on the + +same dimension are not included . + +We considered various schemes for activating the sentence -structure units . One possible scheme would be to use a strict deterministic activation rule , so that a particular SS unit would be turned on only if both of the features the unit stands for were on in the feature vector . This use of the SS units would allow the model to learn to respond in a finely tuned way to particular conjunctions .of microfeatures . However , we wished to see how well the model could function using an inherently noisy input representation . Furthermore , as discussed in Chapter 18 , we knew that generalization is facilitated when units that only partially match the input have some chance of being activated . In the present case , we considered it important to be able to generalize to words with similar meanings . Therefore , the SS units were treated as stochastic binary units , like the units used in Chapter 18 . Each SS unit received excitatory input from each of the two features that it stands for , and we set the bias and variance of the units so that when both of a SS unit ' s features were active , the unit came on with probability .85 ~ and when neither was active , it came on with probability .15 . These cases are represented in the figure by " 1" and " ." , respectively . Units receiving one excitatory input came on with probability .5~ these units + +286 PSYCHOLOGICAL PROCESSES + +The use of the 55 units in conjunction with these particular activation assumptions means that the input representation the model must use as the basis for assigning words to case roles is both noisy and redundant. Each feature of the input is represented in the activation of many of the 55 units, and no one of these is crucial to the representation. A drawback of these particular activation assumptions, however, is that they do not allow the model to learn to respond to specific conjunctions of inputs. While the model does well in our present simulations, we presume that simulations using a larger lexicon would require greater differentiation of some of the noun and verb representations. To handle such cases, we believe it would be necessary to allow tuning of the input connections to the SS units via back propagation (Chapter 8) so that greater differentiation can be obtained when necessary. In principle, also, higher-order conjunctions of microfeatures might sometimes be required. Our use of broadly tuned, pair-wise conjunctive units illustrates the style of representation that we think is appropriate for the input , but the present version is only an approximation to what we would expect a model with a tunable input representation to build for + +itself . + +Case role representation. The case role representation takes a slightly different form than the sentence-structure representation. To understand this representation, it is useful to drop back to a more abstract viewpoint , and consider more generally how we might represent a structural description in a distributed representation. In general, a structural description can be represented by a set of triples of the form (A R B) where A and B correspond to nodes in the structural description, and R stands for the relation between the nodes. For example, a class-inclusion hierarchy can be represented by triples of the form (X IS-A Y) , where X and Yare category names. Any other structural description, be it a syntactic constituent structure, a semantic constituent structure, or anything else, can be represented in just this way. Specifically, the case role assignment of the constituents of the sentence The boy broke the window with the hammer can be represented + +as: + +Broke Agent Boy Broke Patient Window Broke Instrument Hammer + +The constituent structure of a sentence such as The boy ate the pasta + +with the sauce would be represented by: + +Ate Agent Boy Ate Patient Pasta Pasta Modifier Sauce + +In a localist representation , we might represent each of these triples by a single unit . Each such unit would then represent the conjunction of a particular head or left -hand side of a triple , a particular relation , and a particular tailor right-hand side. Our more distributed approach is to allocate groups of units to stand for each of the possible relations (or roles ) , namely , Agent , Patient , Instrument , and Modifier , and to have units within each group stand for conjunctions of microfeatures of the first and third arguments (the head and the tail ) of the triple . Thus , the triple is represented not by a single active unit , but by a pat- + +tern of activation over a set of units . + +In our implementation , there is a group of units for each of the four relations allowed in the case structure . In Figure 3, the Agent , Patient , Instrument , and Modifier groups are laid out from left to right . Within each group , individual units stand for conjunctions of one microfeature of the head of each relation with a microfeature of the tail of each rela tion . Thus , for example , Broke - Agent - Boy is represented by a pattern of activation over the left -most square block of units . The unit in the ith row and jth column stands for the conjunction of feature i of the verb with feature j of the noun . Thus all the units with the same verb feature are lined up together on the same row , while all the units with the same noun feature are lined up together in the same column . For the Modifier group , the unit in the ith row and jth column stands for the conjunction of feature i of the modified NP and feature j of the modifier NP . Letters indicating the dimension specifications of the + +units are provided along the side and bottom edges. + +The figure indicates the net input to each case role unit produced at the end of the training described below , in response to the sentence The boy broke the window with the hammer . (We will see very shortly how these net inputs are produced .) As before , a 1 indicates that the net input would tend to turn the unit on with probability (p) greater than or equal to .85, and a " ." indicates that the net input would tend to turn it on with probability of .15 or less. A "+ " indicates that the net input has a tendency to turn the unit on (.85 > p > .5) , and a "- " indicates that the net input has a tendency to turn the unit off + +(.5 > p > .15) . + +The correct case-frame interpretation of the sentence is provided to the model by a specification that lists , for each of the four possible case roles , the label corresponding to the head and tail of the role . These are shown below each of the four blocks of case role units . The "# " is used to indicate a null slot filler , as in the Modifier role in the present example . From this it is possible to compute which units should be on in the case role representation . Here we simply assume that all the correct conjunctions should be turned on and all other units should + +PROCESSES + +In this example, the pattern of net inputs to the case role units corresponds quite closely to the correct case role representation of the sentence. The features of boy may be seen in the columns of the block of Agent units~ the features of window in the columns of the block of Patient units~ and the features of hammer in the columns of the block of Instrument units. The features of the Agent- Verb- Patient reading of the verb broke can be seen in the rows of each of these three sets of units. There are no features active in the fourth set of units, the Modifier units, because there is no Modifier in this case. In both the Agent and the Patient slots, the model tends to turn on (p > .5) all the units that should be on, and tends to turn off (p < .5) all the units that should be off . In the Instrument slot, there are some discrepancies~ these are indicated by blackening the background for the offending units. All of the discrepancies are relatively mild in that the unit has either a weak tendency to go on when it should not (+ on a black background) or to go off when it should be on (- on a black background) . Several things should be said about the case-frame representations. The first thing is that the slots should not be seen as containing lexical items. Rather, they should be seen as containing patterns that specify some of the semantic properties assigned by the model to the entities designated by the words in the sentences. Thus, the pattern of feature values for the verb break specifies that in this instance there is contact between the Instrument and the Patient. This would also be the case in a sentence like The hammer broke the window. However, in a sentence like The boy broke the window, with no Instrument specified, the pattern of feature values specifies contact between the Agent and the Patient. Thus, the verb features provide a partial description of the scenario described by the sentence. The noun features, likewise, provide a partial description of the players (to use Fillmore 's analogy) in the scenario, and these descriptions, as we will see later on, may actually be modulated by the model to take on attributes appropriate for the + +scenario in question. + +288 PSYCHOLOGICAL + +Details of Sentence Processing and Learning + +The model is very much like the verb learning model (Chapter 18) . When a sentence is presented, a conventional computer program front end determines the net input to each of the sentence-structure units, based on the feature vectors of the words. Each of these units is then turned on probabilistically , as described above. Each surface-structure unit has a modifiable connection to each of the case-structure units. In addition , each case-structure unit has a modifiable bias (equivalent to a connection from a special unit that is always on) . Based on the sentence-structure pattern and the current values of the weights, a net input to each case-structure unit is computed~ this is just the sum of the weights of the active inputs to each unit plus the bias term . Casestructure units take on activation values of 0 and 1, and activation is a probabilistic function of the net input , as in the verb learning model. During learning, the resulting activation of each case-structure unit is compared to the value it should have in the correct reading of the sentence. The correct reading is supplied as a "teaching input " specifying which of the case role units should be on. The idea is that this teaching input is analogous to the representation a real language learner would construct of the situation in which the sentence might have occurred. Learning simply amounts to adjusting connection strengths to make the output generated by the model correspond more closely to the teaching input . As in the verb learning model, if a unit should be active and it is not, the weights on all the active input lines are incremented and the threshold is decremented. If a unit should not be active but it is, the weights on all the active output lines are decremented and the threshold is incremented. This is, of course, just the perceptron convergence procedure (Rosenblatt, 1962) , whose strengths and weaknesses have been examined and relied upon throughout the + +book. + +The most important thing about the model is the fact that its response to new inputs is strictly dependent upon its experience. In evaluating its behavior, then, it is important to have a clear understanding of what it has been exposed to during learning. We have done a number of different experiments with the model, but we will focus pri- + +marily on one main experiment . + +The main experiment consisted of generating a corpus of sentences derived from the sentence frames listed in Table 2. It must be emphasized that these sentence frames were simply used to generate a set of legal sentences. Each frame specifies a verb, a set of roles, and a list of possible fillers of each role. Thus, the sentence frame The human broke the fragile\_object with the breaker is simply a generator for all the sentences in which human is replaced with one of the words on the list of humans in Table 3, fragile\_object is replaced with one of the words on the list of fragile objects in Table 3, and breaker is replaced with one of the words on the list of breakers in the table. It is clear that these generators do not capture all of the subtle distributional + +19. SENTENCE PROCESSING 289 + +SIMULATION EXPERIMENTS + +290 PSYCHOLOGICAL PROCESSES + +TABLE 2 + +AVP AVPI IVP AVP PV + +AVP AVPM AVPI IVP + +> AVS AVP AVS PV + +GENERATORS FOR SENTENCES USED IN TRAINING AND TESTS + +Sentence Frame Argument Assignment + +The human ate . A VF The human ate the food . A VP The human ate the food with the food . A VPM The human ate the food with the utensil . A VPI The animal ate . A VF The predator ate the prey . A VP + +Note: Argument assignments specify the case role assignment of the constituents of a sentence from left to right . A = Agent, V = Verb , P = Patient, I = Instrument , + +M = Modifier , F = (implied) Food, S = Self. + +properties of referents in real scenarios (e.g ., the model is completely sex and age neutral when it comes to hitting and breaking things , con trary to reality ) , and so we cannot expect the model to capture all these subtleties . However , there are certain distributional facts implicit in the full ensemble of sentences encompassed by the generators . For exam ple , all the breakers but one are hard , not soft (only ball is coded as soft in the feature patterns ) ~ only the humans enter as Agents into scenarios + +The human broke the fragile\_object. + +The human broke the fragile\_object with the breaker. + +The breaker broke the fragile\_object. The animal broke the fragile\_object. + +The fragile\_object broke. + +The human hit the thing. + +The human hit the human with the possession. + +The human hit the thing with the hitter. + +The hitter hit the thing. + +The human moved. + +The human moved the object. + +The animal moved. The object moved. + +human + +animal + +object + +man woman boy girl + +human animal object + +wolf lion + +Ii-chicken sheep + +co-chicken cheese spaghetti carrot + +fork spoon + +plate window vase + +ball bb-bat paperwt hatchet hammer rock vase + +paperwt ball bb-bat hatchet hammer rock + +ball dog bb-bat doll hatchet hammer vase + +TABLE 3 + +NOUN CATEGORIES + +fl -bat Ii-chicken dog wolf sheep lion + +ball bb-bat paperwt cheese co-chicken curtain desk doll fork hatchet hammer plate rock + +pasta spoon carrot vase window + +thing + +predator + +prey food + +utensil + +fragile\_object + +hitter + +breaker + +posseSSion + +are indicated in Table 2 by the sequence of capital letters . These indi cate the assignment of arguments from the sentences to the roles of Agent , Verb , Patient , Instrument , and Modifier ( of the Patient ) . 5 Note that there are some sentences that could be generated by more than one generator . Thus , The boy hit the girl with the ball can be generated by the generator The human hit the human with the possession , in which case the ball is treated as a Modifier of the Patient . Alternatively , it may be generated by the generator The human hit the thing with the hitter . In this case , the ball is treated as the Instrument . Similarly , The bat broke the vase can be generated by The breaker broke the fragile \_ object , in which case its case - frame representation contains a + +5 Two special cases should be noted : For The human ate , the case frame contains a specification ( F ) that designates an implied Patient that is the generic food with unspeci fied shape , as indicated in the feature patterns displayed in Figure 1. For The human mo1-'ed and The animal moved , the case frame contains a specification ( 5 ) that indicates that there is an implied Patient who is the same as the Agent (note that the sense of the + +292 PSYCHOLOGICAL PROCESSES + +baseball bat serving as Instrument . The same sentence can also be generated by The animal broke the fragile\_object, in which case, of course, its case-frame representation contains a flying bat serving as Agent. For the main experiment , we generated all the sentences covered by the generators and then selected eight of each type to use as training sentences. Of these we selected two to be familiar test sentences. In addition , we selected two additional sentences from each generator to be used as novel test sentences. These sentences were never used to + +train the model.6 + +The model was given 50 cycles of training with the set of training sentences. On each cycle, each sentence was presented, the model's response to it was generated, and connection strengths were adjusted + +according to the perceptron convergence procedure. + +After the 5th, 10th, 20th, 30th, 40th, and 50th training cycles, the model was tested on both the familiar and the novel test sentences. No learning occurred during the tests, so that the response to the novel test sentences always represented generalization from the training materials + +rather than the effects of direct experience. + +Basic Results + +Figure 4 gives a very global indication of the model ' s performance on both the familiar and the novel test sentences at each phase of testing . The figure indicates the average number of incorrect microfeatures pro duced by the model as a function of learning trials , for both the fami liar and unfamiliar test sentences . There are a total of 2500 case role units , so on the average the model is getting over 95 % correct , even with unfamiliar sentences , after the first 5 learning cycles , and is down to about 1 % error at Cycle 50 . However , these statistics are somewhat misleading , since on the whole , most of the case role units should be off . A more realistic indication of the absolute performance level is provided by the observation that between 56 and 168 of the units should be on in the correct case role representation of each sentence . In general , the errors that the model does make are about evenly dis tributed between sins of commission ( false alarms ) and sins of + +6 Some of the generators (e.g., The human hit the thing with the hitter ) generate rather large numbers of different sentences (in this case, 756) , but others (e.g., The human ate, The predator ate the prey) generate only very small numbers of sentences (four in each of these cases) . The training materials contained four copies of each of two of these sentences so that even here , there were two familiar test sentences and two unfamiliar test + +UNFAMILIAR SENTENCES + +Number of Cycles of Training + +Input Frame 10 20 30 40 + +a ID~O)- + +~O)It)Q)MID~O) + +It) - + +NcDlt)- + +N~~-N + +OI~InOlOo)C')O~CQ""'"NNr-.CQ....C')InNN + +;~~~~~~~~~Zc8\_..\_.\_\_.\_- + +~ + +~~~IiC + +&T"~.~:t':=':~;: + +~=: + +w,=.il}rH + +FIGURE 6. Number of missed features in output for each unfamiliar sentence, after 5, + +10, 20, 30, 40, and 50 cycles of training. See previous caption for conventions. + +128 9183467652~6047 136 60?7A145~5732265 + +These two sentences happened to be among the unfamiliar test sentences generated by the generators The animal broke the fragile object and The breaker broke the fragile\_object. 7 The patterns of activitY produced by the model in response to each of these two sentences are shown in Figures 7 and 8. We can see that in the case of The dog broke the plate, there is a strong pattern of activation over the Agent units, while in the case of The hammer broke the vase, there is a strong pattern of activation over the Instrument units. In fact, the pattern of activation over the Agent units in the first case corresponds closely to the expected target pattern for broke A VP- agent- dog, and the pattern of + +This example has been described in some detail, in part to explicate our displays of the model's responses to particular sentences. In the process we have seen clearly that dog and hammer trigger the appropriate bindings of arguments to slots. This is also the case for examples of the form The plate broke. There, Figure 9 indicates that the only slot + +in which there is appreciable activity is the Patient slot. + +These examples illustrate that the model has learned quite a bit about assigning fillers to slots on the basis of the microf eatures of the slot fill ers involved . For the word break, animate surface subjects are treated as Agents and inanimate surface subjects are treated as Instruments if an Object is specified~ if not, the inanimate surface subject is treated as Patient. The model seems to capture this fact pretty well in its + +behavior. 10 + +11 Though the model did not actually learn the sentence The boy hit the girl or any other sentence containing bo~v and girl as Subject and Object, it did learn s~veral sentences in which boy was the subject of hit and several others in which ,, bbOOOOOOO + +hnS sgggvvv f f f f PPbOOOOOOOo 8.e83 8.2943 ' + +8.2963 8 . 3683 + +8 . 1867 8 ..2474 8 ..247. + +1,318g 1,3192 I,eeee 8,eee8 e . 3196 + +. .319t e .eeee e .. ee8 + +hhss ~ gvvvffffppbbOOOOOOO + +304 PSYCHOLOGICAL PROCESSES + +of incorrect features for unambiguous words. In the atypical case (The wolf ate the chicken) , the pattern is really much closer to the cooked chicken than the live one that the model was "supposed" to have retrieved. It is difficult to fault the model too much in this case, however. Though it was never given sentences of the form The animal ate the food, it was given sentences of the form The animal ate, where the underlying case frame included (implied) food. Thus the model had considerable reason to treat the object of The animal ate as food. Though it had learned The lion ate chicken referred to a live chicken, it appears to prefer to treat chicken in The wolfate chicken more as cooked food than as a living animal. Some of the properties of the live chicken are weakly present- e.g., its female sex and its natural, animate object- + +type classification- but the predominant pattern is that of food. + +With this exception, the model has shown itself quite capable of handling sentences containing ambiguous words as well as sentences containing only unambiguous words. This is, of course, not really surprising in view of the fact that all the words in the sentence are used to help constrain the features assigned to the fillers of every role in the case frame. When one word does not provide the information to constrain the output , the model can exploit information contained in other + +words. + +Structural Ambiguity + +In this section, we briefly consider another type of ambiguity that sometimes arises even when the words in the sentence are unambiguous. This is the structural ambiguity of sentences such as The man hit the woman with the hammer. In such cases, hammer can either be the Instrument or simply a Modifier of woman. This case-structure ambiguity parallels an ambiguity in the syntactic structure of the sentence as well~ if hammer is an Instrument , it is dominated directly by the VP~ whereas if it is a Modifier , it is dominated by the NP the window. Because hammer was included both in the list of possible possessionmodifiers of human objects and in the list of possible instruments of hitting (designated as possessions and hitters in the sentence frames in Table 2 and in the noun categories in Table 3) , either of these readings is equally possible. Thus, it is not so surprising that the model has considerable difficulty with such sentences, generating a blend of the two + +readings. + +A particularly interesting case of case-structure ambiguity occurs with the sentence The bat broke the window. As already mentioned, the sentence is both lexically ambiguous and ambiguous in case structure, and + +the structural ambiguity hinges on the lexical ambiguity . If bat is a baseball bat then the case frame specifies an Instrument and a Patient, but if it is a flying bat then the case frame specifies an Agent and a + +Patient. + +Figure 13 illustrates the pattern of activation generated in this case. What the model does, quite sensibly, is activate one kind of bat- the flying bat- on the Agent units and the other - the baseball bat- on the Instrument units (see the figure caption for a detailed explanation of + +the use of the black background in this figure) . + +People generally get only one reading of a sentence at a time , even when (as in this case) the sentence is easy to interpret in either of two ways. In a later section of this chapter we explain how crossconnections among the case role units and back-connections to sentence-level units would tend to cause the model to choose a single + +interpretation , even in these ambiguous cases. + +Shades of Meaning + +Another property of the model, related to its handling of ambiguity , is the fact that it can shade the feature patterns it assigns, in ways that often seem quite appropriate. One example of this tendency arises in the model's response to the sentence The ball broke the vase. A summary of the pattern produced is shown in Figure 14. The feature pattern on the Instrument units matches the features of ball fairly closely. The value on each dimension that is most strongly activated is the correct value, except on one dimension - the hard/ soft dimension. On this dimension, we can see that the model has gotten ball completely + +wrong- it has strongly activated hard, instead of soft. + +In one sense, this is clearly an ,t error " on the model's part~ all the balls that it learned about were soft, not hard balls. But in another sense, it is a perfectly sensible response for the model to make. All of the other instruments of breaking (called breakers in Table 3) were, in fact, hard. The model picked up on this fact, and shaded its interpretation of the meaning of the word ball as a result. As far as this model is + +concerned, balls that are used for breaking are hard, not soft. + +This kind of shading of meaning is just another manifestation of the process that fills in missing arguments, chooses appropriate verb frames, and selects contextually appropriate meanings of words. It is part and parcel of the mechanism that generally results in the activation of the nominally correct feature pattern. It is a mechanism that naturally blends together what it learns into a representation that regularizes slot fillers , in the same way that the verb learning model discussed in + +FIGURE 14. Summary of the activations on the case role units for the sentence The ball + +broke the ~'ase. + +moved itself In the third case, the case frame contained the subject only as Patient. The model had some difficulty with these constructions, but generally put inanimate subjects into the Patient role only (as in The desk moved) , and animate subjects into both the Agent and Instrument role. With The doll moved, however, the case-frame representation shows considerable activation in the Agent slot. The pattern of activation there (Figure 15) seems to be pretty much that of a small (though fragile and nonhuman) girl - or perhaps it is simply an + +animate doll . + +Generalization to N oyel Words + +We have already seen that the model can generalize quite well from particular sentences that it has learned about to new ones that it has not seen before. It is, obviously, important to be able to generalize in this way, since we cannot expect the training set of sentences to cover all possible word combinations in the language~ even if they contain onl)' a single clause. Thus far, however, we have only considered generalization to sentences made up of familiar words. What would happen, we wondered, if we tested the model using new words that it had never seen before? To examine this issue, we tested the model on the verb touch. Touch differs from hit in only one feature, namely, intensity ~ otherwise all of the same verb features are appropriate to it . We assumed that the model already knew the meaning of touch- that is, we assumed that the correct input microfeatures were activated on presentation of a sentence containing it . We then took all of the test sentences containing the \\I10rd hit, replaced hit with touched, and tested the model on each of these sentences. Overall, performance was somewhat worse than with hit, but the model was still able to assign arguments to the correct underlying roles. In particular, it had no difficulty assigning animate Subject NPs to the role of Agent and the Object NP to the role + +Tn. b~11 brok. ~n. V~S. . + +brOk. IV' V~S. brOk. IVP b~11 - - - - - - . . - ~ - . . . - - --- . - - .....,.,................. .1.1..11-:-:-:-1;-;-:11-:-:-:-:-.1.-:- .tt ...11..I....I.I.!..... ......................... hhssgggvvvf f f fppbbOOOOOOO hhssgggvvvf f f fppbbOQOOOOO hhSSgggvvvf f f fpPbbOOOOOOO hhsSgggvvvf f f fp~ OOOO . e,ee19 e.2St8 - .182e e.eeee v~s. 8.3831 e.8112 \_.1~67 e.3197 b~11 e.2931 e.2S79 1.lese 8.3197 . e..e19 e.2seo e.1&2e e.eeee ~G~NT ~~TlfHT IHST~~ NT ~ 1~lf ~ + +Th. h~tch . t touCh . d th . p~. t ~. + +touCh . dI ~ p~st . touch ~ IY~ h~t'Ch. t' + +Th. gir1 touc ~. a t ~. bO~ . + +toyc ~ a~V~ g; r1 ~OYCh~ V~ + +" ~TIe:HT I NST~UMENT MOOIf' Ie:~ ~GfNT + +FIGURE 16. Summary of the pattern of activation produced by the model in response to + +features. In a much less redundant set of verbs, the model would be forced to learn to rely on just the right features of the sentence-level pattern to predict the features of the case role representation correctly. The second reason is that the deviant feature on the word touch does not fall inside a subspace delineated by a set of related exemplars that behave in similar ways. What we are seeing here, essentially, is assimilation to a single familiar verb that is near the novel verb in feature space. When a novel word is presented that more nearly falls inside the subspace delineated by a set of related exemplars, the model is better able to correctly represent all the features of the novel word in the case role representation. To show this, we defined a new fragile object, a lamp, that was nonhuman, hard, neuter, medium-sized, onedimensional, not pointed, fragile, and furniture . This set of features matches at least one of the breakable objects on every dimension, but matches none of them on all of the dimensions. We then tested the model by taking all of the familiar test sentences containing any of the familiar breakable objects (window, vase, and plate) and then testing the model on these sentences with the word lamp in the place of the familiar breakable object. In many cases, as in the first example shown in Figure 17, the model activated all the features correctly. That is, the correct feature for lamp on each dimension was more strongly activated than any other. The model was most vulnerable to error on the VOLUME and FORM dimensions, as in the second example shown, where it differed from two of the three familiar fragile objects in each case. The example indicates, then, that the desirable tendency of the model to shade the meanings of the words it encounters to fit the typical features it expects in certain contexts need not lead to severe distortions of novel words, as long as their feature patterns fall inside the + +...... '.3195 ...... + +--- girt 1.1191 8.'769 8.318S 8.3'32 ~O~ 1.1739 8.8279 8.31eS 8.3'86 . 1.1e67 8.1763 1."'1 8."86 . 8.1e67 '.1763 ,..... '..8.6 + +The hatchet touched the pasta and The girl touched the boy. + +- - - - - . . . . - . ... ~ . - ..........,." " ,........ ,11,..11...1...11.1...,.. .1.1..11...&,.1..1..1" " ,...,.,.,....,........... hhSSgggvvvf" fppbbOOOOOOO hhSSgggvvv' f" ppbbOOOOOOO hhSSgggvvvffffPPbbOOOOOOO hhSSgggvvvf" fppbbOOOOOOO + +e.eeee 8.1328 8.1291 e,3197 8.8.82 8.2~e3 . .3191 e.2265 8.86~2 e..t.e e.1328 e.1291 + +bO~ + +. . - - . . . . ..... -- - . . . . ~ - 1,1.,1,,1....1.1.1...,.1. 1.1.1,..1....1.1.1.....1. ,............." ,....." , .........,............... hhSSQQQvvv ' fff ~ booooooo hhsSiggvvv" " ppbbOOOOOOO hhSSiggvvv' fffppbbOOOOOOO hhSSiiivvv" ffppbbOOOOOOO + +D ~ St ~ h ~ tCh . t . 310 PSYCHOLOGICAL PROCESSES + +brok . ~ V ~ 1 . . , ~ ~ ~ . . - . . l . l . . l . l . . l . . . l1 . . . . . l . . tV"Is s ~ i gvvv f' f' f' f' ppI ) bOOOO 000 + +~G! NT ~~TI ! NT IH\$T~UM! HT MOOJ"' J~~ + +FIGURE 17. Summary of the response of the model to The woman broke the lamp and + +The bovv broke the lamp. + +space spanned by a set of similar words that are treated by the model in + +a consistent way. + +Straightforward Extensions + +The model does many things well, but it is really just the first step toward a POP model of sentence processing. In the general discussion we will consider some of the more general issues that confront the attempt to extend a model of this type further . Here, we will just mention some straightforward extensions that should be fairly easy to implement . We have not yet implemented these changes, so our dis- + +cussion is somewhat speculative. + +One straightforward set of extensions to the model would involve adding cross-connections among the case role units. The crossconnections would allow argument co-occurrence constraints that are verb-frame specific to be captured more effectively than they can now. In the present version of the model, the influence of one argument on another can only essentially add together with the influence of the verb on that argument. This will ultimately prove insufficient , we believe, because different verbs carry with them radically different interdependencies among their arguments. For example, see imposes some restrictions between the Instrument and the Object (as in Bill saw the man with the telescope and Bill saw the man with the revolver~ the first is ambiguous, the second is not) that are different from those posed by hit (Bill hit the man with the telescope and Bill hit the man with the revolver seem equally ambiguous) . The present version of the model would not + +- + +. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . hhssgggvvvf f fipp~ oooo nhss~~~vvvf f f fPPbbOOOOOOO + +' , . . 39 ' , ~934 ' . 3186 8 .3198 ' , 5271 ' ,' 213 ' ,31' 3 ' .319. ' , 2931 ' .2498 1 .' . ' 2 . .. . . . ' .. 931 8 .. 498 ' .' . 82 . .. , . . + +~ bOI~MP '.4S86 8.e48S e.317S 8.3199 ~ '.882e '.47QI 8.3183 '.3199 . '.3.e~ '.2693 ...... ...... . '.3eeS '.2693 e.'." ...... + +Th. bO~ brOk. th. I~m~. + +brOk.~V~ bO~ brOk.~~ lAMP + +~ . . . . . . . . ~ - --- . 1.1.1...1....1.1.1.....1. .1.1..1.1..1...11.....1.. ......................... ......................... hhS sggg~vvf' fPPbbOOOOOOO hhSS~gg~~~f" fPPbbOOOOOOO hhssg ~vvvff' 'PPbbOOOOOOO hhS S999 ~vv' f f fDObbooooooo + +easily capture these kinds of verb-contingent argument constraints because each argument is encoded separately from the verb at the sentence level, and it is only connections from units at the sentence level that determine the input to the case role units. This means that conjunctions of noun characteristics with verb characteristics are not directly at work in determining case role unit activations. "fhe case role units, however, do provide just such a conjunctive encoding. It seems likely , therefore, that connections among these units would be able to capture verb-specific (or, more exactly, verb-feature specific) con- + +tingencies between slot fillers and their assignments to roles. + +Cross-connections among the case role units would add a number of other advantages, as well. They would allow competition among alternative interpretations of the same word at the case-frame level, so that the stronger of two competing interpretations of the same word could + +effectively suppress the weaker. + +A second straightforward extension would be the addition of backconnections from the case role units to the sentence-structure units. This, too, could have several beneficial effects on the performance of the model. In an extended version of the model with cross-connections and back-connections, the computation performed by the present version of the model would be just the first step in an iterative settling process. This settling process could be used to fill in the features of one reading or another of an ambiguous word at the sentence level, based on the emerging pattern at the case role level. Once filled in, these features could then add to the support for the "dominant " reading over other, initially partially activated readings- the whole network would, in effect, drive itself into a stable "corner" that would tend to represent a coherent interpretation at both the sentence and the case role level. Kawamoto (1985) has observed just such effects in a simulation of word disambiguation based on the brain-state-in-a-box model of J. A . Anderson, Silverstein, Ritz , and Jones (1977) . (Cottrell , 1985, and Waltz & Pollack, 1985, have also observed such effects in their more + +localist sentence-processing models.) + +Back connections would also allow case role activations to actually specify the semantic features of novel or unfamiliar words occurring in constraining contexts. Consider, for example, the sentence, The girl broke the shrafe with the feather. The context provides a considerable amount of constraint on the properties of shrafe. The existing version of the model is able to fill in a plausible interpretation at the case level, but with feedback it would be able to pass this information back to the + +sentence level. + +Another way of passing information back to the surface-structure level would be to use the back-propagation learning algorithm . The use of back propagation to train the sentence-structure units could allow the + +19. SENTENCE PROCESSING311 + +312 PSYCHOLOGICAL PROCESSES + +right features to be constructed at the surface level with only a phonological representation of the words as the predefined input . Back propagation might also allow us to cut down on the rather excessive numbers of units currently used in the surface-structure level. Right now there are far more SS units than are strictly necessary to do the work that the model is doing. While many units could be eliminated in a straightfor ward way (e.g., many of the sentence units could be eliminated because they stand for unlikely conjunctions of features across dimensions, such as human and tool) , many more are simply redundant ways of encoding the same information and so could be consolidated into fewer units. On the other hand, for a larger vocabulary, some conjunctive units will turn out to be necessary, and pair-wise conjunctive units ultimately will probably not suffice. Indeed, we feel quite sure that no predefined coding scheme of the kind we have used could provide a sufficient basis for learning all the sentences in any real language without being immensely wasteful, so it will become crucial to train the sentence and case role units to represent just the needed conjunctions of features. + +Distributed Representation of Roles + +We mention a final "straightforward " extension of the model under a separate heading because it is both more speculative and perhaps somewhat more difficult to understand than the previous suggestions. This is the idea of using a distributed representation of the roles. The idea was first suggested by Hinton (1981 a) , and is currently under exploration by Derthick and Hinton at Carnegie-Mellon University . The essence of the idea is to think of roles not as strictly separate, monolithic objects, but as sets of role descriptors. Thus the role of Agent has certain properties: It specifies an active participant in the scenario, one that may be volitional ~ it specifies the instigator of the action. The role of Patient, on the other hand, specifies a passive participant, one whose volitional involvement is (pretty much) irrelevant , but who is + +the one that experiences the effects of the action. + +Various problems arise with treating these roles as unitary objects. One is that some but not all of the Patient properties generally hold for the role nominally identified as Patient. Similarly , some but not all of the Agent properties generally hold for the role nominally identified as Agent. In certain cases, as with sentences like The boy moved, enough of these properties hold that we were led to assign the boy to both roles + +at once. + +traditional cases. This leads, of course , to a proliferation of roles that is ungainly , unwieldy , and inelegant , and that detracts considerably from + +the utility of the idea of roles as useful descriptive constructs . + +Here , distributed representation can provide an elegant solution , just as it has in other instances where there appears to be a temptation to proliferate individualized , unitary representational constructs (see Chapter 17) . If each role is represented by a conjunction of role prop erties , then far more distinct roles can be represented on the same set of role units . Furthermore , what the Agent roles of two verbs have in common is captured by the overlap of the role features in the represen tations of their roles , and how they differ is captured by their differ ences. The notion of a role that represents a combined Agent / Patient as in The boy moved is no longer a special case, and we get out of + +assigning the same argument to two different slots . + +So far , the vision outstrips the implementation of this idea , but we will sketch briefly one very rudimentary instantiation of it , in what really amounts to a rather slight modification of the model we have described above . Currently , our case role units stand for conjunctions of a role , a feature of the verb , and a feature of the filler of the role . The suggestion , quite simply , is to replace these units with units that stand for a feature of a role , a feature of the verb , and a feature of the filler of the role . The first NP in The boy broke the window with the hammer will produce a pattern of activation over one set of these triples (corresponding pretty much to the canonical features of agenthood ) , while the boy in The boy moved would activate some units from other role feature sets, as well as many of the typical agent feature units . + +Again , we stress that we do not yet have much experience using this kind of distributed representations of roles . However , Oerthick and Hinton (personal communication , 1985) are exploring these ideas in the context of a POP implementation of the representation language KL -TWO (Brach man & Schmolze , 1985~ Moser , 1983) . They have already shown that at least one version of the idea can be made to work and that the coarse coding of roles can be used to allow inheritance of + +constraints on role fillers . + +DISCUSSION + +Now that we have examined the model in some detail and considered some possible extensions of it , we turn to more general considerations . We consider three issues. First , we examine the basic principles of operation of the model and mention briefly why they are important and useful principles for a sentence -processing model to embody . Second , + +314 PSYCHOLOGICAL PROCESSES + +we consider some of the implications of the model for thinking about language and the representation of language. Third , we address the limitations of the present model. This part of the discussion focuses on a key question concerning the feasibility of our approach, namely, the requirement that any plausible model of language processing must be + +able to handle sentences containing embedded clauses. + +Basic Features of the Model + +We emphasize before we begin that the basic features of the present model are shared with a number of other distributed models, especially those of Hinton (1981a) and those described in Chapters 3, 14, 17, and 18 of this book. The two most important properties of the model are its ability to exploit the constraints imposed by all the arguments in a sentence simultaneously and its ability to represent shades of meaning. These aspects are basic~ we believe~ to any attempt to capture the flexi - + +bility and context-sensitivity of comprehension. + +The first of these properties is~ perhaps, just as easily capturable using local rather than distributed connectionist networks. These local connectionist models capture this property much more effectively than they have been captured in nonconnectionist mechanisms (e.g., Small's~ 1980~ word expert parser~ cf. Cottrell & Small, 1983) . Such networks have been applied to sentence processing, particularly to the problems of ambiguity resolution and role assignment (Cottrell , 1985~ Waltz & Pollack, 1985) . Both models use single units to stand for alternative meanings of words or as "binders" to tie words to alternative roles, and use mutual activation and inhibition to select between alter- + +native meanings and alternative role assignments. + +The present model exhibits many of these same properties, but uses distributed representations rather than local ones. What the distributed representations have that local representations lack is the natural ability to represent a huge palette of shades of meaning. With distributed representations, it is quite natural to represent a blend of familiar concepts or a shaded version of a familiar concept that fits a scenario (Waltz & Pollack, 1985, do this with their context microfeatures) . Perhaps this is the paramount reason why the distributed approach appeals to us. To be sure, it is possible to represent different shades of meaning in a localist network . One can, for example, have different units for each significantly different variation of the meaning of a word. A problem arises, though, in specifying the meaning of "significantly different ." We will probably all agree that there are different readings of the word bat in the sentences The bat hit the ball and The bat flew round the cave. But what about the word chicken in the sentences The + +woman ate the chicken and The wolf ate the chicken? Or what about the word ball in The baby kicked the ball and The ball broke the window? There is no doubt that we think of different balls in these cases~ but do we really want to have a separate unit in memory for the soft, squishy, rubber ball the baby kicks and the small, hard ball that can break a + +window? + +With distributed representations, we do not have to choose. Dif ferent readings of the same word are just different patterns of activation ~ really different readings, ones that are totally unrelated, such as the two readings of bat simply have very little in common. Readings that are nearly identical with just a shading of a difference are simply + +represented by nearly identical patterns of activation. + +These properties of distributed representations are extremely general, of course, and they have come up before, particularly in the chapter on schemata (Chapter 14) . We also just invoked them in suggesting that we might be able to use distributed representations instead of some fixed set of case roles. In both of these other cases, as in the case of distributed representation of word senses; the use of distributed representation allows for all shades and degrees of similarity and differ ence in two representations to be captured in a totally seamless way. A final basic feature of the model is the gradualness of acquisition it exhibits. We have not stressed the time course of acquisition, but it was, of course, a crucial property of the verb learning model, described in Chapter 18, and it is quite evident that acquisition is gradual from Figure 4. As with the verb learning model, our model also seems to pick up on the strongest regularities first . This is seen most easily in Figures 5 and 6 by comparing NVN sentences from the hit and broke generators. Those with animate preverbal NPs, which are Agents, are learned more quickly than those with inanimate preverbal NPs, which are Instruments . This is because a far greater number of constructions have animate, Agent subjects than have inanimate, Instrument subjects. These three basic properties- exploitation of multiple , simultaneous constraints, the ability to represent continuous gradations in meaning, and the ability to learn gradually, without formulating explicit rules, picking up first on the major regularities, are hallmarks of parallel distributed models, and they are no less applicable to comprehension of language than they are to any other aspect of cognitive processes. + +Do Words Have Literal Meanings? + +There is one further aspect of the distributed approach to representation of meaning that should be mentioned briefly . This is the stand our model takes on the issue of whether words have literal meanings. It is 316 PSYCHOLOGICAL PROCESSES + +normal and natural to think of words as having literal meanings, but it is very difficult to say what these meanings really are. For, as we have noted throughout this chapter, the apparent meanings of words are infinitely malleable and very difficult to pin down. An alternative view is that words are clues to scenarios. This view, which has been proposed by Rumelhart (1979) among others, never made very much impression on us until we began to study the present model. However, in exploring the model, we have found that it embodies Rumelhart ~s idea exactly. A sentence assembles some words in a particular order, and each provides a set of clues that constrains the characteristics of the scenario, each in its own way. The verb, in and of itself , may specify a range of related scenarios and certain constraints on the players. The nouns further restrict the scenario and further constrain the players. But the words themselves are no longer present in the scenario, nor is there necessarily anything in the scenario that corresponds to the literal meaning of any of the words. Thus in the case of The doll moved ~ the (partially activated) Agent is not a copy of the standard doll pattern, but a pattern appropriate for a doll that can move under its own steam. The crucial point , here, is that all the words work together to provide clues to the case frame representation of the sentence, and none of the words uniquely or completely determine the representation that is assigned to any of the constituents of the underlying scenario. Certainly , the word hammer most strongly constrains the filler of the Instrument role in The boy broke the vase with the hammer, but the other words contribute to the specification of the filler of this role, and hammer contributes to the specification of the fillers of the other roles. Compare The prisoner struck the rock with the hammer and The boy broke the vase with the feather: The former suggests a heavier hammer~ the latter suggests an extremely fragile vase (if we give an instrumental + +reading to the with - NP) . + +Toward a More Complete Model of Sentence Processing + +As we have already made clear, the model that we have described in this chapter is far from a complete model of the psychological processes involved in sentence processing. It does not deal with the fact that sentence processing is an on-line process, a process that unfolds in real time as each word is heard. It does not deal with the integration of processed sentences into larger contextual frameworks. It does not handle anaphora and other referential phenomena, or tense, aspect, or number. No attempt is made to deal with quantification or scoping issues. The model even lacks a way of distinguishing different tokens + +with identical featural descriptions . Thus it does not explicitly desig nate separate dogs in dog eat dog and only one dog in The dog chased himself Finally , the model completely ignores the complexities of syn tax . For the present model , a sentence can come in only one rigidly structured form , and no embedded clauses , cleft sentences , or passive + +constructions are allowed . + +Clearly , we have much work to do before we can claim to have a model that is in any sense complete or adequate . The question is , can it be done at all ? Is there any fundamental limitation in the POP approach that will prevent the successful development of a full - scale model of language processing that preserves the positive aspects of the + +distributed approach ? + +Obviously , the proof is in the pudding . But we think the enterprise can succeed . Rather than discuss all of the issues raised above , we will discuss one that seems quite central , namely , the application of POP models to the processing of sentences with embedded clauses . We con sider several different ways that POP models could be applied to the + +processing of such sentences . + +Interfacing PDP mechanisms with conventional parsers . We start with what might be the simplest view , or at any rate the most conven tional : the idea that a model such as ours might be interfaced with a conventional parser . For example , we might imagine that a parser simi lar to Marcus ' s PARSIFAL ( 1980 ) might pass off the arguments of completed ( or possibly even incomplete ) clauses to a mechanism such as the one we have proposed for case role assignment and PP attach ment . In this way , the " role - assignment module " could be used with any given sentoid and could be called repeatedly during the processing + +of a sentence containing embedded clauses . + +Interfacing our model with a conventional parser would perhaps pro vide a way of combining the best of both conventional symbol process ing and parallel distributed processing . We are not , however , particu larly inclined to follow this route ourselves . For it appears that it will be possible to implement the parser itself as a POP mechanism . As we shall see , there are at least three ways this might be done . One involves implementing a true recursive automaton in a POP network . We describe this method first , even though we suspect that the human parser is not in fact such a machine . After describing the mechanism , we will explain our objections to this view of the human sentence processing mechanism . This will lead us to suggest two other mechan isms . One relies on the connection information distribution mechanism described in Chapter 16 to program a parallel net to process sentences of indefinite length and embeddedness ~ the other operates iteratively rather than recursively . It is more computationally limited in some + +A PDP model that does recursion. It turns out that it is not difficult to construct a parallel network that does true recursive processing. Hinton (personal communication ) worked out the scheme we will describe here and implemented a rudimentary version of it in 1973. While such a mechanism has not been applied directly to parsing, the fact that recursive processing is possible suggests that there is no reason, in principle, why it should not provide a sufficient basis for imple- + +menting some kind of parser. + +The mechanism consists of a large network of units. Patterns of activation on these units are distributed representations of a particular state in a processing sequence. Processing occurs through the succession of states. The units are divided up into subnets that represent particular parts of the state. One important subnet is a set of units that provides a distributed pattern corresponding to a stack-level counter. The connections in the network are set up so that successive states of a routine are associated with their predecessors. Thus, when one state is in place, it causes another to follow it . States may also be used to drive actions, such as output of a line segment, say, if the automaton is a mechanism for recursively drawing figures, as Hinton 's was. Processing, then, amounts to carrying out a sequence of states, emitting + +actions (and possibly reading input) along the way. + +Calling subroutines in such a mechanism is not particularly difficult , since all that is required is to associate a particular state (the calling state) with the start state of some routine . Passing parameters to the called routine is likewise not particularly difficult ~ in the simplest case they can be parts of the calling state that are carried along when the + +routine is called. + +To implement recursion in such a network, all that is required is a way to reinstate the calling state when a routine is done. To do this, the mechanism associates the state of the stack-level units with the state that is in place over the rest of the units, using an associative learning rule to adjust connection strengths while processing is taking place. These associations are implemented by rapidly changing a shortterm component of the weights whose long-term values implement the associations that allow the model to cycle through a sequence of states. The temporary associations stored in these short-term weights are not strong enough to overrule the long-term weights, but they are suffi ciently strong to determine the next state of the network when the long-term weights leave several possibilities. So, at the end of a routine at stack level N , the network associatively reinstates stack level N - 1, with the rest of the state cleared. This associative reinstatement + +respects than the other mechanisms, but the limitations appear to con- + +form to those of the human parser, as we shall see. + +of the previous stack-level state would be based on long-term , relatively permanent associations between states corresponding to adjacent depths in the stack. This reinstated stack-level state, which was associated in the short-term weights with the calling state just before the subroutine call occurred, would then simply use this short-term association to reinstate the pattern that existed before the call. (A "done" bit would have to be set to keep the process from doing the call again at this point .) There is no apparent a priori limit to the number of embedded calls that could be carried out by such a network , though for any fixed size of the stack-level subnet, there will be a corresponding maximum number of associations that can be learned without error . Of course, similar limitations also occur with all other stack machines~ the stack is always of finite depth. There would also likely be interference of previous calling states when returning from any particular level, unless the learning were carefully tuned so that earlier associations with a particular stack level were almost completely wiped out or decayed by the time a new one must be used. Care would also be necessary to avoid crosstalk between stack-level representations. However, these problems can be overcome by using enough units so that very different states are + +used to represent each level of the stack. + +Drawbacks of true recursion. The scheme described in the previous section has several fairly nice properties and deserves considerably more exploration than it or some obvious variants have received to date. However, it does have one drawback from our point of viewone that it shares with other, more conventional implementations of truly recursive automata. The drawback is that the calling state is not present and active during the subroutine call~ it is effectively inaccessi- + +ble until it is reinstated after the return . + +This property of truly recursive schemes limits their ability to simultaneously consider binding a prepositional phrase at each of two levels + +of embedding. Consider the sentences: + +(14) The boy put the cake the woman made in the kitchen. (15) The boy saw the cake the woman made in the kitchen. + +Our preferred reading of the first of these two sentences has the boy putting the cake in the kitchen , rather than the woman preparing it there~ while in the second case, the preferred interpretation appears to be that the woman made the cake in the kitchen, and the boy saw it at some unspecified location. Since the material is the same from the beginning of the embedding in both cases, it appears that the demand the matrix clause material (The boy put the cake . . .) makes for a locative argument influences the decision about whether in the kitchen should be bound into the subordinate clause. While it may be possible to arrive at these two different readings in a conventional parser by backtracking or by passing aspects of the calling state along when the subroutine is called, it would seem to be more natural to suppose that the matrix clause is actively seeking its missing locative argument as the embedded material is being processed, and so is prepared to steal in the kitchen from the verb in the embedded clause. Thus, it appears that a mechanism capable of processing at different levels of embedding at + +the same time is needed. + +A fixed -length sentence processor. A connectionist parser that can, in principle, handle this kind of competition among alternative attachment decisions at different levels of embedding has recently been developed and implemented by Fanty (1985) . He describes a mechanism that effectively parses a sentence at many levels at the same time . The parser consists of a fixed network of units. Some of the units represent the terminal and nonterminal symbols of the grammar~ other units, called match units, represent the different possible expansions of each nonterminal . The symbol units are easily represented in a table in which the columns represent starting positions in the input string and the rows represent lengths. There is a unit for each terminal symbol in each position of the bottom row, and there is a unit for each nontermi nal symbol at every position in the table~ that is, there is a copy of each nonterminal unit for every possible portion of the input that it could cover. For each of these there is a set of binder units, one for each pos- + +sible expansion of each nonterminal unit . + +A simple version of the table, for the indicated three-rule grammar, is shown in Figure 18. Only a subset of the units- the ones that would + +become active in the parse of aabbb- are shown. + +The parser can only process strings up to a predefined maximal length. Essentially, it processes the entire sentence in one two-pass processing sweep. In the first , bottom -up pass, all possible constituents are identified , and in the second, top-down pass, the constituents that fit together with the top S and the subconstituents of the top S are rein- + +forced. These active units represent the parse tree. + +A very nice feature of Fanty's parse is that it takes into account all levels of the parse tree simultaneously. This allows it to find a globally satisfactory parse in one pair of sweeps, eliminating possible constit%uents that do not fit together with others to make a globally acceptable structure. With some modifications (different degrees of strength for different rules~ continuous, interactive processing as opposed to a single pair of sweeps) , it would probably be possible to implement a mechanism that could choose the "better" of two alternative acceptable parses, as people seem to do with many ambiguous + +320 PSYCHOLOGICAL PROCESSES + +5 --t AS + +S + +A -- + aA I a B - + be I b + +B + +A B + +a aA b b bB \$ + +len gth + +1 2 3 4 5 + +starting position + +FIGURE 18. Parsing table used in Fanty's multilevel parser. Only the units active in the correct parse of the string aabbb are illustrated. (From Context-Free Parsing in Connectionist Networks [TR-174, p. 3] by M. Fanty, 1985, Rochester, NY: University of Rochester, Department of Computer Science. Copyright 1985 by M. Fanty. Reprinted by permis- + +sion.) + +sentences. The parser of Selman and Hirst (1985~ Selman, 1985) , which is similar to the Fanty parser in structure but uses simulated annealing, appears to have just the right characteristics in this regard. However, this kind of parser does have some drawbacks. Most importantly , it is limited to sentences of a prespecified length. To expand it , one needs not only to add more units, one needs to program these units with the connections that allow them to do the jobs they are needed or potentially needed to do. Second, the size does grow rather + +quickly with the allowable length (see Fanty, 1985, for details) . + +Fanty's model is, in fact, somewhat reminiscent of the TRACE model of speech perception (Chapter 15) in its reduplication of dedicated units and connections. As with TRACE , it may be possible to use connection information distribution (Chapter 16) to program the necessary connections in the course of processing from a single, central network containing the system's long-term knowledge of the rules of English. Indeed, Fanty (1985) has explored an off -line variant of the connection information distribution scheme~ his version learns new productions locally, and sends the results to a central network which then distributes the results to the rest of the net, off -line. If the programming of the connections could be made to work on-line in the course of processing, as with the programmable blackboard model of + +sentence . + +reading , we would have a mechanism that still needs large numbers of units and connections , but crucially , these would be uncommitted units and programmable connections . The computational capability of the machine would be expandable , simply by increasing the size of the pro - + +grammable network . + +Myths about the limitations of PDP models. We hope that these last two sections will help to dispel some widely held beliefs about com putation and POP models . We will briefly consider two variants of these beliefs . The first , quite simply , is that POP models cannot do recursion . Hinton ' s recursive processor needs considerably more development before we will have a working simulation that proves that this belief is wrong , but it seems clear enough that a recursive POP processor will be available fairly soon . In fact , it is likely that a slightly different approach will be explored more fully first : Touretzky and Hin ton ( 1985) have recently developed a POP implementation of a produc tion system that can do rudimentary variable binding , and at present it appears that they may be able to extend it to perform recursive + +computations . + +The second belief seems to follow from the first : It is that POP models are inherently incapable of processing a full range of sentences . We say it only seems to follow because it depends upon accepting the assumption that in order to process sentences it is necessary to be able to do recursion . Most people who have thought computationally about sentence processing are familiar with sentence -processing mechanisms that are in fact recursive , such as the A TN (Woods , 1970) or the Marcus parser. Since sentences are recursively defined structures , the (implicit ) argument goes, the mechanisms for parsing them must them - + +selves operate recursively . + +Fanty 's ( 1985) parser , or an extension of it incorporating connection information distribution , begins to suggest that this may not be so. In a programmable version of Fanty ' s parser , we would have captured the essential property of a recursive automaton - that the same procedural knowledge be applicable at any point in a parse tree . But we would have captured it in a very exciting new way, a way that would free the mechanism from the serial processing constraint that prevents conven tional recursive mechanisms from being able to exploit constraints from many levels at the same time . Connection information distribution may actually permit us to reap the benefits of simultaneous mutual con straints while at the same time enjoying the benefits of being able to apply the same bit of knowledge at many points in processing the same + +considerable number of units and connections are required to handle the input to and output from the central knowledge structures (see Chapter 12 for further discussion ) , and the resource demands made by even a fixed version of Fanty 's parser are quite high already . There may turn out to be ways of reducing the resource demands made by the Fanty parser . In the meantime , it is worth asking whether some other + +approach might not succeed nearly as well with fewer resources . + +Context -sensitive coding , iteration , and center embedding . There is one more belief abollt sentences , this one even more deeply ingrained than the last, that we have tacitly accepted up to this point . This is the belief that sentences are indeed recursively defined structures . Clearlv ~ sentences are recursively definable , but there is one proviso : Only one level of center embedding is allowed . It may be controversial whether the " true " competence grammar of English accepts multiple center embedded sentences , but people cannot parse such sentences without the use of very special strategies , and do not even judge them to be acceptable (G . A . Miller , 1962) . Consider , for example , the + +" sentence " : + +( 16) The man who the girl who the dog chased liked laughed . + +The unparsability of sentences such as ( 16) has usually been explained by an appeal to adjunct assumptions about performance limitations (e.g., working -memory limitations ) , but it may be, instead , that they are unparsable because the parser , by the general nature of its design , is + +simply incapable of processing such sentences . 13 + +It should be noted that parsers like the A TN and the Marcus parser are most certainly not intrinsically incapable of processing such sentences . Indeed , such parsers are especially well suited for handling an indefinite number of center embeddings . Such mechanisms are clearly necessary for processing such things as Lisp expressions , such as this one taken from a program (actually , itself a parser) written by Jeff + +Sokolov : + +( (and (eq (car (explode arg) ) '/ ) + +(eq (car (reverse (explode arg) ) ) '/ ) ) (implode (reverse (cdr (reverse (cdr (explode arg) ) ) ) ) ) ) + +13 This argument has been made previously by a number of other authors, including Reich (1969). In fact, Reich proposed an iterative approach to sentence processing that is + +324 PSYCHOLOGICAL PROCESSES + +But sentences in natural language are simply not structured in this way. Perhaps, then, the search for a model of natural language processing + +has gone down the garden path, chasing a recursive white rabbit. + +One approach to sentence processing holds that we should ask much less of a syntactic parser and leave most of the work of sentence processing to a more conceptual level of processing. This position is most strongly associated with Schank (1973) , and Charniak (1983) is among + +the recent proponents of this view. + +Let us assume that the job of the parser is to spit out phrases encoded in a form that captures their local context, in a way that is similar to the way the verb learning model, described in Chapter 18, in a form that captures their local context.14 Such a representation may prove sufficient to allow us to reconstruct the correct bindings of noun phrases to verbs and prepositional phrases to nearby nouns and verbs. In fact, we suspect that this kind of local context-sensitive encoding can capture the attachments of NPs to the right verbs in "tail-recursive" + +sentences like + +This is the farmer that kept the cock that waked the priest that married the man that milked the cow that tossed the dog that worried the cat that killed the rat that ate the malt that lay in + +the house that Jack built . is + +(17) + +Locally context-sensitive coding will begin to break down, however, when there is center embedding- specifically, more than one level of center embedding. Local context can be used to signal both the beginning and the end of an embedding, but cannot be used to specify which beginning of an embedding the material just after the end of an embed- + +ding should be bound to. Thus if we read to the last word of + +(18) The man who the girl who the dog chased laughed + +we may not know whether to bind laughed (just after the end of the embedding) to the man (NP before an embedding) or to the girl (a different NP before an embedding). If we bind it to the man, we may + +14 For this to work it will be necessary to code units, not in terms of the adjacent words, but in terms of neighboring constituents more abstractly defined. Thus, in The girl in the hat saw the mouse on the floor, we will want to encode the complex NP the girl in the hat as adjacent to the verb saw. Thus, local context will have to be defined, as it is in Marcus (1980), in terms of constituents, not merely in terms of words. Getting this to + +experience a false sense of closure - this sentence is ungrammatical + +because it has only two verbs for three clauses . + +These suggestions lead us to the following conjecture : It may be pos sible to build a PDP language - processing mechanism that works itera tively along a sentence , building constituents represented by distributed patterns conjunctively encoded with their local context of occurrence . The mechanism would need a way of unifying constituents on two sides of an intervening embedding . Exactly how this would be done remains to be established , but as long as it is done in terms of a mechanism sensitive only to the local context of the constituents before and after the embedding , it may succeed where there is a single embedding but fail in multiply embedded sentences where there are two suspended , incomplete constituents that the mechanism must choose between + +completing . + +We hope it is clear that these ideas are speculative and that they are but pointers to directions for further research . Indeed , all three of the directions we have described in this section are only just beginning to be explored systematically , and it is unclear which of them will prove most attractive on closer scrutiny . We mention them because they sug gest that ways of overcoming some of the apparent limitations of PDP mechanisms may not be very far beyond our present grasp , and that it may soon be possible to retain the benefits of parallel distributed pro cessing in mechanisms that can cope with the structural complexity and + +semantic nuance of natural language . + +ACKNOWLEDGMENTS + +This work is supported by ONR Contract NOOO 14 - 82 - C - O3 74 , NR 667 -483 , by a Research Scientist Career Development Award ( MHOO385 ) to the first author , and by grants from the Sloan Founda tion and the System Development Foundation . We would like to thank Liz Bates , Gene Charniak , Gary Cottrell , Gary Dell , Mark Derthick , Mark Fanty , Geoff Hinton , Ron Kaplan , Brian MacWhinney , Dave Rumelhart , Bart Selman , and Michael Tanenhaus for useful comments + +and discussions . + +BIOLOGICAL MECHANISMS + +PART V + +One of the appeals of parallel distributed processing is the fact that it seems closer to the neural basis of cognition than most other approaches to cognitive processes . The idea that intelligent processing can emerge from the interactions of a large number of simple computa tional units and their interactions is , of course , directly inspired by what we know about the way the brain works . Further , several of the specific assumptions embodied in particular models have been inspired + +by observed characteristics of neural function . + +This part of the book explores the neural mechanisms underlying parallel distributed processing in three different , though interrelated ways . First , it examines what we know and do not know about relevant aspects of the brain . Second , it considers the precise nature of the rela tion between concepts at a neural level of analysis , and concepts at higher , more cognitive levels . Third , it presents three specific attempts to bring PDP and neuroscience closer together by capturing aspects of neural function in simulation models based on the POP framework laid + +out in Chapter 2 . + +The relevant neurophysiology . There is , of course , a vast body of data about the details of human brain function , and it would be hope less to try to summarize all of this information within the confines of our book . However , among these data are some emerging principles and observations about the characteristics of the mammalian brain that + +328 BIOLOGICAL MECHANISMS + +In Chapter 20, Crick and Asanuma describe the principles and obser vations they see as most salient , based on their ongoing s~jrvey of the neurophysiology of the mammalian brain . The focus is on the details of neuronal interaction and on the developing state of knoweldge about the regional architecture of the visual system , as revealed through physiological and anatomical experiments , primarily in primates . The material in this chapter is useful background for any POP modeler , and will be of particular interest to anyone interested in modeling the + +detailed properties of real neural circuitry . + +In Chapter 21, Sejnowski takes a somewhat different approach , and considers several general questions about brain function . By and large , neurophysiological data do not answer such questions in a definitive way , but they do suggest several principles of brain function that should continue to help steer our efforts to capture the essential features of + +the computational processes that take place in the human brain . + +The relation between PDP models and the brain . There are several different ways in which PDP models relate to the brain . Different pieces of work represented in this book have different relationships to the details of brain structure . All share in common that they are " neu rally inspired " models and are explorations of " brain -style " processing . Beyond this , however , there are some important differences . Here , we briefly outline some of these different approaches , and say how they + +relate to the chapters in Part V . + +Some PDP models are intended to explore the computational proper ties of " brain - like " networks . The models described in Parts II and III are generally of this type . They consider sets of units with specified characteristics , and study what can be computed with them , how many units are required to do certain computations , etc . These models focus on parallel processing mechanisms more or less in their own right , quite apart from facts about the details of brain structure or the details of + +human behavior and cognition . + +There are two principle kinds of motivations for this computational tvne of work . One is that the mechanisms under study are sufficiently .. abrain -like that they may shed light on the actual way in which computa tion is done in the brain . The fact that these models generally idealize various properties of the brain may in many cases be a virtue for under standing brain function , since idealization , as Sejnowski points out in Chapter 21, can often facilitate an analysis that leads to deeper under standing of the emergent properties of complex systems . Indeed , some of this work is driven by the goal of exploring the implications of ~- ----- .. --- wspecific properties of brain function , such as the stochastic nature of neural firing , as explored in harmony theory (Chapter 6) and in Boltzmann machines (Chapter 7) . The other motivation is to explore + +INTRODUCTION TO PART V 329 + +the computational capacities of networks trdt appear on their surface to be well suited to certain kinds of information -processing tasks, such as + +search or representation building . + +Other PDP models- and here we have in mind primarily the models in Part IV - attempt more directly to build accounts of human informa tion processing capabilities , at a level of abstraction somewhat higher than the level of individual neurons and connections . In such models , the relationship between particular brain structures and particular elements of the models is not generally specified , but since the models attempt to capture the behavioral products of the activity of human brains , it is assumed that there is some relationship to real activity in the brain . The basic idea is that there is a mapping between elements of the model and the brain , but it is unknown and probably only approximate . A single unit may correspond to a neuron , a cluster of neurons , or a conceptual entity related in a complex way to actual + +neurons . + +It might be thought that by adopting this more abstract approach , these models lose all contact with the underlying neurophysiological mechanisms . This is not the case. While models of cognitive processes may be developed without detailed regard for the underlying physiol ogy , some of the characteristics of the brain clearly place constraints on the cognitive mechanisms . Some examples are the speed and precision of the basic computational elements , the general characteristics of their patterns of interconnection , the nature of the operations they can perform , the number of elements available in the brain , etc. (Chapter 4 provides a fuller discussion of these points ) . It becomes imoortant - & , then , to develop some way of relating the more abstract , cognitive -level theory to the underlying neurophysiology. More fundamentally , this relation is central to conceptions of the relation between mind an brain . It is therefore of considerable importance to have an explicit theoretical framework for conceptualizing the exact nature of this relation . Thi ~ + +point is addressed by Smolensky in Chapter 22. + +In still other cases, the goal is to do neural modeling - to account for the facts of neuroscience rather than (or in addition to ) the facts of cognition . This use of PDP models involves less idealization of the neural elements and more attention to the details of brain structure . Crick favors these applications for he feels that building up from the facts about real neural function is the best way to find out the way things really work - as opposed to the way things might work - in the + +brain . The last three chapters of Part V take this approach . + +We hasten to add that we do not think anyone of these uses is the " right " or " only " way to employ POP models . Rather , we believe that work at each of these levels complements and reinforces work at the other levels , and that work at all of these levels will eventually allow us + +off plasticity. + +Chapter 25 is not concerned with modeling data on the behavior of individual neurons~ rather, it is concerned with reconciling neuropsychological evidence about amnesia with distributed models of memory. In distributed models, such as the one described in Chapter 17, information of different ages is stored in superimposed form, in the same set of connections. This fact provides a natural way of accounting for one aspect of amnesia: the fact that amnesics exhibit the residual ability to learn, gradually, from repeated experiences, even though their memory for individual episodes is extremely weak. Distributed memory, however, seems incompatible with another aspect of amnesia: namely, the temporally graded nature of the retrograde amnesia - the loss of prior information- that accompanies the reduction in the capacity to learn new material. If all memories are stored in the same set of + +to converge on an understanding of the nature of the cognitive processes that the brain supports and the neural mechanisms underlying these processes . We believe that the use of the common POP frame - + +work for all of these applications will facilitate this process . + +PDP models of neural mechanisms. Chapters 23 through 25 each take their own approach to modeling information -processing activity in the brain . Chapters 23 and 24 are explicit attempts to develop models that capture aspects of what is known about the behavior of neurons , + +while Chapter 25 focuses on neuropsychological data. + +In Chapter 23, Zipser takes as his goal the development of biologi cally plausible models of place learning and goal localization in the rat . The goal of the models is to account for localization and place learning behavior , and at the same time , incorporate knowledge gained from single -unit recording experiments . The first model described in the chapter accounts for the behavior of so-called I' place-field " cells in the hippocampus of the rat , and is closely tied to the physiological data. Two other , more speculati ve models work toward an account of goal + +localization , about which less of the physiology is known . + +In Chapter 24, Munro considers the plasticity of neural mechanisms , as revealed through studies of single units in visual cortex after various schedules of visual deprivation and other forms of intervention . He shows how a very simple neural model that focuses on the plasticity of individual units can account for much of the data on the critical period . The account is based on the simple observation that changes in the connections of a neuron will make more difference if its prior connec tions are weak than if they are strong . The critical period is seen, on this account , as a simple manifestation of the natural consequences of the strengthening of connections through experience , and not as a man ifestation of some sort of preordained maturational process that turns + +INTRODUCTION TO PART V 331 + +connections, why should more recent ones be more susceptible to loss or disruption than older ones? Chapter 25 reports simulations of various aspects of anterograde and retrograde amnesia, based on one possi- + +ble answer to this question. + +CHAPTER 20 + +Certain Aspects of the + +Anatomy and Physiology of the Cerebral Cortex + +F. CRICK and C. ASANUMA + +Our aim in this chapter is to describe some aspects of our present knowledge of the anatomy and physiology of the cerebral cortex of higher animals which may be of interest to theorists. We shall assume that readers have at least an elementary knowledge of this subject, so that they know, for instance, about the structure of neurons and the basis of neuronal excitation and synaptic transmission. The text by Kandel and Schwartz (1981) could be used to cover this background + +knowledge. + +It is clearly impossible to describe most of what is known, even though this represents a tiny fraction of what one would like to know. We shall select examples to illustrate the general points we want to make. It will soon emerge that while some things are known with reasonable certainty, much is unknown or, even worse, surmised only on rather incomplete evidence. For this reason alone, the object of this chapter is not to dictate to theorists what "units " they must use in their modeling. It might turn out that theory will show that a particular process, or implementation of a process, gives a very advantageous performance, even though the experimentalists can, as yet, see no sign of it . The wise thing at that point would be to look for it experimentally , since it may have been overlooked for one or another technical reason. This aside, theorists should at least try to learn whether the features they wish to use for their implementation do actually occur in the relevant part of the brain, and they should be duly cautious if the + +20. THE CEREBRAL CORTEX 335 + +merely to point out certain features of the cortex which should not be + +overlooked in theoretical modeling . + +Another general point that should be made is that in many cases theorists choose problems associated with either language or the human visual system without recognizing that there is at least one important difference between them . Put briefly , there is no animal model for language , nor is it possible to carry out many types of experiments on the language centers of the human brain for obvious ethical reasons . Most of the really useful new methods used in neuroanatomy , such as + +tritiated amino acid autoradiography i horseradish peroxidase histochem- istry, and metabolic mapping with [ 4C] deoxyglucose can only be used effectively on animals . We are in the embarrassing position of knowing a lot about the neuroanatomy of the macaque monkey while having only a very limited amount of similar information about the human brain . Similarly , the most powerful neurophysiological technique - the use of microelectrodes for isolating the electrical acti vi ty of single neu rons (or small groups of neurons ) - is not suited for extensive use on humans . This disadvantage is partly offset by the greater ease with which human psychophysical experiments can be done . There are also a number of techniques which can be used to study aspects of the neural activity from the outside . These include position emission tomography (PET scanning ) , magnetic field detectors , electro encephalography , (EEG ) and scalp recordings of evoked potentials . Unfortunately either the spatial or the temporal resolution of these methods is usually inadequate , and , as a result , the interpretation of the + +results is often not clear cut . + +In the long run , a theoretical model in biology can only be validated by a detailed comparison with experiment . All psychophysical tests show that the performance of the visual system of the macaque mon key is roughly comparable to our own . From this point of view , there fore , the solutions of visual problems should be easier to bring down to earth than linguistic ones . This does not mean that linguistic problems may not suggest valuable ideas about the working of the brain . It does mean that they may be more difficult to test at the level of neuronal + +organization and function . + +The Neuron + +The " classical " neuron has several dendrites , usually branched , which receive information from other neurons and a single axon which out puts the processed information usually by the propagation of a "spike " or an "action potential ." The axon ramifies into various branches that make synapses onto the dendrites and cell bodies of other neurons . + +336 BIOLOGICAL MECHANISMS + +This simple picture (Figure 2A ) has become complicated in several ways: (For a more thorough , yet general account , see the book by + +Shepherd , 1979.) + +. A neuron may have no obvious axon but only " processes" that seem to both receive and transmit information (Figure 2B) . An example of such neurons is the various amacrine cells found in the retina (Cajal , 1892) . Although neurons without axons also occur in the olfactory bulb (Cajal , 1911) , they have not been convincingly demonstrated in other parts of the ner - + +vous system . + +. Axons may form synapses on other axons . In the cerebral cor tex these synapses have been found only upon the initial segments of the axons of certain cells (Figure 2C) (Peters , Proskauer , & Kaiserman -Abramof , 1968 ~ Westrum , 1966) . + +. Dendrites may form synapses onto other dendrites (Figure 20 ) . Examples of this are known in the retina (Dowling & Boycott , 1966) , the olfactory bulb (RaIl , Shepherd , Reese, & Brightman , 1966) , the thalamus (Famiglietti , 1970) , the superior colliculus (R . D . Lund , 1972) , and the spinal cord (Ralston , 1968) , but such contacts appear to be rare or absent in the + +cerebral cortex . + +. An axon may not propagate a spike but instead produce a graded potential . Because of attenuation , we should expect this form of information signaling not to occur over long distances , and indeed it is found largely in such places as the retina , where the distances between connected neurons are shorter than in many other neural tissues ~ possibly because the time requirements are different (Figure 2E) (Werblin & Dowling , 1969) . It is also conceivable that graded potentials occur at more local levels (Figure 2F) . For example , an axon terminal forming a synapse on a given cell may itself receive a synapse. The presynaptic synapse may exert only a local potential change which is therefore restricted to that axon terminal . (The existence of this sort of a mechanism has been suggested for the spinal cord [Kuno , 1964] and the thalamus [Andersen , Brooks , Eccles , & Sears, 1964] , but to date , no examples of this + +20. THE CEREBRAL CORTEX 337 + +A. + +B. c . + +\ - + +D. + +E . Axon F.I ,Axon #1\,/#2 + +FIGURE 2. Highly schematized diagrams of the "classical" neuronal profile (A) and some of its variants (B-F). A: The "classical" neuron receives synapses on its dendrites and generates action potentials which travel down the axon. The axon subsequently branches and forms synapses on the dendrites and cell bodies of other neurons. B: There are neurons with no obvious axons. C: The initial segments of axons of neurons in the cerebral cortex may receive synapses. Note the highly strategic position of this kind of synapse. D: Dendrites forming synapses directly onto the dendrites of other neurons occur in the olfactory bulb and the thalamus. E: Graded potentials (instead of action potentials) can be effective if the axon is short. F: Graded potentials can also be effective at local levels. Here, Axon # 2 can modulate the efficacy of the synapse formed by Axon + +# 1 by producing a local potential change in the terminal of Axon # 1. + +20. THE CEREBRAL CORTEX 339 + +The importance of the classification into the two morphological types (originally recognized by Gray , 1959) is that Type I synapses seem to be excitatory , whereas Type II synapses seem to be inhibitory . We should add that the foregoing statement , though generally accepted by experimen talists , has not been systematically tested . In systems where the excita tory or inhibitory nature of a given synapse is well established , this correlation of morphology with physiology appears to be absolute + +(Uchizono , 1965) . + +There is another possible criterion for determining the character of synapses: This is the transmitter they use. In general , one is apt to assume that a given transmitter (or apparent transmitter ) will usually do the same thing in different places, though there are well -established exceptions (depending on the nature of the postsynaptic receptors ) . Glutamate and aspartate always seem to excite , GABA (gamma -amino butyric acid) always seems to inhibit (Krnjevlc & Phillis , 1963) . (It may come as a surprise to the reader to learn that for most cells in the brain we do not yet know what neurotransmitter they use.) The iden tity of the transmitters is usually determined immunocytochemically . Thus , an antibody staining for the enzyme glutamic acid decarboxylase (G AD ) , which is necessary for the production of G ABA , can be used + +to identify some of the inhibitory synapses in that tissue . + +Various other methods have been used to identify possible neuro transmitters , for example : injecting the putative transmitters on to neu rons while recording from them , microassays to determine their level in the tissue , labeling of high affinity uptake systems , etc . Each technique has limitations on what it can show . At the moment it is difficult to identify the transmitters involved and their postsynaptic effects at most synapses in the central nervous system . That said , we can make a ten tative list of possible generalizations about synapses, although most of + +them are only supported by our ignorance : + +. No axon makes Type I synapses at some sites while making + +No axon in the mammalian brain has been shown to release two different nonpeptide neurotransmitters . (But it seems likely that many neurons, including cortical neurons, may release a II conventional " transmitter and a neuropeptide, or in some + +cases two or more neuropeptides.) + +. + +There is no evidence so far in the mammalian brain that the same axon can cause excitation and inhibition at different synapses, but this is certainly possible since the effect of a given transmitter ultimately depends on the kinds of receptors + +. + +Type II at others. + +Peptides + +In some cases it has been shown that peptides act not at their place of release but at some distance away. This distance may be perhaps some tens of micra or further if carried by a vascular system (as in the path from the hypothalamus to the pitui tary) . Diffusion takes time . The slow time of onset would be compatible with the possible time delays produced by diffusion . + +. + +. + +It has been argued that peptides form a second, slower means of communication between neurons that is more economical than using extra neurons for this purpose. Different peptides are used in the same tissue to enable this communication to have some degree of specificity. (We should remark that so far very little is known about either the receptors for peptides or the physiological role of most neuropeptides.) + +THE CEREBRAL CORTEX + +We shall assume that the reader has some familiarity with the structure of the cerebral cortex and with the behavior of the neurons it contains. For an excellent review of the functional architecture of the primary visual cortex, see Hubel and Wiesel, 1977. This section aims to expand that knowledge. We shall not deal here with the non-neuronal + +There are many examples now known of a single neuron producing (and presumably releasing) more than one neuropep- + +tide. + +A remarkable discovery over the last ten years or so has been the existence of many distinct peptides, of various sorts and sizes, which can act as neurotransmitters (see Iverson, 1984, for review) . There are, however, reasons to suspect that peptides are different from more conventional transmitters such as acetylcholine or norepinephrine : + +. Peptides appear to "modulate" synaptic function rather than to + +activate it by themselves. + +. The action of peptides, in the few cases studied, usually appears to come on slowly and to persist for some time . That is, for times up to seconds or even minutes rather than for a few milliseconds or less as is the case for conventional transmitters . + +20. THE CEREBRAL CORTEX + +The neocortex consists of two distinct sheets of neurons, one on each side of the head. Each sheet is relatively thin (typical thicknesses run from 1.5 to about 5 mm) and continuous. This is illustrated in Figure 4. Although it is highly convoluted in most of the larger mammals, the neocortex has no slits in it and, as far as we know, no insulating barriers within it . Since it is a continuous finite sheet, it must have an edge. This edge is surrounded by allocortical areas and by various noncortical structures. The sheets on either side of the head are connected by a massive fiber bundle, the corpus callosum. In humans, each sheet has an area of roughly 1000 cm2 (Henneberg, 1910) . In the macaque + +monkey the figure is nearer 100 cm2. + +Each sheet of the neocortex is highly stratified . An example of the stratification in a typical cortical area is shown in Figure 5A. Histori cally and didactically, the neocortex has been subdivided into six layers (Lewis, 1878) , although a more convenient parcellation can be made into four main layers, which can then be divided further . These four layers are listed below, along with their most prominent features. + +341 + +General Organization + +. + +An upper layer (layers II and III ) . This layer contains the smaller pyramidal neurons which send their main axons to other cortical areas, either in the same hemisphere or on the + +. + +cells in the cortex (the glial cells, which may outnumber the neurons by 10-50 times) nor with its blood supply, though both these topics are + +of considerable practical and clinical importance. + +The cerebral cortex is conventionally divided into the allocortex (comprising olfactory and limbic cortical areas) and the phylogenetically more recent neocortex, which is all the rest. We shall be concerned almost exclusively with the neocortex, the extensive development of which is characteristic of the mammalian brain, especially the + +behaviorally more interesting primates. + +A superficial layer (usually referred to as layer I) . This layer has rather few cell bodies and consists mainly of axons and apical dendrites. (The presence of this superficial cell-poor layer seems to be characteristic of a "cortical" arrangement of neurons, be it the neocortex, the allocortex, or the cerebellar + +cortex.) + +344 BIOLOGICAL MECHANISMS + +arborizations in the neocortex (Figure 6) . Not only do most of the incoming and outgoing axons travel vertically across the layers to enter or exit from the deep aspect of the cortical sheet , but many of the den dritic and axonal processes of neurons in the neocortex are vertically oriented (the ascending dendrites of pyramidal cells are particularly + +good examples of this - see Figure 14A ,B) . + +The number of neurons per unit volume of the neocortex varies somewhat , but the total number of neurons underlying a given unit of surface area is remarkably constant from one area of the cortex to another and from species to species (Rockel , Hiorns , & Powell , 1980) . In the unshrunken state , this figure is about 80,000 per mm2 (Powell & Hendrickson , 1981) . An exception is the striate cortex of primates , where the figure is about 21/2 times as large (Rockel et al., 1980) . The + +reasons for this regularity (and the exception ) are not known . + +FIGURE 6. The pronounced vertical orientation of many of the dendritic and axonal processes in the neocortex is evident in this diagram of the parietal cortex of an adult mouse. At the left is a diagrammatic representation of all neuronal cell bodies within one very thin section~ at the center are the cell bodies and dendrites of some pyramidal neurons, and at the right are some different types of cortical input axons. The surface of the brain is at the top. (From "Cerebral Cortex: Architecture, Intracortical Connections, Motor Projections" by R. Lorente de No. In Physiology q( the Nervous System, p. 282, edited by J. F. Fulton, 1943, New York: Oxford University Press. Copyright 1943 by + +20. THE CEREBRAL CORTEX 345 + +Cortical Areas + +The neocortex , as already implied , appears to consist of several distinct areas, or " fields " (Rose , 1949) . These differ somewhat in their histological appearancel (the striate cortex , for example , can be easily recognized in cross section by the presence of a distinct stripe through the middle layer [Figure 50 ] , although most areas are not so easily recognized .) , anatomical connections , and the functions they perform . The hope is that in time it will be possible to parcel out unambiguously the entire neocortex into a number of distinct functional areas. Within each such area we may expect there to be considerable homogeneity of cell types , connections , and functions , all of which are likely to change rather abruptly when one crosses the border of each area and passes into another area. The number of distinct areas in the neocortex of humans (on one side) is likely to be of the order of 100. Presently , the most commonly accepted cortical parcellation scheme is the one that was established by Brodmann ( 1909) and is illustrated in Figure 7. Although extremely accurate in certain places, this map will undoubt - + +edly be refined in future years . + +It has yet to be shown that this simple concept of cortical area may not break down in parts of the neocortex . If it holds up , we should be able to count their exact number , so that we could say that in humans there are, say, 137 and not 136 distinct cortical areas. Eventually it should be possible to distinguish each area and thus construct a four - + +color map of the cortex . + +This concept of cortical area appears to hold up fairly well in those cortical areas concerned with early visual processing . In primates there appear to be at least ten of them , covering the region occupied by Brodmann 's areas 17, 18, and 19 (Figure 8) It applies very well to the striate cortex (area 17) , sometimes called the first visual area (or VI ) , and to the area known as MT (or the middle temporal area) . In the macaque , VI is an exceptionally large area, whereas MT is rather small , being less than 10% the size of VI (Van Essen, Maunsell , & Bixby , 1981 ~ Weller & Kaas, 1983) . The size of the other early visual areas will probably fall between these limits . It is important to not lose sight of the basic definition of a cortical area: ridiculously small subdivisions that do not reflect real functional differences can obscure the utility of + +this concept . + +1 The common terms used for these differences are cytoarchitectonics and myeloarchitectonics. The former refers to the differences in neuronal density and to the relative development of individual cortical layers~ the latter refers to differences in the distributions of axons (especially myelinated axons) within the cortex which varies from area to + +20. THE CEREBRAL CORTEX 349 + +FIGURE 10. A schematic diagram demonstrating part of the systematic relationship of the thalamus with the cerebral cortex and the thalamic termination of several input systems in macaque monkeys. The cerebral cortex (top center) is viewed from the left side, and several frontal cross-sections of the thalamus are illustrated, with the caudalmost section at top left and the rostralmost section at bottom right. Similarly marked parts on the left sides of the thalamic sections and the cerebral cortex have thalamocortical connections. The terminations of afferent systems are represented on the right sides of the thalamic sections as follows: inputs from the cerebellum by heavy cross-hatching, somatic sensory inputs from the leg area by short heavy dashes, somatic sensory inputs from the arm area by heavy lines, and somatic sensory inputs from the face by heavy dots and dashes. Abbreviations in the thalamic sections indicate histologically identifiable nuclei. (From The Primate Thalamus, p. 189, by A. E. Walker, 1938, Chicago: University of Chicago Press. Copyright 1938 by the University of Chicago Press. + +Reprinted by permission.) + +center through which the cerebral cortex has access to outside informa tion . The thalamus is, therefore , often referred to as the "gateway" to + +the cerebral cortex. + +- ' . . . . , , :" + +" , " .. . . , . . , . . . , . , . " , ' . . . . . . . , ' . . . - . . . . . , ' , - . . . . . . , . . , , - 0 . . , . ' - . . . . . . . . . ' . . . . ' . . . . . . 0 . . . . . ' , ' . . . . . .. . . . . 0 . . . , . - . . . ' . . . . . . . . . . f ?M . . . . . . - . . . . . . " . . ' . - . . ' , . . . . . . " ' . . ' . . . ' . . . . . ~. " . ..\ .... ' . . . . . n ' . ' . ' . . . . , ' . . . . . . . . . . 0 . " . . . . . 0 . 0 ' " . " . . . . . . . , . ' . pPO " '. . ' . 0 ' LJ', G : - 00. .: . . . , . . . ' . - . . : , , , ' . 0 . . ' . . . . . " , . O . . . . ' ' looo . :MG ' . . 0 " , . . . " 0 : ' . . 0 + +",.......::.':::."7: .'. , ,..:,::77~~~~ ,. .'.:.'.' , . . . ' . . . . . ' . ' , . . , ' , . . , " " , , . . , . , . . . . . 0 ' ' . " , . , . , " " , , . , " " , . , . . . , ' , . . " " , . . . . . " , ' , - - , . , ' , . . . . . . .O, . .' , " , " " " . , ' LP " , ' , . LP . . . . . . . 0 . . 0 ' . , " " . ' . " . , , . , . . . , ' , ' . ' . f? . 0 ' . " ' G:" ' . ' . . " " " , , , - - - -" ' , ' - \_ . . . , , , , + +. . . . . ' " " " . - - " " , + +, . . . ' . ' . " , . " , ' " , ' - ' , . , , " . . . - - - ' . ' . . . . - . ' Q. ' .,. , . . ', ', " ' , : '. ': " . , . = = \_ . : , , ' , " " , , - , - - - \_ . . - ' . .. . " .. . ' ~ D " " ," " " MD ,- , - - - ~ . , . , . ' " - - - - . " ' . " - \_ . Q . ' . , " - " " " . \_ , - - - - .' :; : : = : ., . , ., :: ,. " ,': .-- = ~--: \_- =====:--=-: , ' :': :' :,': :- : : = - - - =. : + +----.-. , , 0 ,-, --- ---- ,-,..'", ,-, -VPL :" ."' - - - - . ', , , . : . ;~-: '= ----: . ' .- - - - '\_ . ' . ' ." . . . " " . . - - - - - ' . - - - - .- ' , , ,- - - - '- ' C " j VPM - - - - , . - . - . ' - - - - ' - - - - \_ . ! VI . ' - - - - . ' VPl ; : =,\_ . C;: M ~- ,~ f:>~ :-,- . - - - \_ .\_ '- ' .. ...'\_ .\_ ,- - - ~ ,: - - - - ' - ' , - - - - ' - ' - ' . \_ ' - - - - . + +t.~'--- :-:-':-"" ,~. MG,: '.' --:,-"-' ,-'. "~ O:..." \_ ."~:' :":::: + +. . . + +MD ' " + +, , + +. , + +GP : " . ." .,'. ' , GP , ' . ." S ." .. . :... . .' " . ' , ':'.." ....'.. + +. 0 T ' . ' ,.' .' .; + +A structure called the claustrum- situated deep to the insular region of the cortex, receives inputs from (Carman, Cowan, & Powell, 1964) and projects to (Macchi, Bentivoglio , Minciacchi, & Molinari , 1981) almost all areas of the cortex. Since, apart from its diffuse innervation from the brain stem, it receives no other input , it could well be described as a satellite of the cortex. Only the visually responsive part of the claustrum has been intensively studied, and it has been shown to be systematically connected with the striate cortex and the adjacent visual + +area (LeVay & Sherk, 1981 a) . + +The thalamus comprises a number of specific nuclei~ these have welldefined inputs and project to restricted portions of the cerebral cortex. The thalamic nuclei, like the cortical fields, can be differentiated in terms of histological appearance, connections, and function . The lateral geniculate nucleus, for example, is the relay center for inputs from the retina that pass on to the striate cortex. It is a distinct , laminated nucleus which can be easily differentiated histologically from the surrounding structures (Figure 5E) . Neurons in the lateral geniculate nucleus receive visual signals from the axons of ganglion cells in the + +350 BIOLOGICAL MECHANISMS + +Diffuse innervations to the cortex arise in a number of brain stem and basal forebrain areas (Figures 9B,C) . Among them are a noradrenergic system that arises principally in the locus coeruleus (Anden et al., 1966) , a serotonergic system that arises mainly in the dorsal raphe nucleus (Bobillier et al., 1976) , and a cholinergic system that arises in the basal forebrain (Mesulam & Van Hoesen, 1976) . These systems spread throughout the cortex both horizontally and vertically and do not appear to be organized with any topographic finesse. In addition to these, it has been suggested recently that there may be a diffuse GABAergic system innervating the neocortex, which arises in the hypothalamus (Vincent , Hokfelt , Skirboll , & Wu, 1983) . The exact function of these diffuse inputs is not known, but it is important for theorists to be aware of their + +existence. + +. + +. + +Restricted neocortical projections arise in the hippocampus (Swanson, 1981) and amygdala (Porrino , Crane, & Goldman-Rakic, 1981) . These tend to terminate most heavily in cortical areas that are removed from the primary sensory and primary + +motor areas. + +. + +absent (as in the motor cortex ) , they usually terminate in the lower part of the upper layer (Jones , 1975a) . In the electron microscope , the terminal boutons of thalamocortical axons are all Type I (Jones & Powell , 1970a) and are known to be excitatory . The axons of the thalamic neurons that project to the cortex rarely have collaterals within the main body of the thalamus (Friedlander , Lin , Stanford , & Sher- + +man , 1981) . + +In addition to the specific nuclei , there are a number of less specific (sometimes called nonspecific ) thalamic nuclei . The most prominent group of the less-specific nuclei is known as the intralaminar nuclei and occupies a thin , vertical , sheet -like zone extending anteroposteriorly through the center of the thalamus . While most of these are rather small , one - the centromedian nucleus - is very prominent in the human brain . The neurons of the intralaminar nuclei project both to the striatum and to the cerebral cortex (Jones & Leavitt , 1974~ Powell & Cowan , 1967) . Their cortical projection , instead of terminating in the middle layer of the cortex , terminates mainly in the superficial layer (layer I) . Moreover , the cortical projections of the intralaminar nuclei are not confined to a single cortical field , but tend to be rather widespread . Our present knowledge of the less-specific thalamic nuclei + +and their role in cortical function is quite vague . + +Each of the specific thalamic projections to the cortex is accompanied by a reverse projection from the cortex to the thalamus . The spatial organization of the reverse projection reciprocates , fairly precisely , the forward one . This reverse projection arises from cells at the bottom of the deep layer and terminates directly on the peripheral dendrites of thalamocortical relay cells . Their terminations are also Type I (Guil lery , 1969~ Szentagothai , Hamori , & Tombol , 1966) . Although they are very numerous , the function of these reverse projections is not known . A very remarkable nucleus , called the thalamic reticular nucleus forms a thin shell around the main body of the thalamus . It is only a few cells thick . Its neurons are very large , with protrusions on their dendrites called spines (M . E. Scheibel & A . B. Scheibel , 1966) . This nucleus does not project to the cortex but projects back into the thalamus (Jones , 1975b) . It appears to receive small collaterals from most of the axons that pass between the thalamus and the cortex . It also gets some input from the traffic between the thalamus and the stri atum . Its axons are inhibitory (Houser , Vaughn , Barber , & Roberts , 1980~ Montero & Scott , 1981) , and they have extensive axon collaterals within the reticular nucleus (Scheibel & Scheibel , 1966) . Obviously this nucleus occupies a very strategic place in the brain . It deserves more attention , both from experimentalists and theorists (Crick , 1984) . + +20. THE CEREBRAL CORTEX 351 + +352 BIOLOGICAL MECHANISMS + +which case they are called associational inputs) or in the opposite hemisphere (where they are known as commissural inputs) . It is important to note that a typical cortical area is not connected directly to all or even most other cortical areas. Usually it projects to a handful of other areas, although the areas that are removed from the primary sensory or motor areas tend to project more widely (Jones & Powell, 1970b~ Pandya & Kuypers, 1969) . But if a cortical area projects to another cortical area, its projections are usually topographically organized, at least on a coarse scale. That is, as far as position in the sheet is concerned, connections between areas are not random~ neighboring neurons in a field tend to project to neighboring regions in other fields in some systematic way. Moreover , as a general rule, projections from one field are usually matched by a reciprocal projection from that field which is also topographically organized. To a considerable extent the forward and backward mappings coincide, at least on a coarse scale, but are not symmetrical in all details. Rockland and Pandya (1979) and Maunsell and Van Essen (1983) suggest that for the early visual areas, a forward projection (forward with respect to the retina) is likely to project predominantly into the middle layer, whereas the reverse projection is likely to avoid the middle layer and instead terminate largely in the superficial + +and deep layers (Figure 11) . + +Topographically organized maps occur in many cortical areas. Anatomical and electrophysiological studies show that in most cortical areas there is a more or less topographic representation of the periphery upon the cortical surface . Detailed maps of cortical representation patterns are available for the areas concerned with sensory input (and motor output ) . As might be expected , such maps vary somewhat from individual to individual . Their broad topography is usually not linear ~ the extent of cortex representing a given region of the periphery is roughly proportional to the peripheral innervation density . Thus , the fovea is heavily over -represented in the striate cortex (Figure 12A ) , and the hand occupies a bigger region than the trunk in the somatic sensory (Nelson , Sur , Felleman , & Kass, 1980~ C. N . Woolsey , Marshall , & Bard , 1942) and motor cortical areas (C . N . Woolsey et al., + +1952~ see Figure 12B) . + +All this makes good sense. Because neurons in the cortex cannot act directly on more distant neurons in the same area (see later ) , such " maps " bring into proximity neurons which are likely to have related inputs . They also allow more space for the more densely innervated + +regions . + +This systematic mapping of the periphery is likely to be a feature of many cortical areas, not merely those near the sensory input . In general terms , as one proceeds further from the sensory input , the + +... + . . . . - - - - - - - - - - - -;;;:;"- - - - - =~~~==~== ~====== ------=-- ----=---- + +F rARD CAW + +20. THE CEREBRAL CORTEX 353 + +. . . + +=- ------~.- i~~----- -------- --------- -------- -------- + +. . . . + +- - - - - - ~ = - - - - - - - . . . + +- - + +FEEDBACK + +FIGURE 11. A schematic diagram of the characteristic laminar distributions of cell bodies and terminals in forward and feedback cortico -cortical pathways . Forward path ways arise mainly from the upper layer and terminate mainly in the middle layer . Feed back pathways arise from both upper and lower layers and terminate mainly outside the middle layer . Triangles represent cell bodies , and axons are represented by thin lines . (From "The Connections of the Middle Temporal Visual Area and Their Relation to a Cortical Hierarchy in the Macaque Monkey " by J. H . I~. Maunsell and D . C . Van Essen , 1983, Journal Qf Neuroscience , 3, p. 2579 . Copyright 1983 by The Society for Neurosci - + +ence . Reprinted by permission .) + +mapping of the periphery becomes more diffuse . At the same time the + +neurons respond to more elaborate " features " of the input . + +There are irregularities within a cortical area. It should not be inferred from the abo\'e description that cortical areas are relatively uni form . On the contrary , on the scale of 1 mm to 2 mm , patchiness is almost always the rule . The patchiness can, in many instances , be attributed to disjunctive distributions of inputs . Dense foci of termina tions , separated by zones that are relatively free of terminations , have been described for the inputs from the thalamus and from other cortical + +areas . + +This is especially clear in cases where the inputs are not continuous but discrete . For example , the thalamic input from either of the two eyes form nonoverlapping stripe patterns (not unlike fingerprints when viewed from the surface ) in the middle layer of the striate cortex (Fig ure 13) (Hubel , Wiesel , & LeVay , 1977~ l ,eVay , Connolly , Houde , & Van Essen, 1985) . In the somatic sensory system of rodents , inputs + +356 BIOLOGICAL MECHANISMS + +irregular. Stripe-like patterns of terminations have been described for thei r projections to area 18 (Gilbert & Wiesel, 1981 ~ Maunsell, N ewsome & Van Essen, 1980) . In the primary auditory cortex, there are irregular rows of commissural terminations which in cross-section appear as multiple column-like clusters. Such clusters contain neurons that display certain kinds of binaural interaction (Imig & Brugge, 1978) . The various kinds of patches outlined above appear to underlie a tendency of neurons aligned vertically to display certain similarities in functional properties. Other response properties, not necessarily correlating with input signals, are also aligned vertically . For example, in the visual system of monkeys, the cells that project to the cortex have center-surround receptive fields, and the neurons in the upper and lower layers of the striate cortex respond specifically to lines oriented in a particular orientation (Hubel & Wiesel, 1968) . Furthermore , neurons with similar orientation preferences are often aligned vertically , though this may not always be true . However, in a general sense it has been found that when recordings are made with a microelectrode inserted perpendicular to the surface of the cortex, the response properties of all the neurons encountered throughout the depths of the cortex tend to + +be similar . + +These various types of patchinesses have suggested to some authors that the cortex is organized on a "modular " basis, either involving columns about 1/2 mm or so in diameter or into minicolumns , some 50 microns or so across (Mountcastle, 1978) . In the cortex there is really no evidence for true modules of the type found , for example, in the fly 's eye and rather little for more irregular modules. The exact basis + +on which the cortex is organized remains to be discovered. + +Cortical Outputs + +All the axons that leave a cortical area make Type I (excitatory) synapse in their projection fields. The subcortical projections of the cortex, in contrast to the subcortical inputs, are not subject to the constraint of always relaying through the thalamus. Thus, the cortex can project directly to the spinal cord or superior colliculus , but the spinal + +and collicular inputs to the cortex always relay in the thalamus. + +As mentioned earlier, there is a close relationship between populations of cortical output neurons and their laminar positions. This is particularly evident for the populations of neurons that project subcortically. For example, the cortical neurons which project to the thalamus are situated at the bottom of the deep layer, whereas those that project to the striatum and brain stem tend to be concentrated in more + +20. THE CEREBRAL CORTEX 357 + +superficial portions of the deep layer ( Jones & Wise , 1977 ~ J . S . Lund , + +R . D . Lund , Hendrickson , Bunt & Fuchs , 1975 ) . + +As with the input systems , most of the output systems of the neocor tex are patchy . Patches of neurons have been demonstrated to project to other cortical areas and others to project subcortically ( Jones & Wise , 1977 ~ Murray & Coulter , 1981 ) . Although the groups of cells giving rise to the various projections are segregated into layers , physiological studies indicate that neurons producing similar outputs are vertically aligned . This has been most convincingly demonstrated in the motor cortex , where microstimulation points producing isolated contractions of given muscles have been shown to be organized in cylindrical zones which extend throughout the depths of the cortex ( Asanuma & Rosen , + +1972 ) . + +THE NATURE OF NEOCORTICAL NEURONS + +Experimental Methods + +The shape of neurons in many areas of the brain has traditionally been studied in Golgi - stained material . The Golgi method stains , in their entireties , a few cells here and there , apparently " at random ." The haphazard selectivity of this method allows investigators to visualize clearly most of the dendritic processes of individual neurons . Unfor tunately , though , the technique is capricious and does not always stain the axon and axon collaterals completely . A more recent method , using intracellular injections of an appropriate marker such as the fluorescent dyes procion yellow or lucifer yellow or the enzyme horse radish peroxidase ( HRP ) , is capable of producing a similar picture with better reliability and control , but is not suited for sampling large popu lations of neurons since each neuron must be separately injected . + +Very fine details , such as the morphology of the synapse , cannot be seen using the light microscope . The electron microscope is necessary for this . The extremely high magnifications needed to differentiate such details , however , make it difficult to reconstruct ( using a very large number of serial sections ) even a very small neuron in its entirety . ( This problem can be partially alleviated by combining stan dard electron microscopic procedures with the Golgi method or a + +It is important to realize that each of the techniques presently avail able is limited in its sampling capacities . Many of the following conclu sions , therefore , are rather general and apply to broad groupings of + +358 BIOLOGICAL MECHANISMS + +cortical neurons. Except in rare cases, there is little quantitative infor- + +Cell Types in the Neocortex + +The most common and most characteristic neurons of the cerebral cortex are the pyramidal cells (Figure 14A) . Such neurons, as their name implies, have a pyramid-shaped cell body. A thick apical dendrite ascends vertically from the apex of the cell body. It often has tufts of branches that arborize in specific laminae. A number of basal dendrites also extend out from the bottom of the cell~ these branches spread horizontally for some distance. All dendrites of pyramidal cells possess large numbers of dendritic spines. The axons of pyramidal cells emerge either from the bottom of the cell body or from one of the basal den- + +drites and generally leave the area. + +Though these basic features are common to all pyramidal cells, there are a variety of different types of pyramidal cells (Figure 14B) . On the basis of cell body size alone, they range from about 10 microns up to 100 microns in diameter (Cajal, 1911 ~ Conel, 1939) . The branching patterns of the apical and the basal dendrites also differ tremendously, as do the target sites of the projection axons and the arborizations of axon collaterals which participate in local circuits. These variations do not appear to be random, and a number of classes of pyramidal cells have been described (Cajal, 1911~ Lorente de No, 1943~ J. S. Lund , 1973) . Unfortunately , the information presently available for differen tiating the various types of pyramidal cells is far from complete. It is unlikely that there are as few as ten distinct types: There could be as + +many as a thousand. + +All axons that leave the cortex belong to pyramidal cells. The converse, however, may not be true. Though all pyramidal cells were once considered to be projection neurons (Cajal, 1911) , recent data suggest otherwise. Using intracellular HRP injections, Gilbert and Wiesel (1983) have found a few pyramidal cells with extensive local axonal + +arborizations that do not project out of the striate cortex. + +The remainder of the neurons in the cerebral cortex can be broadly categorized as 'I nonpyramidal cells" (Figure 14C) . By definition , they comprise all neurons whose cell bodies are not pyramid-shaped. They constitute a large number of cell types which can be differentiated on the basis of the shape of the cell body, size, dendritic arborizations, and axonal ramifications . For example, some have relatively spherical cell bodies with dendrites that radiate in all directions and therefore are star-shaped, or 'I stellate." Others are spindle-shaped and have dendritic + +mati on on specific cell types. + +. IneS. + +360 BIOLOGICAL MECHANISMS + +Neurons With Spines + +on their sp only a single Type I synapse~ + +Neurons Without Spines + +arborizations which are aligned vertically . Again , the number of distinct types is not known . It is unlikely to be as few as ten ; it could run + +to several hundreds . + +Instead of discussing in detail the varieties of nonpyramidal cells that are known , we should like to draw the reader ' s attention to two charac teristics of nonpyramidal cells that are of significance in the context of this chapter . One is that the nonpyramidal cells are local circuit neu rons , viz ., they do not project out of a given cortical area. The other is that there are two basic types of non pyramidal cells according to their dendritic morphology . One type has numerous spines on its dendrites , + +and the other has few or no spines . + +A convenient categorization combines the entire population of pyramidal cells and also the spiny nonpyramidal cells into a group called II neurons with spines ," and the remaining nonpyramidal cells into a group called " neurons without many spines ." The following generaliza tions are applicable when cortical neurons are categorized in this way + +(see Table 1) . + +The neurons with spines are the pyramidal cells , the star pyramids , and the spiny stellate cells . Such cells receive Type I synapses mainly + +---- - . Usually , each spine has + +TABLE ! + +Neurons With Spines + +Usually one Type I Input to Spines Occasionaliy one Type I plus one Type II + +Input to Dendrites Both types Both types Input to Soma Type II only Both types + +Multiple Type lIon many + +Input to Axon Hillock pyramidals in layers II and III (see text ) + +20. THE CEREBRAL CORTEX361 + +a minority of spines has an additional Type II synapse. No spine seems + +to have only a Type II synapse by itself (Colonnier , 1968) . + +The Type II synapses on spiny cells tend to be fewer in number than Type I synapses. They do, however, occupy sites that are suited for effectively influencing impulse generation by the neuron (which generally takes place at the axon initial segment) . They usually occur on the proximal shafts of the dendrites or on the cell bodies (Gray, 1959) . A special type of Type II synapse is found on the initial segment of the + +axon of many pyramidal cells (Peters et al., 1968) . + +The axon of a spiny cell forms only Type I synapses (LeVay, 1973) . Pyramidal cells almost always send the main branch of their axon out into the white matter below the cortex. Spiny stellates almost always have a local axon which does not leave the cortex but ramifies instead + +in close proximity to its cell of origin . + +Neurons Without Many Spines + +Although neurons without spines may have transient spines on their dendrites early in development , in the mature state they have relatively + +few , if any , spines . + +Such cells , of which there are several obviously different morphologi cal types , receive both Type I and Type II synapses on their dendritic shafts and on their cell bodies ( Gray , 1959 ) . The axons of nonspiny neurons do not descend to the white matter but ramify locally . Their axons are believed , in most cases , to form only Type II synapses + +( LeVay , 1973 ) , but there may well be exceptions . + +It remains to say that spiny cells are in the majority ( 80 % ) . Of these , a fair number , perhaps as many 25 % can be non pyramidal in some cort ical areas . The nonspiny cells are in a minority ( 20 % ) . Unfortunately + +these percentages are only very approximate . 3 + +3 These approximations are derived from the results of Tombol ( 1974 ) , who found 59 % of the neurons in the visual cortex of monkeys to be pyramidal neurons , 7 .4% to be large stellate neurons , and 33 .6% to be small stellate neurons . Of the population of small stel late neurons , 63 % were found to occur in the middle layer . These results did not take into account the spiny stellate neurons which also need to be included in the spiny category . Since spiny stellate neurons are small (Cajal , 1911 ) , restricted to the middle layer (1. S. Lund , 1973 ) , and constitute the major component of the middle layer (1. S . Lund , 1973 ) , we have added 21 % to the overall percentage of pyramidal neurons reported by Tombol , to obtain a very rough figure of 80 % for our estimate of spiny neu - + +We shall now discuss these generalizations (summarized in Table 1) on the assumption that most Type I synapses excite and most Type II synapses inhibit . The main point to grasp is the asymmetry between + +excitation and inhibition . + +Excitatory neurons and excitatory synapses are clearly in the majority . Only excitation is sent out of any area of the cortex to other places. On the other hand, the inhibitory synapses are more strategically placed on the cells, being nearer the impulse initiating site at the axon hillock , at least for spiny cells. This is almost a necessity if the system is not to get out of hand, since any area of the cortex feeds back excitation to itself in large amounts. The synapses formed by axons entering the cortex are in a minority , sometimes a very small minority . The great majority come from the axons of other cortical cells: mostly, but not + +entirely , from those within a few hundred microns. + +Inhibition seems to have priority in two ways. Inhibitory neurons have excitatory inputs on their cell bodies, so that they can be brought into action quickly . Excitatory neurons, on the other hand, receive inhibition at strategic sites. This preference for inhibition must be set against the fact that (excluding some of the diffuse innervation ) the inputs entering the cortex are all excitatory. Thus any inhibition needed must be generated from this excitation . This requires an extra step and therefore will take time . It seems as if the cortex is arranged so that this time delay is minimized by the regularities discussed above. In special conditions , such as epilepsy and under the influence of hallucinogenic drugs, the cortical system may go into full -scale oscillation , presumably because the balance between excitation and inhibition has + +been upset. + +362 BIOLOGICAL MECHANISMS + +Excitation Versus Inhibition + +Special Cell Types + +Nonspiny neurons are of various types. Many of them are stellate. Here we describe three unusual types of nonspiny neurons whose pro- + +perties may be of special interest. + +Chandelier cells. So-called because their axons ~nd in a set of verti cally oriented beaded terminal segments which make them look somewhat like chandeliers (Szentagothai & Arbib , 1974) . An alternative + +20. THE CEREBRAL CORTEX 363 + +cells (Somogyi , 1977 ) . Each chandelier cell axon has at least 50 to 200 such terminal segments (Somogyi , Freund , & Cowey , 1982 ) , each of which may form 5 to 10 synapses (Fairen & Valverde , 1980 ~ Somogyi et al ., 1982 ) . (There does not appear to be any corresponding cell which makes Type I synapses on axon hillocks .) Each pyramidal cell may receive up to six such terminal segments , presumably from dif ferent chandelier cells (Fairen & Valverde , 1980 ~ Somogyi et al ., 1982 ) . It is difficult to resist the impression that a chandelier cell can veto the output of a whole set of neighboring pyramidal cells . Whether this is really true is not known , but the fact that chandelier cells are prob ably GABAergic (Peters , Proskauer , & Ribak , 1982 ) and form Type II + +synapses strongly implies that they are inhibitory . + +The number of chandelier cells is not known . A not unreasonable guess would be that they form about 1% of the total neuronal popula tion . 4 It is not known how many types of chandelier cells exist . So far + +no stain has been found which selectively stains them . + +Basket cells . These cells have vertically oriented stem axons which give rise to several horizontally disposed collaterals . The collaterals subsequently give off obliquely or vertically directed fine terminal branches , which are commonly clustered and resemble baskets (Cajal , 1911 ~ Marin -Padilla , 1969 ) , though not all terminal branches resemble baskets (Jones , 1975c ) . These terminal branches often form loops of boutons around the cell bodies of pyramidal cells ( 10 to 20 terminal branches may converge upon certain pyramidal cells ~ Martin , Somogyi , & Whitteridge , 1983 ) . The characteristic fine axonal sprays of these cells are rather difficult to visualize , so it is not certain that basket cells occur in all cortical areas . The terminal boutons of basket cells are Type II in morphology and are thought to contain GABA (Martin et al ., + +1983 ~ Somogyi , Kisvarday , Martin , & Whitteridge , 1983 ) . + +Again , one cannot resist the impression that the basket cell is likely to exert a veto (or at least a partial veto ) upon the output of the corti - + +cal projection neurons . + +Bipolar cells . These are cells whose dendrites and axons form a very long thin bundle in the vertical direction (M . L . Feldman & Peters , 1978 ) . Some of them have been shown to contain peptides such as somatostatin , cholecystokinin (CCK ) , and vasoactive polypeptide (VIP ) + +4 This guess is based on three arbitrary assumptions: (a) all pyramidal neurons receive initial segment synapses from chandelier cells, (b) every chandelier cell innervates about 200 pyramidal neurons, and (c) every pyramidal neuron is innervated by about five different chandelier cells. Together, these suggest that there are about 40 pyramidal neurons for each chandelier cell. Since pyramidal neurons account for about 60% of the neurons in the visual cortex of monkeys (TOmbOI, 1974) , the above assumptions would suggest that chandelier cells form about 1.5% of the neuronal population of the monkey + +364 BIOLOGICAL MECHANISMS + +(Emson & Hunt , 1981 ~ Fuxe , Hokfelt , Said, & Mutt , 1977) . These cells can be stained immunohistochemically . About 1350 VIP cells are estimated to occur under 1 mm2 of surface in the rat visual cortex (this figure is uncorrected for shrinkage ) (Morrison , Magistretti , Benoit , & Bloom , 1984) , thereby making up about 1% of the total neurons . Whether bipolar VIP cells also have other nonpeptide transmitters is not yet known . The type of synapse made by each type of bipolar cell is not clear . Their relationship , if any , to the " columns " reported in the cortex is also unclear . Nevertheless , their narrow shape is intriguing . + +The Behavior of Single Neurons in the Cerebral Cortex + +The behavior of single neurons in the cerebral cortex will depend to some extent on the exact nature of the neuron concerned . Here we + +will treat only the general problem . + +It is widely believed that the dendrites of most neurons behave in a largely passive manner . Their cable constants can be estimated from passive membrane transients that can be recorded intracellularly . In the cortex the total soma -dendritic input resistance ranges from 6.7 to 78 megohms with a mean of 24 megohms , while the membrane time con stant tends to be relatively constant at around 8.2 milliseconds (Con nors , Gutnick , & Prince , 1982) . If the specific membrane capacitance is assumed to be about 1 JL F / cm2 (K . S. Cole , 1968) , then the mean specific membrane resistance is relatively high at about 8,200 ohm -cm2. This implies a relatively large length constant for most neurons in the + +cerebral cortex . + +However , there are disturbing reports that the dendrites of some neurons (for example , the Purkinje cells of the cerebellum and the pyramidal cells of the hippocampus ) may have spike generating patches (Llinas & Nicholson , 1969~ Spencer & Kandel , 1961) . Unfortunately , the experimental techniques to look for this are not easy and the + +interpretation of the results is not straightforward . + +Clearly , it would make a tremendous difference if the dendrites of a neuron were not purely passive . To give just one example , if its den drites are passive it might be argued that the apical dendrites of a pyramidal cell may mainly serve to " modulate " the inputs of the basal dendrites , because the apical dendritic shaft would attenuate any change of potential produced by synapses in the apical tuft so that , by itself , it might not be able to fire the cell . If the apical dendrite had spike generating capabilities , this argument would not be valid . It is clearly an urgent matter to decide just how potential changes are propagated in + +Another important theoretical parameter is the "weight" of individual synapses~ that is, the size (and time course) of the potential change that synapse produces in the postsynaptic cell. Since in many theories these weights not only determine the behavior of the neuron but are thought to be important for memory, they are obviously of considerable signifi cance. Such weights could be influenced by many factors, both presynaptic and postsynaptic. Moreover , the weights could be subject to transient changes due to many different biochemical processes. Parenthetically we may point out that there is a problem concerning long-term memory and the synaptic weights that may be associated with it . How do synapses manage to remember anything over a period of years in the face of relentless molecular turnover ? This makes one wonder whether some single structural feature, either at the molecular level or at a higher level, might embody the "long-term weight." A naive guess might be that it is simply the area of the synapse, since in the neocortex this varies, from synapse to synapse, by a factor of 10 + +(Peters & Kaiserman-Abramof , 1969) . + +Type II synapses tend to be nearer the axon hillock than do Type I synapses. Thus, it can be argued that such inhibitory synapses on a given dendrite can exercise a partial veto on more distal excitation and thus the exact arrangement of the various synapses could be significant . On this view, a single neuron, rather than being a single integrating device for distributed excitation and inhibition , may be a more complex processing unit , with each dendritic branch acting, in a loose sense, as an integrating unit for its own inputs (Koch, Poggio, & Torre , 1982) . It remains to be seen whether this new concept is really valid. Whether it is or not, it should be noted that it is a lot easier to implement addition , subtraction, and division than it is to implement multiplication in a single neuron. In logical terms, AND -NOT seems easier to implement than AND . However, because of the uncertainties in our + +knowledge, such generalizations are precarious. + +In any single neuron a synapse nearer the cell body is likely to have a larger effect than one near the ends of the dendrites, but even this rather obvious deduction has been questioned for neurons whose dendrites generate action potentials. It is obvious that a lot needs to be learned about dendritic behavior before theorists have a solid body of + +facts to build on. + +20. THE CEREBRAL CORTEX 365 + +The Behavior of Groups of Neurons in the Cerebral Cortex + +366 BIOLOGICAL MECHANISMS + +As we have already seen, in the cortex there are extensive axon col laterals . Many of these only extend laterally for relatively small distances - less than mm - but a significant fraction spread for several millimeters (Gilbert & Wiesel , 1983~ Rockland & J. S. Lund , 1983) . However , they never seem to spread as much as a centimeter , though this is not true for the diffuse inputs such as those from the brain stem . Thus , in mathematical terms , for one cortical area the connections seem to be "near -diagonal ," assuming that we have a two -dimensional arrangement of cells and a four -dimensional connection matrix . Whether excitatory axons spread more or less than inhibitory axons is + +not clear . The data on this point are confusing . + +A favorite theoretical model is one in which all cells of one type con nect directly to all other cells of the same type . It seems very rare for a cell to connect to itself (the diagonal term ) , although occasional axon collaterals that terminate upon their parent cell have been described (Van der Loos & Glaser , 1972) . A more disturbing criticism is that , among the sea of axon collaterals , we really have no evidence that cells of one type connect to other cells of the same type . A better guess would be that the collaterals usually contact cells of other types in that area of cortex , often to cells in a different layer . Our ignorance springs partly from the fact that we lack convenient experimental methods for + +studying which cell types actually connect to which . + +Are there any general rules about the connection in the neocortex ? An outline model , based on recent studies of the visual cortex (Gilbert , 1983~ Wiesel & Gilbert , 1983) , might be that the main extrinsic input to a cortical area (from the thalamus ) is to the middle layer . From there the excitation spreads largely to the upper layer , and from there to the deep layer - first to layer V and then to layer VI . The flow of information for other inputs is less clear . Inputs from other cortical areas tend to end in the upper layer and presumably spread from there to the deep layer . This description is certainly grossly oversimplified in almost every respect but it may turn out to have an element of truth + +in it . + +Rates of Firing + +The average discharge rate of neocortical neurons is relatively slow - perhaps only 50 to 100 spikes per second , though the rate for a brief time can rise as high as several hundred spikes per second (see e.g., Lynch , Mountcastle , Talbot & Yin , 1977) . This means that the time between spikes is often 10 to 20 milliseconds . Bearing in mind how much II computation II the brain can do in 100 milliseconds , this + +20. THE CEREBRAL CORTEX367 + +seems to suggest that the average rate of firing of an individual neuron can only be transmitted rather approximately and that computations involving many reiterations are unlikely , at least for the initial process ing of an input . The precise nature of this limitation deserves further + +study . + +Most , but not all , cortical neurons have very low resting discharges : only a few spikes a second ( see , e .g . , Abeles , 1982 ) . This is likely to cause problems when one needs to signal both positive and negative values of a function . One obvious way is for one set of neurons to sig nal the positive values and another to signal the negative ones . In the visual system this appears to be initiated by the retinal ganglion cells ( which have separate ON - center and OFF - center receptive fields , Kuffler , 1953 ) which signal information from the retina to the lateral geniculate body ( Cajal , 1892 ) and from there are relayed to the primary + +visual cortex and elsewhere . + +A large " soma - dendritic " spike generally follows an action potential which is initiated at the axon hillock . This large spike is believed to take place at the cell body and possibly invade the proximal parts of the dendrites ( Brock , Coombs , & Eccles , 1952a ) . This might conceivably wipe clean the slate each time a neuron fires , as well as tell each synapse that the cell had fired . There is evidence suggesting that such a mechanism might exist in spinal motoneurons . Virtually complete destruction of pre - existent postsynaptic potentials have been seen fol lowing soma - dendritic spikes in spinal motoneurons ( Brock , Coombs , & Eccles , 1952b ) . Further data on this important point would be + +welcome . + +Feature Detection + +In certain parts of the neocortex , especially those near the sensory inputs , it has been shown that a particular neuron will respond best to a certain set of " features " in the input . Thus a so - called " simple cell " in the first visual area responds best to a line or edge of a particular orien tation in a particular place in the visual field ( Hubel & Wiesel , 1968 ) . It may prefer a certain small range of spatial frequencies ( Schiller , Fin lay , & Volman , 1976 ) . It may respond better to movement in one direction rather than that in the opposite direction ( Hubel & Wiesel , 1968 ) . Some cells are sensitive to the horizontal " disparity " between the input to the two eyes ( Hubel & Wiesel , 1970a ) . Other cells may respond better to some wavelengths of light than to others ( Michael , + +368 BIOLOGICAL MECHANISMS + +The description and classification of features are matters of the first importance , but even for the early parts of the visual system our knowledge is still very incomplete . These details are of the greatest interest to theorists actively studying a particular system . Here we can + +only mention them in passing . + +As one proceeds further from the sensory input , the mapping of the periphery becomes more diffuse . At the same time most of the neu rons tend to respond to one or another feature of the stimulus movement , color , etc . - while still others respond to more elaborate features in the input . For example , Zeki has shown that in the visual area V 4 of the macaque , a cell 's response to the wavelength of the light depends somewhat on the wavelength coming from fairly distant regions in the visual field (Zeki , 1978) . In the first visual area, on the other hand , a neuron 's response to wavelength is much more local (Michael , 1978) . This makes sense since although the axon collaterals spread a similar cortical distance in both areas, V 4 is smaller than VI , so that in the former the collaterals can reach more distant parts of the visual field , especially as the " mapping " in V 4 is more diffuse than it is + +in VI (Van Essen & Zeki , 1978) . + +As one proceeds further into the system it becomes increasingly diffi cult to discover exactly what "feature " a cell likes best . A few neurons in the cortex , lining the superior temporal sulcus and in the inferior temporal cortex of monkeys , appear to respond to pictures of faces (Bruce , Desimone , & Gross , 1981 ~ Desimone , Albright , Gross , & Bruce , 1980~ Perrett , Rolls , & Caan , 1982) . If the eyes are blocked out in the pictures , the neurons fire less. If the features of the face are jumbled , the neurons do not respond at all . The exact location and the orientation of the pictures do not appear to be critical to the response of these neurons . It is claimed that other neurons in these complex cortical areas respond specifically to hands (Desimone et al., 1980) , but for most of the neurons in these cortical areas , the best type of stimulus has eluded discovery . This is a case where a good theory might give useful pointers to an experimentalist . Since a neuron 's out put is simply the spikes it sends down its axon , the same pattern of spikes can conceivably be produced by a whole variety of different but related inputs . Thus , in a very real sense the firing of a single neuron conveys somewhat ambiguous information . It is widely believed that it is the pattern of a set of neurons which is best thought of as conveying information . It thus becomes important to know whether the input from a single cortical neuron can, by itself , fire a particular cell in its projection field or whether several neurons are required to do this . There is little evidence in the neocortex that a single neuron can, by itself , fire a cell , but exactly how many are needed can only be guessed at . Even where we know that the axon of one neuron contacts the + +dendrites of another neuron, we usually do not know how many distinct synapses it makes on the second cell. Methods that could answer this + +Question would be very valuable. + +Conceptually the problem is not straightforward , since the background "noise" (the occasional random firing of many neurons) is likely to bring a neuron closer to threshold and thus reduce the number of more active neurons required to fire the cell. Spontaneous, transient fluctuations of the membrane potential have been seen in all intracellu larly examined cortical neurons (Connors, Gutnick , & Prince, 1982) . There seems to be rather little correlated firing of neurons in the neocortex. (For details, see the monograph by Abeles, 1982.) That is, neighboring neurons seldom fire at precisely the same time . When neurons do fire with some degree of synchrony, as they appear to do to produce alpha-waves in the EEG, they do so mainly when the mind appears to be idle. This apparent lack of synchronized firing suggests that the brain is not organized, as a modern digital computer is, on a repeating time cycle. However, the thalamus does appear to impose a degree of rhythm on its output , so it is possible that more subtle time + +effects exist and have been missed. + +An important unresolved question concerning feature detection is whether it is inborn or learned. This is a difficult topic and we can only touch on it . At the moment it seems likely that "feature detectors" are to a considerable extent inborn but can be tuned up by experience, especially during certain "critical periods" in development. The neocortex does not appear in its details to be a general-purpose computing machine. Each area (with its connections) seems designed to carry out a specific function , even though this can be modified somewhat by experience. Natural selection has had every opportunity to develop the necessary neuronal machinery to cope with issues which, because of the nature of the external world , have changed little in evolution . Theorists almost always assume that they are cleverer than natural selection. + +This is usually a mistake. + +In spite of the above remarks, it is reasonable to assume that the neocortex has evolved because it is good at a particular sort of computation and that, with appropriate local variations, it may be broadly the same in all parts. We may also expect that these basic processes will be complicated by somewhat elaborate neural gadgetry designed to make for better performance. What these basic computational processes are + +remains to be discovered. + +Other sections of this book concern models constructed out of "units." These units often have properties similar in some respects to neurons in that they have multiple inputs, some sort of summation rule, a threshold rule, and a single output which is usually distributed to several other units. However, their inventors are always careful to + +20. THE CEREBRAL CORTEX369 + +370 BIOLOGICAL MECHANISMS + +point out that they are not intended to represent real neurons. Indeed, at this stage in the game, it would be foolish to attempt to do this. Nor are most of the units used satisfactory idealizations of real neurons. If the properties of real neurons present useful gadgets to neural modelers, they should not be mixed together in combinations that + +never occur together in the brai n. + +Another explanation offered by modelers in defense of their units is that a single unit really stands for a group of neurons. This might be acceptable to neuroscientists if it were carefully stated how this group might be built out of more or less real neurons, but this is seldom if ever done. Consequently, it is difficult to know whether a given II unit II + +is plausible or not. + +Another approach to the difficulty is to claim that II units are placeholders for informational states" (J. L . McClelland , personal communication) and that the relationship between the neurons and such states may be complex. This may indeed be plausible, but from the neuroscientist's point of view it makes it almost impossible to test the + +models unless the relationship is spelled out in detail. + +Another difficulty is that neural modelers seldom state exactly what their models are supposed to demonstrate. This difficult question is + +addressed more fully in the last chapter of this book. + +Meanwhile we list here briefly some of the devices loved by theorists which, if interpreted literally , are not justified by the available experi- + +mental evidence: + +. Neurons that excite some cells and inhibit others. + +. Neurons that merely " change sign." For example, a neuron that accepts excitation from one neuron only and whose onput pro- + +duces inhibition on one neuron only. + +. Neurons that connect to all other cells of the same type. + +. Neurons with distinctive synapses that do elaborate computations. Apart from spines which sometimes have both a Type I and a Type II synapse, such complications are rare or absent in the neocortex, though they do occur in the thalamus. However, separate dendrites may perform such a role in the cortex. + +. A neuron that, by itself , can fire another cell. This does occur in the cerebellum (the climbing fiber on a Purkinje cell) (Eccles, Llinas, & Sakaski, 1966) . It is not certain that it does not occur in the neocortex but the available evidence suggests that it is not common. However, chandelier cells and basket cells may, by themselves, be able to veto the firing of another + +20. THE CEREBRAL CORTEX 371 + +The following are features found in the neocortex but often not used + +in theoretical models: + +. Veto cells, which appear to veto many other cells and which probably need the summated activity of several distinct inputs + +to fire them. + +. The various diffuse inputs , from the brain stem and elsewhere , which may be important , not only for the general level of arousal of the cortex ( as in sleep ) but also for potentiating the synaptic modification involved in laying down a memory . + +ACKNOWLEDGMENTS + +We thank our colleagues at the Salk Institute for many helpful dis cussions . We are especially grateful to W . Maxwell Cowan and Jay McClelland for their detailed comments on the manuscript . We also + +thank Betty Lang for her careful typing of the various drafts . + +This work was supported by the J . W . Kieckhefer Foundation , the Samuel Roberts Noble Foundation , the System Development Founda - + +tion , and NIH Fellowship NS - O7061 . + +CHAPTER 21 + +Open Questions About + +Computation in Cerebral Cortex + +T. J. SEJNOWSKI + +In Chapter 20~ Crick and Asanuma have attempted the difficult task of summarizing what is presently known about the physiology and anatomy of cerebral cortex. Here I will attempt to summarize what is not known. The goal of this chapter is to provide a framework within + +which to ask computational questions about cerebral cortex. + +QUESTIONS ABOUT CEREBRAL CORTEX + +Different areas of cerebral cortex are specialized for processing infor mation from different sensory modalities, such as visual cortex, auditory cortex, and somatosensory cortex, and other areas are specialized for motor functions ~ however, all of these cortical areas have a similar internal anatomical organization and are more similar to each other in cytoarchitecture than they are to any other part of the brain. The relatively uniform structure of cerebral cortex suggests that it is capable of applying a general-purpose style of computation to many processing domains, from sensory processing to the most abstract reasoning. Whether the similarity between different areas of cortex is merely superficial or extends to the computational level is an experimental + +question that depends on theoretical issues. + +Information processing and memory share the same circuitry in cerebral cortex, in contrast with digital computers where the memory and central processing unit are physically separated. The style of + +Almost all information that must be transmitted by neurons over distances greater than 1 millimeter is coded into action potentials. These all-or-none spike discharges last for about 1 millisecond and carry infor mation by their presence or absence. When the technique for reliably recording action potentials from single cortical neurons was introduced, it was a surprise to many that the response from some cortical neurons in somatosensory cortex and visual cortex could be correlated with simple features of sensory stimuli (Hubel & Wiesel, 1962~ Mountcastle, 1957) . This early success put a special emphasis on the cellular level rather than either the subcellular or network levels and led to the idea that single neurons coded simple sensory features and perhaps simple + +percepts as well (Barlow, 1972) . + +It should be emphasized, however, that rarely does a single neuron respond solely to a single feature dimension and that the tuning curves along feature dimensions are usually broad. Thus, single neurons in sensory cortex can be thought to represent volumes in a highdimensional space of features: The firing rate of a single cortical neuron no longer represents the analog value of a variable directly , but rather the probability of a variable lying within some volume of the + +21. COMPUTATION ICEREBRAL CORTEX 373 + +computation and the style of memory must therefore be closely related. This requirement is a very powerful one and should help narrow the range of possible candidate computational styles because, in addition to showing that a class of algorithms has significant processing capabilities, it is necessary to also show that the performance of the algorithms can be seamlessly improved by experience. This intimate relationship between the hardware and the software may make it possible to use constraints from both the computational level and the implementational level to investigate experimentally the representations and algorithms used in each cortical area (Ballard, in press~ Sejnowski, in press) . + +The key issue about which we know least is the style of computation in cerebral cortex: How are signals in neurons used to represent infor mation ? How do networks of neurons cooperate in transforming the information ? How are the results of a computation stored for future use? These Questions will be the focus of this chapter, which concludes with some remarks on the role of computational models in + +understanding complex systems like cerebral cortex. + +REPRESENTING INFORMATION + +374 BIOLOGICAL MECHANISMS + +response of a single neuron were to represent not merely a conjunction of local features , but an interpretation of those features in the context of the image , then the response should be influenced by parts of the image outside the classical receptive field . Recently , evidence has been found for strong surround effects in visual cortex which are antagonis tic to the response properties of the receptive fields (Allman , Miezin , & + +McGuinness , 1985) . + +What makes these new surround effects especially interesting is that they are selective . As shown in Figure 1, some neurons with direction ally selective receptive fields in extrastriate cortex can have their best responses modulated 100% depending on the direction of movement of the surrounding visual field (Allman et al., 1985) . The surround effects in the middle -temporal area (MT ) , where receptive fields are typically 5- 100, can extend 40- 800. Significant surround effects related to illusory contours have also been reported in area V -II (von der Heydt , Peterhans , & Baumgartner , 1984) , as shown in Figure 2. In another region of visual cortex , the V 4 complex , neurons have been found whose surrounds are selectively tuned for orientation , spatial fre quency , and color (Desimone , Schein , Moran , & Ungerleider , 1985) . Some of the neurons in this area appear to be selective for color over a wide range of illumination : The wavelength -dependent response in the receptive field is influenced by the color balance of the surround . + +(Zeki , 1983a, 1983 b) . + +These surround effects may be important for perceptual phenomena like motion parallax and color constancy that require comparison of local features within a larger context of the visual field (Allman , et al., 1985) . The basis of these long -range influences is not known , but several sources may contribute : First , stimulus -specific information could spread laterally within cortex through intrinsic horizontal axonal arborizations that extend 2- 4 mm (Gilbert & Wiesel , 1983 ~ Rockland & J. S. Lund , 1983) ~ second , reciprocal connections between cortical maps , particularly the descending feedback projections , could have extensive spread ~ third , inputs from noncortical structures such as the claustrum (LeVay & Sherk , 1981b) could influence the surrounds ~ and fourth , transcollosal connections might carry surround information , particularly between regions across the vertical meridian (Desimone et al., + +1985 ) . + +The discovery of large nonclassical surrounds provides an important opportunity to explore the collective properties of cortical processing . The response properties within the classical receptive field probably represent local , intrinsic processing , but the surround effects represent the long -range pathways and the spread of information within cortical areas. The spread is stimulus specific and should prove to be as impor tant as the primary response properties of the receptive field itself . For + +- - - 330 3000 - + +- - 27if ~ .J 2400 + +~ 2100 + +~- I 1800 + +~ 1500 1200 ~ 900 - ~ + +~ - 800 + +300 - + +00 + +~ ~ ~ BACKGRaN : > DOTS MOVE AT 00 + +~ - + +21. COMPUTATION IN CEREBRAL CORTEX375 + +~ o + +- ~ - D ) + +- ~ 2700 L ~ - 2400 + +~ - 2100 + +1~ 0 + +- -- - - - - - + +- BACK ~ a . N ) DOTS STA ~ Y + +FIGURE 1. Responses of a neuron in middle temporal (MT ) cortex to a bar moving in different directions superimposed on a background of random dots. The bar was oriented orthogonally to the direction of movement . The results of each of the 12 directions (00 through 330 ) are shown in histograms consisting of a before period, an underscored stimulus presentation period, and an after period. The largest histogram bin contains 26 spikes. When the background is moving in the same direction as the bar the response is entirely abolished, but when its movement is opposed to the direction of the bar the response is enhanced. (From "Stimulus Specific Responses From Beyond the Classical Receptive Field: Neurophysiological Mechanisms for Local-Global Comparisons in Visual Neurons " by J. Allman , J. Miezin , and E. McGuinness, 1985, Annual Re~'iew q( Neuroscience, 8, p. 416. Copyright 1985 by Annual Reviews, Inc. Reprinted by permission.) + +- - - - - + +900 + +- - - 600 + +- ~ o + +00 + +-~ - 12d ' + +- - - - ~ + +3000 2700 + +- ~ - + +. - ~ 1500 . ~~ - - 1200 + +- + +- - + +9( ) + +- - - - - 600 - + +3( ) - - - - - - ~ -- - - d + +BACK ~ DOTS MOVE AT 1800 + +- - + +2400 + +- - - - - = 21 ~ 1800 - - - - + +1& f + +376 + +- 90 - 45 0 45 90 0 2 4 e Orlentat 'ion ( deg ) Number of IIne8 + +FIGURE 2. Top: Illusory contours . Apparent contours are perceived in A , B , and D at sites where the stimulus is consistent with an occluding contour . Small alterations in the stimulus can have dramatic effects on the appearance of these contours , as in C where thin lines have been added to B . Bottom : Responses of neurons in extrastriate visual cortex (area 18) of the monkey to edges , bars and stimuli producing illusory contours . The stimuli (insets ) were moved back and forth across the receptive fields (ellipses ) . In each line of the raster scan a white dot indicates the occurrence of an action potential as a function of time . The mean number of spikes per stimulus cycle is indicated to the right . Neuron 1, which responded to the lower right edge of the light bar (A ) , was activated also when only the illusory contour passed over its classical receptive field (B ) . Either half of the stimulus alone failed to evoke a response (C and D ) . Spontaneous activity is shown in E. Neuron 2 responded to a narrow bar (F ) and , less strongl }', to the illusory bar stimulus (G) . When the ends of the " bar " were intersected by thin lines , however , the response was nearly abolished (H ) . In Neuron 3, the border between two abutting gratings elicited a strong response . The orientation tuning curves show corresponding peaks for bar and illusory contour (/ ) . When the lines inducing the contour were reduced in number to less than three , the response disappeared (1) . In contrast , neurons in primary visual cortex (area 17) did not respond to any of these stimuli . (From 'I Illusory Contours and Cortical Neuron Responses " by R. von der Heydt , E. Peterhans , and G . Baumgartner , 1984, Science, 224 , p. 1261. Copyright 1984 by the American Asso - + +21. COMPUTATION IN CEREBRAL CORTEX 377 + +example, different orientation -sensitive neurons could respond dif ferently to a local edge depending on the meaning of the edge within the context of the surrounding image: whether it represents an occluding contour , surface texture , or a shadow boundary (Sejnowski & Hin - + +ton , in press) . + +The analysis of a single image requires the processing power of the entire visual system~ in a sense, the interpretation of the image is the state of all the neurons in the visual system. In the language of features one would say that the object is internally represented by the particular combination of features currently activated. A problem arises when it is necessary to compare two objects, such as faces, seen at dif ferent times. One needs some means for binding together the most important combination of features at one moment and storing them for + +future use. + +This binding problem is particularly difficult because most regions of cortex are only sparsely interconnected. If two groups of neurons have few direct connections then it is difficult to imagine how a conjunction of two facts represented in the two regions can somehow be stored. Several solutions to this binding problem have been suggested, but no one yet knows how it is actually solved in the nervous system. The binding problem is a touchstone for testing network models that claim to have psychological validity . For a discussion of binding in the con- + +text of shape recognition see Hinton (1981c) . + +One approach to the binding problem is to represent a complex object by the activity of only a few neurons, a so-called local representation similar to the "grandmother cell " hypothesis (J. A. Feldman, 1981) . In this case the binding of two facts can be accomplished by dedicating one or more intermediate links between the neurons representing the features and the neurons representing the object. One problem with this approach is the combinatorial explosion of neurons and links that must be dedicated to the representation of even modestly complex objects. One consequence of the localist solution to binding is that some decisions to take an action may be based on the state of very few links between very few units. There is no convincing evidence for such II command fibers" anywhere in cerebral cortex. An alternative solution to the binding problem, based on a " searchlight of attention " is + +discussed in the section on temporal coincidence. + +In summary, it appears from studies of single neurons in visual cortex that they generally respond to a conjunction of features on a number of different dimensions. The sharpness of the tuning for values on different dimensions varies, but in general, each neuron is rather coarsely tuned, and its receptive field overlaps with the receptive fields of other neurons. Coarse coding of features also holds for other sensory areas of cortex and motor cortex (Georgopoulos, Caminiti , + +378 BIOLOGICAL MECHANISMS + +Kalaska , & Massey , 1983 ) , although the evidence there is not nearly as good as in the visual system . These observations are consistent with the ideas about distributed representations described in Chapters 3 , 7 , + +and 18 . + +NEURONAL PROCESSING + +The time available for processing puts strict constraints on the types of algorithms that could be implemented in cerebral cortex . Following a briefly presented image , the information coded as a pattern of hyper polarizations in the photoreceptors is processed in the retina and coded into trains of action potentials by the retinal ganglion cells . Within about half a second following presentation of the image we can recog nize an object in the image . Because photoreceptors are slow , a signifi fant fraction of the response time , about 25 - 50 milliseconds , is required for the information to reach cortex and several hundred milli seconds are required for the motor system to produce a response , which leaves about 200 - 300 milliseconds for visual processing . This is a severe restriction on algorithms , such as cooperative ones , that require extensive exchange of information between local neurons . David Marr + +( 1982 ) concluded that : + +cooperative methods take too long and demand too much neural hardware to be implemented in any direct way . The problem with iteration is that it demands the circulation of numbers around some kind of loop , which could be carried out by some system of recurrent collaterals or closed loops of neu ronal connections . However , unless the numbers involved can be represented quite accurately as they are circulated , errors characteristically tend to build up rather quickly . To use a neu ron to represent a quantity with an accuracy of even as low as 1 in 10 , it is necessary to use a time interval that is sufficiently long to hold 1 to 10 spikes in comfort . This means at least 50 ms per iteration for a medium - sized cell , which means 200 ms for four iterations - the minimum time ever required for our cooperative algorithm to solve a stereogram . And this is too + +slow . ( p . 107 ) + +The timing problem is even more severe than Marr states because the responses of single neurons in cortex often vary from trial to trial and there are usually only a few spikes in a single response ( Figure 3 ) . 21. COMPUTATION IN CEREBRAL CORTEX 379 + +Trials I + +1:III + +~ + +10 II 12 + +POST-STIMULUS TIME HISTOGRAM + +-50 + +Time in Milliseconds + +2 ~ ~ n - l -" = - T ~ - lLtlH1 ~ r - lL ~ - t -~ ~ r ~ " t ~- - 11 r - =-- . - - --- t = - - t ~ - : frt ~ - - t - ~ - t - .~ - -~ ~tf r1Ht 11urm -ti ---- - - t 4 + +. - t --I . -i8..Jr t- - 1t1 tt11tti,-1i. --1-1 + +1 - -\_I t- irtt -- - r-lrtll r- + ~t t + +t I - 50 mile + +FIGURE 3 . Extracellular recordings from a single neuron in extrastriate visual cortex of the cat . This neuron responded best to a slit of light obliquely oriented in a particular part of the visual field . The first 12 successive responses of the neuron to 50 exposures of the light are shown above , and the average response for 20 trials is shown below ( Post - Stimulus Time Histogram ) . Even before the onset of the stimulus the neuron was spontaneously active . Although the pattern of firing varied from trial to trial , the ensem ble average of the responses is repeatable . ( From " Integrative Properties of Parastriate Neurons " by F . Morrell , in Brain and Human Behavior , p . 262 , edited by A . G . Karczmar and J . Eccles , 1972 , Berlin : Springer . Copyright 1972 by Springer - Verlag . Reprinted by + +permission . ) + +Therefore , in many experiments the spike train is averaged over a number of responses ( typically 10 ) to obtain a post - stimulus time histo gram . The histogram represents the probability of a spike occurring during a brief interval as a function of time following the stimulus . This suggests that for short intervals ( 5 - 10 milliseconds ) and especially during nonstationary conditions , stochastic variables may be more appropriate than the average firing rate ( Hinton & Sejnowski , 1983 ~ + +Sejnowski , 1981 ) . + +A probabilistic code means that the probability of firing , rather than being represented by a number that must be accurately transmitted , can be represented directly as the probability for a neuron to fire during a + +. .\_ - 111- - 115 ' r - - 1 - - ~ ~ ~ ~ ~ , ij ~ ~ + +380 BIOLOGICAL MECHANISMS + +short time interval . The use of a probabilistic code rather than one based on the average value of spike firing reopens the possibility of cooperative algorithms because in 200 milliseconds it is possible to perform 40 or more iterations with 3- 5 milliseconds per iteration , the minimum interspike interval . This is enough time for some cooperative algorithms to converge to a steady state solution through a process of relaxation (Sejnowski & Hinton , in press) . Interestingly , it was found that adding noise to the system during the relaxation often improved the convergence by helping the system overcome locally inappropriate configurations and achieve the best overall global state. Some of the details and consequences of these probabilistic algorithms are + +discussed in Chapter 7. + +Nonetheless, "single-shot" algorithms that converge in one pass through a network , such as a linear transformation followed by thresholding (Duda & Hart, 1973~ Kohonen , 1977) , remain attractive, especially for the early stages of visual processing that are fairly automatic. Even for problems that require the global comparison of features, it would be desirable wherever possible to minimize the number of passes that information must make through a circuit without new information being added. However, contextual influences on processing might still require iterative computation , as illustrated in models like the interac- + +tive activation model of word perception. + +The single-shot and relaxation strategies have been presented as alternatives, but a better way to view them is as extremes in a continuum of strategies, any of which may be adopted by cortex depending on the level in cortex and the nature of the problem. For the recognition of common objects, a network that can process the image in a single-shot may be learned through experience. For novel or more complex objects, a relaxation strategy may be more flexible and have a higher capacity. Since the relaxation strategy must start out with a guess anyway, it may as well be a good one and get better with practice. This is also a graceful way to use the finite resources available in visual memory. In Chapter 7, an example is given of a relaxation strategy + +which can improve its performance with practice. + +Several nonlinear parallel models (1. A. Anderson, 1983 ~ McClelland & Rumelhart , 1981 ~ see also Chapters 14 through 17) make use of units that have continuous activation values. While the membrane potential of a neuron does have an approximately continuous value, the interaction between neurons with action potentials is clearly not continuous . Several ways have been proposed to relate the variables in these models more closely with neural properties. First, the continuous value may be considered an average firing rate~ however, as explained earlier, the time average firing rate is ill -defined over short time intervals. Second, a single unit could correspond to a population of + +neurons , and the activation would then represent the fraction of the neurons in the ensemble that are firing during a short time interval (Wilson & Cowan , 1972) . A third possibility is that the units are den - + +dritic branches that interact nonlinearly . + +Until recently , the dendrites of most neurons were thought to be governed mainly by the passive linear properties of membranes (Rail , 1970) and to serve mainly in the integration rather than processing of synaptic signals . If , however , there are voltage -dependent channels in dendrites , then the signals represented by membrane potentials are nonlinearly transformed and the dendrites must then be studied in smaller units , perhaps as small as patches of membranes (J. P. Miller , RaIl , & Rinzel , 1985~ D . H . Perkel & D . J. Perkel , 1985~ Shepherd et al., 1985) . The membrane patches and dendritic branches still have an integrative function , but to analyze that function requires a finer -grain + +analysis (Figure 4) . + +At an even finer level individual synapses may themselves interact nonlinearly because the conductance change at one synapse may serve as a current shunt and alter the driving force for other nearby synapses (Koch , Poggio , & Torre , 1982~ RaIl , 1970) . This is particularly true for synapses that occur on dendritic shafts but is less important for synapses that are electrically isolated on spines . With nonlinear interac tions between synapses and between patches of dendritic membrane many more processing units are available but this advantage is partially offset by the limited topological connectivity of dendritic trees . We need to explore the range of transformations that can be performed inside neurons and build up a vocabulary of elementary computational + +operations (Shepherd , 1978, 1985) . + +Whether nonlinear computations are performed at a subneuronal level is of fundamental importance to modeling parallel networks . If , at one extreme , each neuron acts like a classical linear integrator , then the sigma -pi units discussed in Chapters 2, 10, and 16 would have to be implemented in the brain using a single neuron for each multiplicative connection . If , on the other hand , nonlinear interactions can be imple mented at a subneuronal level , our estimate of the computational power of a fixed number of neurons would be greatly increased , and it would be possible to directly implement several proposals that require multiplicative connections , such as Ballard 's ( 1984) implementation of Hough transforms ~ Hinton 's ( 1981c) mapping from a retinocentric to a viewer -centered frame of reference ~ or McClelland 's ( 1985) method for " programming " the weights between one set of units using signals set up in another set of units . It is worth noting , though , that these schemes would generally require very precise anatomical connectivity and \'ery accurate timing of signals to get the most out of the nonlinear + +21. COMPUTATION IN CEREBRAL CORTEX 381 + +382 BIOLOGICAL MECHANISMS + +A B c + +] 50 jJ.m + +S1 521 - . \ 1\ \,;\," + +\ ~ + +FIGURE 4. Top: ,4: Pyramidal neuron in the cerebral cortex stained by the Goigi method of impregnation. B: Schematic diagram of the terminal segment of an apical dendritic branch in the most superficial cortical layer in ,4. Only three spines out of the total array are indicated., spaced 50..u m apart. C: Diagrammatic representation of a compartment model of B. Dendritic compartments are symbolized by D., the necks of spines by N., and the spine heads by S. In addition to passive membrane resistance and capacitance, active sodium and potassium currents, following the Hodgkin-Huxley model., were incorporated into the spine heads. This is a simplified model of only a small portion of the apical dendrite. Bottom: Current pulses were injected into spine head S 1. The traces show the simulated membrane potential in various compartments of the dendrite and spines following either a subthreshold current pulse or a suprathreshold current pulse. Note that when a spike occurs in S 1 it propagates by saltatory conduction through the dendritic compartments down the chain of spines. Spines may also interact if they simultaneously receive input currents: The combination may reach threshold even though the inputs individually produce only subthreshold membrane potentials. (From 'I Signal Enhancement in Distal Cortical Dendrites by Means of Interactions Between Active Dendritic Spines'! by G. M. Shepherd., R. K. Brayton., J. P. Miller ., I. Segev., J. Rinzel, W. RaIl, 1985~ Proceedin,~s q{ the lVational Ac'ademy q/'Sc'ienc'es USA., 82., p. 2193. Reprinted by + +Digital computers have a central clock that synchronizes the processing of signals throughout the central processing unit . No such clock has been found in the central nervous system on the millisecond time scale, but this does not rule out the importance of small time differ ences in neural processing. For example, the information about visual motion in primates at the level of the retina is represented as time differences in the firing pattern of axons in the optic nerve. In visual cortex, the relative timing information is used to drive cells that respond best to edges that are moving in particular directions (Koch & Poggio, 1985) . In the realm of learning, the timing of sensory stimulation in the 10- 50 millisecond range is known to be critically important for classical conditioning (Gluck & Thompson, in press~ Sutton & Barto, 1981) . Unfortunately , very little is known about the coding and processing of information as spatio-temporal patterns in populations of + +neurons. A few of the possibilities will be mentioned here. + +The arrival time of impulses is extremely important in the auditory system where slight temporal differences between spike trains in the two cochlear nerves can be used to localize sound sources. It also appears that information in the relative timing of impulses in the same nerve is essential in carrying information in speech at normal hearing levels (Sachs, Voigt , & Young, 1983) . Although it is difficult for neurons with millisecond time constants to make accurate absolute timing measurements, differences between arrival times down to 10 microseconds can be detected (Loeb, 1985) and therefore submillisecond timing information could also be important in cortex. This raises the possibility that the timing of arriving impulses might also be + +important in the cerebral cortex as well. + +The transformation between the input current and the firing rate of the neuron has a range between threshold and saturation over which the relationship is fairly linear. However, at any given time only a small fraction of all cortical neurons is operating in the linear region. Therefore only a subpopulation of neurons is sensitive to the timing of synaptic events, namely, those neurons that are near the threshold region. This leads to the idea of a skeleton filter - the temporary network of neurons near threshold that can linearly transform correlations between spikes on input lines (Sejnowski, 1981) . This is a way for temporarily changing the effectiveness with which some synapses can transmit information on the timing of synaptic events without actually altering their strength. It is not as flexible as a general modification scheme, such as the one suggested by McClelland (1985) , because all + +21. COMPUTATION IN CEREBRAL CORTEX 383 + +TEMPORAL COINCIDENCE + +, . \_ . - - . . . . . ~ ~ + +PLEX ..I + +384 BIOLOGICAL MECHANISMS + +the synapses originating from one neuron are modified by the same + +factor. + +Recently, von der Malsburg (in press) has suggested a scheme for binding together distributed circuits that represent a set of facts by their simultaneous activation . He speculates that this temporal binding is implemented by the rapid changes in the strengths of synapses between neurons that are co-active within a few milliseconds. Crick (1984) has modified this proposal by suggesting that the binding occurs during longer intervals of about 50 milliseconds during which bursts of impulses, produced by "searchlights" of attention in the thalamus, provide the signal for rapid synaptic changes (Figure 5) . The advantage of this approach is that the representations are distributed over a population of neurons and that simultaneous co-activation of a group of neurons in one area will impose simultaneous co-activation in another + +group that receives a projection from the first . + +~;---.\_;;-=--:~-NEO"C~ ', ~ , ' ,]-~~ + +RETICULAR + +FIGURE 5. The main connections of the reticular complex, highly diagrammatic and not drawn to scale. Solid lines represent excitatory axons, dashed lines show inhibitory axons, and arrows represent synapses. The principal neurons in the thalamus that project to the neocortex have two modes of response depending on the membrane potential. If the membrane potential is initially depolarized, then ascending input to the thalamus (from the retina~ for example) causes the principal neuron to fire at a moderate rate roughly proportional to the input. If, however, the neuron is initially hyperpolarized, for example by inhibitory inputs from the reticular complex, then the output from the principal cell is a rapid burst of spikes. According to the searchlight hypothesis, focal inhibition arising from the reticular nucleus produces sequentially occurring bursts in subsets of active thalamic neurons. The bursts are thought to last about 50 milliseconds and to produce short-term transient alterations in the synaptic strengths in cerebral cortex. (From "Function of the Thalamic Reticular Complex: The Searchlight Hypothesis" by F. H. C. Crick, 1984, Proceedings q( the National Academy q( Science.S' USA, 81, p. 4587. Reprinted + +21. COMPUTATION IN CEREBRAL CORTEX 385 + +If a temporal code is used in cortex, then spatio-temporal correlations should show up in recordings from groups of neurons. In recordings from nearby cortical neurons, spatio-temporal correlations have been observed between spike trains, but the significance of these correlations is unclear (Abeles, 1982; Abeles, de Ribaupierre, & de Ribaupierre, 1983; Gerstein, Bloom, Espinosa, Evanczuk, & Turner , 1983~ Shaw, Silverman, & Pearson, 1985~ Ts'o, Gilbert , & Wiesel, 1985) . However, it is already clear from these pioneering observations that the complexity of spatio-temporal signals from two or more neurons will require new techniques for data analysis and presentation. Several groups now have the technical ability to record simultaneously from many isolated neurons in cerebral cortex (Gerstein et al., 1983~ Kuperstein & Eichenbaum, 1985~ V . B. Mountcastle, personal communication , 1985~ Reitboek, 1983) . It will be especially interesting to record from alert animals attending to sensory stimuli and to search for correlated bursts + +of spikes and temporal coherence between spike trains. + +NEURONAL PLASTICITY + +Not only does cortex provide the capability of fast processing but it can be partially reconfigured with experience. There are experimental hints that the functional connectivity within cerebral cortex is far more fluid than previously thought . In a series of careful studies, Merzenich, Kaas and their colleagues have demonstrated that the spatial map of the body surface on the surface of primary somatosensory cortex of mon- + +keys can be significantly altered by changes in activity . + +In one series of experiments the map of the hand in somatosensory cortex was determined by multiple electrode penetrations before and after one of the three nerves that innervate the hand was sectioned (Merzenich et al., 1983) , as illustrated in Figure 6. Immediately fol lowing nerve section most of the cortical territory which previously could be activated by the region of the hand innervated by the afferent nerves became unresponsive to somatic stimulation . In most monkeys, small islands within the unresponsive cortex immediately became responsive to somatic stimulation from neighboring regions. Over several weeks following the operation, the previously silent regions became responsive and topographically reorganized. In another set of experiments a hand region in somatosensory cortex was mapped before and after prolonged sensory stimulation of a finger ~ the area represented by the finger on the surface of cortex expanded and the average size of the receptive fields within the finger region diminished + +21. COMPUTATION IN CEREBRAL CORTEX387 + +The uncovering of previously " silent " synapses is the favored expla nation for these experiments because the maximum shift observed , a few millimeters , is about the size of the largest axonal arborizations within cortex . The apparently new receptive fields that were " uncovered " immediately after nerve section could represent a rapid shift in the dynamical balance of inputs from existing synapses, and the slower reorganization could be caused by changes in synaptic strengths at the cortical and subcortical levels . This raises several crucial ques tions : First , what fraction of morphologically identified synaptic struc tures are functionally active in cerebral cortex ? It is not known , for example , how many quanta of transmitter are released on average at any central synapse. Second , how quickly if at all can a synapse be transformed from a " silent " state to an active state , and what are the conditions for this transformation ? Finally , how is this plasticity related to the representation and processing of sensory information ? Perhaps the most serious deficiency in our knowledge of cerebral cortex con cerns the physiology of individual central synapses, which are inaccessi ble by conventional techniques owing in part to the complexity of the cortical neuropil . New optical techniques for noninvasively recording membrane potentials and ionic concentrations may someday make it possible to study dynamic changes at central synapses (Grinvald , 1985) . The evidence for a rearrangement of the body map on the surface of cerebral cortex during experimental manipulations raises interesting questions about perceptual stability because this reorganization is not accompanied by confused or mistaken percepts of the body surface (Merzenich & Kaas, 1982) . This suggests that as a neuron shifts its input preference , other neurons that receive information from it must reinterpret the meaning of the signal . If the connectivity of cerebral cortex is as dynamic under normal conditions as these experiments suggest, then many of the issues that have been raised in this chapter must be re-examined from a new perspective (Changeux , Heidmann , & + +Patte , 1984~ Crick , 1984~ Edelman , 1981) . + +ROLE OF COMPUTATIONAL MODELS + +A complete description of every neuron , every synapse, and every molecule in the brain is not synonymous with a complete understanding of the brain . At each level of description the components must be related to the phenomena which those components produce at the next highest level , and models are a succinct way to summarize the relation ships . A classic example of a successful model in neuroscience is the Hodgkin -Huxley model of the action potential in the squid axon . Here + +the bridge was between microscopic membrane channels (hypothetical at the time) and macroscopic membrane currents. The first step in making a model is to identify the important variables at both the lower and upper levels~ next, a well-defined procedure must be specified for how these variables interact (an algorithm) ~ and finally , the conditions under which the model is valid must be stated so that it can be com- + +pared with experiments. + +The models that have been explored in this book do not attempt to reconstruct molecular and cellular detail. Rather, these connectionist models are simplified , stripped-down versions of real neural networks similar to models in physics such as models of ferromagnetism that replace iron with a lattice of spins interacting with their nearest neighbors. This type of model is successful if it falls into the same equivalence class as the physical system~ that is, if some qualitative phenomena (such as phase transitions) are the same for both the real system and the model system (Ma, 1976) . When they are successful these simple models demonstrate the sufficiency of the microscopic variables included in the model to account for the macroscopic + +measurements. + +The emergence of simple parallel models exhibiting nontrivial computational capabilities may be of great importance for future research in neuroscience because they offer one of the few ways that neuroscientists can test qualitative ideas about the representation and processing of information in populations of neurons. Suppose that single neurons in an area responded to features of the visual input that could be important for computing, say, optical flow . Knowing the goal of the computation , one could design a parallel algorithm for implementing the computation of optical flow and then test it with a wide range of inputs. The process of specifying and testing an algorithm often reveals unexamined assumptions and refines the original motivation for the model. If one successful algorithm is found then the computational feasibility of the original proposal is strengthened~ to test whether some form of the algorithm is actually implemented in cortex would be much more difficult ~ ultimately , the performance of the algorithm has to be + +compared with psychophysical testing. + +Some neuroscientists may feel uncomfortable because connectionist models do not take into account much of the known cellular properties of neurons, such as the variety of membrane channels that have been found . What if the processing capabilities of cerebral cortex were to depend crucially on some of these properties? In this case it may not be possible to get networks of oversimplified model neurons to solve difficult computational problems, and it may be necessary to add new properties to the model neuron. The added capabilities would yield a better understanding of the roles played by these neural properties in + +388 BIOLOGICAL MECHANISMS + +21. COMPUTATION IN CEREBRAL CORTEX 389 + +processing information , and suggestions could emerge for useful prop erties which have not yet been observed . The present models are guideposts for thinking about the computational capabilities of neural networks and benchmarks that set the standards for future models . + +One of the key insights that has already emerged from studying one class of simple nonlinear networks with recurrent collaterals is that amongst the large number of possible states of a network , only rela tively few of these states, called attractors , are stable (J. A . Anderson , 1983~ M . A . Cohen & Grossberg , 1983~ Hinton & Sejnowski , 1983~ Hogg & Huberman , 1984~ Hopfield , 1982~ Hopfield & Tank , 1985~ Sejnowski , 1976~ Wilson & Cowan , 1972) . The existence of stable attractors is a feature that is likely to generalize to more complex net works . Objects and their relationships can be internally represented by these attractors , and the search for the best match between the world and the internal representation of the world by the dynamics of the net work is much more powerful than previous template -matching pro cedures . This opens a large number of research problems , such as the issue of local vs. distributed representations and the binding problem , both of which have been discussed in this chapter . The identification and study of these issues in simple network models will greatly help us in understanding the principles that went into the design of the cerebral + +cortex . + +ACKNOWLEDGMENTS + +I am grateful to Neal Cohen , Francis Crick , Mark Gluck , Geoffrey Hinton , Chip Levy , and Gordon Shepherd who provided valuable suggestions on earlier versions of this chapter , and I especially wish to thank Jay McClelland for helping to shape the chapter in many ways, + +large and small . + +Mind and brain provide two quite different perspectives for viewing cognition . Yet both perspectives are informed by the study of parallel distributed processing. This duality creates a certain ambiguity about the interpretation of a particular POP model of a cognitive process: Is each processing unit to be interpreted as a neuron? Is the model supposed to relate to the neural implementation of the process in some + +less direct way? + +A closely related set of questions arises when it is observed that POP models of cognitive processing divide broadly into two classes. In local models, the activity of a single unit represents the degree of participation in the processing of a known conceptual entity - a word, a word sense, a phoneme, a motor program. In distributed models, the strength of patterns of activity over many units determine the degree of participation of these conceptual entities. In some models, these patterns are chosen in a deliberately arbitrary way, so that the activity of a single unit has no apparent "meaning" whatever- no discernible relation to the conceptual entities involved in the cognitive process. On the surface, at least, these two types of models seem quite different . Are they + +as different as they seem? How are they related? + +This chapter begins with a brief consideration of the neural interpretation of POP models of cognition . These considerations serve mostly to layout a certain perspective on the POP modeling world , to make some distinctions I have found to be valuable, to introduce some + +CHAPTER 22 + +Neural and Conceptual + +Interpretation of PDP Models + +P. SMOLENSKY + +22. NEURAL AND CONCEPTUAL INTERPRETATION391 + +terminology , and to lead into the main question of this chapter: How are distributed and local POP models related? The chapter ends with a discussion of how, using the framework of POP models, we might forge a mathematical relationship between the principles of mind and + +brain. + +The following technique will be used to relate distributed to local models. We take a distributed model of some cognitive process, and mathematically formulate a conceptual description of that model, a description in terms of the conceptual entities themselves rather than the activity patterns that represent them. From some perspectives, this amounts to taking an account of cognition in terms of neural processing and transforming it mathematically into an account of cognition in terms of conceptual processing. The conceptual account has a direct relation to a local model of the cognitive process~ so a distributed + +model has been mapped onto a local model. + +The mathematical formulation of the conceptual description of a distributed model is straightforward ~ and the mathematical results reported in this chapter are all Quite elementary, once the appropriate mathematical perspective is adopted. The major portion of this chapter is therefore devoted to an exposition of this abstract perspective on POP modeling, and to bringing the consequent mathematical observations to bear on + +the cognitive issues under consideration. + +The abstract viewpoint presented in this chapter treats POP models as dynamical systems like those studied in mathematical physics. The mathematical concepts and techniques that will be used are those of linear algebra, the study of vector spaces~ these techniques are discussed in some detail in Chapter 9. The formal parts of the discussion will be confined to footnotes and italicized passages~ these may be skipped or skimmed as all results are discussed conceptually in the main + +portion of the text , which is self-contained. + +NEURAL AND CONCEPTUAL INTERPRETATIONS + +The interpretation of any mathematical model involves the mapping of a mathematical world into some observable part of the real world . The ambiguity in the interpretation of POP models arises because the mathematical world of the model can be mapped into f~'o observable + +The neural world relevant here is discussed in Chapter 20- a world of receptor cells, neurons, synaptic contacts, membrane depolarizations, neural firings , and other features of the nervous system viewed at this + +392 BIOLOGICAL MECHANISMS + +level of description. The mathematical world is that described in Chapter 2- a world of processing units, weighted connections, thresh- + +old and sigmoidal functions , and activation. + +Least precisely prescribed is the world of cognitive behavior. This world is mapped by experiments that probe perceptual behavior, reasoning and problem solving behavior, skilled motor behavior, linguistic behavior, memory task behavior, and the like . POP models have been interpreted in terms of all these aspects of behavior, and to understand the common basis for these interpretations we must adopt a fairly + +general- and rather imprecise- way of speaking about cognition . + +The connection between the formal structure of POP models and cognitive behavior rests on theoretical knowledge constructs hypothesized to underlie this behavior. Consider perception first . Interpreting sensory input can be thought of as consideration of many hypotheses about possible interpretations and assigning degrees of confi dence in these hypotheses. Perceptual hypotheses like "a word is being displayed the first letter of which is A ," "the word ABLE is being displayed," and "the word MOVE is being displayed" are tightly interconnected~ confidence in the first supports confidence in the second and undercuts confidence in the third . Thus assignment of confidence- injerence- is supported by knowledge about the positive and negative evidential relations among hypotheses. This same kind of knowledge underlies other cognitive abilities; this kind of inference can support problem solving, the interpretation of speech and stories, and also motor control . The act of typing ABLE can be achieved by letting "the word ABLE is to be typed" support "the first letter to be typed is + +A" and inhibit "the first letter to be typed is M ." + +This way of thinking about cognition can be summarized by saying that behavior rests on a set of internal entities called hypotheses that are positively and negatively related in a knowledge base that is used for inference, the propagation of confidence. The hypotheses relate directly to our way of thinking about the given cognitive process~ e.g., for language processing the hypotheses relate to words, syntactic categories, phonemes, meanings. To emphasize that these hypotheses are defined in terms of our concepts about the cognitive domain, I will call them conceptual hypotheses or the conceptual entities, or simply concepts~ they are to be distinguished from the mathematical and neural + +entities - units and neurons- of the other two worlds. + +The internal structure of the neural, mathematical, and conceptual worlds we have described are quite similar . Table 1 displays mappings that directly relate the features of the three worlds. Included are all the central defining features of the POP models- the mathematical world - and the corresponding features of the portion of the neural and + +22. NEURAL AND CONCEPTUAL INTERPRETATION 393 + +TABLE 1 + +positive/ negative + +weight + +approximate additivity of evidence + +independence from irrelevant information + +limited dynamic range + +sigmoidal function F limited range of processing strength + +THE MAPPINGS FROM THE MA THEMA TICAL WORLD TO THE NEURAL AND CONCEPTUAL WORLDS + +Neural Mathematical Conceptual units + +activation + +spread of activation + +connection + +hypotheses + +degree of confidence + +propagation of confidence: inference + +conceptual - inferential - + +interrelations + +positive/ negative inferential relations + +approximate additivity of depolarizations + +spiking thresholds + +summation of inputs + +activation spread threshold G + +In Table 1 , individual units in the mathematical world are mapped on the one hand into individual neurons and on the other into individual conceptual hypotheses . 1 These two mappings will be taken to define the local neural interpretation and the local conceptual interpretation of PDP models , respectively . These are two separate mappings , and a particular PDP model may in fact be intended to be interpreted with only one of these mappings . Using both mappings for a single model would imply that individual concepts , being identified with individual units , would + +also be identified with individual neurons . + +In addition to the local mappings there are also distributed mappings of the mathematical world into each of the neural and conceptual worlds . In a distributed conceptual interpretation , the confidence in a + +1 What is relevant to this chapter are the general features , not the details , of Table 1. The precision with which the mappings are described is sufficient for present purposes . For a more precise account of the relation between the mathematics of certain POP models and the mathematics of inference , see Hinton , Sejnowski , and Ackley ( 1984) . + +394 BIOLOGICAL MECHANISMS + +conceptual hypothesis is represented by the strength of a pattern of activation over a set of mathematical units. In a distributed neural interpretation , the activation of a unit is represented by the strength of + +a pattern of neural activity of a set of neurons. + +It must be emphasized that the choices of neural and conceptual interpretations are truly independent. Some neural models (e.g., Hopfield , 1982) may have no direct conceptual interpretation at all~ they are intended as abstract models of information processing, with no cognitive domain implied and therefore no direct connection with a conceptual world. The reading model of McClelland and Rumelhart (1981 ~ Rumelhart & McClelland , 1982~ see Chapter 1) has an explicit local conceptual interpretation ~ we can choose to give it no neural interpretation , a local neural interpretation (implying individual neurons for individual words) , or a distributed neural interpretation . The Hinton (1981 a) and J. A . Anderson (1983) models of semantic networks have explicitly distributed conceptual interpretations ~ they can be given a local neural interpretation , so that the patterns over units used in the models are directly interpreted as patterns over neurons. They can also be given a distributed neural interpretation , in which the units in the model are represented by activity patterns over neurons so that the concepts- patterns over units - correspond to new patterns over neu- + +rons. + +The nature of the patterns chosen for a distributed interpretation either neural or conceptual- can be important (although it is not always~ this is one of the results discussed later) . A distributed interpretation will be called quasi-local if none of the patterns overlap, that is, if every pattern is defined over its own set of units. Quasi-local distributed interpretation , as the name implies, forms a bridge between local and distributed interpretation : a quasi-local neural interpretation associates several neurons with a single mathematical unit , but only a + +single unit with each neuron. + +Since quasi-local interpretations are special cases of distributed representations, the methods applied in this chapter to the general case of distributed representations could also be applied to quasi-local repre~entations. Certain similarities to local representations can be expected to emerge, but the general results to be discussed suggest that it is a mistake to assume that the mathematical properties of the local + +and quasi-local cases will be essentially the same. + +The primary reason for displaying Table 1 is to emphasize that the neural and conceptual bases for interest in POP models are completely independent. Even if all neural interpretations are eliminated empiri cally, or if no neural interpretation is given a model at all, a conceptual interpretation remains a strong independent source of cognitive + +22 . NEURAL AND CONCEPTUAL INTERPRETATION395 + +At the same time , the independence of the neural and conceptual mappings makes it quite striking that both contact exactly the same class of mathematical models. Why should this be? Is it that we have ignored crucial features of the two worlds, features which would lead to Quite different mathematical abstractions? A more encouraging possibility is this: Perhaps we have captured the essence of neural processing in POP models. Perhaps implicit in the processing of neural firing patterns is another mathematical description, a description in terms of the concepts represented in those patterns. Perhaps when we analyze the mathematics of this conceptual description, we will find that it has the mathematical structure of a POP model- that because of special properties of POP models, at both the neural and conceptual levels of descrip- + +tion , the mathematical structure is the same. + +This wildly optimistic scenario (depicted schematically in Figure 1) will be called the hypothesis of the isomorphism of the conceptual and neural levels- the isomorphism hypothesis for short. We will find that it is in fact exactly true of the simplest- one might say the purest- POP models, those without the nonlinear threshold and sigmoidal functions . For models with these nonlinearities , we shall see how the isomorphism + +Neural World Conceptual World + +- - - - + +fi nat state + +. . . - - - -::::..... + +. .. ... .. + +- - - - - - - + +pdp model # 1 " lower level model " + +pd p model #2 "higher level model" + +FIGURE 1. The dashed line indicates a mapping from a POP model representing neural states to a POP model representing conceptual states. The mapping is an isomorphism if 'l when the two models start in corresponding states and run for the same length of time , + +396 BIOLOGICAL MECHANISMS + +hypothesis fails , and explore a phenomenon within these models that + +distinguishes between the neural and conceptual levels . 2 + +It is an open empirical question whether the conceptual entities with which we understand most cognitive processes are represented by the firing of a single neuron , by the firing of a group of neurons dedicated to that concept , by a pattern of firing o 'ler a group of neurons involved in representing many other concepts , by neural features other than firing , or by no neural features at all . The purpose of this chapter is to show how to use POP models as a mathematical framework in which to compare the implications of assumptions like those of local and distrib - + +uted models . + +The plan of attack in this chapter is to compare two related mathematical models , each of which can be given either neural or con ceptual interpretations . They can be thought of as describing a single neural net with both a local and a distributed model , or as implement ing inference over a single set of conceptual hypotheses using both a local and a distributed model . The comparison of these two models will thus tell us two things . It will show how a description of a neural net in terms of its patterns compares with a description in terms of its indi vidual neurons . It will also provide information about how behavioral predictions change when a local model of a set of concepts is converted + +to a distributed model . + +The comparison between the two mathematical models will constitute an investigation of the isomorphism of levels hypothesis . Model 2 will be a description of the dynamics of the patterns of activation of Model 1 ~ the hypothesis is that the description at the higher level of patterns ( Model 2 ) obeys the same laws as - is isomorphic to - the description at the lower level of individual units ( Modell ) . To permit all the relevant interpretations to apply , I shall call Modell simply the lower - + +level model and Model 2 the higher - level model . + +2 Strictly speaking , an isomorphism insists not only that there be a mapping between the neural and conceptual world that preserves the dynamics , as indicated by Figure 1, but also that the map establish a one -to -one correspondence between states in the two worlds . Actually , it seems reasonable to assume that the neural world is a larger space than the conceptual world : that a conceptual state lumps together many neural states , or that the set of possible neural states includes many that have no conceptual counterpart . This would render the "conceptual level " a " higher " level of description . These con siderations will manifest themselves formally in the section " Pattern Coordinates ," but for now the relation of isomorphism , despite its symmetry , serves to emphasize the true + +INTERPRETATION + +This section introduces the perspective of PDP models as dynamical systems. Traditionally , a PDP model is viewed as a network of processors communicating across links ~ I will call this the computational viewpoint. To illustrate the difference between the computational and dynamical system perspectives, it is useful to consider a prototypical dynamical system: a collection of billiard balls bouncing around on a + +table. + +A common exercise in object-oriented computer programming is to fill a video screen with billiard balls bouncing off each other. Such a program creates a conceptual processor for each billiard ball. Each "ball" processor contains variables for its "position " and "velocity," which it updates once for each tick of a conceptual clock. These processors must exchange messages about the current values of their vari- + +ables to inform each other when "bounces" are necessary. + +Billiard balls can be seen from a computational viewpoint as processors changing their local variables through communication with other processors. Physics, however, treats the position and velocity values simply as real variables that are mutually constrained mathematically through the appropriate "laws of physics." This is characteristic of the + +dynamical system viewpoint . + +To view a POP model as a dynamical system, we separate the data and process features of the units. The activation values of the units are seen merely as variables that assume various values at various times, like the positions and velocities of billiard balls. The changes in these variables over time are not conceptualized as the result of prescribed computational processes localized in the units. In fact the processes by which such changes occur are unanalyzed~ instead, mathematical equa- + +tions that constrain these changes are analyzed. + +The equations that determine activation value changes are the analogs of the laws of physics that apply to billiard balls~ they are the " laws of parallel distributed processing" that have been described in Chapter 2. A version of these equations can be written as follows . Let Uv (t ) denote the activation of unit v at time t . Then its new value one unit + +of time later is given by + +22. NEURAL AND CONCEPTUAL 397 + +FROM NETWORK OF PROCESSORS TO + +uv(t+ 1) = F [LWv/1.G(U/1. (t))]. /1. (IA) + +Here F is a particular nonlinear sigmoid function , an increasing Sshaped function that takes a real number as input (the net activation flowing into a unit ) and gives as output a number in the range [- m, M ] + +DYNAMICAL SYSTEM + +398 BIOLOGICAL MECHANISMS + +(the new activation of the unit ) . G is a nonlinear threshold function : G (-,X' ) = x unless x is less than a threshold, in which case G (x ) = O. + +W Vjl is the strength of the connection from unit J..t to unit v . + +The "knowledge" contained in a PDP model lies in the connection strengths {W v,u} or weight matrix, W . The nonlinear functions F and G encode no knowledge about the cognitive domain of the model, and serve to control the activation spread in non-domain-specific ways. + +Thus the heart of a PDP model is its weight matrix ~ the rest of the machinery can be viewed as bells and whistles added to get the weight matrix to be "used properly" during inference. The purest PDP models, from this point of view, consist only of the weight matrix ~ + +from the preceding equation, F and G are removed: + +u v (t + 1 ) = L W v IL UIL ( t) . /.L + +The absence of the controlling nonlinearities make these models diffi cult to use for real modeling, but for our analytic purposes, they are extremely convenient. The main point is that even for nonlinear models with F and G present, it remains true that at the heart of the model is the linear core, W . For this reason, I will call the dynamical systems governed by the preceding equation quasi-linear dynamical systems. In this chapter, the analysis of POP models becomes the analysis of quasi-linear dynamical systems. These systems will be viewed as ela- + +borations of linear dynamical systems. + +KINEMATICS AND DYNAMICS + +Investigation of the hypothesis of the isomorphism of levels is a purely mathematical enterprise that bears on the questions of interpret ing POP models. This section provides an introduction to the + +mathematical structure of dynamical systems. + +There are two essential components of any dynamical system. First , there is the state space S, the set of all possible states of the system. In our case, each state s in S is a pattern of activation, i. e. ~ a vector of activation values for all of the units. The second component of a dynamical system is a set of trajectories s t , the paths through S that obey the evolution equations of the system. These trajectories can start at any point So in S. For activation models, So is the initial activation pattern determined by the input given to the model (or its history prior to our observation of it) , and the corresponding trajectory S t is the ensuing sequence of activation values for all later times, viewed as a path in the state space S. (This " path" is a discrete set of points because the values of t are~ this fact is not significant in our + +considerations .) The evolution equations for our quasi-linear dynamical + +systems are Equations 1 A of the previous section . + +Corresponding to these two components of dynamical systems are two sets of questions . What is the . state space S? Is it finite or infinite ? Bounded or unbounded ? Continuous or discrete ? How can the points in S be uniquely labeled ? What structures relate points to one another ? These properties define the geometry of state space, what I will call the kinematics of the dynamical system . In kinematics , the evolution equations and trajectories are ignored ~ time plays no role . Only the proper - + +ties of the points in state space themselves are considered . + +The questions in the second set pertain to the trajectories . Are they repetitive (periodic ) ? Do they tend to approach certain special states (limit points ) ? Can we define quantities over S that differ from trajec tory to trajectory but are constant along a trajectory (conserved quanti ties) ? These are the questions about the system 's dynamics , and their answers depend strongly on the details of the evolution equations . + +It may seem that the questions of dynamics are the real ones of interest . However , it is useful to consider kinematics separately from dynamics for two reasons . First , the link between kinematics and dynamics is strong : The kinds of evolutionary equations that can sensibly be assumed to operate in a dynamical system are limited by the geometry of its state space. For example , geometrical structures expressing the symmetries of spacetime or elementary -particle state spaces restrict severely the possible evolutionary equations : This is the basis of the theory of relativity and gauge field theories of elementary particles . In our case., imposing boundedness on the state space will eventually lead to the breakdown of the isomorphism of levels . The second reason to emphasize kinematics in its own right is that the questions of interpreting the dynamical system have mostly to do with inter - + +preting the states, i.e., with kinematics alone . + +In this chapter we are concerned primarily with interpretation , and the discussion will therefore center on kinematics ~ only those aspects of dynamics that are related to kinematics will be considered . These aspects involve mainly the general features of the evolution equations - the linearity of one component (W ) and the nonlinearity of the remaining components (F ,G ) . More detailed questions about the trajectories (such as those mentioned above ) address the behavior of the system rather than its interpretation , and will not be considered in this + +chapter . 3 + +3 J. A. Anderson, Silverstein, Ritz, and Jones (1977) show the power of concepts from linear algebra for studying the dynamics of POP models. Some of their results are closely related to the general observations about nonlinear models I will make in the last + +KINEMATICS + +The first question to ask about a state space is: How can the points - states- be labeled ? That is, we must specify a coordinate system for S , an assignment to each activation state s of a unique set of + +numbers . + +Each such s denotes a pattern of activation over the units . Let us denote the activation value of the vth unit in state s by Uv (s) ~ this was formerly just denoted liv. These functions {uv} form the unit coordinates for S . Each function Uv takes values in the set of allowed activa tion values for unit v . In the standard POP model , this is the interval [- m, M ] . One could also consider binary units , in which case the func tions Uv would take values in the set {O,l } (or {- I , I} ) . In any event, if all units are of the same type , or , more specifically , if all have the same set of allowed values , then all unit coordinates take values in a + +single set. + +It is sometimes helpful to draw a very simplified example of a state space S . Using unit coordinates , we can plot the points of S with respect to some Cartesian axes . We need one such axis for each uv , i.e., each unit . Since three axes are all we can easily represent , we imagine a very simple network of only three units . The state space for such a network is shown in Figure 2. In Figure 2A , the case of activa tion values in [- m, M ] is depicted . In this case, S is a solid cube (with side of length m + M ) . Figure 2B depicts the case of binary activation values {O, I} ; in this case, S is the eight vertices (corner points) of a cube . Except where specified otherwise , in the remainder of this chapter the standard case of continuous activation values will be + +assumed . + +Thus if the network contains N units , S is an N - dimensional space that can be thought of as a solid hypercube . Any other point of N space outside this hypercube is excluded from S because it corresponds to activation for at least one unit outside the allowed range . Thus , + +states with " too much " activation have been excluded from S . + +" Too much " has so far been defined according to each unit individually ,' it is interesting to consider whether states should be excluded if they correspond to "too much " activation among the units collectively . This would amount to excluding + +from S even some of the points in the hypercube. + +Here are two ways one might eliminate states with too much activation in total . The first way is to require that Qf the complete set of N units, only N max can be active (i.e., have nonzero activation ) at anyone time. As Figure 3 shows, this removes much of the hypercube and leaves S with a rather bizarre shape. This S is + +- m 0 M + +0 + +M I + +. / + +22 . NEURAL AND CONCEPTUAL INTERPRETATION401 + +LI uvl + +> a max. + +A less unusual approach is to d~fine II too much activation in total" by the + +condition + +This results in an S that is depicted in Figure 4. Unlike the bizarre S Qf Figure 3, + +Imposing this kind Q! limitation on total activation would turn out to have much less of an e.f!ect on the dynamics Qf the model than would the limitation on the + +FIGURE 2. A: The solid cube bounded by - m and M forms the standard state space for POP models containing continuous units. B: The eight corners of the cube bounded bv 0 - . and 1 forms a modified state space., corresponding to POP models containing binary + +units. + +402 BIOLOGICAL MECHANISMS + +If only two of three units are allowed to have nonzero activation, the state + +Red~fining the "total activation" to be the Euclidean distance q[ the plotted point ,[rom the origin would not change the conclusion that S is not topologically distinct ,[rom the hypercube. In ,[act, limiting the Euclidean distance or the sum of activations, or using the original hypercube, are all special cases Q[ d~fining S to be a "ball" with respect to some metric in N -space. It is a fact that all such balls are + +topologically equivalent (e.g., Loomis & Sternberg, 1968, p. 132) . + +In the remainder of this chapter, S will denote the standard hypercube as depicted in Figure 2A, the state space of the general nonlinear activation model. The state space of the simplified , linear, activation model will be denoted SL' This space, as we shall see in the next section , is simply all of N -dimensional Euclidean space, where N is again the number of units in the network . (For example, there is no need to draw S[ because, for N = 2, it is the entire plane of the paper!) S is clearly a subset of S[ ~ in S, the unit coordinates of any state fall within the restricted range [- m, M ] , while in S[ the unit coordinates can be + +any real numbers. + +The unit coordinates provide a convenient description of S for many purposes. However., it is important to realize that points of S can also be described with an infinitude of other coordinate systems. In a distributed interpretation ., new coordinates that give a simple description of these patterns will turn out to be better than unit coordinates for interpreting states of the system. We shall construct these pattern + +FIGURE 3. + +space is formed from three intersecting planes. + +22. NEURAL AND CONCEPTUAL INTERPRET A TION 403 + +This solid octahedron is the state space obtained by restricting the sum of + +coordinates hortly, but this construction uses a property of S we must + +VECTOR SPACE STRUCTURE + +A central feature of parallel distributed processing is its exploitation of superposition of knowledge during computation . Each unit that becomes active exerts its influence in parallel with the others, superimposing its effects on those of the rest with a weight determined by its level of activation. As we shall see, in linear models, this is a mathematically precise and complete account of the processing. As emphasized in the section "From Network of Processors to Dynamical System," even nonlinear POP models are quasi-linear systems, and knowledge is used in the same fashion as in linear models. Thus super- + +position plays a crucial role in all POP models. + +Superposition is naturally represented mathematically by addition. In the simplest case, addition of individual numbers represents superposition of unidimensional quantities. Adding multidimensional quantities (like states of activation models) is mathematically represented by + +FIGURE 4. + +the magnitudes of the units' activations to be less than Gmax' + +now discuss: its vector space structure. + +vector addition. The concepts of vector and vector addition are best viewed together, as data and process: "Vector" formalizes the notion of "multidimensional quantity " specifically for the purpose of "vector + +addition." 4 + +Actually , the notion of superposition corresponds to somewhat more than the operation of addition : Superposition entails the capability to form weighted sums. This is important for parallel distributed processing, where the complete state of the system typically corresponds to a blend of concepts, each partially activated. Such a state is mathematically constructed by summing the states corresponding to the partially activated concepts, each one weighted by its particular degree of + +activation. + +Using unit coordinates, the operation of weighted summation is simply described. The activation of a unit in a state that is the weighted sum of two other states is simply the weighted sum of the activations of that unit in those two states. In other words, the unit coordinates of the weighted sum of states are the weighted sum of the unit coordinates of the states. Given two states s 1 and S2, and two weights wI and + +w2, the weighted sum s is written + +Uv(St+l) = F [L, WV/.l-G(u/.l-(St ]. ..u + +The reason all the unit coordinates Uv of the state S t + 1 are guaranteed to lie in the allowed range [ - m , M ] is that the function F takes all its values in that range . This nonlinear function is what ensures that the trajectories do not leave the bounded cube S of states . If F were absent , then the coordinate Uv would just be the weighted sum ( with weights Wv , u for all values of JL ) of the quantities G ( u /l. ( t ) ) ~ this need + +4 It is common to use the term " vector " for any multidimensional quantity ., that is , a quantity requiring more than one rea ] number to characterize completely . This is ., how ever .. not faithful to the mathematical concept of vector unless the quantity is subject to superposition . The precise meaning of " superposition " is captured in the axioms for the + +22 . NEURAL AND CONCEPTUAL INTERPRETATION405 + +The linear evolution equation can be written more transparently in terms of state + +vectors rather than unit coordinates. D~fine N vectors W.u by + +Uv(Wiu) = Wviu' + +W..u is the vector of weights on connections from unit ,u. It is also the activation vector that would exist at time t + 1 if at time t , unit ,u had activation 1 and all other units had activation O. No ~v because the evolution is linear , the state at time t + 1 produced by a general activation pattern at time t is just the weighted sum Qf the patterns that would be set up by individual unit activations at the units, with the + +weights equal to the actual activation of the units. That is, + +LUJL (St) W JLO + +JL + +St+ 1 + +u (t+ 1) = Wu (t ). (28) + +is extended to all of N -space, i.e. SL, then the linear dynamical equa- + +tion above is permissible. + +notation: + +5 By imposing special restrictions on the weights , it is possible to ensure that the weighted sum lies in S , and then the nonlinearity F can be eliminated . But like F , these + +not lie in the allowed range . 5 So in the simplified linear theory in which + +F and G are absent , the evolution equation + +UV(Sf+ l) = L, WVf.LUf.L(Sf ) (2A ) + +f.L + +imposes no restriction on the range of values of the coordinates ; trajec - + +tories may wander anywhere in N -space. + +Thus we see that the kinematical restriction of state space to the bounded region S has lead to the insertion of the bounded (and there fore nonlinear ) function F into the dynamical equation . If state space + +(This vector can be seen to obey the linear evolution equation given above by evaluating its v th unit coordinate, using the rule for coordinates of weighted sums, + +and the defining coordinates of the vectors w ,u.J + +This equation explicitly Sl10WS the blending of knowledge that characterizes parallel distributed processing. The vector W,u is the output of unit ,u,. it is the II knowledge" contained in that unit, encoded as a string of numbers. The state of the system at time t + 1, Sf+ 1, is created by forming a weighted superposition of all the pieces of knowledge stored in all the units. The weight for unit ,u in this superposition determines how much in:/luence is exerted by the knowledge encoded by that unit. Tllis weight, according to the previous equation, is U,u (S f ) . That is just the + +degree to which unit ,u is active at time t . + +Another useful form for the linear evolution equation uses matrix + +406 BIOLOGICAL MECHANISMS + +u is the N x 1 column matrix of unit coordinates uv, and W is the N x N matrix of values W V,u. This matrix is relative to the unit coordinates~ shortly we shall switch to other coordinates, changing the + +numbers in both the square matrix Wand the column matrix u . + +PATTERN COORDINATES + +Now we consider activity patterns used in a distributed neural or conceptual interpretation . For concreteness, consider the pattern < + 1,- 1,+ 1,- 1> over the first four units. To denote this pattern, we define a vector p the first four unit coordinates of which are < + 1,- 1,+ 1,- 1 > ~ the remaining unit coordinates are zero. Now consider the state s with unit coordinates < .3,- .3,.3,- .3,0,0, . . . , 0> . This state can be viewed in two ways. The first is as the superposition of four states: u 1 with unit coordinates < 1,0,0, . . . , 0> , U 2 .with unit coordinates < 0,1,0, . . . , 0> , etc., with weights respectively + .3, - .3, + .3, and - .3. This is the unit view of s . The second view is + +simpler: s is simply .3 times p : + +s = .3p . + +S = .9 1 + .6 2 + .9 3 + .6 4 + +or as + +s = .15PI + .75P2. + +This is the pattern view of s . + +The general situation is comparable. If there is a whole set of distributed patterns, each can be represented by a vector Pi . Any given state s can be represented in two ways: as the superposition of the vectors uv, with weights given by the unit coordinates of s , or as a superposition of pattern vectors Pi . If the patterns comprise a distributed conceptual interpretation , the weights in this latter superposition indicate the system's confidence in the corresponding conceptual + +hypotheses. + +Let's consider a slightly less simplified example. Let PI be the vector p above, and let P2 correspond to the activation pattern < + 1,+ 1,+ 1,+ 1> over the first four units. Then the state s with unit + +coordinates < .9,.6,.9,.6,0,0, . . . , 0> can be viewed either as + +22 . NEURAL AND CONCEPTUAL INTERPRETATION407 + +It is useful to consider this example geometrically as well as algebraically. In Figure 5, s is drawn (only the first two unit dimensions are depicted) . The projections of this vector onto the unit axes (defined by the vectors uland u 2) are .9 and .6, while the projections onto the vectors PI and P2 are .15 and .75. These conceptual vectors define the + +axes of the pattern coordinate system for state space. + +In a PDP model with a distributed interpretation , the interpretation of the state of a system requires the use of the pattern coordinate system. The mathematics of linear algebra (discussed in Chapter 9) tells how to convert state descriptions from unit coordinates to pattern coordinates, and vice versa. All that is required is the specification of the + +patterns. + +Before considering the conversion between unit and pattern coordinates, one observation needs to be made. Consider a distributed conceptual interpretation. (Exactly the same considerations apply to a distributed neural representation.) If confidence in a group of conceptual hypotheses are to be separable, then the pattern + +FIGURE 5. The unit basis vectors" 1 and" 2 define the axes for the unit coordinate system. The state s has unit coordinates < .9,.6> . The pattern vectors PI and P2 define the axes for the pattern coordinate system. The state s has pattern coordinates < .15,.75> . + +22. NEURAL AND CONCEPTU AL INTERPRETATION409 + +p = p - l u . (3B) + +p =[1 i]. + +Thus the state S 1 representing . 5 of pattern one and . 3 of pattern two has pattern + +coordinates < .5, .3 > and unit coordinates + +u 1 = 2 1 . 3 = 1 .3 . [ 1 3] [ . 5] [ 1.4] + +The two coordinate s} 'stems ands 1 are shown in Figure 6. + +The existence Qf an inverse olP is guaranteed by the linear independence Qf the + +{ Pi } . + +Let's consider a simple case with two units supporting the two patterns < 1,2> + +and < 3, 1> . Here the pattern matrix is + +computed from the conceptual components of s, the components of s + +with respect to the pattern basis {Pi } , by + +u = Pp . (3A) + +In this matrix equation, u and p are the N x 1 column matrices of coor- + +dinates of s in the unit and pattern systems, respectively. + +To compute the pattern coordinates from the unit ones, we need the + +inverse matrix of P : + +22. NEURAL AND CONCEPTUAL INTERPRETATION 411 + +Thus, Iij is the interconnection strength from pattern j to pattern i . In a distributed conceptual interpretation , this number expresses the sign and strength of the evidential relation from the j th conceptual hypothesis to the i th conceptual hypothesis. Thus I governs the propa- + +gati on of inferences. + +The important result is that the evolution equation for the linear model has exactly the same form in the pattern coordinate system as it had in the + +unit coordinates. + +THE ISOMORPHISM HYPOTHESIS HOLDS IN LINEAR + +SYSTEMS + +s = .6PI + .3P2 + +then the corresponding state in the higher-level model would have activation . 6 in + +Unit 1, .3 if! U'1it 2, and 0 elsewhere. + +The analysis at the end of the preceding section shows that for a linear model the evolution equation has exactly the same form in pattern coordinates as in unit coordinates. In other words, there is an exact isomorphism between the lower and higher levels of description in linear + +models. + +This isomorphism has been viewed so far as a mapping between two descriptions of a given model. It can also be viewed as a mapping between the behavior of two different POP models. One is the original model with which we began, a model supporting a distributed interpretation , having N units with interconnection weight matrix W . Let's call this the lower-level model, Mi . The higher-level model Mh has a unit for every pattern of the distributed interpretation and has interconnection matrix I . The law governing its processing (Equation 4) is exactly the + +same as that of the lower-level model (Equation 2) . + +The isomorphism maps states of the lower-level model into states of the higher-level model. Take any state Sf of the lower-level model. To find the corresponding state Sh of the higher-level model, express Sf in pattern coordinates. The coordinate for the ith pattern- its strength in state Sf - gives the activation in state Sh of the ith unit of Mh . (In other words, the i th pattern coordinate of Sf equals the i th unit coordi- + +nate of S h .) + +So for example if the state s of the lower-level model is a superposition ofthe,/lrst + +two patterns, say, + +the evolution equation of the other, so that the behavior of one model is exactly mapped onto that of the other. That is, if the two models start off in corresponding states, and are subject to corresponding + +inputs, then for all time they will be in corresponding states. 6 + +The significance of the behavioral equivalence of the two models can be brought out in an example. Consider a linear version of the letter perception model (that is, remove the nonlinearities from the equations of the model, maintaining the original nodes and interconnections) . As originally proposed, this model, Mh , has a local conceptual interpretation . Suppose we wanted to rebuild the model with a distributed conceptual interpretation , with hypotheses about words and letters + +represented as activation patterns over the units of a model M, . + +First, each conceptual hypothesis (i.e., unit in the original model) would be associated with some specific activation pattern over units in M, . The inference matrix of Mh , which gives the positive and negative strengths of connections between conceptual hypotheses in the original model, would be algebraically transformed (following Equation 5) , using the activation patterns defining the distributed interpretation . This new matrix defines the correct weights between units in M, . This + +sets up the lower-level model. + +To run the model, inputs are chosen and also an initial state. Both are originally specified in conceptual terms, and must be algebraically transformed to Mi (following Equation 3A) . This defines the inputs and initial state of the lower-level model. Then the lower-level model is run for a length of time . The model's response to the input is determined by taking the final state, representing it in pattern coordinates, and reading off the activations of the corresponding conceptual + +hypotheses. + +What the isomorphism tells us is that after all this effort , the result will be exactly the same as if we had simply run the higher-level model. The higher-level model can be viewed as a conceptual description of the lower-level model in which details of the "implementation patterns" have been ignored. The behavioral isomorphism implies that these details have no effect at all on the behavior of the model. However, the two. models do implement the same processing differently , and they will differ in how they respond to modifications of the processing mechanism itself . Thus the behavioral effect of destroying a unit will + +412 BIOLOGICAL MECHANISMS + +6 If the lower-level model has external inputs to the units, exactly the same transformation that maps sfafe.S' of Mj to states of Mil also maps inpuf.S' of M{ to inputs of ~ 1' This + +can be verified by taking the matrix form of the new linear evolution equation, + +22 . NEURAL AND CONCEPTUAL INTERPRETATION413 + +LOCALIZED DAMAGE AND THE ISOMORPHISM OF + +Suppose we remove one unit from the lower-level model. What will be the corresponding modification in the isomorphic higher-level model? That is, what will be the effect on the model's ability to process the patterns that are meaningful in the distributed interpretation ? Removing unit v can be viewed as insisting that it have activation zero and no incoming connections. This amounts to allowing only + +states s that have + +Uv (8) = o. + +1 - op oJ. + +(Here 1 is the unit or identity matrix , and T is the matrix transpose operation .) The + +new evolution equation becomes + +0 ( 1+ 1) = Do W 0 (I ) . + +Dov + +Introducing D is equivalent to the more obvious step q[ replacing the v th row q[ W by zeroes, or q[ simply' removing it altogether, along with the v th element q{ u . However, it is difficult to map these surgeries onto the higher-level model to see what they correspond to. By instead performing the "damage" by introducing a new linear operation (multiplication by D ) , we can again use simple linear algebra and trans- + +LEVELS + +be different for the two models, and the demands on connection adaptation , i.e., learning will differ . Understanding these phenomena in terms of the lower- and higher-level models provides an opportunity to exploit more of the power of the techniques of linear algebra. They will be discussed in the following two sections, which can be skipped without diminishing the comprehensibility of the subsequent + +discussion. + +This change in the kinematics of the system brings with it a change in the dynamics. We need to follow this change through , transforming it + +to the higher-level model. + +The evolution equation must be changed so that only allowed states are reached,. this amounts to saying that the activation of unit v will ne~'er change .from zero. This can be done as follows. The column matrix W u (I ) has .for its v th element the inputs coming in to unit v,' rather than this .for the v th element in u (I + 1) we want zero. So we apply a "damage matrix" that" prQjects out" the component along + +uv: + +414 BIOLOGICAL MECHANISMS + +We can view D as a projection onto the states orthogonal to Uv if we introduce the inner product in which the unit basis vectors are orthonormal. Then the inner product of two states sand s' , (s , s '), can be easily computed using the column + +matrices U andu' of the unit cooordinates of these states: + +(5 ,S ') = or 0' . + +While the unit basis is orthonormal, the pattern basis may not be. The relevant + +matrix is M with elements + +Mij = (p i ' P j ) = L U v (p i ) U v (p j ) = L P viP v j, + +v v + +I.e., + +M = pT p . + +IfM is the unit matrix 1, then the pattern basis is orthonormal, also, and the inner product of two states sand s' can be computed using the column matrices p and p' of their pattern coordinates using the same simple formula as in the unit coordinates: + +(s ,s ') = pT p' [orthonormal patterns only]. + +Otherwise one must use the general.formula of which this is a special case: + +(s ,s ') = pTMp ' . + +(Since u = Pp, this is just u T uiJ + +Now we apply the standard procedure for changing the dynamical equation to the + +pattern basis. This gives + +p (t+ 1) = Dd I p (t ). + +Here, the "damage vector" d is the column matrix of pattern coordinates ofuv: + +d = p - lu v + +and Dd is again the matrix that orthogonally projects out d: + +Dd = 1 - d dT M . + +(If the pattern basis is not orthonormal, the inner product matrix M must appear in the orthogonal projection matrix D " if the pattern basis is orthogonal, then M = 1 + +so it has no effect.) + +So the corresponding damage in the higher-level model is removal of the pattern represented by d.. All allowed states will be orthogonal to this pattern. Introducing D here is equivalent to making a change in the inference matrix I that is more complicated than just converting a row to zeroes. All connections coming into the patterns that employ the deleted unit will be altered in a rather complicated way,' I is replaced + +by Dd I . + +22. NEURALND CONCEPTUAL INTERPRETATION 415 + +[- . .4 .2 OJ 2 - . 6] [ 11 + +(The weighted sum of the two patterns, with weights < - .2,.4> , is seen to be 0 on the second unit, 1 on the first .) Thus in the pattern coordinates, the damage has been to remove the state < - .2,.4> , leaving only states orthogonal to it. This of course is just a different description of exactly the same change in the state space: + +see Figure 9. + +Thus removing a lower-level unit corresponds to removing a pattern of activation over the higher-level units~ under a distributed conceptual interpretation , this amounts to removing "pieces of concepts" - the + +pieces relying on that unit . + +The same analysis can be run in reverse, to show that "removing a higher-level unit " (e.g., a concept) amounts to performing a rather complicated change in the weight matrix that has the effect of eliminat ing from the state space those states not orthogonal to the pattern + +> damaged state space + +> > U1 + +p = + +model that are not orthogonal to a particular state of the higher -level units . This state corresponds under the isomorphism to OJ) ~ it represents exactly the superposition of lower -level patterns in which the activations on all lower -level units exactly cancel out to 0, except for + +the removed unit , which ends up with an activation of 1. + +destroy unit 1 . . . + +damaged state space + +416 BIOLOGICAL MECHANISMS + +FIGURE 9. + +corresponding to the deleted higher-level unit . In short, localized damage in one model is distributed damage in the other. Geometrically , the picture is similar in the two cases~ localized damage removes the states orthogonal to a coordinate axis, while distributed damage removes the states orthogonal to a vector that is not a coordinate axis. Since the higher-level coordinates simply employ different axes than + +the lower-level coordinates, the picture makes good sense. + +LEARNING OF CONNECTIONS AND THE + +One major conceptual distinction between local and distributed interpretations is that in the former case the individual elements of the interconnection matrix can be readily interpreted while in the latter case they cannot. In a version of the reading model with a local conceptual interpretation , the positive connection from the unit representing II the first letter is A'I and that representing I'the word is ABLE " has a clear intuitive meaning. Thus the connection matrix can be set up intui tively , up to a few parameters that can be adjusted but which have clear individual interpretations . By contrast, the interconnection matrix of the modified reading model defined in the section "The Isomorphism Hypothesis Holds in Linear Systems," with a distributed conceptual interpretation , had to be obtained by algebraically transforming the original interconnection matrix : This matrix cannot be obtained by intuition , and its individual elements (the connection strengths between individual units in the distributed model) have no conceptual + +In pattern coordinates, the destruction of Unit 1 is described as the removal + +of the state < - .2,.4> , leaving only the states orthogonal to it . + +ISOMORPHISM OF LEVELS + +remove state < - .2,.4 > . . . + +22. NEURAL AND CONCEPTLT AL INTERPRETATION 417 + +however , another way to produce the interconnections in the distrib uted model : through a learning procedure . The two procedures I will discuss are the original Hebb learning procedure and its error -correcting + +modification , the delta rule . + +I will only briefly and imprecisely discuss these two learning pro cedures ~ a fuller discussion is presented in Chapter 2, Chapter 8, and Chapter 11. In the Hebb procedure , the interconnection strength between two units is increased whenever those units are simultaneously active . This can be implemented by adding to the strength the product of the units ' activation . In the delta rule , this is modified so that what is added to the strength is the product of the input unit 's activation and the difference between the output unit 's activation and the value it + +should have according to some outside " teacher ." + +The relevant results about these procedures , for present purposes , are these : The delta rule will eventually produce the interconnection matrix that minimizes the error , measured relative to the teacher . The Hebb procedure will give essentially the same result in the special case that the activation patterns the model must respond to are mutually orthogonal . In this case, the error -correction feature of the delta rule is + +superfluous . + +There is an intuitive explanation of this result . Suppose a new input activation pattern must be associated with some output pattern . Iil general , that input pattern will , by virtue of previously learned associations , produce some output pattern . The delta rule adds into the interconnec tions just what is needed to modify that output pattern , to make it the correct one . The. Hebb procedure adds connections that will themselves produce the output pattern completely from the input pattern , ignoring connections that have already been stored . If the new input pattern is orthogonal to all the already learned patterns , then a zero output pattern will be produced by the previously stored associations . 7 That is why , + +with orthogonal inputs , the simple Hebb procedure works . + +The point is that in general , the delta rule will produce the correct interconnection matrix for .a distributed model , as it will for a local model . This represents a degree of parity in the status of the two models . However , this parity has its limits . The Hebb rule will in general not produce the correct matrix for a distributed model , unless the patterns have been carefully chosen to be orthogonal . (A simple exam ple of such orthogonality is a strictly local model in which each input is + +uniquely represented by a single unit .) + +Thus the lower - and higher -level models may differ in whether Hebb learning works ~ this is because what is local to the connection between + +418 BIOLOGICAL MECHAN[SMS + +two units in one model will in general not be local in the other, and some special arrangement- orthogonality of patterns- is needed to + +ensure that nonlocalities do not cause any problems. + +This issue of the orthogonality of the patterns relates back to kinematics. To analyze what the individual components of the interconnection matrix need to be, it is necessary to add to the vector space of states the additional geometric structure of an inner product; it is this that tells whether states are orthogonal. The inner product is defined so that the unit basis is orthonormal. When the pattern basis is orthonormal as well, the transformation from unit to pattern coordinates is a rotation, and it preserves the constraints on the interconnection matrix elements. In particular, the adequacy of the Hebb procedure is invariant under the transformation from the lower- to higher-level model. In the general case, when the pattern basis is not + +orthonormal, this invariance is broken. + +NONLINEARITYAND RESTRICTED STATE SPACE + +Having established the validity of the isomorphism of levels hypothesis for linear POP models, it is time to consider quasi-linear systems with nonlinearities . To understand the effects of these non- + +linearities, it is helpful to go back to kinematics. + +The state space SL of linear POP models is all of N -space, where N is the number of units in the model. By contrast, the standard state space S of general POP models is the solid hypercube in N -space described in the section "Kinematics." This represents states in which each unit has activation within the limited range [- m, M ] . Such a restriction is motivated within the neural interpretation by the limited range of activity of individual neurons~ it is motivated within the conceptual interpretation by the desirability of limiting the possible influ ence of a single conceptual hypothesis. (POP models are feedback systems that tend to be difficult to control unless activation values have a ceiling and floor . Nonlinearities also allow multilayer POP networks to possess greater computational power than single-layer networks: see + +Chapter 2.) + +Whatever the motivation , the restriction of states to the cube S , instead of allowing all states in N -space SL, means that the general linear evolution equation (with unrestricted weight matrix W ) is unacceptable. Introducing the nonlinear sigmoidal function F of Equation + +Unlike SL, the hypercube S looks quite different in different coordinate systems. In unit coordinates, all coordinates are limited to [- m, M] ~ with a different set of axes, like those of pattern coordinates, the allowed values of a given coordinate vary, depending on the values of the other coordinates. (See Figure 10.) No longer is it possible for the description of the system to be the same in the two coordinate systems. As we shall see explicitly , the exact ismorphism of levels that + +holds for linear models breaks down for nonlinear models. + +Another characterization of the kinematic effect of restricting S to a hypercube is that now states can be distinguished according to their position relative to edges, faces, corners, and so on. Choosing to represent a concept, for example, by a point in the corner of S will produce different behavior than choosing a point in the middle of a face. These distinctions simply cannot be made in the linear state space SL . A crucial effect of limiting the state space to S is that now some superpositions of states will be in S while others will not~ it will depend on the position of the states relative to the boundary of the hypercube. Because some patterns cannot superimpose, i.e., coexist, they must instead compete for the opportunity to exist. Other patterns can coexist, so the choice of patterns in an interpretation will matter. In particular, + +22. NEURAL AND CONCEPTUAL INTERPRETATION419 + +U2 P, + +: # + +M / / + +/ / / / + +/ / + +u , + +- M + +" - " / " + +> " " " " - " " " " " " " " + +P2 + +FIGURE 10. In unit coordinates, the allowed values of U2 are [- m ,M ] regardless of the value of u 1. In the pattern coordinates shown, the allowed values of P2 depend on the value of PI , as shown by the two diagonal bars. These bars correspond to two different + +420 BIOLOGICAL MECHANISMS + +and + +the choice of nonoverlapping patterns ( e . g . , over single units ) - a local or quasi - local interpretation - will produce different behavior than the choice of overlapping patterns - a genuinely distributed interpretation . + +Take for concreteness the allowed unit coordinate range [ - m , MJ to be + +[ - 1 , + 1 ] . + +Consider for example a local conceptual interpretation in which Concepts 1 and 2 are represented by Units 1 and 2 , respectively . In unit coordinates , then , the representation q ! the hypotheses are < ] , 0 , 0 , 0 , . . . , 0 > and < 0 , 1 , 0 , 0 , . . . , 0 > . Then the superposition q ! these two states is simply < 1 , 1 , 0 , 0 , . . . , 0 > . This falls within S , and is there . [ ore kinematically allowed . By contrast , consider the simple distributed representation in which the t } VO hypotheses are respectively represented by < 1 , 1 , 0 , 0 , . . . , 0 > and < 1 , - 1 , 0 , 0 , . . . , 0 > . Now the superposition Q ! the t ' o states is < 2 , 0 , 0 , 0 , . . . , 0 > which is kinematically forbidden . The situation is graphi - + +cally depicted in Figure 11 . + +The basic observation is that superimposing states representing maximal confi - + +dence in two conceptual hypotheses is kinematically allowed when the corresponding patterns do not overlap - always true in a local interpretation - but kinematically . ! orbidden when the } ' do overlap - sometimes true in a genuinely distributed + +interpretation . + +The kinematic restriction that states stay inside the hypercube has a dynamical consequence in the sigmoidal function F . It will now be verified that F does indeed lead to a greater difficulty in superposing < 1 , 1 > and < 1 , - ] > than in super posing < 1 , 0 > and < 0 , 1 > . ( All coordinates in this note will be unit coordinates . ) Let F be the function that takes a vector , passes all its unit coordinates through F , and uses the resulting numbers as the unit coordinates of the output . I will show that F retards the growth in length ofa vector along the edge ( the < a , 0 > direction or e ) more than along the diagonal ( the < { 3 , { 3 > direction or d ) . These retardation + +factors are + +lei a + +Re = I F ( e ) I = - F - ( ~ ) + +- I d I - J2 { 3 - - \_ . . & \_ - Rd - IF ( d ) I - J2F ( { 3 ) - F ( f3 ) . + +As shown in Figure 12 , these retardation factors are the reciprocals of the average slope of the F curve between the origin and the x values a and f3 , respectively . Since the F curve is concave downward , as x increases , this average slope dimin ishes so its reciprocal increases . That is , the retardation will be greater as a and f3 grow ; F squashes vectors more and more strongly the closer they get to the edge of the state space . A fair comparison between the retardation along e and d requires that these vectors be of equal length . In that case , a is greater than f3 ( by a factor + +22 . NEURAL AND CONCEPTUAL INTERPRET A TION 421 + +P1 + P2 + +FIGURE 11. A: In a local interpretation in which Concepts 1 and 2 are represented by vectors uland u 2., the superposition u 1 + u 2 lies in S (along the diagonal). B: In a distributed interpretation in which Concepts 1 and 2 are represented by vectors PI and p 2., + +the superposition PI + P2 lies outside of S (in the direction of an edge). + +Competition of patterns that are forbidden to superimpose- what I will call natural competition- does not exist 1n linear models. The subsequent discussion of nonlinear models will focus on natural competition and how it distinguishes between local and distributed models. + +Natural competition resembles inhibition , which of course can be present in linear models. There is a crucial difference , however. Inhi bition is explicitly inserted into the interconnection matrix. Competition arises independently of the interconnection matrix ; it depends on the overlap of patterns and on the nonlinearity . Loosely, we can say that whether two states naturally compete depends only on kinematics (their position in state space relative to the edges of the space) , and not on + +P1 + +S + +p ~ + +U2 U1 + U2 + +S + +U1 + +To investigate the isomorphism hypothesis in nonlinear PDP models, as before we take a model with a distributed interpretation and transform the description from unit to pattern coordinates. We then compare the new form of the evolution equation with the original form ~ if the form has changed, the hypothesis fails. To start with , we restore the nonlinear sigmoidal function F to the evolution equation~ we will + +422 BIOLOGICAL MECHANISMS + +FIGURE 12. The slope of the solid line, F and < 1 , - ] > . A superposition of these two states with weights . 3 and . 2 , respectively , would produce , in a linear model , the state with unit coordinates < . 5 , . 1 > ( this state has pattern coordinates < . 3 , . 2 > of course ) . In the nonlinear model , the numbers . 5 and . 1 are each passed through the function F to get the unit coordinates Qf the new state . Consulting the F .function Qf Figure 13 , we see that F (. 5 ) = . 9 and F (. 1) = . 6 , so the new state has unit coordinates < . 9 , . 6 > . The pattern coordinates of this state , as shown in the section called " Pattern Coordi nates , " are < . 75 , . 15 > . Thus the strength of pattern 1 relative to pattern 2 has + +been amplified by the .factor + +.J5 / . 15 = 3 33 . 3 / . 2 . . + +The dominance of the stronger pattern has been enhanced by the nonlinearity , just as the dominance Qf stronger nodes is increased by mutual inhibition . This is + +natural competition . + +This competitive effect is not present if the patterns do not overlap . In fact the nonlinearity diminishes dominance in this case . ' f the " patterns " are < 1 , 0 > and < 0 , 1 > - i . e . , if the model is local - and we again consider combining . 3 Qfthe .first with . 2 Qf the second , then the weighted sum is < . 3 , . 2 > and the new state , after passing the unit coordinates through F, is < . 78 , . 7 > The " amplification " .factor is + +therl ;'fore + +426 BIOLOGICAL MECHANISMS + +=F(x) / x F(y) / y . F (x ) / F (y ) + +x / y + +This is the ratio of the average slope ofF between the origin and x and between the origin and y ,. as already pointed out in section 1O, the negative acceleration of F implies that this slope will be less for the greater interval (x ) , so the local amplifica- + +tion is always less than one. + +than one. + +The local amplification is simply + +FIGURE 14. The slope of the solid line is [F(w) - F(z )]/ (w - z). The point marked x is the midpoint of this line- the vector average of the eTldpoints- with coordinates + +< J/2[\I1.,'+Z],1/2[F(w)+ F(z)]> . Thus the slope of the dashed line is + +1/2 [F(~v) + F(z)] 1/2 [W + z] . + +For these patterns , the conclusions that the amplification factor is greater than one for the distributed model and less than one for the local model is not dependent on the particular F values used above ; they hold for any negatively ' accelerated F ,[ unction . The distributed amplification is ( letting . 3 be replaced by x and . 2 by y ) : 1/ 2 [ F ( x + y ) + F ( x - y ) ] / 1/ 2 [ F ( x + y ) - F ( x - y ) ] - + +x / y . + +Letting x + y = wand x - y = Z , this becomes + +1/ 2 [ F ( w ) + F ( z ) ] / 1/ 2 [ F ( w ) - F ( z ) ] - 1/ 2 [ F ( w ) + F ( z ) ] / 1/ 2 [ W + Z ] + +1/ 2 [ W + Z ] / 1/ 2 [ W - Z ] [ F ( w ) - F ( z ) ] / [ w - z ] . + +As shown in Figure 14 , this is the ratio of the slopes of two lines that can be drawn on the graph of F , and because F is negatively accelerated , this ratio must be greater + +22. NEURALND CONCEPTUAL INTERPRETATION 427 + +It is useful to explicitly relate natural competition to mutual inhibition ,. we shall do this for the above case. The pattern coordinates of the state created in the nonlinear model by superposing < 1, 1> with strength X and < ] ,- ] > with strength yare + +> P 1 = 1/2 [F (X + .,v) + F (X - y ) ] P2 = 1/2 [F (x + .,V) - F (x - y ) ]. + +Now let us substitute + +F (x + y ) = S + [x + y ] F (X - y ) = S - [X - y ] . + +s+ is the average slope of F between the origin and X + y ,. this is less than S\_ , the average slope ofF between the origin and X - Y (see Figure 15) . This substitution + +. . gives , on regrouping , + +> PI = aX - ' Y Y P 2 = ay - ' Yx + +where + +a = 1/2 (s+ + s\_) 'Y = 1/2 (s- - s+) . + +These equations, displayed graphically in Figure 16, show that the effect of the nonlinearity on the < x , y > combination is the same as having an inhibition of strength ' Y between units representing the initial and final strengths of the different patterns , along with an excitation of strength a between units for the initial and final values of the same patterns . The magnitude of the inhibition 'Y depends on the difference in average slope of F between the origin and X - Y on the one hand and X + Y on + +F + +. . . . . ' s + + +x + y + +428 BIOLOGICAL MECHANISMS + +a a + +FIGURE 16. + +The conclusion, then, is that with overlapping patterns like those occurring in truly distributed models, F amplifies differences in the strengths of patterns~ with nonoverlapping patterns like those of local or quasi-local models, F has the opposite effect. This is natural com- + +petition at work . + +When viewed at the higher level of patterns, natural competition acts like inhibition between overlapping patterns. The nonlinearities automatically create significant inhibition between strong patterns but insignificant inhibition between weak patterns. So for a distributed conceptual interpretation , it is impossible to have a high degree of confi dence in more than one conceptual hypothesis represented on a given set of units, but the system can simultaneously entertain without diffi culty a low degree of confidence in several such hypotheses. If we think of the units on which conceptual hypotheses are represented as some kind of semantic features, then two hypotheses that call for dif ferent values of the same features- two hypotheses represented by overlapping patterns- are hypotheses that are semantically incompatible. Thus distributed representation offers an attractive form of + +automatic inhibition between mutually incompatible hypotheses. + +These considerations suggest that we could try to make a higher-level POP model approximately behaviorally equivalent to a distributed nonlinear lower-level POP model by inserting additional inhibitory weights between units representing competing patterns. These extra weights might approximately serve the function of the complicated nonlocal nonlinearity in the truly isomorphic non-POP higher-level model. Of course, assigning fixed magnitudes to those weights would only approximate the real situation in the lower-level model in which the degree of + +A network displaying the effective inhibition produced by natural competi- + +tion between overlapping patterns PI and Pl' + +the other. In the region sufficiently close to the origin that the graph Qf F is nearly linear , ' Y is zero. Thus .for sufficientl } ' weak patterns there is no competition ; how + +weak is "sl{fflcient " "-till depend on how large the linear range ofF is. + +22 . NEURAL AND CONCEPTUAL INTERPRET A TION 429 + +competition varies with the strength of the patterns. With nonlinear models, it does seem that higher-level models must incorporate some form of complexity that goes beyond the standard POP framework in order to really capture the subtlety of the interaction of patterns in the lower-level model~ the degree of failure of the isomorphism hypothesis + +seems to be significant . + +The failure in the isomorphism hypothesis induced by F is compounded by the nonlinear thresholding function , G. In the previous section we saw that the nonlinearity introduced by F becomes nonlocal in the higher-level model. Exactly the same analysis applies to the non- + +linearity introduced by G. + +It is interesting to consider whether a local thresholding of the activation of patterns in the higher-level model, since it can't be created by putting a local G in the lower-level model, can be affected some other way. Natural competition functions like a threshold on inhibition . When a concept is weakly present, it creates essentially no inhibition ~ when it is strongly present, it generates considerable inhibition . Thus, it is as though there were a threshold of activation below which a concept is incapable of influencing other concepts inhibitively . The threshold is not sharp, however, as there is a gradual transition in the amount + +of inhibition as the concept strengthens. + +CONCLUSION + +If mind is to be viewed as a higher-level description of brain, some definite procedure is needed to build the higher-level description from the lower. One possibility is that the higher level describes collective activity of the lower level, for example, patterns of activation over multiple lower-level units. In the analysis of dynamical systems, it is customary to create such higher-level descriptions, using higher-level units that are collective aspects of many lower-level units. The higher-level description employs new mathematical variables, each of which is defined by combining many variables in the lower-level description. This requires that the lower-level description be expressed in terms of + +mathematical variables. + +POP models constitute an account of cognitive processing that does rest on mathematical variables: the activation of units. Thus these models can be described at a higher level by using the preceding method. The lower-level description of the system amounts to a set of variables and an evolution equation~ the higher-level description is created by defining new variables out of many old ones and substituting + +430 BIOLOGICAL MECHANISMS + +Analyzing POP models in this way leads to several observations . The core of the evolution equation , where the knowledge of the system is employed , is linear . The dynamical systems corresponding to POP models are quasi -linear . A central kinematic feature of these systems is that the state spaces lie in vector spaces, and linear operations playa very special role . Superposition is fundamental to the way parallel distributed processing works . Linear algebra gives us both concepts for understanding POP models and techniques for analyzing them . It tells us that there are many equally good coordinate systems for describing the states, and how to transform descriptions from one coordinate system to another . In particular , it suggests we consider a coordinate system based on the patterns , and use this to frame our higher -level description . It tells us how to transform the knowledge (interconnec tion matrix ) from one level of description to the other . Linear algebra tells us that linear operations are invariant under this kind of transfor mation , and therefore if the evolution equation is linear , its form will be the same in the two descriptions . This is the isomorphism of levels + +for linear POP models . + +Linear algebra also alerts us to the fact that edges to the state space interfere with superposition . This leads to an evolution equation that modifies pure linear superposition by adding nonlinear operations . The breakdown of superposition at the boundaries of state space leads to competition between states that cannot superpose . The lack of invari ance of the bounded state space under linear operations leads to a breakdown of the isomorphism of levels in the corresponding nonlinear + +POP models .lO + +The concepts of linear algebra add considerably to our understanding of POP models , supplementing the insight that comes from simulating POP models on computers . We can analyze with precision , for exam ple , the effects of localized damage or of synaptic modification upon the higher -level description of the processing . We can understand why the choice of patterns doesn 't matter in linear models and why it does in nonlinear models . We can even get some handle on what kind of effects these choices have for nonlinear models , although the picture + +needs much more clarification . + +10 Note that the nonlinearity in quasi -linear systems is minor compared to that in highly nonlinear systems . In POP models , the knowledge is contained in the linear part - it is this part that is learned , for example , in adaptive models - while the nonlinearity is uni form across the units , and fixed from the outset . In a highly nonlinear model , the activa tion value of a unit would be a nonlinear function of the other activations , with parame ters encoding the unit 's knowledge that are used in arbitrary ways , rather than merely as coefficients in a weighted sum . In such a model , superposition and linear algebra might + +22. NEURAL ANDCONCEPTUAL INTERPRETATION431 + +The isomorphism of levels hypothesis constitutes a mathematically analyzable Question about the mind / brain duality , within the framework of POP models of cognition . These models serve well because of their independent interpretations as models of neural and conceptual + +. processing . + +While the isomorphism of levels hypothesis speaks to a fairly philo sophical issue , the analyses of this chapter show that no strong argu ment about the hypothesis can have validity unless it makes sharp enough distinctions among models to differentiate between linear and nonlinear POP models : The matter demands a certain degree of mathematical care . From an appropriate formal viewpoint , however , we have seen that conceptual accounts of mind and physiological accounts of brain can be two descriptions of a single cognitive system . + +ACKNOWLEDGMENTS + +While I carry full responsibility for the views expressed in this chapter , the critical role played by insights of Jay McClelland and Dave Rumelhart is fully and gratefully acknowledged . This chapter is actually in major part the result of a joint effort , and I thank Dave and Jay for the ideas and understanding they have shared with me . Many thanks , too , to Eileen Conway and Mark Wallen for excellent graphics and computer support . The work was supported by the Systems Develop ment Foundation , the Alfred P . Sloan Foundation , National Institute of Mental Health Grant PHS MH 14268 to the Center for Human Information Processing , and Personnel and Training Research Programs of the Office of Naval Research Contract NOOO14 - 79 - C - O323 , NR 667 - + +437 . + +CHAPTER 23 + +D. ZIPSER + +Biologically Plausible Models of + +Place Recognition and Goal Location + +In this chapter I describe three parallel network models that deal with some elementary aspects of spatial cognition - namely , recognizing places and locating goals . The performance of these models was exam ined using computer simulations in which the networks guide the movements of a simulated observer . These models are constrained by both the requirements of accomplishing the tasks and by a desire to achieve some degree of biological plausibility . The requirement of bio logical plausibility has the advantage of generating models that can have immediate relevance to psychology and neurobiology but it has the disadvantage of limiting the range of problems that can be approached . This limitation is not one of principle , but grows out of our currently limited understanding of how computation is organized in the brain . More general problems can often be attacked when the constraint of biological plausibility is not invoked and unrestricted symbol manipula tion is allowed . Before tackling biologically plausible models , it is use ful to look at what has been done in this unrestricted computing con text because it will give some insight into the major issues in spatial + +cognition . + +From the realm of II pure I' artificial intelligence research , for example , we have the fuzzy map theory ( Davis , 1981 ~ McDermott , 1980 ) . The + +The first third of this chapter is a modification of the article "A Computational Model of Hippocampal Place Fields" by D. Zipser, which appeared in Behavioral Neuroscience, 1985, 99, 1006- 1018. Copyright 1985 by the American Psychological Association, Inc. + +goal here was to develop a system that could deal with the spatial relations between objects so that queries about them could be answered in the context of a language understanding system. Among the questions the fuzzy map system is designed to answer are: "Am I headed towards home? How do I get from here to Carnegie Hall ? What buildings are between W oolsie and Sterling? What is the nearest Chinese restaurant to here? What street is the best route from Yale to the hospital?" These questions are answered in a linguistic framework and new infor mation is assimilated through language so no attempt was made to guide actual navigation behavior or to learn from the environment . + +Clearly, the range of possible facts about the spatial relationships between objects necessary to answer questions of this kind is far too great to be explicitly stored in memory. What is needed is a representation that stores basic information so that inference can be used to determine the required facts when the system is questioned. In the fuzzy map system, each landmark or object has its own reference frame fixed rigidly to it . The combination of object and associated reference frame is called a frob . Frobs are connected to each other to form maps by storing mquants, each of which contains information about the translation , rotation , or scale factors relating a pair of frobs. Queries about spatial relations are answered by searching a data structure consisting of mquants. An important feature of the fuzzy map formulation is that it separates the components of the transformation relating frobs so that rotation , translation, and scale factors are in separate mquants. This has a number of advantages, one of the most important of which is that partial information about the spatial relations between frobs can be used. For example, two frobs connected only by a scale factor can be compared with respect to size even if their other spatial relations are unknown . Another important feature of the fuzzy map concept is its "fuzziness." The components of the transformation between frobs are not specified exactly, but are specified as ranges. This allows inexact, semiqualitative information to be incorporated into the map data + +structure. + +Another approach to spatial processing, in large scale environments , is found in the work of Kuipers (1978, 1983) who is concerned with developing psychological models. A particularly interesting feature of Kuipers' approach is the concept of view, which he defines as "the sensory image received by the observer at a particular point " (Kuipers, 1983, p. 217) . The critical importance of views is that they are used to recognize places. Places are important because their representation can serve as a node to which related information can be attached. The criti cal operation on views is comparison to determine equality. For example, by comparing the current view with a data base of stored views, it is possible to gain access to all the information associated with the + +23. PLACE RECOGNITION AND GOAL LOCATION 433 + +current place. The concept of view is very relevant biologically because there are neurons in the brain that fire only within the context of a particular view. One of the important things that can be associated with a place is information about getting from that place to another place. Kuipers represents the paths between places as a sequence of actions and views. The idea is that if you are at a particular place, and take a certain action, it will generate a new view. This view, in turn , can be used to index a new action, which will produce a new view, and so forth , tracing out a path to the goal. This strategy almost certainly + +corresponds to one of those used by humans and animals. + +In addition to path information , it is also possible to associate actual knowledge about the direction and distance to a goal with a place. The existence of absolute knowledge of goal location, relative to external landmarks, has been clearly demonstrated in the case of rats that are forced to swim in a tank of milky water (Morris , Garrud, Rawlins, & O'Keefe, 1982) . A small platform is placed below the surface of the cloudy water so that it is invisible to the rat. The rat is then put into the tank and swims around randomly until it locates the platform . The rat climbs up on the platform , rises up, and observes the landmarks in its environment . On subsequent immersions, the rat no longer searches randomly but swims directly to the remembered position of the platform . Since the rat will swim directly to the platform from any initial position in the tank, it must be computing the location of the platform , using remembered information about the location of external + +landmarks. + +The models described in this paper were designed to emulate the kind of goal seeking behavior seen with the rat in cloudy water. Such models require that a place, or more generally, an environmental context , can be recognized. In addition , they need a mechanism to bind goal location to place representations and a way to use this information to guide behavior. Finally , the models need a mechanism to assimilate new information so that goals can be located in unfamiliar environ ments. The first model discussed is concerned with place recognition and it can be quite biologically plausible because a lot is known about the neurobiology of place recognition . The subsequent models of goal location must be more speculative since much less is known about the + +mechanism of this activity . + +Place Recognition + +23. PLACE RECOGNITION AND GOAL LOCATION 435 + +hippocampus (Becker , Walker , & alton , 1980~ O' Keefe , 1976~ O' Keefe & Dostrovsky , 1971 ~ Olton , Branch , & Best, 1978) . In the rat , for example , there are single units that fire at their maximum rate only when the animal is at a particular location relative to a set of distal landmarks . These locations are called place fields . Removing too many landmarks or radically altering their spatial relations abolishes the place-field response of these units (O' Keefe , 1979~ O' Keefe & Nadel , 1979) . Recently , it has become possible to make accurate measure ments of the location , size, and shape of place fields , and to determine how they change when the environmental landmark cues are manipu lated (Muller , Kubie , & Ranck , 1983) . Quantitative experiments of this kind show that the response of place-field units is determined in a systematic , rule -governed manner by the configuration of the surround ing scene. Muller , Kubie , and Ranck have demonstrated this in a particularly elegant fashion . They showed that when every feature of the environment is scaled to a different size, the relative location of place fields and their areas scale with the environment . This , as we will see later , places a nontrivial constraint on the computational mechanisms + +that can be used to model location in rats . + +To account for these experimental observations , I have developed a computational model that relates the configuration of distal landmarks to the location , size, and shape of place fields . The input to this model is the configuration of landmarks in the environment together with the location of the observer . The output of the model represents the activity of a place-field unit in the observer 's brain . The model can be used to simulate experiments on a computer , the results of which can be compared with real experiments to test the correctness of the model . For example , suppose it is known from experiment that an animal can use a set of simple objects - such as rectangular cards - as place cues, and it is also known that the size of the retinal images of these cards is used as an indicator of location . Then the model can use this informa tion to provide Quantitative predictions of how the shape and location of place fields will change when the size , tilt , or location of these cards is changed . Conversely , suppose that the way in which place fields change when the environmental cues are manipulated has been deter mined experimentally . Then the model can help to determine what features of the environmental cues are being measured to locate the + +animal . + +It might seem strange to try to construct a model to do this since so much information processing takes place between the input of sensory information and the excitation of place-field units . Obviously , no theory currently feasible can account for all this processing in detail , and I make no attempt to do so. Rather , my model employs a biologi cally plausible architecture to compute the activity of place-field units + +436 BIOLOGICAL MECHANISMS + +from the configuration of distal landmarks using only the geometrical constraints inherent in the problem itself and as few specific hypotheses about brain structure and function as possible. This approach implies that even if the model proves to be a valid predictor, it will not directly provide new physiological knowledge. What it will do is give a precise description of the computations being carried out by the place-field system. Once these computations are understood, the task becomes to explain how neural networks in the brain actually implement them. I feel that trying to explain how neurons might accomplish a clearly defined computation is a more tractable task than trying to relate an + +animal's behavior directly to the functioning of its neurons. + +The Model + +The basic question that the model must address is: How do the place-field neurons know that the observer, in whose brain they reside, is at the location where they are supposed to fire ? I consider this to be a pattern-recognition problem in which a stored representation of a scene is compared to a representation of the current scene. Roughly speaking, the better the match between these two representations, the closer the viewer is to the viewpoint of the stored scene. The activity of place-field units can be thought of as reflecting the closeness of this match. A matching task of this kind could be very complicated if details from the entire scene had to be considered. However, the experiments show that only a few discrete objects need to be used. This greatly simplifies the modeling problem and also makes sense since location information about only a small set of objects is sufficient to locate a viewer in the environment . An example of how several measurements combine to specify location is shown in Figure 1 where the point P is uniquely located by its distance from the three landmarks + +a, b, and c. + +In order to see how a place-field unit might make use of this kind of information , imagine that at some time when an observer was at location P, in Figure 1, representations of the objects a~ b~ and c were recorded in some way in memory. Further assume, that the descriptions of each of these objects contained the value of the distance to P. Suppose that at some later time the observer returns to the vicinity of P. The observer~s sensory system can now generate a set of current descriptions representing the objects~ together with their current distances. If these representations, other than their distance components~ are not affected too much by the viewing position, then the current representation of each object will differ from its stored representation + +b . + +a . . . . " + +23. PLACE RECOGNITION AND GOAL LOCATION 437 + +FIGURE 1. The location of point P is uniquely determined by its distance from the three landmarks located at G, b, and c. The circles are parametric curves along which the dis tance of an observer from a landmark remains the same . Other measures of location such as the size of the retinal image of a landmark also give parametric curves , but these are not generally circles centered at the landmark . (From I' A Computational Model of Hippocampal Place Fields " by D . Zipser , 1985, Behavioral Neuroscience , 99, p. 1007. Copyright 1985 by the American Psychological Association . Reprinted by permission .) + +only to the degree that the object ' s current distance from the observer differs from its distance to P . A neuron whose output response is a summated measure of the similarity between these current and stored representations for each landmark will have the properties of a place - + +field unit . + +The model deals with the problem of implementing a place - field unit that can carry out the required matching by breaking the task into two stages , each of which is carried out by a II layer " of simple processors roughly analogous to neurons or small neural networks . This arrange ment is shown in Figure 2 . Each unit in the first layer is specific for one landmark and one place field , and each is able to compare the current value of a location parameter with a value of the same parame ter stored in the unit . The output of these units remains 0 while their landmarks are not in the current scene . When a first - layer unit ' s 438 BIOLOGICAL MECHANISMS + +Sensory System + +Layer 1 + +Layer 2 + +FIGURE 2. The model is shown here as implemented in a network of processors. The "sensory system" processes input from an environmental scene and produces two outputs. These are X, which is a description of a landmark in the current scene, coded so that it will be recognizable by units in Layer 1, and dx, which is the value of a location parameter, such as distance, valid for the current position of the observer and landmark X. Each unit in Layer 1 is concerned with just one landmark and place field . When a description of this landmark appears at the output of the sensory system, the current value at the dx output is compared with the value, da, stored in the unit . Thus, if the value at X = A , then the unit labeled Ap will generate an output by applying its response function to dx - da. The procedure used to evaluate the model assumes that the whole scene is scanned while the observer remains still , and it also assumes that the outputs of Layer 1 units, once computed, remain fixed until the observer moves again. The Layer 2 unit integrates the outputs of the Layer 1 units to get an overall measure of how closely the current scene matches the scene as viewed from the place field centered at P. (From " A Computational Model of Hippocampal Place Fields" by D. Zipser, 1985, Behavioral Neuroscience, 99, p. 1008. Copyright 1985 by the American Psychological Association. + +Reprinted by permission.) + +landmark is detected by the sensory system, its response increases as the current and stored location parameter values become closer. The response of these first -layer units reaches its maximum value when the current and stored location parameters are equal. The task of the sensory system is to detect the landmarks and generate descriptions of them that can be recognized by the processors in the first layer. The sensory system must also measure the current value of whatever parameters are used to determine location. The model, however, is not + +SCENE + +X dx + +concerned with the details of how this is done. It is also not concerned with how this information is represented or transmitted to the processors in the first layer. The computations involved in the model do not + +require any detailed knowledge of these processes. + +The output of the processors in the first layer serves as input to the unit in the second layer, which acts like a place-field neuron. Only one of these is shown in Figure 2 because the current model is only concerned with the output of a single place-field unit . The output of the second-layer unit must be a monotonically increasing function of the sum of its inputs from the first layer in order to represent the similarity between the current scene and the scene as recorded at the center of the place field . The output of this second-layer unit is used to define + +the location and shape of place fields in simulated experiments. + +So far, the response functions for the units in each of the two layers have only been specified in general terms. In order to precisely define the model for computer simulation , some real functions must be chosen for these roles. The properties of the model are not very sensitive to the exact nature of these functions so long as they have the required general properties. This insensitivity to detail is illustrated in Figure 3 where place fields have been calculated using the two different + +first -layer tuning functions shown below: + +R 1 = 1 otherwise I 0 if I dx - d; I > (T + +R 1 = exp- [ ( dx - d; )2/ (]"2] (1) + +where R 1 is the first -layer unit response function , dx and dx \* are the stored and current values of a location parameter (distance from landmark X to P in the case of Figure 3) , and (T is the matching criteria + +parameter. The second-layer unit response function is + +0 i f L R 1 (x ) - 8 ~ 0 ( 2 ) + +x R2 = ~,LI R 1 (x ) - 8 otherwise + +x + +where R 2 is the second-layer unit response function , x is the set of all landmarks used for the match, and e is the threshold parameter. The outlines of the place fields in Figure 3 indicate the curves along which the function R 2 = e . While the two place fields are not identical , the outlines and locations generated by the two different first -layer matching functions are Quite similar . Since the step function and the Gaussian function used are about as different as this kind of monomodal + +440 BIOLOGICAL MECHANISMS + +FIGURE 3. The boundaries of the place fields centered at P have been computed using two different Layer 1 response functions. The location parameters used were the distances to landmarks at A, B, and C. The two Layer 1 functions used are plotted in the insert and the arrows indicate which function generates which place-field boundary. (From It A. Computational Model of Hippocampal Place Fields" by D. Zipser, 1985, Behavioral Neuroscience, 99, p. 1009. Copyright 1985 by the American Psychological + +Association. Reprinted by permission.) + +tuning function can get, the similarity in place-field shape indicates the general insensitivity of the model to the nature of these functions . While the outlines of the place fields generated are similar , the internal structure of the fields are different . The Gaussian matching function (Equation 1) gives the kind of smooth peak observed experimentally in + +place fields. + +It is clear that what has been described is not a single model but a class of computational schemata related by the way in which they use location parameters in a two-layer architecture. The individual models in the class differ in just what features are measured to serve as 23. PLACE RECOGNITION AND GOAL LOCATION 441 + +location parameters and in which response functions are used in each + +layer. + +Location Parameters + +In Figure 1, distance was used as a measure of landmark location. Any other measurable feature whose value is a function of observer location can also be used. Somewhat more formally , a location parameter is a function depending on the relative location of landmark and observer that has a single value for each point in the environment . The inverse is not true. That is, a single value of a location parameter may map to many different locations. In the examples used so far, distance has been the location parameter, but in fact, distance is probably not being used by the rats in the Kubie , Muller , and Ranck (1983) experiments. This is demonstrated in Figure 4 which shows what happens when a triangle of landmarks a , b , c , is expanded by dilation to a larger triangle a ', b ', c '. The experimental results on environmental dilation predict that the place field should increase in size and still be centered at P . However, if the remembered distances are used, there is no longer a triple intersection at P . Actually , there is no triple inter section anywhere, which implies that there will be either no place field at allor , at best, one with a greatly reduced size, just the opposite of what is actually observed. This suggests that remembered values of the absolute distance to landmarks are not being used by the rat to activate + +place-field units in the dilation experiments. + +If distance is not being used as a measure of landmark location, what is? Something is required that, like distance, defines curves in the en vironment whose intersections can be used to localize the viewer, but , unlike distance, scales properly with dilation . Among the measurable features that have these properties are the visual angle subtended by two points on a landmark and the retinal area of the landmark image. Angle and area differ from distance in several ways. Unlike distance, they cannot refer to single points but require landmarks with some finite extent. Also, unlike distance, angle and area can be determined by a single measurement. Distance requires either two measurements or knowledge of the absolute size of the landmark. Because the notion of " landmark" is somewhat arbitrary, measurements can often just as easily be made that reflect the relationship between landmarks. For example, the gap between two trees could make just as good a landmark as each of the trees themselves. Retinal area, it should be noted, is a very simple thing for a visual system to compute since after a figure-ground separation, all that is required is that the number of + +, . + +b . . + +a - . ' + +. . . . . + +c , + +- . c . + +442 BIOLOGICAL MECHANISMS + +FIGURE 4. The scene from Figure 1 characterized by landmarks at G, b, and c has been dilated by a factor of 1.5 which has relocated the same landmarks at a', b', and c'. The circles indicate the curves along which the location parameters (the distances, indicated by the dotted lines in this case) have their undilated values. These circles no longer intersect at P making it unlikely that a place-field mechanism that dilates with the scene could depend on remembered distances. (From II A Computational Model of Hippocampal Place Fields'l by D. Zipser, 1985, Behavioral Neuroscience, 99, p. 1010. Copyright + +1985 by the American Psychological Association. Reprinted by permission.) + +units in the figure be totaled. Of course, other factors must be included to explain conscious perception that corrects for apparent reti- + +nal size. + +Since location parameters, by definition , have a single value at each point in space, the properties of a particular parameter can be visualized by plotting the locus of a single value of the parameter. Examples of the curves generated in this way for distance, angle, and area are given in Figure 5. These are the curves that arise assuming the landmark is a square card that looks the same from both sides. Actually , most natural landmarks look different from the back, so that generally only the curves on one side of the landmark will playa role in place-field location. The shape of these location parameter curves will depend on + +23. PLACE RECOGNITION AND GOAL LOCATION 443 + +p + +Area = 4(2 arctan J tan (Sf 2) tan (S- A )f 2) tan S- B)f 2) tan ((S- C)f 2) where.f is the focal length~ A, B, and C, are the visual angles of the three sides of the triangle~ and S = V2 (A + B + C) . Since A, B, and C are dilation invariant, so is the retinal area of the object. (From 'I A Computational Model of Hippocampal Place Fields" by D. Zipser, 1985, Behavioral Neuroscience, 99, p. 1011. Copyright 1985 by the American + +Psychological Association. Reprinted by permission.) + +Simulated Experiments + +In order to see how well the model works, experiments of the kind used to study place fields were simulated on a computer. The simulated experimental environment , as detailed above, is shown in the computer generated display in Figure 6 (details of the simulations are given in the legend to this figure) . The outer rectangle, which represents the limit of the simulated environment , contains the landmarks (shown as straight lines). The simulation assumes that the animal has a place field centered at point P. The location of the simulated observer is systematically moved over a uniform lattice of points + +FIGURE 5. L is a landmark and P is a viewpoint . Curve 1 is a locus of all viewpoints a constant distance from the center of L . Curve 2 is a locus of all viewpoints from which a square standing vertically on L would have a constant area on a spherical retina. Curve 3 is a locus of all viewpoints where a line of length L would subtend a constant visual + +angle. The visual angle, A, subtended by a line of length a is given by: + +A = 2 arctanJ (5- b ) (5- C)/ 5 (5- a ) + +where band c are the distances from the endpoints of the line to the focal point and s = 'h (a + b + c) . Note that A is invariant to dilation by a factor d since replacing a, b, and c by do, db, and dc does not affect the value of the above equation. The area of any object can be approximated by the sum of the areas of a set of triangles which cover its + +visible surface. The retinal area of a triangle is: + +444 BIOLOGICAL MECHANISMS + +FIGURE 6. This figure shows the output from a typical simulated experiment on the screen of a Symbolics 3600 LISP machine. The experiment is initialized by first placing landmarks, (simulated square cards in this case) in the outer square. The size, position, and number of landmarks can be input explicitly as a set of numbers or determined interactively by the use of a "mouse." Once the scene is set, an initial viewpoint P, which will be the center of the place field, is chosen. Then \falues for (T and @ are picked and the simulation is started. First, the simulation program calculates the areas of the landmarks from the viewpoint P. These areas are used as the stored values of the location parameter. Then the viewpoint is systematically scanned through a raster of 145,000 points in the inner rectangle. At each of these points the retinal areas of landmarks are computed and used as the current value of the location parameters in evaluating the response of the Layer 2 unit that represents the place-field unit. A mark is placed in the inner rectangle wherever the value of the Layer 2 unit just crosses threshold. The curve generated by these marks is the border of the place field. The landmarks in this figure are quite symmetrically placed around the scene that leads to a fairly symmetrically shaped place-field border. Asymmetrically placed landmarks would produce a less symmetrical field (see Figures 7 and 8). The size and, to some degree, the shape of the place field are determined by the choice of (T and 8 . See the text and Figure 7 for more about (J" and (.). (From ,t A Computational Model of Hippocampal Place Fields" by D. Zipser, 1985, Behavioral Neuroscience, 99, p. 1012. Copyright 1985 by the American Psychological + +Association. Reprinted by permission.) + +covering the inner rectangle. The observer is limited to this inner rectangle so as to keep the landmarks distal because the model cannot deal with either proximal landmarks or the complexities of having the observer wander around in between landmarks. At each viewpoint , + +23. PLACE RECOGNITION ANDGOAL OCATION445 + +the activity of the place-field unit is computed using the model. In this, and all following simulations , the Gaussian matching function (Equation 1) and a threshold function (Equation 2) are used for the response functions of the first - and second-layer units respectively, and retinal area is the location parameter. The shape and location of place fields are visualized by plotting their boundaries. At each viewpoint scanned in the inner rectangle, information from all landmarks is used. That is, no account is taken of viewer orientation . The significance of + +this simplification will be discussed later. + +More About Landmarks + +In the experiments that originally demonstrated the dependence of place-field unit activity on distal landmarks, a variety of objects such as a fan, a white card, a buzzer, and a light , all arranged at 900 intervals around the experimental area, were used (O'Keefe & Nadel, 1979) . The only manipulation carried out on these cues was either to remove them or to interchange their locations. While this served well to demonstrate the basic phenomenon in a qualitative fashion, a more precisely defined set of landmarks and closer control over their location is required to determine the quantitative relationship between landmark configuration and place-field unit activity . At the present time not enough information is available to determine what would constitute a good, simple set of landmarks. In the computer simulations described here, planar, square landmarks of different sizes, that stand vertically at any position in the outer rectangle, are used. As viewed from above, in the computer-generated display, these square landmarks appear as straight lines. Squares were chosen because the computation of their projected retinal areas is reasonably tractable. The computation of the projected retinal area of an arbitrarily shaped object from a large number of different positions is quite complex. In all the rest of the simulations described here, the retinal area of these squares will be the location parameter used. It seems reasonable that a set of such square cards of different sizes, textures, and reflectances might well serve as adequate cues in real place-field experiments. Indeed in the Kubie , Muller , and Ranck (1983) experiments, a rectangular card played an + +important role as an environmental cue. + +Place-Field Shape and Size + +446 BIOLOGICAL MECHANISMS + +(T and 8 affect place fields is shown in Figure 7, in which (T and 8 are systematically varied while the landmarks and place-field ,center are kept fixed . The results shown in Figure 7 indicate that although these two parameters do not have identical effects on the shape and size of place fields, their effects are quite similar , particularly in the region of moderately high 8 and moderately low (T, which give realistic looking place fields. Real place-field units are probably subject to a good deal of inhibitory interaction with other hippocampal units and many other modulating influences. For this reason, the model described here is unlikely to give a very accurate picture of the shape variation of place + +fields with landmark manipulation . + +Place-Field Location + +Extensive simulations indicate that both the location, shape, and size of place fields is affected by the number, size, and location of the landmarks. The effect of landmark manipulation on the shape of place fields is relatively small and might be difficult to observe experimentally. However, the much larger effects of changing landmark location, size, or orientation on the location and size of place fields can easily be detected experimentally and will serve as the main test of the model. + +FIGURE 7. This figure was generated in the same way as Figure 6 except that rather than displaying the place-field boundary for just one set of values of (1' and 0 , a range of values was used to create a contour map of the place fields. A: (1' has been scanned while O is held at 2.4. The (T values for the different curves are: (1' 1= 0.1, (1'2= 0.25, (1')= 0.4, (1'4= 0.55, (1' 5= 0.7, (1'6= 0.85. B: (1' is fixed at 0.6 and O is scanned: 01= 3.9, + +23. PLACE RECOGNITION AND GOAL LOCATION 447 + +For example, the one hard Quantitative experimental result that we have in this area comes from the dilation experiments (Kubie et al., 1983) . Experiments similar to this were simulated using the model described here. The results of this simulation are shown in Figure 8. First , a place field centered at P was generated using landmarks A , B , and C . All the coordinates specifying the location of A , B , and C were then multiplied by 2 to give a dilation . The dilated scene was then translated back to a convenient location in the outer rectangle to + +FIGURE 8. This figure shows the result of a simulated dilation experiment. First, the landmarks A, B, and C of the indicated size were set up and the viewpoint P chosen as the place-field center. The field centered at P was generated by the simulation. Then the dilation, which increased the size of each landmark and the distance between them by a factor of two, was computed using the known coordinates of the landmarks. This enlarged scene was then shifted so that it could be put in the outer rectangle. This resulted in landmarks A', B', and C'. A place-field boundary was then computed by the simulation using the same values of the stored location parameters originally determined at P. This led to the generation of a new larger place field at a different location. When the point P was dilated and translated by the same amount as the landmark A', B', and C', it mapped to a location indicated by P'. The fact that P' occupies the same position in the new place field as P did in the original, together with the fact that the new place field is a two-fold magnification of the original, are consequences of the dilation properties of retinal area used as a location parameter. (From II A Computational Model of Hippocampal Place Fields'l by D. Zipser, 1985, Behavioral Neuroscience, 99, p. 1015. Copyright + +448 BIOLOGICAL MECHANISMS + +give landmarks A " B ', and C '. The same dilation and translation were applied to the point P itself to give the point P '. The landmarks A " B ', and C ' were used to generate a new place field using the same recorded values of the location parameters employed to generate the original place field centered at P . The new place field is centered at P ' and has the same shape but is twice the size of the original . This result demonstrates that when retinal area is used as a location parameter, the model gives the expected result for a dilation experiment . While the actual shape and size of a place field depends on model parameters, the way it dilates is the result of the inherent mathematical properties of the location parameter used - area in this case. (See the caption of Figure 5 for proof that the area has the expected dilation properties.) Other simulations in which the size or location of landmarks was changed in ways other than uniform dilation , produced large shifts in the location and size of the place fields. The finding of similar placefield position shifts accompanying corresponding landmark manipulations in real experiments serves as strong confirmation that the model described here embodies the correct rules relating landmark configura- + +tion to place-field properties. + +Scope of the Place-Field Model + +The model place-field described here is both oversimplified and incomplete, yet within its domain of applicability , it is testable by experiment. One way in which the model is incomplete is that it ignores the problem of left -right asymmetry. Early experiments that indicated that distal landmarks determined place fields also showed that interchanging the landmarks on the right and left side extinguished the location-specific activity of place-field units. This indicates that the animal has the ability to distinguish right from left , whereas the model as described is symmetrical. The ability to distinguish right from left is a relatively straightforward feature to incorporate into the model and one way of doing this is described later in this chapter in connection + +with goal-finding models. + +Another oversimplification of the place-field model is that it ignores the problem of viewer orientation . It is known from experiment that many place-field units show sensitivity to the orientation of the observer (McNaughton , Barnes, & O'Keefe, 1983) . For example, a rat running through a maze arm in one direction may excite a place-field unit at a particular location that is not excited when the rat runs back through the same location in the opposite direction . Orientation is important for goal location and a mechanism for incorporating it into a + +23. PLACE RECOGNITION AND GOAL LOCATION 449 + +Goal Location + +Knowing where you are is only worthwhile if this information can be used for some useful cognitive purpose. For example, to answer the question "How do I get home from here?", information about the location of a goal (home in this case) must be available. For the rest of this chapter, I will deal with the problem of developing mechanisms that can answer th!s question. The problem is trivial , of course, if the goal is perceivable from the current location. The problem becomes interesting only when the goal is too far away or too inconspicuous to detect. In all of what follows , it will be assumed that the observer must find the way home using a set of locally visible landmarks and that the observer has no access to absolute direction information such as "Which way is north ?" and so forth . This does not significantly reduce the generality of the problem, since the determination of an absolute direction such as north would, in general, depend on knowledge about the con- + +figuration of the local landmarks anyway. + +The unoriented place fields described above are insufficient for goal location. The reason for this is that in the absence of absolute direction information , the location of a goal must be given relative to both the location and orientation of the observer. One way to approach this issue is to incorporate orientation into the place field itself . I call an oriented place field a viewjield. Many of the place fields observed in the hippocampus are, in fact, oriented as pointed out above. That is, some hippocampus neurons fire at a particular place only when the rat is pointed in a specific direction . Orientation can be incorporated into place fields by adding some weak, topological constraint, such as classifying landmarks as being either on the right , in the center, or on the left . Distinguishing right , left , and center is a fairly straightforward task for the sensory system of any bilaterally symmetrical animal. + +In the following sections I describe two models of goal-finding . One, the distributed view-field model, uses a large number of oriented placefields, each with associated goal location information , scattered around the environment . The other model is based on a more extensive computational analysis and requires fewer units but more elaborate + +calculations. + +The Distributed View-Field Model + +The distributed view-field model for goal location is based on the network shown in Figure 9 which is used as the " cognitive map" to guide an observer to a goal. The first layer of units, called object units, VISUAL SYSTEM + +left center right + +. . . + +1: v - + +. . . + +Ig .v - 9 = 1 1 Iv - + +450 BIOLOGICAL MECHANISMS + +OBJECT UNITS + +YIEW- FIELD UNITS + +> GOAL UNITS + +MOTOR SYSTEM + +FIGURE 9. Network used in the distributed view-field model. The visual system output consists of three sets (left, center, and right) of three numbers representing an object's type, distance, and orientation relative to the observer. The output of an object unit is 0 unless its recorded type number matches its current input from the visual system. In this case, the output is the product of two Gaussian tuning functions (see Equation 1), one for distance and one for orientation. The output of the view-field units is the same kind of sum given in Equation 2. The output of the goal units is two components of a vector + +pointing to the goal each multiplied by the input from a view unit. + +is analogous in function to the Layer 1 units of the preceding placefield model shown in Figure 2. The primary difference is that the object units in Figure 9 are divided into left , center, and right groups. Object units are gated on only when the landmarks they recognize appear in the appropriate region of the visual field , i.e., left , center, or right . The view-field units in Figure 9 are analogous to the Layer 2 units in Figure 2. Together, the object units and the view-field units recognize an oriented place field , i.e., a view field , in the same general way as the corresponding units in Figure 2. However, now the output of the view-field unit also depends on orientation as well as location. Once a view-field unit for a particular place is created, information + +about the location of a goal can be associated with it . In the network shown in Figure 9, goal location is encoded in an additional unit whose output is interpreted by the motor system as the direction of the goal. To actually head to a goal from any particular location, an observer with this kind of network would first examine the landmarks in front of it , which would lead to the activation of a set of object units and then to the activation of an associated view unit . This in turn would activate a goal unit , the output of which could direct the observer to the goal. + +There are several problems to be solved before this general strategy can actually be applied to controlling the movements of an observer. First , it is impossible to have a unique ,,'iew-field unit for every place and orientation in the environment . At best, one could hope to have a rich supply of view-field units whose place fields spanned the environ ment. Another problem is that even with a large number of view-field units, it is unlikely that the observer is ever at the exact center of a place field . This means that some form of interpolation is required to compute the location of the goal from the current position of the observer. Another problem is to specify how information about the environment gets assimilated by the network in Figure 9 in the first place. Aside from the technical issues of recruiting the appropriate units and connecting them together with the desired weights, there is the conceptual problem that arises from the need to know the location of a goal at the time that its association with a particular view field is made. There is no trivial solution to this problem. One approach is to remember and constantly update the location of a particular goal as the observer moves through the environment . This active memory of goal location can then be used to establish the place-field goal relationships when new units are recruited. Once enough units have been instantiated, the territory can be thought of as familiar and it will no longer be necessary to have an active memory of the location of a goal in order to find it . This is the strategy used in the distributed view-map model described here. This approach has the drawback that it demands both processing resources and memory accuracy. These requirements could possibly be met for modest periods of time and over short distances with no distractions, but they could cause problems in more + +extended situations. + +In the distributed view-map model, the viewer has a large set of view fields scattered over the environment . Associated with each of these view fields is a vector pointed towards the goal. If the observer is in the center of one of these view fields and oriented in the optimal direction , the associated goal unit indicates the direction of the goal. However, the observer is seldom at the center of a view field so information from a set of nearby view fields must be interpreted . The first step in this process is recognition of the currently visible set of left , center, + +23. PLACE RECOGNITION AND GOAL LOCATION 451 + +452 BIOLOGICAL MECHANISMS + +and right landmarks that are used to gate the appropriate ensemble of view fields. Associated with each of these view fields is a vector pointing home. This is illustrated in Figure 10, which shows a viewer, V, oriented towards the central landmark, C , and nine view fields, each labeled In . Of course, the oriented view fields are not actually written on the ground in the environment but are encoded in the brain of the observer. Although the whole ensemble of view fields that have the same set of three landmarks will be gated on, the activity of each individual unit will depend on how closely its parameters match the current situation . The closer the viewer is to the center and orientation of any particular view field , the more active the unit representing it becomes. In the distributed view-field model, the observer interpolates the location of the goal by using a weighted average of the direction vectors of all of the active goal units. The way this weighted average is formed is that each goal unit multiplies its output vector, indicating goal location by its input from a view-field unit . The motor system then sums all of these weighted vectors and normalizes them to the sum of the activity + +FIGURE 10. A diagrammatic representation of the view-field model. G is the goal, V is the obser\rer, L, C, and R are landmarks. The positions at which view fields have been recorded by the observer are indicated by ms. Each view field consists of a line representing the orientation of the observer when the view field was recorded and an + +of all the view-field units (see Figure 9) . Thus, the goal vectors associated with close-matching view fields playa large part in the sum, since their associated units are highly active, whereas the vectors from less closely fitting view fields playa smaller role. This strategy requires the view fields to be reasonably well distributed around the environment . In order to test the model, the network of Figure 9 was used to actually control the behavior of a simulated observer moving around in a model environment . Before describing this simulation in detail, it's necessary to deal with the problem of getting environmental informa tion into view fields. Rather than building in spatial information , a procedure for assimilating it while the viewer moves around was incorporated into the model. The naive viewer was supplied with a network similar to that shown in Figure 9, but in which all object units and goal units had zero values for all their relevant parameters. At fixed time intervals, while the observer explored the environment at random, a signal is sent to recruit object and goal units. Upon receipt of this signal, the object units being recruited record the values necessary to recognize and locate the currently visible set of landmarks, while the goal unit records the location of the goal relative to the current position and orientation . The object units receive their information from the current output of the visual system, whereas the goal unit to be trained obtains its values from a working memory. Once all the available units are recruited, no more view fields can be learned and all subsequent goal-directed travel is dependent on the existing set of view fields. + +To observe the properties of the distributed view-field model, a simulated observer was developed with two motivational states, "curiosity " and "guilt ." In the curiosity state, the observer explores the environment by a random pattern of movement . In the guilt state, the observer attempts to return home using the information recorded in its network of view-field units. The assimilation of new information takes place at all times, independent of the motivational state of the observer. Thus, new information can be assimilated either during random + +exploration or during return to home. + +The actual simulation program to carry out all this is quite complex, because in addition to simulating the cognitive mapping network of Figure 10, the environment , together with some information about the observer's location and visual system, had to be modeled. This project was expedited by the availability of a general purpose parallel simulating system called P3 (Parallel Process Programmer) . The P3 system is described in more detail in a separate chapter of this book, but briefly , P3 is used to simulate networks consisting of an arbitrary number of unit processors connected together by signal lines. The complete network of interconnected units is called a P3 plan. Each unit in the plan must have a computer program, called a method, associa1ed with it that + +23. PLACE RECOGNITION AND GOAL LOCATION 453 + +updates its outputs according to some function of its current inputs and state variables . The input to units described in a P3 plan can come only from other units in the plan . That is, there is no outside world in the P3 description of a network . This means that the environment , as well as the nervous system network within the model , must be described by individual units . The simulated model can interact with the outside world in two ways . It can be initialized and observed as it functions , using facilities provided by the P3 simulation system . In addition , the method programs can communicate with the investigator through the keyboard and display using the available features of the method language . The methods can also use the file system . However , all communication between units must be via connections described in the + +P3 plan . + +A simplified view of the P3 plan used to simulate the model described here is shown in Figure 11. There is one very complex unit called the environ unit which carries out a multitude of tasks . It keeps a record of and displays for observation the current position of the viewer , the location of the goal (home in this case) , and the position of all relevant landmarks . The output of the environ unit provides the viewer -centered information necessary to activate the object units in the model . In this way , the environ unit serves as the sensory system of the viewer . Another output of the environ unit is working memory , which has the current goal location used by goal units when they are assimilating new information . The input to the environ unit comes from the mover unit which serves as the motor system for the viewer . The environ unit uses this information to update the location and the orientation of the observer . Thus , we see that the environ unit serves as the entire world outside the particular part of the brain being simu lated by the mapping network under test , that is, it constitutes the mus culature , the visual system , and the short -term memory of the observer together with the physical world outside the viewer . Obviously the method program for the environ unit is quite complex . The shaded units in Figure 11 represent the major parts of the cognitive map net works under test . These are the elements that are changed significantly when different models of the viewer 's space representation system are studied . The rest of the P3 plan can remain essentially the same, con - + +stituting a major saving in effort . + +The model and the associated methods were coded in the P3 system . An example of what the screen of the Symbolics 3600 LISP machine looks like during the progress of a simulation of the model is shown in Figure 12. Information about the state of various units , at one time cycle , is displayed in the large panel on the left . The " world display " window of the environ unit appears in the panel on the right . The behavior of the model is most easily analyzed by examination of the + +454 BIOLOGICAL MECHANISMS + +23. PLACE RECOGNITION AND GOAL LOCATION 455 + +FIGURE 11. A simplified plan of the P3 simulation of the distributed view-field model. The shaded boxes represent the part of the model that contains the specific map informa tion . The mover is actually comprised of several units that compensate for the delay between observation and resulting movement . This compensation is required because other motions may occur during this period. The symbols in the world display window of the environ unit are those used in the computer display that it drives (see Figure 12). + +world display window. The observer, marked V in the figure, is just about to reach the goal at the center, having started towards the goal at a point marked S. The path of the observer during the "guilt" state, when it is trying to go home, is characterized by evenly spaced dots. The path of the observer during the "curiosity" state is seen as a set of much more arbitrarily spaced dots. One dot is added to these paths at each cycle of the simulation. At the outer extremes of the field, the landmarks appear as rectangles. In this particular simulation, eleven landmarks were used. Al though they all look the same on the screen, + +456 BIOLOGICAL MECHANISMS + +FIGURE 12. Symbolics 3600 LISP machine display of the distributed view-field model. + +they are in fact distinguished by the viewer. The three landmarks that constitute the current view are highlighted by making them hollow rec- + +tangles slightly larger than the unviewed landmarks. + +Figure 12 represents the state of the system after 216 iterations of the simulation . Only 10 out of the pool of 100 view units have been recruited, so this is relatively early in the exploration phase. Examining the path from S to V in the world display window, shows that the viewer is able to go directly home along a moderately straight path. In + +See the text for explanation. + +general, this is the case early in a simulation , before many view fields have been recruited. The panel on the left shows the output activity of the object units, the view-field units, and the goal units. No informa tion is being displayed about the teach unit , the environ unit , the state unit , or the mover unit . Actually , the mover unit consists of a group of several units that work together to provide the appropriate motion information based on the output of the array of goal units. Some caution needs to be used in looking at a state display of this type since there is a delay of one cycle between each layer of the network . Thus, what's seen at the output of the goal units is a consequence of events occurring one cycle earlier in the view units, and two cycles earlier in the L , C , and R object units. The important point to notice here is that only two goal units show any output activity at all, and both of these have activity of the same sign. This means that at this point the movement of the viewer is being controlled by only a small set of view fields. This is consistent with the fact that the simulation is early in the + +assimilation phase. + +After the assimilation phase is over and all units have been recruited, the pattern of view fields is as shown in Figure 13. This figure was generated from the world display window of the environ unit , which has the option of showing the actual positions corresponding to the observer's store of view fields. Figure 14 shows the path of the observer attempting to get home after simulation cycle 3081 when the assimilation phase is long over. The path starts at S, and the observer, after much thrashing about, has reached point V, and not yet gotten close enough to home for the home detector to have triggered. Note that the path starts at S and continues in a relatively straight fashion, but not directly towards home. Before passing too far beyond the goal, the observer has made a sharp turn to the left and moved towards the goal on a very uncertain and constantly changing path. Then, after approaching quite close to the goal, the observer again turned, this time in a path that took it somewhat away from the goal. As we look at Figure 14 at the current cycle, the observer has been thrashing around in the general vicinity of the goal but has not been able to actually reach it . Eventually (he observer will get home, but it will take a great many cycles. This behavior is quite typical of what happens when an attempt is made to go home after alII 00 view-field units have been recruited. To the right of the world display window, the current states of the array of the view-field units and goal units are shown. These are not both from the same cycle, rather the view-field units are shown from one cycle before the goal units so that the active view-field units are the ones that determined the activity of the goal units in the lower array. Notice that a large number of view-field units are active and that a correspondingly large number of goal field units are active. However, + +23. PLACE RECOGNITION AND GOAL LOCATION 457 + +some goal units have positive output values as indicated by solid rectangles, while others have negative values as indicated by open rectangles. The reason for this is that some of the view fields are on opposite sides of the goal, which provides the observer with conflicting information about the sign of the direction of the goal. This conflicting information is the cause of the viewer's inability to get to the goal in a smooth fashion. This conflict situation only causes a serious problem when the observer is quite close to the goal because when it is further away, information from view fields on the opposite side of the goal contribute very little to the weighted sum of goal vectors. Although the problem is inherent in the model, by adjusting various parameters that control the density of view-field placement and the strength of their interaction , it is possible to reduce the size of the region of ambiguity to the point where it is small compared to the area in which the goal is directly + +perceivable. + +The distributed view-field model simulated above has the virtue of simplicity , since the viewer is not required to carry out any complex 23. PLACE RECOGNITION AND GOAL LOCATION 459 + +FIGURE 14. Behavior of observer, V, in the distributed view-field model with all units recruited. The state of the view-field units, V, on the 3080th cycle and of the goal units on the next cycle are shown on the left . The reason for the complex path followed by + +the observer is given in the text . + +computations to navigate. Its algorithm for assimilating new informa tion is extremely unsophisticated, operating only on the basis of time . One price paid for this simplicity is the need for a large number of units to store assimilated information . One way in which this algorithm might be improved is to assimilate new information only when the present information is inadequate. This inadequacy is easy to detect since the unit that sums the activity of all the view-field units can also be used to determine when there is insufficient information available. The way this is done is to take advantage of the fact that when the sum of the activities of the view-field units is high, the observer is in familiar terri tory ~ when this sum is low, the viewer is in unfamiliar territory where it would be wise to assimilate some new information . This would do away with redundant view fields that are generated by the clock method. On balance, the distributed view-field model meets the criterion of biological plausibility since it is based on the concept of place-field units that are known to exist. These units may well playa role in goal navigation since the hippocampus, where they are located, + +In this section, a navigation scheme called the 13 -coefficient model (f3 model for short) is described that overcomes some of the drawbacks of the distributed view-field model described previously. Rather than requiring many separate view fields , the f> model needs to record infor mation about a set of landmarks and a goal only once. This recorded information can then be used to locate the goal anywhere the landmarks are visible. The {3 model also indicates goal location unambiguously, so the problem of sign that caused confusion near the goal in the view-field model is eliminated . Since only one recording is required, the actual number of units needed for the {3 model can be much less than for the view-field model. The {3 model can do away with the need for an updated memory of goal location whenever the set of landmarks to be used are visible from the goal itself since in these cases the recording can be made at the goal. If additional recordings of new sets of landmarks are made at locations where both a new and an old set are visible , the rteed for an updatable memory of goal location can be elim inated because the old set of landmarks can be used to establish the goal location for the new set. The price paid for these good features is an increase in computational complexity together with a loss of an immediately obvious link to current neurobiological data. Both of these drawbacks could be more apparent than real. More about this after the + +{3 model has been examined in detail. + +To understand the f3 model, it 's necessary to delve a little more deeply into the computational aspects of representing location. The problem we wish to solve is illustrated in Figure 15. An observer located at position V records the position of the three landmarks L , C , and R together with the location of the goal G . At some later time , the same observer is imagined to be at point V' at which the locations of the landmarks L , C , and R can be determined. The observer's problem is to locate the goal G , which cannot be seen from the position V', using the information recorded at point V. It can be shown that there exist three constants, {3L, {3c, and f>R, which depend only on the + +is required for navigation to unperceived goals. The magnitude of the ambiguity problem that this model has in the vicinity of the goal can probably be reduced to a point where it is not any more troublesome than the uncertainties about goal location that would arise from other + +sources of error in any model. + +The 13 -Coefficient Model + +23. PLACE RECOGNITION ANDGOAL OCATION461 + +FIGURE 15 . The observers at Vand at V ' can both locate the landmarks L , C , and R in their viewer -centered reference frames but only at V can the goal G be perceived . The + +problem is to solve for T so that the observer at V ' can locate G. + +relative locations of L , C , Rand G , and have the following nice + +properties : + +x 'G = .BLX L + .BCX'c + {3RX 'R y 'G = .BLy 'L + {3cY 'c + {3Ry 'R + +1 = .BR + .Bc + .Bc + +where x 'G , Y 'G, XL , Y L , x 'c , Y IC' and x 'R , y 'R are the coordinates of G , L , C , and R in the reference frame of the observer at V '. (For a derivation of the /3 s see Appendix A .) Since the /3 s depend only on the relative locations of the landmarks and the goal and not on the location of the observer , they can be computed at any place where the location of the landmarks and the goal are known , that is, at V in our example . Because the {3s are constant , it is only necessary to have a single record of their values to locate the goal from anywhere the landmarks can be viewed . The significance of this set of {3 equations relating the location of G to the location of the landmarks is that the coordinates of the goal can be obtained as a linear combination of the current values of the landmark coordinates and the remembered /3. This means that neural like elements can perform the computations if their synaptic weights + +correspond to the values of {3 . + +A network using the {3 -coefficient concept and consisting of three units is shown in Figure 16. The job of the context gate unit is to determine that the current left , center , and right landmarks are the same as were used to originally program the /3 units . When the context unit recognizes the appropriate set of landmarks , it gates on the {3 units . 462 BIOLOGICAL MECHANISMS + +FIGURE 16. A pair of units that compute the x and y componef1ts of goal location using the method of f3 -coefficients. In the units, the f3 s are implemented as weights or lines coming from a sensory system that can measure the current values of the coordinates of three landmarks, L, C, and R. Each of the triangular {3 units is gated by a context gate unit (oval shape) which has an output of 0 unless the desired goal is G and the current landmarks are L, C, and R in the appropriate configuration, in which case the output of the gate unit goes to 1. If the value of w = 1 also, the correct value of the goal coordi- + +nates appears at the output of the {3 units. + +These units perform the appropriate linear summation operations and their output represents the coordinates of the goal. One of the sets of units in Figure 16 is required for every combination of three landmarks with a goal. The output of the appropriately gated {3 units is an exact indication of the location of the goal from any point in the environ ment. This means that there will be no problem approaching the goal from any angle and there will be no confusion from information coming from the opposite side of the goal as there was in the previous example. Note that only one set of {3 units and a context unit is required for each goal-landmark combination as opposed to many units for each combination in the distributed view-field model described above. If information about the configuration of the environment is recorded at the goal itself , as may be the case for the rat on the platform in cloudy water, no working memory of goal location is required. + +XL + +X C ( }: X'. 6.) w . 1 1 1 + +X 'R + +{ GAlACAR } CONTEXT GATE + +y ' L + +y ' + +C ( }: y~ Ii . ) w . 1 1 1 + +YR + +23. PLACE RECOGNITION AND GOAL LOCATION 463 + +An important issue in the f3 model is how the f3s are initially computed and recorded. Since we can get no hints from neurobiology, a wide range of possibilities are available. For example, we might imagine that the f3 s are computed locally by each f3 unit when it is recruited. Such a computation could take the form of a learning rule that adjusted the value of the f3s in accordance with an error signal generated by comparing the current output of a f3 unit with the correct output, i.e., the coordinates of the goal that, of course, must be known when the f3s are programmed. Another approach is to have a single, central /3 computer that calculates the appropriate values of f3 and transmits them to the newly recruited /3 units for recording. In the absence of hard data, it is a matter of taste which of these one consid- + +ers to be more biologically plausible. + +There is a completely different way to go about programming the f3 units that does not involve setting the values of /3 at all. In this approach it is assumed that there is a pre-existing pool of /3 units each with a set of fixed f3 values. It is then the values of the strengths of connections between a context unit and the f3 units in the pool that are set to produce the desired result. The idea is that the output of each f3 unit is weighted by the value of the weight, w, which connects it to a context unit . If these w s are chosen correctly, the sum of the weighted outputs of all the {3 units in the pool gives the appropriate goal coordinates. In this system a set of w s rather than a set of {3 units have to be learned. This could have some advantages, for example, the number of f3 units in the pool is fixed and can be much smaller than the number of context units. This means that fewer units are required to instantiate a w programming version of the model than a {3 programming version.. Another advantage of the w version is that setting the w values is synonymous with recruiting the f3 units so that recruitment and programming are accomplished as a single operation rather than as two separate ones. As with the computation of {3, the determination of the w s can be local to the {3 units or carried out by a central w computer. In the simulation used here to test the /3 model, a version of w programming that had a pool consisting of only four /3 units with a central w computer was used. The way this system worked to program the {3 units with the correct connection strengths to the context units is + +explained in Appendix B. + +A simulation analogous to that used to test the view-field model was employed to evaluate the /3 -coefficient scheme. Only those parts of the P3 plan that determine the representation of the spatial map were changed. The plan of this model is shown in Figure 17. The context units are very simple recognizers. Their output is 0 unless the particular set of left , center, and right landmarks to which they are sensitive is currently being viewed, in which case their output goes to 1. The teach + +ENVIRON UNIT + +world disploy window e - , . Y1eVer home landmark + +goa1 viewer 1 t - visual " t " oca10n t pos110n sys em memory updote + +T + +I mover unit + +~ . . + +T .~ + +.. tonte :)Ct S t 8 .t e .. . unIt + +units + +~~ ~.. 1 + +~ ~ + +te8 ~h ... 6~rr -8Y.~ + +un1t .. unlt :S ~ L - :~ comp + +: unit . . T + +464 BIOLOGICAL MECHANISMS + +FIGURE 17. A simplified diagram of the P3 pian used to simulate an observer with a {3 array map of its environment. The shaded units constitute the map and they are the only + +significant difference between this pian and the one shown in Figure 11. + +unit supplies a signal to the context units and the {3 units to recruit them when new contexts are assimilated. The teach unit requires modification since it no longer makes sense to teach at uniform time intervals. The teach unit produces a pulse only when no context units + +are active, that is, when the current view is unfamiliar . + +The performance of this model is superb. The viewer always goes exactly home at the appropriate time . The results of a typical simulation episode are shown in Figure 18. Notice the straight paths heading directly towards the center of the goal. The number of context units required in this model is roughly equal to the number of landmarks, plus a few extra to take care of cases where a landmark can be the central object with different sets of flanking objects. The loops in the paths, found near the environment window borders in Figure 18, are + +23. PLACE RECOGNITION AND GOAL LOCATION 465 + +FIGURE 18. The performance of the {3 array model simulated with P3 and shown on + +the display of a Symbolics 3600 LISP machine. See text for details. + +due to that fact that the state unit can detect when the observer leaves the area with landmarks. When this happens, the context unit instructs the move unit to turn the observer left until a set of three landmarks become visible. This feature is only included to keep the observer on the screen and has no significance for the network being tested. Even when the number of context units is insufficient to assimilate all possible views of the landmarks, the observer manages to find its way home. It simply searches until it finds an appropriate view for which it has assimilated information and then proceeds to use it to head home. Behavior degrades quite gracefully in this case and the number of landmarks has to exceed the number of context units by a great deal before + +serious difficulties are encountered. + +Aside from being able to accomplish the task in an efficient and accurate fashion, the f3 -coefficient network has some other attractive features. It is, for example, able to explain the behavior of rats in the cloudy water experiment , since while on the platform , the rat can assimilate the appropriate f3-related information for groups of room cues. The distributed view-field model described earlier has a much more difficult time with the cloudy water paradigm. It would require that the rat jump off the platform and swim around the tank to pick up + +a large set of view-field information . The problems that arose in the view-field scheme near the goal would be particularly annoying to the rat in this case since there are no visual cues to serve in goal detection, which become apparent as the rat approaches the submerged platform . + +The three models that have been presented here differ from each other in the degree to which they encompass known experimental observations. The first model of place fields is based so strongly on neurophysiological data that its predictions are immediately amenable to testing. The second model, which adds a goal vector to place fields, is more speculative in the sense that it hypothesizes an explicit output role for the place-field neurons. It seems very likely that these neurons do playa role in navigation since removal of the hippocampus, which contains them, cripples navigational ability (Morris et al., 1982) . Both of these models clearly meet the criterion of biological plausibility since they attempt to explain observable data in terms of neural-like models. The {3 model is of a different sort. It attempts to explain the observed data by proposing a novel representational and computational scheme. This scheme is biologically plausible in the sense that it is implementable with neural-like elements operating in a highly parallel fashion. However, the {3 model can draw neither support or opposition from current experimental data. Indeed, this is just what we would expect from a theory that proposes a mechanism that is not completely intuitive but derives from a formal analysis of the problem domain. This is to be expected since it is very unlikely that experimentalists would find data relevant to the {3 model, even if it is correct, until they are specifically looking for it . This, of course, is exactly what theory is supposed to do, ask Questions which would not be asked in the normal + +course of experimentation . + +466 BIOLOGICAL MECHANISMS + +Conclusion + +23. PLACE RECOGNITION AND GOAL LOCATION 467 + +APPENDIX A + +, + +XL XL X = Xc X ' = X ' C XR X R + +Then, T = X- I X I where X- I is the inverse of X that exists as long + +x 'G = xG T + +or substituting for T , + +x 'G = xGX - l X '. (1) + +Equation 1 points out an interesting fact. Namely, the first two terms on the right-hand side are independent of viewer location and can be computed once- at the initial siting of the landmarks. This + +as L , C, and R are distinct and not collinear. + +Now we have T defined in terms of the coordinates of the three landmarks recorded at V and the coordinates of the same landmarks observed from V'. Since we are using homogeneous coordinates, the + +third coordinate of all objects can be taken as 1. + +The observer at V' is now able to compute T . Applying T to the recorded coordinates of the goal G will give the coordinates of G in the + +observer's current reference frame. That is, + +To see where the f3 s come from , we solve for the transformation T that maps all points in the V system to the V ' system and then divide the expression for T into a constant part that depends on landmark and goal configuration and a variable part that depends on observer loca tion . T must be found using only information about the recorded and current location of the landmarks L , C , and R . Once T has been obtained , it can be applied to the coordinates of the goal G in the V system to map them into the coordinates of G in the V ' system . If information about three landmarks is used in two dimensions , homo geneous coordinates can be employed and T can be a linear transforma tion (Foley & VanDam , 1983 ) . Having T linear will greatly simplify the nature of the computations necessary to use the transformation and will make the networks that carry it out much more biologically plausi - + +ble . The derivation of T is shown below : + +Let Xi = (Xi Yi Zi) be the homogeneous coordinates of the i th , , object . (In the case of Figure 15 , i = L , C , R , or G .) Then T is + +defined so that X 'i = Xi T . To solve for T let + +468 BIOLOGICAL MECHANISMS + +Define: + +{3 = (f3L ,f3C,f3R) = XGX- l, + +then : + +x 'G = f3LX L + f3cx'c + f3Rx'R y 'G = !3LY L + !3cY'c + {3Ry'R + +1 = !3L + !3c + !3R' + +computation , in fact, yields three constants. Once determined, these three constants are sufficient to locate the goal G in any reference frame in which the locations of the landmarks L , C , and R can be determined. I call these constants /3 -coefficients and their definition is + +given below: + +470 BIOLOGICAL MECHANISMS + +In this chapter I discuss the state dependence of learning rate using the development of ocular dominance in visual cortex (Area 17) as a model system. Several qualities make this system an excellent example of neural plasticity. Foremost and most obvious of these qualities is the clear and abundant evidence of plasticity in Area 17. Secondly, the susceptibility of ocular dominance properties to a very broad range of manipulations has been extensively analyzed and the circuitry connecting the retina to visual cortex is better understood than any other neural system of comparable complexity . Furthermore , for the purposes of this analysis, the system can be characterized in terms of two-dimensional "ocularity states," which serve to illustrate many of the mathematical concepts in this book with a relatively simple + +representation. + +An account of early learning is presented in this chapter that can be described at several different levels. While the underlying concepts are actually quite simple, they are also in their essence mathematical and are thus expressed in mathematical language. To help make the presentation more understandable to all readers, I have tried to ela- + +borate most of the points in more intuitive terms. + +The aim of this chapter is to suggest that the high plasticity frequently observed in the early stages of a learning process may reflect, at least in part, an expected reduction in the modifiability of neuronal + +CHAPTER 24 + +PLASTICITY AND LEARNING + +S tate - Dependent Factors + +Influencing Neural Plasticity : + +A Partial Account of the Critical Period + +P. W. MUNRO + +Focus on single-unit learning . Unlike most of the chapters in this book, which explore the behavior of whole networks, the present chapter is focused at the level of the single neuron and its afferent synapses. This does not reflect a difference in belief about the appropriate level of analysis, but rather it is grounded in the simple pragmatic observation that at the single-unit level, a fairly good account of the relevant phenomena can be given. Put another way, the critical period is not seen as an emergent property of an interactive network in this approach, but as a phenomenon that Inight be traceable to the + +effects of prior experience on the behavior of individual units. + +Learning rate as a factor in PDP models. Notions of learning rate (in general) and the critical period (in particular) bear on models for learning by parallel distributed processing systems and have not been extensively studied by theorists apart from specific applications. A popular approach to selecting a learning rate is the pragmatic strategy in which one chooses a step size that yields a good solution in an acceptable time frame~ however, rate properties of adaptive systems deserve more attention, as they may provide an important link between theoretical models and empirical data. Several existing theories of plasticity in cortex are concerned with the sequence of learning and ignore the rate of learning, either ignoring the critical period or making ad hoc assumptions to account for it . Conversely, in and of themselves, the scope of the ideas to be presented in this chapter is limited to rate and do not include an explicit rule for synaptic modification . Since it lacks such an explicit learning rule (that could be used to predict final states) , it must + +response characteristics as their synaptic connections are strengthened as a result of experience. This contrasts with previously proposed alternative possibilities that this phenomenon is either maturational or that + +it is centrally gated by global modulatory signals. + +The organization of the chapter is as follows: The present section introduces the reader to the subject and the approach of the chapter. The following section describes a general developmental phenomenon called the critical period during which neural networks are observed to be relatively plastic, then focuses on how plasticity is manifested during the development of ocular dominance in visual cortex, both during and after the critical period. In the third section, the reader is introduced to the notion of state-dependent plasticity, a concept that is then applied to give an account of the time course of ocular dominance plasticity. In the fourth section, these ideas are compared with experimental data. In the final section, the ramifications of state-dependent plasticity are discussed in relation to experimental data, existing theories, and their + +predi cti ve power. + +24. NEURAL PLASTICITY473 + +THE CRITICAL PERIOD + +be emphasized that the present partial account is not sufficiently complete to constitute either a theory or a model of cortical plasticity. + +Two cautionary notes regarding terminology. First , it should be noted that although the terms plasticity and learning are used interchangeably in this chapter, there is a difference in nuance between them. Plasticity carries with it a sense of physical modifiability but not necessarily toward adaptation, whereas learning has a flavor of storing information from the environment with less emphasis on the neural (synaptic) substrate. Both, however, refer to adaptation, an environment -driven metamorphosis that enables a system to generate responses appropriate to that environment . Second, one should be particularly careful in interpreting the term state (especially as in "state of the system") here. In many of the network models, the state describes the instantaneous activation levels of all the units. Here, the same term refers to the connectivity values of the afferents to a unit . In the context of a network model, the activation state is generally changing very rapidly as the assembly of units settles in response to a particular stimulus according to information implicit in the connectivity state, which modifies more slowly under the influence of some self- + +organizing adaptive principle . + +It is well established that plasticity varies over the course of onto genetic development . During so - called critical or sensitive periods of plasticity , certain perceptual ! mechanisms have been found to be more susceptible to adaptive modification by the stimulus environment , whereas the susceptibility is low or nonexistent at other times . Sensi tive periods have been demonstrated in many systems , such as song learning in birds ( Konishi , 1978 ) , socialization in dogs ( Scott , 1962 , 1968 ) , and phoneme discrimination in humans ( Eimas , 1978 ; Miyuwaki et al ., 1975 ) . However , the phenomenon has been most extensively analyzed with respect to the development of binocular interaction in + +mammalian ( particularly cat and monkey ) visual cortex . + +It is certainly not expected that all of these examples will necessarily have the same physiological substrate , nor would it be correct to + +1 Weak evidence exists for sensitive periods at " higher " (i.e., more cognitive ) levels of mental function . The most compelling results are based on findings that children recover from trauma -induced aphasia more rapidly and completely than adults (who rarely , if + +474 BIOLOGICAL MECHANISMS + +assume that any behavioral observation of sensitive periods in learning should be reflected by sensitive periods in neurophysiological measures of single-unit plasticity. However the converse inference, namely, that plasticity in single units is sufficient (but not necessary) for macroscopic learning phenomena, seems valid. Therefore the reader should keep in mind that the framework to be presented below for neuronal plasticity is not restricted to visual cortex, but might be applicable much + +more generally. + +Ocular Dominance and its Susceptibility to the Environment + +Interest in visual system plasticity and the generation of relevant data enjoy a symbiotic relationship that has led to the production of a great deal of both. A brief overview is given in this section of a part of this data that is based on measuring changes in the ocular dominance (OD) statistics of a large sample of neurons (from about 50 to over 1,000, depending on the experiment) . This method, devised by Wiesel and Hubel (1963) , consists of assigning each unit to one of seven ocular dominance classes based on the relative values of its optimal responses to monocular inputs from both eyes. Since there is an innate statistical bias for a neuron to respond preferentially to the eye on the opposite side of the head, the ocular dominance classes are ordered according to the influence on the neuron of the ipsilateral eye relative to the contralateral eye. A Class 1 neuron responds exclusively to input from the eye contralateral to it , a Class 7 neuron responds only to the ipsilateral eye, a Class 4 neuron gives roughly equal responses to each eye, and neurons in the other classes are responsive to both eyes with + +corresponding degrees of preference. + +The stimulus environment can be crudely controlled by suturing shut neither , either, or both of the eyelids. The resulting paradigms are respectively called normal rearing (NR) , monocular deprivation (MD ) , and binocular deprivation (BD) . These can be combined into rearing schedules such as reverse suture (RS) in which a period of MD is fol lowed by opening the closed eye and suturing shut the previously open eye, and alternating monocular occlusion (AM ) which consists of + +several such reversals. + +Several results can be interpreted in terms of an age-defined critical period, though the boundaries of the critical period seem to vary somewhat with the particular details of the experimental procedure. Hubel and Wiesel (1970b) found that MD drives all neurons to strongly prefer the open eye, provided the animal is still sufficiently young- neuronal sensitivity to MD seems to peak at about 4 weeks and disappears by about 3 months (see Figure 1) . More recently, other researchers + +(Cynader, Timney , & Mitchell , 1980) report an ocular dominance shift in kittens subjected to monocular deprivation for 3 months after rearing under normal conditions from birth to 5 months of age. Because it is such a striking effect, requiring only 24 hours or less during the height of the critical period (Olson & Freeman, 1975; Peck & Blakemore, 1975) , the ocular dominance shift under monocular deprivation is often + +used as a test for assessing cortical plasticity. + +With the exception of BD, other rearing schedules distort the relatively uniform ocular dominance histogram (ODH ) of normal kittens and cats. Binocular deprivation generally leads to a histogram with all OD classes represented, as in newborn and normally reared cats. However, unlike normally reared cats, newborn and BD cats have neuronal responses described as "sluggish" and "unpredictable" with ill -defined receptive fields (Cynader, Berman, & Hein , 1976; Wiesel & Hubel, 1965) . In another rearing paradigm, artificial strabismus (AS) , the eyes receive noncorrelated inputs. Both surgical (severing some of the extraocular muscles) and optical (attaching eyeglasses with prisms) techniques have been used to simulate strabismus. Strabismic kittens exhibit V-shaped ocular dominance histograms, i.e., the neurons become highly monocular, but do not show an overall preference for one eye over the other. While AS yields a sensitivity time course that closely matches MD (Hubel & Wiesel, 1965) , the same cannot be said + +of all procedures. + +The results reviewed thus far appear consistent with a fairly strict maturational hypothesis for cortical sensitivity . However, evidence against this view comes from a very interesting result that has been obtained by Cynader et al. (1976) who have raised binocularly deprived + +24. NEURAL PASTICITY 475 + +FIGURE 1. The ocular dominance histogram (DOH) shift associated with monocular deprivation (MD). The classic result of Hubel and Wiesel is shown in this figure adapted from their 1970 paper. The DDH is shown for a kitten deprived of vision in one eye from Day 10 to Day 37. Units that cannot be driven through either eye are classified as visually unresponsive (VU) and are represented here by an unfilled bar. (The DOH of a + +normally reared [NR] kitten is nearly symmetric.) + +476 BIOLOGICAL MECHANISMS + +kittens throughout and beyond the period associated with plasticity (up to 10 months) and then opened just one eye. They observed a strong shift in ocular dominance after a 3-month period of monocular experience. Cynader (1983) extended this result by raising the kittens in the dark for up to 2 years, followed by 9 to 18 months of monocular experience. This phenomenon, described at the end of this section, provides the most compelling evidence for a link between a neuron's + +connectivity state and the plasticity of the state. + +Plasticity-Modulating Processes + +The hypothesis that plasticity is strictly age-related falls down in the face of another kind of evidence as well ~ it has been found that plasticity can be modulated by a variety of chemical and/ or physical processes (see Table 1) . One might suppose that the critical period is explicitly controlled by one or more of these processes (i .e., it is part of the "design" of the system) . However, as will be seen, this is not the only alternative hypothesis. For now, consider the following evidence concerning the roles of a variety of modulators of plasticity, focusing on + +norepinephrine in particular. + +Norepinephrine . Catecholamines attracted attention as potential modulators of neuronal plasticity during the 1960s (see, for example, Crow, 1968) . The catecholamine norepinephrine (NE) is pervasively distributed throughout the central nervous system from a localized region in the brain stem, the locus coeruleus (LC) ~ thus the anatomy of the norepinephrine system makes it an attractive candidate for a global + +TABLE 1 + +PROCESSES THAT MODULATE CORTICAL PASTICITY + +References + +e]ectrica] Singer (1979) + +Experimental Stimulus Modality + +> pharmacological mechanical + +Natural Site of Modulation + +Kasamatsu & Pettigrew (1979) + +Freeman & Bonds ( 1979) Buisseret et at. (1978) + +Locus Coeruleus + +Proprioception (Extraocular) + +Reticular Formation + +24. NEURAL PASTICITY 477 + +modulator of plasticity . The LC / NE system has been implicated in maze-learning behavior of rats by Anlezark , Crow , and Greenway ( 1973) , who showed that bilateral LC lesions impaired learning and resulted in decreased cortical concentrations of NE . Neurophysiological evidence that NE modulates neuronal plasticity has been found recently in rat hippocampus by Hopkins and Johnston ( 1984) and earlier in cat + +visual cortex by Kasamatsu , Pettigrew , and Ary ( 1979) . + +In a series of experiments (see Kasamatsu , 1983, for a comprehen sive review ) , Kasamatsu and his colleagues showed that when applied to visual cortex , 6-hydroxydopamine (6-0HDA ) , a neurotoxin that locally destroys LC projections , prevents the ocular dominance shift in MD kittens . They went on to show that plasticity could be restored with direct injections of norepinephrine . Kasamatsu et ale ( 1979) also attempted to induce plasticity in normally reared adult cats via NE injections . This experiment yielded an asymmetric V -shaped histogram biased toward the open eye. That is, NE was shown to produce observ able plasticity in a system that otherwise would not demonstrate + +environmentally driven modification . + +Attempts to replicate and extend these results have had mixed out comes . Consequently , the role played by NE in modulating plasticity is very controversial at the present time . While NE certainly has some effect on the susceptibility of neurons to their stimulus environments , the situation is not as simple as one might think on the basis of Kasamatsu 's initial reports . A study by Bear et ale ( 1983) exemplifies the mixed nature of the results and provides a partial explanation . They obtained catecholamine depletion using two different techniques to administer 6-0HDA . One group of kittens received 6-0HDA using the osmotic mini pump procedure of Kasamatsu et ale ( 1979) and the other group received injections intraperitoneally (into the abdomen ) before the third postnatal day . Plasticity was disrupted only in the former case~ however , subsequent biochemical analysis (HPLC ) revealed that the depletion was more effective in the latter group . The results were quite surprising : While the former group replicated the earlier result , the latter group showed no observable disruption of plasticity even though pharmacological analysis indicated that the NE + +depletion was more severe . 2 + +Other examples of induced plasticity . Stimulation of at least three different sites has been shown to enhance plasticity in visual cortex of adult cats. Mechanical stimulation of the extraocular muscles generates + +2 By way of explanation, Bear et al. suggest hat if the LC mechanism is disrupted sufficiently early, a compensatory mechanism may be activated. Such a mechanism, they + +478 BIOLOGICAL MECHANISMS + +a proprioceptive (feedback) signal which has been shown to be suffi cient for plasticity with respect to both orientation selectivity (Buisseret, Gary-Bobo, & Imbert , 1978) and ocular dominance (Freeman & Bonds, 1979) . Plasticity-gating capabilities as revealed by electrical stimulation techniques have also been reported for the reticular formation (Singer, 1979~ Singer & Rauschecker, 1982) and the medial nuclei of the + +thalamus (Singer, 1982~ Singer & Rauschecker, 1982) . + +The Effect of the Environment on the Critical Period + +The conjecture that NE is a global modulator of neural plasticity does not necessarily imply that it governs the sensitive period. In this chapter an alternative conjecture is entertained~ namely, that the potential for change possessed by a neuronal state is a function of that state. (It may perhaps be influenced by global factors as well.) The following result, mentioned earlier, of Cynader et al. (1976) provides supporting evidence. Kittens were raised in total darkness for periods as long as a year, after which rearing continued under the MD paradigm. Complete shifts to the open eye were found in each case, suggesting that visual input influences not only the response properties of the visual system by way of some plasticity mechanism, but the functioning of the mechanism itself . Ramachandran and Kupperman (in press) have taken these results further to show that the ocular dominance shift under MD is not the only plasticity phenomenon to be delayed (or prolonged) by dark rearing. They have not only obtained ocular dominance shifts in dark-reared animals, but they have observed dominance reversal upon reverse suture in animals at ages up to 6 and 6.5 months. The details of how much and what kind of experience are necessary and/ or sufficient to delay the critical period are far from clear at this time . Mower, Christen, and Caplan (1983) report that 6 hours of binocular experience at 6 weeks eliminates the plasticity-preserving effect of dark rearing~ but Ramachandran and Kupperman (in press) have shown that kittens raised normally for a full month and subsequently reared in + +darkness show plasticity in Area 17 for at least 6 months. + +THE OCULARITY STATE AND ITS EFFECT ON + +The theoretical formulation in this chapter is intended to serve primarily as a partial explanation of the sensitive period for the development of ocular dominance in visual cortex. The central concept is that + +PLASTICITY + +retino-cortical connectivi ties are weaker in the newborn and are hence more susceptible to change than the stronger synaptic connectivities that develop as a result of experience. Assuming that the ocular dominance class depends on the relative synaptic weights (the direction of the synapse vector) , this means that the effect on the ODH of a given change in connectivity is greater when the absolute values of the weights (the magnitude of the synapse vector) are relatively small. This notion can be supported by a very diverse variety of learning rules (i.e., synaptic modification rules) , and so the specific formulae used here are secondary to the major theme. They are included for illustrative + +purposes. + +Let the response r of an ideal neuron be given by a continuous nondecreasing function (T of its net depolarization x , and let x in turn be a weighted sum of the neuron's stimulus components S; ; i.e., the units + +have a semilinear (see Chapter 2) activation function : + +24. NEURAL PLASTICITY 479 + +The Model Neuron + +[#lW; (t )S; (t) I + +(1) + +r (t) (T (x (t ) ) (T + +The weights Wi are collectively designated by the weight vector w , and the stimulus elements Si are collectively designated by the stimulus vector s. Since the weights are associated with synaptic connectivities , w is called the synaptic state. One can clearly see that under this assumption the neuron's response characteristics, as measured by a set of test stimuli , are determined by w . Adaptive learning (i.e., plasticity) is a dynamic process in which the synaptic state is driven by the stimulus environment such that the response characteristics with respect to the same environment approach some optimizing criterion . Several theoreticians (see Chapter 2) have analyzed the adaptive capabilities of various networks (idealized anatomical configurations) that self-organize according to rules (idealized physiological processes, usually at the scale of the synapse) that express the time rate of change of synapse weight + +Wi as a function v of local variables: + +dw.I + +-"dt = v (r (t ) , Wi ( t), Si (t ) , . . . ). (2) + +480 BIOLOGICAL MECHANISMS + +incorporated. Global modulators such as NE can also be factored into + +the rule by appropriate independent functions . + +However, as will be seen, no such ad hoc description is necessary. Rather, for certain initial conditions on w , there exist modification rules from which plasticity decreases naturally under the influence of + +patterned input . + +The Ocularity Plane + +4 Sanderson and his colleagues found that only about 9% of geniculate neurons in the cat could be excited from the nonpreferred eye, but that only 18% are truly monocular, the remaining majority having inhibitory fields in the nondominant eye. In monkey the LGN seems to maintain a higher degree of segregation~ Marrocco and McClurkin (1979) + +report that 87% of neurons in macaque LGN are strictly monocularly driven . + +5 This is actually a special case of a more general formulation in which the ocularity state W is given by the net depolarizations of the neuron by arbitrary (fixed) monocular stimuli to each eye. Namely, this is the special case in which the test stimuli are uniform activations of all afferents. The typical laboratory procedure is quite different . In a given neuron the optimal stimulus is found for each eye. Then the two corresponding responses are compared in order to determine the ocular dominance class. Hence, the test stimuli are state dependent. A more detailed theory (such as Bienenstock, Cooper, & Munro , 1982) would be required to simulate this experimental method . However, the + +Figure 2 is a schematic view of the retino - geniculo -cortical pathway , the most direct Gust two synapses ) from the ganglion cells of the retina to the visual cortex . Note that the individual components of the stimulus vectors incident to a cortical cell are actually the activities of neurons in the lateral geniculate nucleus responding to retinal signals . 3 Despite findings that some LON cells respond binocularly ( Sanderson , Bishop , & Darien - Smith , 1971 ) , 4 the components Si are idealized as being strictly monocular . Let C (I ) be the set of all afferents to a given neuron from LON neurons responsive to the contralateral ( ipsilateral ) eye . Let each neuron ' s ocularity state W :=: ( W C , WI ) be given by its net input connectivities from each eye , and let the ocularity plane be the + +associated state space : 5 + +Wc == L Wi WI == LWio ( 3 ) + +iEC iEI + +3 The retina is not the only neural structure that projects to the LG N . Other sources of LGN input include the reticular complex and feedback from Layer 6 of visual cortex + +(Gilbert & Kelly , 1975) . + +Optic Chi8sm + +> Right lGN + +CORTEX ~ If + +1111111111 + +Shad ] ng ~ y- + +Right visual field information Left visual fjeld information Tectocortical pathway + +[ ~~~~= =J + +FIGURE 2. Circuitry of the visual system. Of the information pathways from retina to visual cortex, the retino-geniculo-cortical pathway, shown here in gray and white, is the most direct and the most well understood. The optic nerves approach the optic chiasm in two bundles, one associated with each eye. Here, they are separated and recombined into two groups according to whether they originate from the left or right side of the retina- i.e., they are grouped as a function of which "side" of the world they look at, such that information from the left side of the visual field is generally directed to the right side of the brain and vice versa. Other pathways from retina to cortex exist, for example, the tectocortical pathway: retina --.. superior colliculus --.. pulvinar nucleus --.. + +cortex (shown here in black). + +Figure 3 depicts these assumptions with respect to a neuron in visual cortex. Macy, Ohzawa, and Freeman (1982) define a continuous measure of neuronal ocular preference, the ocular dominance index (001 ) + +483 + +mapped + +(5) + +24. NEURAL PLASTICITY + +(T (WI) z (W) == + +Using this index, the ocular dominance categories can be mapped onto regions of the ocularity plane (Figure 4) . Two prominent aspects of the diagram are determined by the particular function (T. These are: (a) a threshold connectivity W () for both components of W below which no action potentials are elicited by the corresponding test stimuli and (b) the curvature of the iso-ocularity contours. (These are straight + +radial lines if - a z - a z - - - p = < ~ E = aw-;; Vc +-a-w;- VI = '\7z.V + +where V : = < dW / dt > E is the average "velocity " of the state in the W -plane and Vz is a vector pointing in the direction of steepest change in z with magnitude equal to that change (the components of Vz are simply the partial derivatives of z with respect to W c and WI) . The plasticity can thus be represented as the inner (dot) product between two vectors: the velocity of the state and the gradient of the 001 . The + +Given z , a scalar measure of the neuronal state, the plasticity p associated with a particular state W can be defined for any stimulus environment E . The plasticity is the time rate of change in z under the + +influence of E : + +A2. As it is molded under the influence of a structured stimulus environment , the pattern of synaptic weights is refined and + +reinforced with experience, and thus tends to grow. + +A3. The rate of change of synaptic weights may decrease or remain invariant , with changes in the magnitude of the weight vector~ in fact, the rate of change of synaptic weight may even grow as the magnitude of the weight vector grows, as long as it grows + +less rapidly than the weight vector itself . + +24. NEURAL PLASTICITY 485 + +(7) ~ = L ~ ~ ~ = L ~ (T/(Xi)sj. a Wj i art dxl a Wj i ar + +inner product of two vectors can be expressed as the product of their magnitudes and the angle between them (see Chapter 9) . These are + +considered separately below . + +Dependence on the magnitudes of \7z and V . Whether the loss of plasticity associated with the critical period is a function of neuronal state ultimately depends on the behavior of the product between the magnitudes of these two vectors for large magnitudes of W . Since ' V'z I decreases with IWI (I \7z I goes ~ s IWI- 1 on average) , the issue reduces to the relationship between IV I and IW I. This is exactly the issue addressed in Assum.E.tion A3 above, since IW I is the magnitude of the weight vector and IV I is its speed in the ocularity plane. In keeping with the conventional Hebb -like approach (i.e., the change in each synaptic weight depends only on the activities of the corresponding presynaptic and postsynaptic units ) , consider the indirect effect of W on V mediated by the neuronal activity rather than any explicit dependence of V on the weights . It now becomes very important to consider the form of the function (T relating the response r to the quantity x (see Equation 1) . This function is sometimes called a squashing function since it tends to saturate for high values of x (as shown , for example , by Chapman , 1966) because of the upper limit on the neuronal firing rate (i.e., the absolute refractory period ) . Hence , if V depends on r + +(not x ) , it will (like r ) level off as x increases . + +It would be sensible for V to decrease with increasing x . The argu ment supporting this possibility is based teleologically on the assumption that each unit optimizes some function of its stimulus en vironment according to a gradient descent process. In Chapter 8, it is shown that optimization of least square error in a multilayered system leads to an explicit rule for learning in which each synapse modifies according to a function separable into three factors : the presynaptic (afferent ) activity , an error signal propagated from higher levels , and the derivative of the squashing function of the postsynaptic unit . More generally , one can show that the derivative (T '(x ) is a factor regardless of the function being optimized , whether it be a least square error (as in Chapter 8) ~ selectivity for orientation , direction , or spatial frequency (as in many cells in visual cortex ) ~ or some other quantity . This is demonstrated quite easily . Let Q be the optimized function , a quantity measured over the set of response values ri evoked from a given unit by a set of test stimuli Si . If ri =: (T (Xi ) (where ..Xi =: w .s i ) , then the gradient V Q breaks down + +as follows : + +486 BIOLOGICAL MECHANISMS + +a ( + +x + +B + +x + +FIGURE 5. A squashing function and its first derivative . A: An easily computed function that incorporates the salient features (namely, a threshold, (), and monotonic approach to an asymptote, ..u) of neuronal response characteristics is given by the function that is defined by a- (x ) == ..u(x - 0)/ (.x-l/ 2+ X - 20) for x > 0 and vanishes for x < 0, where x 1/2 is the value of x at which the function attains half its maximum value (i.e., a- (x 1/ 2) = ..u/ 2) . B: The derivative (T '(x ) of this particular function is shown for x > (). The decay in the derivative as x increases can be implicated in a decay in learning rate for systems that follow gradient descent. This effect is potentially quite substantial as + +JL + +e + +a ' + +e + +With increasing exposure to the world, units may become highly selective so that they come to respond at intermediate levels where in cat visual cortex vation (Blakemore, (1978) reports the + +FIGURE 7. Trajectories corresponding to reverse suture. Two examples are shown. One path (that closer to the origin) starts from a weaker, and hence presumably less mature state. This state travels from Class 1 to 7 without entering the intermediate + +classes. + +7 Evidence supporting the existence of s by sudden removal of the open eye after a Hawken , & Mark , 1982~ Kratz , Spear , & + +;uch input has been found l period of monocular depri Smith, 1976), but Drgger + +NEURAL PLASTICITY + +24. NEURAL PASTICITY 493 + +WI + +Wc + +FIGURE 10. Ocular dominance and responsivity as polar-like coordinates. Accurate measures of W may be difficult to come by. One can only calculate rough approximations on the basis of the corresponding responses. Some estimates might be made on the basis of existing data by using ocular dominance as an indication of the "angle" and + +responsivity as a rough measure of the II magnitude" of W . + +the concept of critical period far beyond the original work by Hubel and Wiesel . Of the many differences between these two approaches , there is one which is fundamental to the nature of learning by biological systems - namely , that while the rate of learning in biological information -processing networks can be made subject to extrinsic fac tors , it may well be influenced by intrinsic properties of the learning mechanism , the information patterns as they are learned , and interac - + +tions between them . + +It has been established in this chapter that a theory of plasticity need not presuppose the existence of a global modulator to account for the critical period . What role , then , does the norepinephrine system play ? After all , it has been well demonstrated , both experimentally and on + +teleological grounds , that it can modulate plasticity . + +The conjecture that the LC releases NE as part of an attentional mechanism 8 seems to resolve the issue . Rather than acting as a clock controlling the developmental sequence of plasticity , the activity of NE probably fluctuates on a finer time scale . Under this assumption , non recognition of a stimulus might trigger a " novelty alarm " in the form of an LC / NE plasticity signal . Thus , another factor in the critical period + +8 The notion that NE is a medium for externally gated plasticity originated in the early 1960s based on studies of the reward system (Poschel & Ninteman , 1963). Whether and how catecholamines are implicated in reward and reinforcement remains controversial. + +. + +,..." + +1IIIIIIIi ~ + +~ . ~ ' . + +11111111 + +- . . II + +may be the loss of novelty brought about by experience~ this suggests an explicit experience-dependent mechanism for plasticity- one that would amplify the effect described in this chapter and would therefore + +be difficult to analyze independently. + +Grossberg (1980) offers a comprehensive description of the critical period that incorporates all of the mechanisms in Table 1. This is quite different from the approach taken in this chapter, in which I have attempted to separate the critical period from these other factors. Given the broad disparity between these two points of view, an experiment to discriminate between them should not be difficult to design. For example, what are the states of these mechanisms in cats reared in + +darkness for several months from birth ? + +494 BIOLOGICAL MECHANISMS + +D ISCUSSI ON + +State Dependence and Existing Modification Rules + +Assumptions AI , A2 , and A3 can be incorporated into many dynami cal models of plasticity in cortex , as can hypotheses based on global modulation ( see next subsection ) . Consider three varieties of mathematical formulations , characterized by the factors determining the magnitudes of the vectors representing the final equilibrium states ( see + +Figure 11 ) : + +. Case 1 . . Throughout modification , the magnitudes of the neural states are explicitly constrained ; for example , the sum of the com ponents is held constant ( e . g . , Perez , Glass , & Shlaer , 1975 ~ von der Malsburg , 1973 ~ Chapter 5 ) . Unfortunately , explicit con - + +straints on magnitude are not consistent with the assumption + +that the state vectors grow during learning . Certain models of this kind employ such constraints because of a tendency for the weights to grow without limit ~ for these models , only an upper bound is really needed and the inherent tendency for growth may provide the necessary reinforcement . However , some models do require that strict magnitude constraints be imposed ( e . g . , those with even less stable dynamical equations ) . While it may not be impossible to adapt these models to Assumptions + +AI , A2 , and A3 , the solution is not likely an elegant one ; for example , a requirement that the magnitude be conserved at a fixed value M might be altered such that M increases accord ing to some complex ad hoc rule up to some maximum value + +Case 3.. There is no minimum radius such as that in the previous case; equilibrium states exist arbitrarily close to the origin (e.g., Munro , 1984) . A dynamical system of this variety presents a particularly hostile context for Assumptions A l - A3. There is no reason to expect the weights to grow no matter how small the initial weights are. This highlights the fundamental depen- + +dence of the assumptions on scale. + +496 BIOLOGICAL MECHANISMS + +. + +Global Modulators as Dynamical Variables + +-.: ~ ~ + +dWi dt + +The first of these possibilities is consistent with the data from both Cynader's and Kasamatsu's labs. That is, a global modulatory signal may control the speed (magnitude of the velocity vector) of the neuronal state as it is driven by the environment , but the distance between ocular dominance classes depends on the state. Thus the observed plasticity is a function of both the synaptic state and global factors- e.g., norepinephrine. Destruction of the catecholamine terminals in some region by 6-0HDA might then bring synaptic modification to a com- + +plete halt. + +Secondary global modulatory action via influence of the presynaptic activity is not a very promising approach since it would distort the pattern of afferent activity . This effect would be disastrous except in the trivial case, namely, if it were equivalent to a uniform scale factor. Of course. the :::trtinn would then be formally identical to the third + +Global modulation of cortical plasticity , whether it is mediated by the locus coeruleus , proprioception , the brain stem , or the thalamus , can be integrated into a synaptic modification formula in any of several ways . Let us assume a general modification rule that is separable into a presynaptically dependent function t / I and a postsynaptically dependent + +function <1> : + +dwj ( 8 ) + +- " dt = t / 1 ( Sj ) ( r ) . + +Some simple conjectures as to the role of a modulatory signal ( a ) are that it may influence plasticity in a direct multiplicative fashion or by + +exerting an effect on the presynaptic or postsynaptic activities : + +a t / I ( Si ) ( r ) ( 9 ) + +t / I ( Sj ( a ( r ) . t / I ( Sj ) ( r ( a + +24. NEURAL PASTICITY 497 + +conjecture for the role of a , in which it influences the postsynaptic activity (assuming that r depends monotonically on a variable that is + +linear in Sj, like x in Equation 1) . + +Norepinephrine is known to influence responsivity in neurons of the visual cortex. Kasamatsu and Heggelund (1982) found that this influ ence was not easily characterized~ for example, overall responsiveness would increase, decrease, or not change with roughly equal probability . However, they did notice certain correlations with respect to cell type. Videen, Daw, and Rader (1984) also found that the relationship between NE and neuronal response is quite complicated. Thus the third of the above functions may have some support, though the exact form of the dependence of a on NE concentration has not been + +specified. + +Predictions + +Theoretical neuroscientists are often criticized (often with good reason) for neglecting their duty to suggest experiments that test their theories. They counter with accusations, which also are valid, to the effect that the bulk of theoretical work passes through the literature unnoticed by the experimental community and that many, if not most, predictions remain untested. Arguments assigning blame aside, the interaction of theory and experiment in neuroscience is not in a healthy state. In an effort to improve the situation , this section outlines some crude designs that may lead to laboratory verification of the ideas + +covered in this chapter. + +A very informative experiment would be to analyze the time course of the loss of plasticity along the path of information flow (Layer 4c Ys. other layers in the monkey) after a period of dark rearing. By comparing this result with the observation that Layer 4c loses plasticity for ocular dominance earlier than other layers in monkey Area 17 (Blakemore, Garey, & Vital -Durand , 1978~ LeVay, Wiesel, & Hubel, 1980~ Vital -Durand , Garey, & Blakemore, 1978) , it should be possible to separate the maturational from the environmental influences on the critical period. A strict interpretation of the analysis in this chapter predicts that the entire process should be postponed and hence the results after dark rearing should not substantially differ from the established results. The outcome of the experiment could conceivably be mixed indicating that both environmental / informational and maturational factors exert influence . It seems reasonable, indeed quite likely , that at lower levels (such as the thalamus) , maturational effects on the + +498 BIOLOGICAL MECHANISMS + +Reinstating plasticity after patterned rearing . Cynader ' s experi ments have demonstrated that the visual system is capable of "waiting " in a plastic state for patterned input . This result may be indicative of a more general relationship between responsivity and plasticity . 9 One idea that grows out of the present approach is that plasticity may in fact be reduced in part because cells in the mature animal rarely respond in the intermediate range , where the derivative of the cell ' s response with respect to its net input is relatively large (see Figure 5B) . If , as suggested earlier , synaptic modification depends on this derivative , then cells that are responding vigorously will not modify their connections . Thus these ideas predict that if the cells could be made to respond less vigorously , they could thereby become more plastic , provided the new response level were in the appropriate range . Of course , this is not the only factor that determines plasticity ~ the size of the weight vector plays a very important role in the extent to which a change of a fixed size will alter the ODI . That is, of the two quantities '\7z and (T '(x ) that are candidates for the loss of plasticity , only the latter can be manipulated in the adult . Hence , the observed plasticity resulting from a reduction of response magnitude in adult animals should be weaker than the + +natural plasticity of younger animals . + +The following outline sketches an experimental paradigm for testing the relationship between responsivity and plasticity : One method to reduce responsivity without introducing the potential pitfalls of phar macological techniques would be to apply diffusive contact lenses . Degrading the contrast of the stimuli has the further property of reduc ing orientation selectivity and hence simulates this aspect of kittenhood as well . This has the advantage of further simulating properties of the young animal and the disadvantage of confounding orientation selectivity and neuronal responsivity as factors in neural plasticity . Once the lenses have been calibrated with respect to neuronal responsivity , many different rearing paradigms should be tried since various factors may induce differential effects across different paradigms . Differences in morphological development (at both geniculate and cortical levels ) are, for example , typically observed for different kinds of rearing ~ it may therefore prove advantageous to study the effects of manipulating the environments of normally reared animals since they have not suffered + +9 Cynader plays down the generality of this relationship, citing his observation that neuronal responsivity reaches adult levels before the peak of the critical period for animals raised in patterned environments. However, it should be noted that synaptic weights can continue to grow even after adult levels of responsivity are observed. This will naturally be the case in units whose activation saturates according to the general types of activation + +The ideas which have been described with respect to oculardominance plasticity in visual cortex are abstracted in this section and considered as they might apply to higher (more cognitive) levels of cortex. In general, it seems plausible to assume that the important infor mational content of a stimulus pattern in cortex depends upon the relative values of its components, which define radially oriented regions of the state space, since nearly every level of neural processing shows evidence of lateral inhibition , a known mechanism for pattern normalization . The absolute magnitude of the stimulus loses its relevance in this case and its informational content is reduced by one degree of freedom to the direction alone. Gati and Tversky (1982) refer to the magnitude and direction of a vector stimulus as its qualitative and quantitative aspects, respectively. One can clearly see that in this case the assumptions AI , A2, and A3 may apply under these circumstances. According to this distinction , the plasticity of a self-organizing process is expected to exhibit state dependence as a function of the quantitative aspect of the state across a qualitative measure on the stimulus environment . Small assemblies or modules of such units can be made to evolve to arbitrary regions of the input space (as in Reilly , Cooper, & Elbaum, + +1982) , which can be thought of as categories. + +24. NEURAL PLASTICITY 499 + +the potentially irreversible and possibly plasticity-limiting damage that is + +associated with deprived rearing. + +Regardless of the experimental technique, a clear demonstration that links weak neuronal responsivity to increased plasticity promises to both provide evidence that neuronal response characteristics evolve such that they follow a gradient descent with respect to some environment related variable and lend strong support to the notion that plasticity is + +state dependent. + +BEYOND VISUAL CORTEX + +Stages of Processing + +Environmentally driven sequential development. The state dependence of plasticity has interesting implications for a hierarchically organized system. Consider an organizational scheme in which infor mation passes through a sequence of several neural assemblies, each + +responsible for some stage of processing.1o Assume that synaptic connectivities are initially weak throughout the entire system. Each stage lies in a state of weak connectivity and high plasticity until it receives sufficient exposure to some pattern set. At the onset of exposure to patterned input (e.g., eye-opening in kittens) , only the input assemblies receive strong signals. The earliest stages in the system are therefore the first to lose plasticity, and so increasingly longer sensitive periods may be expected for the development of higher cognitive functions . This consequence of the ocularity plane framework is consistent with data from visual cortex of both cat and monkey. Daw and Wyatt (1976) found evidence that the sensitive period for direction-selective cells is earlier, both in its onset and offset, than the sensitive period for ocular dominance. While these may not represent different stages of processing, the experiment clearly supports the notion of a link + +between plasticity and the nature of the stimulus features. + +In monkey (and in cat as well) , the LGN projection to Area 17 terminates most predominantly in Layer 4c (Hubel & Wiesel, 1972) ~ this layer therefore receives the earliest, most "raw" input to cortex. Considerable evidence, both physiological (Blakemore et al., 1978) and morphological (Vital -Durand et al., 1978) indicates that in monkey visual cortex, plasticity is diminished in this layer earlier than in the other layers. These findings have been replicated by LeVay et al. (1980) , who attribute the effect to maturational factors rather than + +implicit aspects of plasticity. + +Based on developmental data from the rat somatosensory system, Durham and T. A . Woolsey (1984) have formulated a "sequential instruction hypothesis for sensory pathway pattern development" (p. 445) . In spite of their conjecture that "a given station might 'instruct ' the next more central one" (p. 425) , they stick to a more traditional interpretation of their data: " . . . critical periods are linked to developmental periods since they coincide with times during which axons are normally innervating their targets and are segregating" (p. 446) . It is not clear therefore whether the instruction to which they refer is exogenous (i.e., sensory information ) or endogenous (e.g., + +genetically precoded chemical transmission) . + +Another factor in considering the developmental aspects of different levels of the system is the structure of the pattern environments presented to each stage. As successive levels self-organize, the representation of the world becomes more symbolic. During its ascent + +10 The visual system seems to be organized in such a fashion . However , the informa tion flow is not strictly serial , rather it seems to be directed along " functional streams " (Van Essen & Maunsell , 1983) , which have mixed hierarchical / parallel attributes . + +24. NEURAL PLASTICITY501 + +This observation pertains to plasticity in that as stimulus sets become more discrete, and perhaps more orthogonal, their constituents are better separated~ hence learning by feature-detecting units is much more rapid. So it is conceivable that for such systems, the equilibrium points may not be so far from the origin~ thus, these neurons may enjoy extended or indefinite sensitive periods! This, of course is consistent with our experience~ people learn to recognize patterns quite rapidly (relative to the hours or days required for neurons to become orientation selective, for example) and do not generally lose that + +ability . + +SUMMARY + +In this chapter I have proposed a factor that may account for the high rate of learning observed in the early stages of many learning processes. This factor of state dependence may in fact be the principal component responsible for the critical period~ it emerges from three basic assumptions regarding the mathematical relationships between synaptic connectivity values and their time derivatives. The notion of state-dependent learning rate has been discussed here in the context of the observed susceptibility of ocular dominance characteristics to environmental manipulations. This approach suggests an account for several specific observations in visual cortex and also suggests further experimental + +tests of the relationship between ocularity state and plasticity . + +On a broader level, it is hoped that this chapter will contribute to greater interaction between theory and experiment in this field . Toward this end, analytical tools such as the ocularity plane may prove useful both for making experimental data more accessible to theoretical analysis and for examining and describing aspects of the mathematical + +through the system, information is continually recoded in a manner such that the stimulus sets become more discrete. Shepard and + +Podgorny (1975) make this point with the following example: + +Whereas we can continuously shift a color (for example, blue) in brightness, hue, and saturation until it becomes as similar as we wish to any other color (for example, green) , we cannot continuously deform a word 'blue' to another word 'green' without passing through intermediate configurations that are + +not words at all. (pp. 189-190) + +Over the past three years , several individuals were very generous with their time and energy to apply their knowledge and insight to the issues raised in this chapter . These include Leon Cooper , Michael Paradiso , and Alan Saul of Brown University ~ Paul Heggelund of the University of Oslo ~ V . S. Ramachandran of UCSO ~ and several members of the POP research group at the UCSO Institute for Cogni tive Science , in particular , David Rumelhart , Paul Smolensky , and especially Jay McClelland . This work has been supported by United States Office of Naval Research Contract NOOO14- 81 - K -O136 , the Norwegian Council for Science and the Humanities (N A VF ) , the System Development Foundation , and grant PHS MH - 14268- 11 from the National Institute of Mental Health to the Center for Human Informa - + +tion Processing at the University of California , San Diego . + +502 BIOLOGICAL MECHANISMS + +ACKNOWLEDGMENTS + +Amnesia and + +Distributed Memory + +CHAPTER 25 + +J. L. McCLELLAND and D. E. RUMELHART + +In several chapters in this book, we have argued for distributed models of learning and memory . In most of these cases, we have considered primarily psychological and computational reasons to prefer distributed mo--~ls. In this chapter, we ask, can distributed models shed any light on the biological basis of memory ? One possible answer would be "no" - we could fall back on the claim that distributed models are abstract descriptions, not concrete descriptions of the physiology of memory. Indeed, many of the specific distributed models we have considered in this book are somewhat "unphysiological" in several of their details. But the general idea of distributed memory (at least, within localized regions of the brain, as discussed in Chapter 3) does seem sufficiently consistent with what we know about the brain that the hypothesis that memory is physiologically distributed seems worth + +considering. + +In this chapter, we consider this hypothesis in light of the phenomenon of bitemporal amnesia- the deficit in memory that is produced by a bilateral insult to the medial temporal lobes of the brain. Bitemporal amnesia is interesting from the point of view of distributed models because two distinct aspects of the phenomenon seem to suggest very different things about the biological plausibility of distributed + +models. + +One prominent aspect of bitemporal amnesia is that it produces a retrograde amnesia that is temporally graded. After the precipitating insult , the individual is unable to remember recent events, but memory + +504 BIOLOGICAL MECHANISMS + +for remote information appears to be intact. If there is recovery, as there is in many cases of bitemporal amnesia, much of the recent inf or- + +mation that had been lost will return . + +These aspects of amnesia seem to contradict the most basic assumptions of a distributed , superpositional model of memory. These models hold that all memories, old and new, are stored in the same set of connections. If this is so, why is it that an amnesic insult selectively disturbs the newer memories? And why is it that the memories that at first seemed to be lost can later be retrieved? The phenomenon seems to beg for an interpretation in which what is lost is access to that part of the memory store in which recent memories are held, rather than one in which all memories are superimposed in the same set of connections. On the other hand, another prominent aspect of bitemporal amnesia seems to be highly consistent with a distributed model. Bitemporal amnesia produces a profound anterograde amnesia, as well as a retrograde deficit . That is, after the amnesic insult there may be a profound deficit in the ability to acquire new information . This is particularly true when amnesics are tested for their ability to recall or recognize specific individual events to which they have been exposed since onset of the amnesia. However, the amnesic deficit is not so profound , even in the severest cases, that the patient is unable to learn from repeated experience. For example, H. M ., an extremely profound amnesic, is quite aware of his deficit , presumably as a result of repeatedly having been confronted with it . Milner (1966) reports that he often greets people by apologizing for not recognizing them, giving his memory deficit as his excuse. He remembers that he cannot remember, even though he cannot remember any particular occasion when he failed to + +remember. + +This aspect of amnesia is quite naturally and directly accounted for by distributed models. We need only assume that the amnesic insult has resulted in a reduction in the size of the changes that can be made to connection strengths in response to any given event. Smaller changes will result in very weak traces of each individual episode or event, but, over repeated trials, what is common to a number of + +experiences will be gradually learned. + +In summary, we appear to be faced by a paradoxical situation . One prominent aspect of bitemporal amnesia appears to argue against distributed models, while another appears to argue in favor of them. + +In this chapter, we confront this paradox. First , we consider in more detail many of the basic aspects of retrograde amnesia. Then, we propose a model that appears to be capable of accounting for these facts within the context of a distributed model of memory. Several simulations are presented illustrating how the model accounts for various aspects of the empirical data on bitemporal amnesia, including the + +The anterograde and retrograde amnesias produced by the insult appear to be correlated in extent. While there are some reports of dissociation of these two aspects of amnesia, it is well established in cases of amnesia due to electroconvulsive therapy that anterograde and retrograde amnesia are correlated in severity ~ both develop gradually through repeated bouts of electro- + +convulsive therapy. + +25. AMNESIA505 + +Basic Aspects of Amnesia + +The term bitemporal amnesia was introduced by Squire (1982) to refer to the syndrome that is produced by a number of different kinds of insults that affect the medial portions of the temporal lobes in both hemispheres of the brain. The syndrome may be produced by bilateral electroconvulsive therapy (still widely in use as a treatment for severe depression), bilateral removal of the medial portions of the temporal lobes (as in patient H. M.) , head trauma, or in several other ways. The syndrome is marked by the following characteristics (see Squire, 1982, + +for a more detailed discussion): + +. + +. + +The retrograde amnesia consists of an inability to give evidence of access to previous experiences within a graded temporal window extending back over an extended period of time prior to the amnesic insult . The size of the window varies with the severity of the amnesia, and good evidence places it at up to three year's duration based on careful experimental tests. + +. + +temporally graded nature of retrograde amnesia and the ability to extract what is common from a set of related experiences. In a final section of the chapter, we consider some recent evidence suggesting that for certain kinds of tasks, amnesics show absolutely no deficits. + +> The anterograde amnesia consists of a deficit in the acquisition of new knowledge accessible to verbal report or other explicit indications that the subject is aware of any particular prior experience~ somewhat more controversial, it also consists of a more rapid loss of information once it has been acquired to a level equal to normal levels of acquisition through repeated + +exposure. + +506 BIOLOGICAL MECHANISMS + +. + +A Resolution to the Paradox + +Most strikingly , memories that appear to be lost after an amnesic insult are often later recovered. As the ability to acquire new memories returns, so does the ability to remember old ones that had previously been lost. The recovery is gradual, and it is as if the temporal window of retrograde amnesia shrinks. There is generally a residual, permanent amnesia for events surrounding the insult that caused the amnesia, extend- + +ing variously from minutes to days from the event. + +As we have already noted , the temporally graded nature of the retro grade aspect of bitemporal amnesia appears to suggest that recent memories are stored separately from older ones . However , it is possi ble to account for this aspect of the phenomenon in the context of a distributed model if we make the following assumptions . First , we assume that each processing experience results in chemical / structural change in a large number of connections in which many other traces are also stored , but that each new change undergoes a gradual consolidation process , as well as a natural decay or return to the prechange state . Thus , the changes resulting from a particular experience are widely dis tributed at one level of analysis , but at a very fine grain , within each individual connection , each change in its efficacy has a separate consoli dation history . 1 Second , we assume that consolidation has two effects on the residual part of the change : (a) It makes it less susceptible to decay ~ and (b) it makes it less susceptible to disruption . These assump tions can explain not only the findings on the temporally graded nature of retrograde amnesia , but also the fact that memory appears to decay + +more rapidly at first and later decays more slowly . + +So far this explanation simply takes existing consolidation accounts of the amnesic syndrome (e.g ., Milner , 1966 ) and stipulates that the changes are occurring in synapses that they share with other changes occurring at other points in time . However , we need to go beyond this account to explain two of the important characteristics of the bitem poral amnesic syndrome . First , the hypothesis as laid out so far does + +1 When we speak of connections between units, even if we think of those units as neurons, we still prefer to use the term connection somewhat abstractly~ in particular, we do not wish to identify the connection between two units as a single synapse. Two neurons may have a number of different physical synapses. The total strength of these synapses + +not explain recovery~ second, it does not explain the coupling of + +anterograde and retrograde amnesia. + +To capture these two important aspects of the syndrome, we propose that there exists a factor we call 'Y (gamma) that is depleted by insult to the medial temporal lobes. Gamma serves two functions in our model: (a) it is necessary for consolidation~ without 'Y, new memory traces do not consolidate~ and (b) it is necessary for expression~ without 'Y, recent changes in the connection between two units do not alter the efficacy of the connection~ they are just ineffectual addenda, rather than effective pieces of new machinery. Implicit in these assumptions is a third key point that 'Y is only necessary during consolidation. Fully + +consolidated memories no longer need it for expression. + +25. AMNESIA 507 + +Some Hypothetical Neurochemistry + +To make these ideas concrete, we have formulated the following hypothetical account of the neurochemistry of synaptic change. While the account is somewhat oversimplified , it is basically consistent with present knowledge of the neurochemistry of synaptic transmission, though it should be said that there are a number of other ways in which connection strengths could be modulated besides the one we suggest here (for an introductory discussion of current understanding of synaptic function and synaptic modification , see Kandel & Schwartz, 1981) . The account goes as follows . The change to the connection from one unit to another involves adding new receptors to the postsynaptic membrane (the one on the input unit ) (see Figure 1) . We assume that both + +h + +Dendrite . J + +R- + +receptors + +FIGURE 1. A connection between two units, as we conceptualize it in the amnesia model. Note that both positive and negative changes involve addition of new receptors. + +508 BIOLOGICAL MECHANISMS + +positive and negative changes involve the addition of receptors; in both cases, there must be new structure to consolidate for the model to work properly. In the figure , we have drawn the connection between two units as though it occurred at a single synapse and was not mediated by interneurons , though neither of these assumptions is excluded by the + +quantitative structure of the model. 2 + +A cartoon of one of the receptors is shown in Figure 2. Receptors are, of course, known to be the physical structures whereby neurotransmitters released by the presynaptic neuron influence the potential of the postsynaptic neuron. To be functional , though, our hypothetical receptors must be clamped in place at each of several 'Y -binding sites by molecules of 'Y - this is the aspect of the model that is the most speculative. The probability that a site is bound depends, in turn , on the + +receptor + +, gamma + +~ I + +Post - synaptic membrane + +FIGURE 2. A cartoon of a receptor , showing its location in the postsynaptic membrane and illustrating the role of the transmitter substance , and of the hypothetical substance y , + +which acts to bind the receptor into the membrane . + +2 As pointed out in Chapter 20, real neurons are generally thought to have either exci tatoryor inhibitory connections but not both . Our model could be brought into line with this idea if we assumed that negative (inhibitory ) connections between two units actually occurred at excitatory synapses onto inhibitory interneurons , rather than on direct con nections between two neurons . Connections onto these inhibitory interneurons would have to be trained , of course , using something like the generalized delta rule (Chapter 8) . This revision of our assumptions would increase the complexity of the model but would not change its basic properties : therefore we have retained the less realistic assumption that positive and negative increments can be stored in the same connections . + +25. AMNESIA 509 + +A Quantitative Formulation of the Model + +Let us now formalize these assumptions in a quantitative model. We assume that time is broken up into a number of discrete ticks. In the simulations each tick represents about an hour of real time . On each tick , an unconsolidated site is bound by 'Y with a probability p , given by the law of mass action (this law governs a large number of chemical and + +biochemical processes) : + +y . + +p = l - y + +concentration of y in the environment of the synapse. In this model, consolidation amounts to the " hardening" or fixation of the 'Y -binding sites, while they are occupied by a molecule of y . Thus, consolidation can only occur at bound sites. Consolidation is a process like the setting of glue, but it is thought to be probabilistic and all-or-none at each site + +rather than continuous. + +As we have already seen, 'Y is essential for consolidation. In addition , we assume that it is necessary for the receptor to function . Once a site is consolidated, however, 'Y is irrelevant to it , just as a clamp is irrelevant once a glue-joint is set. Thus, unconsolidated sites depend + +on 'Y, but consolidated ones do not. + +On this view, bitemporal amnesia simply amounts to taking away the clamps. Old, fully consolidated synaptic changes no longer require them, and new ones cannot function without them and will decay without becoming consolidated. But what of memories in an intermedi ate stage of consolidation? Here, we assume the consolidation process has gone far enough so that the structures will not break up rapidly without 'Y, but that it has not gone so far that they actually function effectively without it . When 'Y returns, after a period for recovery, they may still be there, so they will be able to function again and even + +continue to consolidate. + +This equation has the property that at high concentrations of y (much greater than 1) , all unconsolidated sites will be bound, but at low concentrations (less than about .2) , the probability of being bound is + +roughly linear with y . + +Now, in each tick , an unconsolidated site may become consolidated or "fixed " with some probability f , but only if it is bound. Thus, the + +510 BIOLOGICAL MECHANISMS + +For a receptor to be functional at a particular tick , all its sites must be either consolidated or bound with ' Y . Each unconsolidated site is assumed to be independent of the others , so the probability that recep - + +tor i will be active , Pa ( receptor ; ) , is just + +Pa ( receptori ) = pu + +where u is simply the number of unconsolidated sites . + +Finally , receptors may be lost from the postsynaptic membrane . Each site contributes multiplicatively to the probability that the receptor will be lost . That is , the probability that receptor i will be lost is simply the product of the susceptibilities for each site . The susceptibility of consolidated sites , c , is assumed to be small enough so that for com pletely consolidated receptors the probability of loss is very very small per tick ~ though over the course of years these small probabilities even tually add up . The susceptibility of unconsolidated sites , u , is rela tively large . For any given receptor , some number c of its sites are consolidated at any given time and u sites are not . The probability of + +receptor loss per tick , PI ( receptorj ) simply becomes + +PI ( receptori ) = ( OC ) c ( OU ) U . + +Relation to Other Accounts of Amnesia + +Most attempts to account for temporally graded retrograde amnesia quite naturally involve some form of consolidation hypothesis , and our model is no exception to this . However , other accounts either leave the nature of the consolidation process unspecified ( e . g . , Milner , 1966 ) or give it some special status . For Wickelgren ( 1979 ) , who has the most concretely specified account of retrograde amnesia , memory trace formation involves a " chunking " or unitization process whereby each memory trace is organized under its own superordinate or " chunk " unit . A number of other authors have proposed accounts with a simi - + +lar flavor ( e . g . , Squire , N . J . Cohen , & Nadel , 1984 ) . + +In keeping with the view that our model can be implemented in a distributed memory system , our model of consolidation does not involve anything like chunking of a memory trace under a single superordinate unit . Instead , it simply involves the fixation of memory traces in a time - dependent fashion , dependent only on a single , global + +generally have not imagined that the hippocampus is the actual site of memory storage, for on that view, it would be difficult to explain why retrograde amnesia is temporally graded, unless only recent memories are thought to be stored there. But the hippocampus is often thought to playa very important role in memory trace formation . To Wickel gren, for example, the hippocampus is the organ of unitization - it is the units in the hippocampus that bind the pieces of a memory trace together into chunks. In our model, we imagine that the primary role of the hippocampus in memory formation is to produce and distribute 'Y to the actual memory storage sites. This does not mean that we believe that this is the only function of the hippocampus. An organ as complex as the hippocampus may well play important information processing roles. However, as we shall see, this role is sufficient to provide Quite + +a close account of a number of aspects of the amnesic syndrome. + +The primary goal of the simulations was to demonstrate that, with the simple assumptions given above, we could account for the main aspects of the coupled phenomena of anterograde and retrograde amnesia, using a single set of values for all of the parameters of the model, only allowing y to vary with the assumed amnesic state of the subject. Since the phenomena range over a wide range of time scales (hours or even minutes to years) , this is by no means a trivial matter. Rather than embedding the assumptions about amnesia in a full -scale distributed model, we have simply computed, from the above assumptions, what the residual fraction (or residual functional fraction ) of the memory trace would be at various times after the learning event, under various conditions. The assumption here, basically, is that each memory trace is made up of a large number of receptors distributed widely over a large number of connections. The fraction of the total that remains and is functional at any particular time gives the "strength" of the memory trace. To relate the results of these simulations to data, it is sufficient to assume that the size of the residual functional fraction of a memory trace is monotonically related to accuracy of memory task + +performance. + +Of course, memory task performance, and indeed the effective residual strength of a memory trace, does not depend only on the hypotheti cal biochemical processes we are discussing here. For one thing , there is interference: New memory traces acquired between a learning event and test can change connection strengths in such as way as to actually reverse some or all of the changes that were made at the time of the + +25. AMNESIA 511 + +Simulations + +original encoding event, producing what were classically known as retroactive interference effects. There will be proactive interference effects as well in a distributed model (see Chapter 3) . Additionally , as time goes by, there will be changes in the mental context in which retrieval takes place~ all of these factors will contribute to the apparent strength of a memory trace as observed in experiments. The point of our model of amnesia is not to deny the importance of such factors~ we simply assume that perf Ofmance in a memory task varies with the resid- + +ual functional fraction of the original trace, all else being equal. + +The values of the parameters are shown in Table 1. The significance + +of the particular values chosen will become clear as we proceed. + +TABLE! + +Value + +nsite.5 .f Or (} u Y Norma ! + +Parameter Name + +3 .00007 .02 .25 1.0 + +PARAMETERS UED IN SIMULATIONS OF THE AMNESIA MODEL + +Anterograde amnesia.. Smaller functional fractions at all delays. As we have said, our model assumes that amnesia amounts to a reduction in the size of "Y. Reducing the size of "Y does not reduce the size of the memory trace- the number of receptors added- but it does greatly reduce their effectiveness: For a receptor to be functional , all of its sites must be either bound with gamma or consolidated. Initially , before any consolidation has occurred, the probability that a receptor + +will be functional , or active, is + +P a (receptor i) = P n + +where n is the number of sites on the receptor. For normals, we take p (that is, y/ (1 - y )) to be .5. Since each receptor has three sites, Pa will be .53 or .125~ if amnesia reduces the concentration of y by a factor of 9, the effect will be to reduce p to .1, and Pa to .001. In general, with nsites equal to 3, reducing p by a particular fraction of the normal + +25. AMNESIA 515 + +8 x la - 6 . It should be noted that these figures are per hour . The consol idation parameter translates into a consolidation rate of about 50 % per year , per receptor site . The average time it takes for all of the sites on a receptor to become consolidated is longer than this , of course , but only by about a factor of 2 for the case of nsites = 3 ; this is essentially the factor that determines where the curve for amnesics will catch up with the curve for the normals . The decay rate from fully consolidated + +memory , which translates into about 7 % per year or 50 % per decade , essentially determines the overall slope of the normal function and the + +tail of the amnesic function . + +Recovery of lost memories . . The return of the partially consolidated + +amnesia is temporally graded is the fact that it recovers as the ability to acquire new memories recovers . In the case of retrograde amnesia induced by electroconvulsive therapy , Squire , Slater , and Miller ( 1981 ) showed that the severe retrograde amnesia for pretreatment memories recovers over the course of several months , at the end of which test performance is back to pretreatment levels . In our model , since retro grade amnesia is due to the fact that loss of ' Y renders traces ineffec tive , it is not surprising that the return of ' Y will render them effective + +for recovery is not generally thought to be complete . There is usually some loss of memory for events in the time period preceding the onset of the amnesia , and the precipitating event is almost never recalled ~ this is particularly striking in head trauma patients , who often do not know what hit them , even if they had seen it at the time ( Russell & Nathan , + +1946 ) . + +To examine how well our model can do at reproducing these aspects of amnesia , we ran the model in the following simulated amnesia - + +and was left in this state until some time If ' at which point we assumed recovery occurred . Of course , real recovery is gradual , but for simplic ity , we assumed that it was a discrete event . We then asked what frac tion of a trace laid down before the onset of amnesia remained , relative to the fraction that would have remained had there been no insult . The results of the simulation are shown in Figure 5 . Each curve shows the strength of the recovered trace , relative to the strength it would have had with no intervening amnesia , as a function of the duration in months of the amnesic episode . Clearly , for memories a year or more old , the trace recovers to nearly premorbid levels at the end of the amnesic episode , even if it lasts as long as a year . For memories laid down within the day of the the amnesic event , however , the bulk of the trace is gone by the end of the amnesic episode , even if it lasts only + +516 BIOLOGICAL MECHANISMS + +mti.i!mT9 + +~ro e ~ 0 z + +i1!.E~r.I;B. + +FIGURE 5. Simulated recovery of premorbid memories as a function of time in the amnesic state and age of memory at onset of the amnesia. The age ranges from an hour + +to a decade, as indicated by the labels on the curves. + +a month . Memories that are a month old at the onset of the amnesia show an intermediate pattern . If the amnesia is relatively brief , they survive quite well ~ but if it lasts several months , they weaken consider ably , relative to the strength they would have had in the absence of + +amnesia . + +The loss of memory trace strength during amnesia is a result of the great reduction in the opportunity for consolidation during the amnesic interval . We now turn to a more direct consideration of this matter . + +Do amnesics forget faster than normals ? A number of studies ( Huppert & Piercy , 1978 ~ Squire , 1981 ) have reported that bitemporal amnesic subjects appear to forget more rapidly than normals , even if equated with normals for the amount of initial learning . The effect is generally rather small , and it is controversial because the equating of groups on initial performance requires giving amnesics considerably + +more training than normals , over a longer period of time . These differ ences could possibly change the basis of learning and other qualitative aspects of the task as experienced by amnesic and normal subjects . It is interesting , then , to consider whether our model would predict such a + +difference . + +The model does predict a difference in rate of trace decay between amnesic and normal subjects . Though ' Y does not influence the rate of trace decay directly , it does influence the rate of consolidation , and + +1 .20 + +1.00 Decade + +Year + +0 .80 + +0 .60 + +0 .40 + +0 .20 + +Day + +0 .00 Hour + +- 0 .20 + +0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Time in Months + +518 BIOLOGICAL MECHANISMS + +and amnesics in day-scale decay rates. However, there are other reasons to believe that there is consolidation on a shorter time scale than we get with our model and the parameters in Table 1. For one thing , a single bout of electroconvulsive therapy that produces a brief and mild amnesia nevertheless appears to produce permanent loss of memory for the shock treatment itself . Such an effect seems to suggest that there is + +consolidation going on over a shorter time-scale. + +The model might capture all of the data if we assumed that there are two separate phases to consolidation, both of them dependent on y : one that occurs on a relatively short time scale and is responsible for the differences in day-scale decay rates, and one that occurs on a very long time scale and is responsible for extended temporally graded retrograde amnesia. As things stand now, traces decay rather slowly over hours, but, over the course of a month , they are reduced to about half of one percent of their original strength. Though we do not know exactly how to scale trace strength against response probability , it seems likely that we forget more quickly over hours but more slowly over + +days and months than in the present version of the model. + +Summary. The model provides, we think , an appealing, unified account of most aspects of anterograde and retrograde amnesia, simply by assuming that the amnesic insult depletes 'Y and that recovery amounts to its gradual return to pretraumatic levels. By adding an additional stage of consolidation, the model could be made to span the very wide range of time scales, ranging from hours to years, of the coupled phenomena of anterograde and retrograde amnesia as they appear in the + +bitemporal amnesic syndrome. + +Most importantly , the model shows clearly that there is no incompatibility between the phenomenon of temporally graded retrograde amnesia and distributed representation. So far, however, our account of amnesia has not really depended on the features of our distributed model. In the next section we will consider aspects of the amnesic syn- + +drome which do seem to point toward distributed models. + +RESID U AL LEARNING AND SPARED LEARNING IN + +BITEMPORAL AMNESIA + +As we noted briefly before, there are some domains in which amnesics exhibit what are generally described as spared learning effects: They show no noticeable deficits when compared to normal subjects. There is now a very large literature on these spared learning effects. + +25. AMNESIA 519 + +The following summary seems to capture the basic characteristics of + +what is spared and what is not . + +While amnesics seem to be highly deficient in the ability to form accessible traces of particular individual episodic experiences , they seem to be completely spared in their ability to learn certain types of skills that require no explicit access to the previous processing episodes in which the skill was acquired ( N . J . Cohen , 1981 ~ N . J . Cohen , Eichen - + +baum , Deacedo , & Corkin , 1985 ) . In addition , they show apparently normal repetition priming effects in experiments involving such tasks as perceptual identification , in which the subject must simply identify a briefly flashed word in a short exposure ( see Schacter , 1985 , for a review ) . These effects may be strongly and strikingly dissociated from the subjects ' verbally expressed recollections . Thus , H . M . has acquired a skill that allows him to perform perfectly in solving the Tower of Hanoi problem , without becoming aware that he has actually ever performed the task before and without knowing ( in a conscious , reportable sense ) even what constitutes a legal move in the Tower Puz zle ( N . J . Cohen et al . , 1985 ) . Also , amnesic subjects show normal effects of prior exposure to words in perceptual identification and related tasks , without necessarily having any awareness of having seen the words or even participating in the priming portion of the task . Between these two extremes lies a gray lone . Within the domains + +however gradually , from repeated experience ( Schacter , 1985 ) . First , we will consider these residual learning effects from the point of view of distributed memory . Then , we will examine the more striking spared + +learning effects . + +Residual Learning in Bitemporal Amnesia + +As we noted early in this chapter , distributed models provide a natural way of explaining why there should be residual ability to learn gradually from repeated experience within those domains where amnesics are grossly deficient in their memory for particular episodic experiences . For if we imagine that the effective size of the increments to the changes in synaptic connections is reduced in amnesics , then the + +basic properties of distributed models - the fact that they automatically extract the central tendency from a set of similar experiences and build up a trace of the prototype from a series of exemplars - automatically provides an account of the gradual accumulation of knowledge from repeated experience , even in the face of a profound deficit in remembering any specific episode in which that information was + +presented. Distributed models are naturally incremental learning models, and thus they provide a very nice account of how learning + +could occur through the gradual accumulation of small traces. + +We call the hypothesis that anterograde amnesia amounts to reducing the effective size of the increments the limited increment hypothesis. For bitemporal amnesics, the effective size of the increments is limited by the depletion of 'Y ~ in other forms of amnesia (which also show similar kinds of residual learning) the size of the increment might be limited in other ways. According to the limited increment hypothesis, residual learning is simply a matter of the gradual accumulation of information through the superimposition of small increments to the connection + +strengths. + +To illustrate this point, we have carried out a simulation analog of the following experiment by N. J. Cohen (1981) . Amnesic subjects and normal controls were seated in front of an apparatus with a movable lever. On each trial of the experiment , the subject was asked to move the lever until it reached a stop set by the experimenter. The experimenter then moved the lever back to the start position and removed the stop. After a variable delay, the subjects were asked to reproduce the previous movement. Such trials are referred to as reproduction + +trials. + +At the end of each group of three trials, subjects were asked to reproduce their impression of the average distance they had been asked to move the lever, based on all of the preceding trials in the experi- + +ment . Such trials will be called averaging trials. + +The results of the reproduction task were as expected from the fact that amnesics have very poor memory for specific experiences~ at very short delay intervals, amnesics did as well as normals, but at longer intervals , they were grossly impaired, as measured by the deviation of the reproduced movement from the training movement (Figure 7) . However, amnesics did no worse than normals at reproducing the average movement. The experiment was divided into four parts: In the first and last parts, the movements were all relatively long~ and in the two intermediate parts, the movements were all relatively short (some subjects had the long and short trials in the other order) . At the end of each block of trials, both groups accurately reproduced the average movement for that block (For the long blocks, movements averaged 42.6 degrees for the normals and 41.3 for the amnesics~ for the short blocks, movements averaged 30.8 for the normals and 30.6 for the + +amnesics) . + +We simulated this phenomenon using the distributed memory model described in Chapter 17. Briefly , that model consists of a single module , or set of units, with each unit having a modifiable connection to each other unit . The units in the module receive inputs from other + +25. AMNESIA 521 + +(see~~ep) ~O~J~ e+nlosqy + +FIGURE 7. Accuracy of reproduction movements by amnesics and normal controls in the lever placement experiment described in text. (From "Neuropsychological Evidence for a Distinction Between Procedural and Declarative Knowledge in Human Memory and Amnesia" by N. J. Cohen, 1981, doctoral dissertation, University of California, San + +Diego. Copyright 1981 by N. J. Cohen. Reprinted by permission.) + +units via the modifiable connections, as well as external inputs from stimulus patterns. Processing in the module begins with all units at a resting activation of 0 and the presentation of an external input pattern. In this case, the module consisted of 16 units, and each input pattern was a vector of 16 excitatory or inhibitory inputs. When a pattern is presented, it begins to drive the activations of the units up or down as a result of its direct effects~ the units then begin to send excitatory and inhibitory signals to the other units via the modifiable connections. For patterns that have previously been stored in the connections among the units, the internal connections produce an enhancement of the pattern of activation over and above what would be produced by the external input alone~ if , however, the external input is very dissimilar (orthogonal) to the patterns that have been stored in the module on previous + +trials, there will be little or no enhancement of the response. + +On each trial of the experiment , a new distortion of the same 16 element prototype pattern was presented to the module , and connection strengths were adjusted after each trial according to the delta rule (see Chapter 17 for details) . We then tested the module in two ways: First, to simulate Cohen's reproduction test, we looked at the magnitude of the model's response to the pattern it had just been shown. For the averaging test, we looked at the magnitude of the model's response to + +12 + +10 Korsakoff [N =2] + +8 Case + +r - - - - - + +- - - - + +- - - + +6 N.A. Co~t; ~l; - - - - - - , - - - - 4 [N = 6] Alcoholic + +Con troIs + +[N= 10] 2 + +0 + +Reproduction Interpolated Movement Movement + +The results of the simulation are shown in Figure 8. As the figure indicates, the larger the size of 'Y1, the more strongly the model responds to the immediately preceding distortion of the prototype. But, after a few trials, the response to the central tendency or prototype underlying each distortion is as good for small values of 'Y1 as for larger ones. In fact, response to the prototype is actually better when the model is II amnesic II (low 'Y1) than when it is II normal " (high 'Y1) ~ in the latter state, the connections are continually buffeted about by the latest distortion , and the model has trouble seeing, as it were, the forest for + +the trees. + +In the figure , there is a gradual improvement in the response to the immediately preceding stimulus for small increment sizes. This occurs only because the stimuli are all correlated with each other, being derived from the same prototype. For a sequence of unrelated stimuli , the response to each new input shows no improvement over trials. + +This pattern of performance is very reminiscent of the pattern seen in several of the experiments performed by alton and his colleagues (see alton , 1984, for a review) . They have trained rats to run in two different mazes, each having two choice points. At one of the choice points, the response was always the same for a given maze (we call this the maze-dependent choice) ~ at the other choice point , the response that had to be made varied from trial to trial , based on the response the rat made on the preceding trial (we call this the trial -dependent choice) . The principal finding of these experiments is that rats with hippocampal lesions show gross impairment in the ability to make the right trial dependent choice, but show no impairment in the ability to make the right maze-dependent choice if they were trained up on the task before surgically induced amnesia. The acquisition of the maze-dependent choice is slowed in rats trained after surgery, but these animals eventually reach a point where they can perform as well as normals. Such animals show near chance performance in the trial -dependent choice + +522 BIOLOGICAL MECHANISMS + +the prototype. Note that these test trials were run with connection strength modification turned off , so each test was completely uncon- + +taminated by the previous tests. + +In keeping with the limited increment hypothesis, we assumed that the difference between amnesics and normals in Cohen's experiment could be accounted for simply by assuming that amnesics make smaller changes to the strengths of the connections on every learning trial . To show that the model shows residual learning of the prototype under these conditions, we ran the simulation several times, with three dif ferent levels of the increment strength parameter 11 from the equation + +for the delta rule, which we reproduce here: + +~ w.. = 'nD' a . lJ . , I J' + +Such a pattern of results is completely consistent with the limited increment hypothesis: Performance in the trial -dependent choice requires, by the design of the task, that the subject rely on a memory trace of the preceding trial of the experiment , whereas performance on the maze-dependent choice can be based on a composite memory trace acquired gradually over repeated experience in the same maze. No separate mechanisms for retaining recent episodes, as opposed to more + +general memories~ is required. + +In summary, there are a variety of phenomena, both in human and animal amnesia, which fit in very well with the kind of gradual, residual learning we see in our distributed model. Distributed models naturally and automatically pullout what is common to a set of experiences, even if , or one might even say especially when, the traces of the indi- + +vidual experiences are weak. + +It is worthwhile to note that this property of distributed models would not be shared by all learning models, especially those that rely on some mechanism that examines stored representations of specific events in order to formulate generalizations, as in the ACT \* model (1. R. Anderson, 1983) , or in Winston 's (1975) approach to learning. For on such models, if the individual traces are impaired, we would expect the generalization process to be impaired as well. Of course, such models could account for these effects by assuming that each episode is stored in two different ways, once for the purpose of learning generalizations and once for the purpose of remembering the details of particular experiences. Thankfully , our distributed model does not require us to duplicate memory stores in this way~ residual learning based on small increments drops out of the basic superpositional char- + +acter of the model. + +524 BIOLOGICAL MECHANISMS + +Spared Learning of Skills + +More striking that these residual learning effects is the phenomenon of spared learning: The fact that the acquisition of a variety of general skills occurs at roughly the same rate in normal and amnesic subjects. This fact has been taken as evidence that the brain maintains a distinction between those structures underlying explicitly accessible episodic and semantic information on the one hand and those underlying gen- + +eral cognitive skills on the other (N. J. Cohen et al., 1985) . + +While this conclusion is certainly plausible, it is worth noting that there are other possibilities. One that we have considered is the possibility that limited increments to connection strengths make a difference for some kinds of tasks but not for others. The simulations reported in 526 BIOLOGICAL MECHANISMS + +This simulation does not capture spared learning of skills perfectly , since our simulated normals approach asymptote more rapidly than our simulated amnesics . However , if such skills really consisted of many small skills , the differences might not be noticeable . We have not yet developed a version of our model in which there are no differences as a function of 11. We still consider it an open question as to whether we will succeed . It may turn out that there are other distributed models ( perhaps involving hidden units ) in which rate of learning is quite insensitive to large differences in sizes of increments on certain kinds of measures for certain kinds of tasks . This is a matter we are continu ing to pursue as our explorations of memory and learning continue . Setting this possibility aside , let us suppose for the moment that episodic and semantic memory are learned in one memory system , dependent on medial temporal lobe structures , and general skills are learned in a different system . This view raises a question : Why should this be ? Why should the brain make this distinction ? We can actually provide one possible answer to this question based on our observations of the properties of the simple distributed model presented in the simu lations . These observations suggest that large changes in connection strengths may be better for storing specific experiences but may do more harm than good for gradually homing in on a generalizable set of + +connection strengths . 3 + +On the basis of these observations , we might propose that the tem poral lobe structures responsible for bitemporal amnesia provide a mechanism that allows large changes to connections to be made in parts of the system in which memories for specific experiences are stored , but other parts of the cognitive system make use of a different mechan ism for changing connections that results in the smaller changes that are at least as good as larger ones for learning what is common to a set of experiences . However , as we have already suggested , we remain unconvinced that such a distinction is necessary . It may turn out that learning of generalizable skills is simply insensitive to the size of the + +changes made in connection strengths . + +3 As noted previously, spared learning effects also show up in single-trial priming experiments. One view of these effects, consistent with the separate systems view, is that they reflect the subtle effects of single trials in those parts of the system where skills and procedures are learned. Again, an alternative would simply be that the priming task is less sensitive to the magnitude of the changes in connection strengths and more sensitive + +25. AMNESIA 527 + +CONCLUSION + +In this chapter , we have considered the phenomenon of bitemporal amnesia in the light of models of distributed memory . We have described a hypothetical mechanism that can account for temporally graded retrograde amnesia without assuming that recent memories are stored separately from older ones . We have demonstrated how the ability to learn gradually from repeated experiences is an automatic consequence of assuming that amnesia simply amounts to the reduction of the effective size of the changes in the connections in a distributed memory . And we have indicated how a distributed approach can allow us to suggest reasons why large changes to connection strengths might make more of a difference in forming explicit representations of facts and episodes than in laying down the connections required for cognitive + +skills . + +Obviously , there is considerable room for further work to test and to extend our views . If our hypotheses are correct , and if y really is a chemical , then we might hope that someday someone may discover just what the chemical is , and will then go on to show that normal memory depends only on "Y and not on some information processing activity that takes place in the hippocampus , as has frequently been suggested (Squire et al ., 1984 ~ Wickelgren , 1979 ) . Considerably more theoretical work will be required to build a tight connection between those tasks in which spared learning is observed empirically and the situations in which large increments to the weights do not result in superior learning . In the meantime , we hope this chapter has demonstrated that what we know about amnesia is not only consistent with the idea of distributed , superpositional memory , but that certain aspects of the amnesic syndrome - in particular , residual learning in domains where amnesics + +show deficits - actually support the idea . + +ACKNOWLEDGMENTS + +The work reported here was supported in part by a grant from ttle System Development Foundation , in part by contracts from the Office of Naval Research (NOOO14 -79 -C -0323 , NR667 -437 and NOOO14 - ~2-C - 0374 , NR 667 -483 ) , and in part by a NIMH Career Development Award ( MHO0385 ) to the first author . We would like to thank Neal Cohen , Morris Moscovitch , Daniel Schacter , and Larry Squire for several useful discussions of various aspects of amnesia on several dif - + +Cognition and Parallel Distributed Processing + +CHAPTER 2 6 + +Reflections on + +D. A. NORMAN + +This book presents a novel approach to the study of cognitive processes. The overall proposal is for a major change that alters the fundamental mechanisms of human information processing. Still , despite the impressive results, it is not always obvious just what impact this work should have upon the study of cognitive mechanisms. Yes, the underlying components might change, but what is the effect on models of cognition ? Why should cognitive scientists care about the class of models discussed in this book- parallel distributed processing models: POP. What difference do they make? What really has been learned about cognition ? Anything ? And what has been left out: Where are the strengths and the weaknesses? Where do we go from + +here? This chapter addresses these issues. + +I start with the issue of level, for I can already hear my colleagues + +muttering - those who are not part of the enterprise, of course: + +So what? So you have this work on low-level processing structures. Why should it make any difference to our work, or to cognitive science in general? After all, the study of cognition is a high-level pursuit and this PDP stuff is awfully low level- all this talk of weights and synapses and connections between lowlevel units. Oh sure, it is all very nice and even significant, but it has nothing to do with cognitive science: It has no effect on anything we are doing. We care about language and thought, + +532 CONCLUSION + +problem-solving and memory, not about neural mechanisms + +and Hebbian rules for adjusting synaptic weights.l + +Well , in many ways those concerns are correct . Most of what is presented in this book differs radically from the kind of studies that are called " cognitive ." Most are what would normally be called " low -level ," concerned with I' implementation details ," with the hardware and the neurophysiology . Why should it be of concern to the normal , everyday cognitive scientist ? And , equally important , how does this work fit with the substantive concerns of the cognitive scientist ? What is use- + +ful , what is questionable , and what has been left out ? + +It is still too early to give firm answers to all these questions . But I can say where I stand . I am an in -between cognitive scientist . I have watched the developments reported in this book with great interest . Much of my work in the last ten years has been in the spirit of these models , some of it , of course , done with my long -time collaborator , Dave Rumelhart . I have long thought this philosophy to be powerful and important . But I have also disagreed with some aspects, for I have had some problems with the work . It is probably useful to discuss these here , at the end of the book . Some of these problems may reflect inherent , fundamental difficulties . Some may just be temporary problems that persist simply because they haven 't been worked on . And some may be pseudoproblems , resulting either from my own misunderstandings or from the current point of view , but that will disappear when the " proper " approach is adopted . Let me start off with the good things : What does this approach - and this book - deliver ? + +Then I will turn to the problems . + +Before discussing " the POP approach ," I must remind you that there really isn 't a single POP approach . No simple listing of either strengths or weaknesses is really fair , for there are many different contributors , each with a somewhat different approach with its own set of virtues and vices . Although much of the work has a common thread , the details and even the operative philosophies are oftentimes quite different . This level of disagreement is healthy for a developing science , although + +it may cause confusion to the unwary onlooker . + +1 I wrote this paragraph without realizing that my prophecy had already been confirmed: See the essay by Broadbent (1985) and the partially responsive answer by + +WHAT IS NEW: THE PDP APPROACH TO THE + +STUDY OF COGNITION + +26. REFLECTIONS 533 + +A major rethinking of the levels at which we must think of cognitive processes, involving , among other things, an intimate + +relationship between neuroscience and psychology. + +. + +A new form of computational model involving large numbers of highly interconnected parallel computational units, a form that takes into account constraints from studies of the nervous system, constraints from psychological data, and a deep under- + +standing of computational requirements. + +. + +Everyone agrees that full understanding of cognition requires a combination of efforts that cut across disciplinary boundaries. Indeed, this is the basic premise underlying the establishment of cognitive science. Nonetheless, even relatively recently, there has been little combination of efforts . Scientists in one field tended to think work in other fields interesting, but irrelevant to their own. Thus, cognitive psychologists tended to think that studies of the brain were interesting but irrelevant ~ + +continual adjustment and learning . + +"This is a difficult book, difficult but important ." With this sentence, Rumelhart and I opened our introduction to the book Parallel Models of Associative Memory, the earlier work on the study of parallel, distributed models of psychological processing edited by Hinton and J. A . Anderson (1981) . The sentence still applies, perhaps with a bit less emphasis + +on the difficult , a bit more on the important . + +This book starts to put it all together, to make significant advances in the mathematics and underlying bases of the approaches and to explore their implications for the study of cognition . The result is a new form of model for understanding the mechanisms of human (and animal) information processing, models that have several important aspects: + +. New conceptualizations of cognition that change the emphasis from symbolic processing to states that reflect the quality of the match between the data to be described and the possible configurations of the underlying processing structures. These lead to new modes of thinking of cognition , modes that use metaphors such as "stability," "harmony," "local" and "global minima ," and + +" temperature." + +. An emphasis on learning- the mechanisms are built around + +neuroscientists acted as if models of cognition or psychological data were too speculative and unrelated to neural activity (amusing pastimes, but not science) ~ those in artificial intelligence thought the emphasis should be on control structures and representation, and paid little attention to other disciplines. This has changed. There is now a spirit of genuine cooperation. The research reported in this book shows the results. Neurological data offer strong constraints and invaluable guides to the model building efforts : The work reported here both builds upon what is known of the nervous system and asks specific questions to be decided by future research. Psychological evidence is taken seriously: The models must be able to reproduce this form of evidence. And the models must reflect the real demands of computational plausibility , which means that the models must work , must produce answers in appropriate times and with appropriate degrees of accuracy. Each field pushes the other. Each field suggests the data that should be provided by the other, suggests questions to be examined, and sometimes even suggests in which directions future efforts should be directed. The overall effort reflects the appropriate interplay of theory and data, with genuine interaction among the disciplines: a good + +model for a cognitive science. + +534 CONCLUSION + +On the Computer Metaphor + +It has always bothered me that models of psychological processing were thought to be inspired by our understanding of the computer . The statement has always been false . Indeed , the architecture of the modern digital computer - the so - called Von Neumann architecture was heavily influenced by people ' s ( naive ) view of how the mind operated . 2 Now that whole debate can finally be put aside : The work presented here in no way can be interpreted as growing from our meta phor of the modern computer . Here , we are talking about a new form of computation , one clearly based upon principles that have heretofore not had any counterpart in computers . These models are highly paral leI , with thousands or millions of elements interacting primarily + +2 Perhaps I had better document this . Simply read the work on cybernetics and thought in the 1940s and 1950s prior to the development of the digital computer . The group of workers included people from all disciplines : See the Macy Conferences on Cybernetics , or " Her Majesty ' s Conference on Thought Processes ." Read the preface to Wiener ' s book on cybernetics . Everyone who was working together - engineers , physi cists , mathematicians , psychologists , neuroscientists ( not yet named ) - consciously and + +For me, the work has been important for several reasons. In my personal opinion , many students of cognition have boxed themselves into corners, forcing themselves to develop ever more complex rule structures, and ever more complex algorithms for dealing with the behavior of people. Each new experimental finding seems to require a new theory. Clearly, some new approach has been needed. But what? + +The POP approach offers a very distinctive counterapproach. Basically, here we have an adaptive system, continually trying to configure itself so as to match the arriving data. It works automatically, prewired if you will , to adjust its own parameters so as to accommodate the input presented to it . It is a system that is flexible , yet rigid . That is, although it is always trying to mirror the arriving data, it does so by means of existing knowledge, existing configurations . It never expects to make a perfect match, but instead simply tries to get the best match + +26. REFLECTIONS 535 + +through activation and inhibition of one another's activity . Each element is highly interconnected, with perhaps tens of thousands of interconnections. Although the processing speed of each element is slowmeasured in milliseconds rather than the picoseconds common in today's computers- the resulting computations are fast, faster than is possible with even the largest and fastest of today's machines. Parallel computation means that a sequence that requires millions of cycles in a conventional , serial computer can be done in a few cycles when the mechanism has hundreds of thousands of highly interconnected processors. These neurologically inspired computational processes pose new requirements on our understanding of computation , suggest novel theoretical explanations of psychological phenomena, and suggest + +powerful new architectures for the machines of the future . + +Although the models reported here are new, they carryon a tradition that has long existed, a tradition of building models of neurological processes. Work in neural networks, in cybernetics, and in brain theory has preceded the present efforts . The studies of perceptrons, a computational device invented by Frank Rosenblatt in the 1950s clearly anticipated many of the results in use today (see Rosenblatt, 1962) . The critique of perceptrons by Minsky and Papert (1969) was widely misinter preted as destroying their credibility , whereas the work simply (but elegantly) showed limitations on the power of the most limited class of perceptron-like mechanisms, and said nothing about more powerful , multiple layer models. Grossberg developed many of the ideas in popularity today with his mathematical models of brain structures, + +starting in the late 1960s through today (see Grossberg, 1982) . + +Strengths of the POP Approach + +536 CONCLUSION + +possible at any time : The better the match, the more stable the system. The system works by storing particular events, but the results of its operations are to form generalizations of these particular instances, even though the generalizations are never stored directly . The result, as has been illustrated throughout the chapters of the book, is that although the system develops neither rules of classification nor generalizations, it acts as if it had these rules. Thus, the system really mirrors experience~ the regularities of its operation result partially from the regularities of the world , partially from the interpretations of the beholder. It is a system that exhibits intelligence and logic, yet that + +nowhere has explicit rules of intelligence or logic. + +These ideas have particular charm for many of us. The attempt always to find a best fit to existing data by maximizing harmony (or minimizing energy or discrepancy) gives mechanism to a common hope among many modern cognitive theorists (e.g., Shepard, 1984) . The heavy dependence upon particular instances and the lack of explicit generalizations fit a reasonable body of evidence about the importance of specific experiences (e.g., see Kahneman & D. T. Miller , in press~ Medin & Schaffer, 1978) . The way by which these systems try to accommodate themselves to the data by minimizing energy or maximizing harmony results in preferred states or interpretations , where the preferences reflect the particular events the system has experienced. This leads to categorization and classification of the input signals, but in a flexible manner- categorization by distance from prototypes, a mode that is consistent with much recent evidence. Here is a system that incorporates learning as a fundamental, essential aspect of its behavior, that makes no attempt to form categories or rules, yet that acts as if it were a prototype-matching, categorization system that has rules and + +strategies. + +The schema. What about the schema, that omnipresent, powerful tool of modern cognitive theory? Well , as Rumelhart , Smolensky, McClelland , and Hinton show in Chapter 14, the schema still exists, but in somewhat different form than that which schema theorists have thought of it (schema theorists such as Rumelhart and I , I might add). I like this new formulation . More than that, I think this an important step in the understanding of thought . Schemas are not fixed structures. Schemas are flexible configurations , mirroring the regularities of experience, providing automatic completion of missing components, automatically generalizing from the past, but also continually in modifi cation, continually adapting to reflect the current state of affairs. Schemas are not fixed , immutable data structures. Schemas are flexible interpretive states that reflect the mixture of past experience and + +26. REFLECTIONS 537 + +Because the schema is in reality the theorist's interpretation of the system configuration , and because the system configures itself dif ferently according to the sum of all the numerous influences upon it , each new invocation of a schema may differ from the previous invocations. Thus, the system behaves as if there were prototypical schemas, but where the prototype is constructed anew for each occasion by combining past experiences with the biases and activation levels resulting + +from the current experience and the context in which it occurs. + +Essential properties of human information processing. Some years ago, Bobrow and I listed some properties we felt were essential components of the human cognitive system (Bobrow & Norman , 1975~ Norman & Bobrow, 1975, 1976, 1979) . We constructed our lists through observations of human behavior and reflection upon the sort of processing structures that would be required to yield that behavior. We concluded that the system must be robust, relatively insensitive to missing or erroneous data and to damage to its parts. Human cognition appears to work well in the face of ambiguity , incompleteness, and false information . On the one hand, the system is not only robust, it is also flexible and creative. On the other hand, the system continually makes errors. Speech is riddled with incomplete sentences, with erroneous words and false starts. Actions are riddled with "slips" and mistakes. People have learned to deal with these problems, in part by elaborate (although mostly subconscious) correcting mechanisms in language, in part through humor and tolerance for the slips that characterize everyday behavior. Nonetheless, these characteristics of human cognition seem to provide important clues about the nature of the processing mechanisms. We argued that the system had to work by descriptions rather than precise specifications, by partial information rather than complete information , and by competition among compet- + +ing interpretations. + +We argued for a set of essential properties: graceful degradation of performance, content-addressable storage, continually available output , and an iterative retrieval process that worked by description rather than by more traditional search. Although these requirements seemed to us to be both necessary and sensible, supported by the evidence, a common complaint was that these were hand-waving speculations, dreams, that there was no method for implementing these concepts. And if they couldn't be built , then they didn't exist- the ideas were wrong. Well , the POP mechanisms described in this book have exactly the + +properties we required. Hurrah for our side. + +538 CONCLUSION + +activity . These metaphors are more important than might be realized . They accommodate the transfer of knowledge from one application domain to another . The metaphors of PDP are of weights and goodness - of - fit , of stability , of local and global minima or maxima , and of the means to move from one stable state ( a local minimum ) to another ( perhaps a global minimum ) by " shaking up the system " or " raising its temperature ." We see why systems have what psychologists call set or functional fixity : The systems are stable , even if in only a local minimum ; it takes much less evidence to get into a stable state than it takes to get out of it . To change a state is not necessarily easy . You have to shake up the system , heat up the temperature . Don ' t let it freeze into position . New interpretations suddenly arise , with no necessary conscious experience of how they came about : a moment of nothing , and then clarity , as the system heats up , bounces out of one stable configuration and falls into a new configuration . The descrip tions flow smoothly from the tongue . Good metaphors and comfort able descriptions are not scientific criteria . But they make a large difference in the psychological acceptance of the system and in the gen - + +eral utility of the ideas . + +Levels of description . And what about the most common complaint of all : Who cares about this low - level stuff ? I think that the answer is clear : all of us . Now , be careful about how this is interpreted . I , per sonally , am not particularly excited by much of the discussions of synaptic adjustment rules and the details of the operation of single neu rons ( and worse , single synapses ) . But careful attention to these low level details is essential in understanding the appropriate primitive + +structures of cognition . + +The whole point for the cognitive scientist is to understand cognition : perception , language , thought , social interaction , action , emotion . . . . To do so , we insist on explanation of the internal processing structures that give rise to cognitive activities . This is why we have spoken of representation , of the mechanisms of memory and attention , of the rule - structures of language , and of the plans , schemas , and beliefs of people . But in developing models of internal activity , we must adopt an appropriate set of primitive descriptors . So far , the primitives have been based upon symbols : symbol manipulating rules , production sys tems , control structures , and representational systems . How do we know these are the appropriate descriptors ? We don ' t . The choice of + +primitive building blocks depends upon the choice of computational device . Selection of the POP computational system changes things dramatically : New conceptualizations emerge , new primitive levels of description are required , new explanations of cognition are possible . + +26. REFLECTIONS 539 + +By attending to the seemingly uninteresting level of the adjustment of synaptic weights , we end up with a whole new conceptualization of how concepts are encoded . The point is that some low -level stuff makes large differences in the way that the e.ntire system operates , which in turn makes huge differences in the types of high -level descrip tions that are most important for the cognitive scientist . Who would have thought that a person interested in problem solving or thinking should be interested in energy states or measures of " harmony " among units at a " neural -like " level ? But guess what ? They turn out to be important . A focus upon these levels turns out to change the way we view cognition . The POP approach forces a re -evaluation of the impor tance of what would otherwise have been thought to be low -level + +concepts . + +Weaknesses of the POP Approach + +The approach has weaknesses . In part , it is hard to see exactly how to apply it to many of the difficult issues in the study of cognition . In general , the closer to perception or to motor output , the easier it is to see how the work applies . Thus , there seems to be no question about the significance for pattern recognition , for vision or speech under standing , or even for categorization . There have been a few studies that show promise for the control of motor movements ( Hinton , 1984 ; Rumelhart & Norman , 1982 ) . The question arises whether there are fundamental limitations in these models or whether the lack of exam ples simply represents the early stage of development and the initial concentration of effort upon the mathematics , the modeling techniques , and examples drawn from more restricted domains . The answers , of + +course , are not known . 3 + +The type - token problem . Among the problems that have long bothered me about the PDP approach are some technical issues in + +3 Yes, it is possible to make a POP network balance a pole (Barto, Sutton, & C. W. Anderson , 1983) , but this is really an exercise in demonstrating learning, and the perceptual input and motor output required are, well, trivial . The study isn't trivial - it is a very nice demonstration - but the theme is the adjustment of weights, not perception, not motor control , and not decision or thought . In this section I examine several of these problems: the type-token problem, the problem with variables, the need for an extra, evaluative structure capable of overseeing and passing judgment on others, and then + +540 CONCLUSION + +computation . There is a list of them, but the two most significant are the type-token distinction and the handling of variables. The typetoken problem is to be able to handle different instances of the same concept, sometimes at the same time . Thus, if the system has the knowledge that "John eats a sandwich" and that "Helene eats a sandwich," the system has to treat these as different sandwiches. This capability is not easy for POP systems. POP networks are very good at representing general properties, properties that apply to classes of objects. This is where their power to generalize, to generate default values automatically, arises. But the complementary skill of keeping + +individual instances separate seems much harder. + +The issue is addressed in the book; it is discussed in Chapter 3, "Distributed Representations," by Hinton , McClelland , and Rumelhart ; in the McClelland and Rumelhart chapters on distributed memory and amnesia; and in McClelland's chapter on "The Programmable Blackboard Model of Reading" (and probably elsewhere that I missed) . All this discussion is somewhat symptomatic of the difficulties : In traditional symbolic representations, for example, semantic network and frame-based approaches to representation, the issue is straightforward - the solution is natural. Here, however, considerable complications must be introduced to handle the issues, and even then it + +is not clear that the problem is entirely solved. + +One question that should be raised, however, is whether we really wish the problem to be solved. It is interesting to note that in our typing model, Rumelhart and I concluded that the kinds of errors people make in typing require a system in which there is no type-token distinction at the level of control for the typing of individual letters (Rumelhart & Norman , 1982) . The lack of distinction gave rise to some difficulties , but we argued that these are exactly the difficulties that humans face. McClelland makes a similar argument in his chapter on the blackboard model of reading. Thus, it may turn out that the problems faced by POP systems in handling the type-token distinction are actually virtues with regard to their ability to model human cogni- + +tion , especially if people have the same problems. + +Variables. Once upon a time I worried about how the nervous system could have evolved to do all the things computational systems seemed required to do. Among them was the ability to call subroutines. The problem with calling subroutines was that it required variables: not only the values of the actions to be performed, but the name or symbol of the thing that had requested the subroutine - this is how the system would know where to resume operations once the subroutine was completed. Symbol processing systems are fundamentally variable-interpretation processes, and I couldn't see how they could + +26. REFLECTIONS541 + +have evolved. 4 Well , now along comes the PDP approach: In one sense, my problem is solved- there are no variables, save for activation values. All that is represented is particular instances. No need to represent variables: The variable is represented by the configuration of + +units that are active. But I still am not satisfied. + +Now I worry about how PDP units can get away without representing variables. Aren 't variables necessary? What about thought ? If I solve a problem mentally don't I have to postulate hypothetical situations in my head, evaluate them, and make decisions? How do I plan my day, deciding which activities should be done first , which last, which require others to precede them, and which can be postponed? How do I compose music, or do science? Don 't I need to have mental variables, symbols that I manipulate? My answer is "yes.I' I think this lack is a major deficiency in the PDP approach. I believe this problem can be solved by having several levels of systems, each specialized for dif ferent things. The PDP system is fine for perception and motor control , fine for categorization. It is possibly exactly the sort of system required for all of our automatic, subconscious reasoning. But I think that more is required- either more levels of PDP structures or other kinds of systems- to handle the problems of conscious, deliberate + +thought , planning, and problem solving. + +The need for an extra, evaluative structure. A problem with the PDP models presented in this book is that they are too specialized, so concerned with solving the problem of the moment that they do not ask how the whole might fit together. The various chapters present us with different versions of a single, homogeneous structure, perfectly well-suited for doing its task, but not sufficient , in my opinion , at doing the whole task. One structure can't do the job : There do have to be several parts to the system that do different things, sometimes com- + +municating with one another, sometimes not. + +The argument seems especially relevant in considering learning. Though many of the learning rules are self-correcting, and therefore tend to converge in one way or another on optimal performance, they seem to be insufficiently sensitive to the global goals and evaluations made by the organism in which they are implemented. While it is now well accepted that the intention to learn, per se, is not a major determinant of learning, this intention mobilizes cognitive activities that result in better learning. Not much is said about these intentions , their + +4 Of course, I can't figure out how the bones and impedance-matching structures of the ears could have evolved, or the complex tendons that control the tens of bones in the hands could ha\'e evolved either: My lack of imagination is not restricted to information + +More than one system at a time is required. A second problem is that because any single POP network can only settle into one state at a time , it is probably the case that multiple systems are required: modules of POP systems, perhaps. Now , this is not really a criticism of the PDP model. In fact, the property that a PDP network reaches a single state at any moment is both interesting and important : It gives rise to some of the strong points of the model. The point is that although the system is highly parallel and very fast when viewed at the level of computational operations, it is highly serial and relatively slow when viewed at the ff higher level f' of interpreting and analyzing the resulting state changes. This dual perspective is a strong virtue for the modeling of human cognition , for this duality reflects current understanding. People interpret the world rapidly, effortlessly . But the development of new ideas, or evaluation of current thoughts proceeds slowly, serially, deliberately. People do seem to have at least two modes of operation, one rapid, efficient , subconscious, the other slow, serial, and conscious. The problem, however, is that people can do multiple activities at the + +542 CONCLUSION + +source, or the ways in which they influence the system's learning and + +performance. + +When it comes to learning, it is frequently the case that something has to watch over the operations and act as a trainer . But this trainer is separate from the learning mechanisms. And it has to be able to evaluate the quality of performance. How does this take place? What is this second, overseeing mechanism? And how did it get started? How did the trainer . know what task it was to train , and when? And how did it acquire the knowledge of what was good performance if it was a task that the person had never before performed ? Even in the competitive learning environment (see Chapter 5 by Rumelhart & Zipser) in which learning can take place without an overseeing, evaluatory mechanism, it is often advantageous to "train " the system by careful presentation of the items that are to be classified. Thus, Rumelhart and Zipser "trained" their system on various stimulus situations- " teaching" is what they called it . But how does this come about? Who does the "teaching" or " training " ? In some cases, it is another person, but not + +always. + +It is often the case that complex behavior has to be monitored to see if things are proceeding well. This requires some sort of evaluation of the output of the system. But what mechanism does this evaluation? And what mechanism decides what the desired output is to be? I believe this requires an "overlooking " system, one that compares expectations with outcomes. This second, evaluative, system might very well also be a PDP structure, but it must be separate from the + +first , overlooking the first and operating upon it . + +The two problems discussed in the previous section come together into a general statement of the problems of learning and consciousness. To be skilled at something requires that the requisite actions be performed smoothly , effortlessly , with minimum conscious thought or effort . In many ways, skilled performance consists of the execution of automated routines. The PDP structures seem like ideal candidates for mechanisms that produce these automated, subconscious behaviors. But how do these structures come about? What are the procedures for learning? This view suggests that we consider "learning" to be the pro- + +gramming of automated routines. + +Under this view, when we learn some new task or skill , two different systems are involved . One involves conscious control and awareness of the task and the contingencies. Call this system DCC (for deliberate conscious control- after Norman & Shallice, in press) . The other involves a POP mechanism, a pre-established, preprogrammed set of procedures that get followed with minimum need for conscious control + +or even awareness. + +The basic idea is this: Learning involves the setting of weights on the associative network structures of a PDP system. However, this weight setting requires some evaluative mechanism that determines when things are going well and when they are not, and perhaps other kinds of judgments that can be used to affect the weight setting and establishment of appropriate connections. This is one role for DCC. In addition , during the time while the weights are being established, before the PDP structure is properly set up~ if the activity is to be performed at all, it must be through DCC. Hence, two roles for DCC are to control activities when the final "programming" has not yet been completed, and also to control the "programming." Norman and Shallice suggested that DCC only controls activities by influencing activation values. Among other things, this means that the control by POP and DCC mechanisms are compatible, so that both may operate at the same time . Thus, partially learned activities may be under control of both modes. Conscious control of activities acts by activating or + +26. REFLECTIONS 543 + +same time , some of them quite unrelated to one another. So, in my opinion , a PDP model of the entire human information processing system is going to require multiple units. That is, the complete model requires that the brain consist of several (tens? hundreds? thousands?) of independent PDP-like systems, each of which can only settle into a + +single state at a time . + +Learning and Consciousness + +inhibiting the POP networks, attempting to direct them into appropriate states, but without full power to cause such a result: Conscious control is simply one more source of activation and inhibition that adds and + +subtracts from the other influences on total activation values. + +These views of learning and of direct conscious control are consistent + +with a number of qualitative phenomena: + +544 CONCLUSION + +. Control by DCC is slow and serial, hence not very effective for some kinds of skills. If DCC control is exerted after appropriate PDP mechanisms exist, then conscious control of activity will be inferior to subconscious control through the PDP mechanisms. Performance improves if done subconsciously, blocking conscious control . This is indeed the procedure taught by a number of athletic training methods: tt Stop thinking about + +your actions and performance will improve." + +Introspection results from the interpretive attempts of deliberate conscious control - by the requirements of the "evaluator" or "trainer " for learning. Introspection is therefore essential for learning, but it is based upon observation of the outputs of a subconscious (POP) system. As a result, introspections are only capable of accurate descriptions of system states. Because there is no information available about how that state was reached, introspection cannot give reasons for the resulting states. People usually do give reasons however, but these reasons are of necessity constructions and self-hypotheses: We have no conscious awareness of how PDP mechanisms settle into states and no vocabulary for describing the weights and synaptic interactions even were we to have that awareness. + +. + +Consider the role of meaning and understanding in learning. Much has been made of the need for the learner to understand the task and activity . Yet , understanding does not seem relevant to the way that skilled performers operate. Moreover , many things we learn have arbitrary relations: the relation between the name of an object and the object, the order of the letters of the alphabet, the fingering of musical instruments , command sequences of computers. I believe the point is that POP mechanisms can set up almost any arbitrary relationship. Hence, to the expert, once a skill has been acquired, meaningfulness of the relationships is irrelevant . However, the conscious, supervisory mechanisms require meaningful and understandable relationships: The OCC mechanisms must watch over actions and evaluate them, and for this, understandable + +. + +26. REFLECTIONS 545 + +TOWARD ANEW UNDERSTANDING OF HUMAN INFORMATION PROCESSING + +The work presented in this book provides the framework for new directions in our understanding of the human information processing system. In the older view, processing was done by separate components that communicated by passing messages- symbols- among themselves. The perceptual system communicated with the memory system. Memory communicated with perception and problem solving. Language systems communicated with the others. The communications consisted of symbolic messages, interpreted through a representational system, that implied a correspondence between the symbol and the referent and, therefore , an interpretive mechanism (see Rumelhart & Norman , in press) . The emphasis was on symbolic representation, and hence the emphasis was on the rules of thought , problem solving, and memory. This led to the development of frame-based schema systems, with slots, fillers , default values, and inference mechanisms as well as + +to production-theory descriptions of human problem solving. + +The new view is quite different . Under this new view, processing is done by POP networks that configure themselves to match the arriving data with minimum conflict or discrepancy. The systems are always tuning themselves (adjusting their weights) . Learning is continuous, natural, and fundamental to the operation. New conceptualizations are reflected by qualitatively different state configurations . Information is passed among the units, not by messages, but by activation values, by scalars not symbols. The interpretation of the processing is not in terms of the messages being sent but rather by what states are active. Thus, it is what units are active that is important , not what messages are sent. In the conventional system, learning takes place through changes in the representational structures, in the information contained in memory. In this new approach, learning takes place by changes in the system itself . Existing connections are modified , new connections are formed , old ones are weakened. In the conventional system, we distinguished between the information being processed and the processing structures. In the POP system, they are the same: The information is reflected in + +and intelligible relationships are important . Understanding is also essential for troubleshooting , but in many ways, this is what the learning process is all about: troubleshooting the perf ormance in order to establish the appropriate connections. + +A large number of issues are now naturally addressed that were diffi cult to deal with before. In turn , a large number of things that were easy to do before now are difficult . This is a combination of evolution and revolution . Many of our old ideas are still applicable. Many of the essential, critical problems are still problems. But we have a new set of tools, powerful tools that can help make major advances on a number of fronts . These new mechanisms are fundamentally subconscious ones. Learning results from the natural adjustments to states: It results naturally from the operation of the system. But in the process of examining what extra mechanisms are necessary to guide the learning and the overall behavior of the system, we appear to be led directly to consideration of the interacting roles of processing mechanisms and evaluative mechanisms, of subconscious and conscious processes. + +A nice fallout . + +I still have concerns. I do not know how to map much of my understanding of cognition onto these new structures. I believe the typetoken distinction is critical , that the cognitive system can and does manipulate variables, that there must be levels of processes, some of which oversee others. None of these problems seem insurmountable to me. Some may go away, being problems forced upon us (me) only because of old habits of thinking , old views of computation . Some may be solved by new developments. Some may get handled by an amalgamation of methods) combining the best of the more conventional mechanisms of human information processing with these newer views + +of information processing. + +Some old questions are put to rest. To ask "why" a particular action was performed or "why" a particular interpretation was placed on an event means to ask "why" a given internal stable state was reached. But there is no simple answer to these questions. To force the questions is to risk confabulation: answers made up after the fact with no necessary connection to reality. In general, there is no single reason why any given cognitive state occurs. The system is multiply connected, multiply controlled . The states are a result of many different factors all impinging upon one another: The state is simply the best match to all the sources of information . This provides a rather nice resolution of many of the arguments that have taken place over the years within cog- + +nitive psychology. + +546 CONCLUSION + +ACKNOWLEDGMENTS + +- + +Future Directions + +Parallel distributed processing has come a long way since we began our explorations. Four years ago, we had no clear idea how PDP models were going to overcome the limitations of the perceptron~ how they could be related to higher level concepts such as the schema~ or how they could be applied fruitfully to language processing. We think it is fair to say that the chapters in both volumes of this book document considerable progress on these and other problems. During this same period, work emerging from other research groups has also produced major advances. Yet, in spite of the progress, these explorations are not complete. The more we have learned, the more questions we have uncovered. Thus, we think of these volumes more as a progress report + +than as a final statement. + +Even as the book is going to press, the work is continuing and expanding. Our own ideas are evolving , and many other researchers are beginning to join in these explorations, bringing new viewpoints and new issues with them. In the following few paragraphs we sketch what we see as the major emerging themes of the next several years of work - the most promising directions and the biggest challenges that lie + +ahead. + +548 CONCLUSION + +From where we stand , three general areas stand out as major foci of + +Higher-Level Processes + +We began our work on POP models with applications that were more perceptual in nature and that focused more on those areas in which conventional sequential symbol-processing models have been least successful. We obviously believe this is only a first step. We believe that PDP models will provide useful insights into such higher-level cognitive processes as thinking and langauge processing. Chapters 14 and 19 offer our initial explorations of these areas. We do not mean to suggest that we believe these chapters provide all of the answers. Indeed, we have already begun to elaborate these ideas. More important , many other researchers have begun to appreciate the benefits of massively parallel processing in these areas, and are beginning to develop models that go beyond the first steps we have taken in these two chapters. Here we indicate a bit more of what we see as the general form these + +new directions will take. + +Sequential symbol processing. It is becoming obvious to many others besides ourselves that parallel processing and sequential symbol processing must somehow occur in the same system. There appear to be three major schemes for integrating these two processing modalities. One of these is our approach to the problem: to develop POP models in which sequential behavior is captured in the successive settlings of a parallel network or set of networks. Touretzky and Hinton (1985) , have been working somewhat along the same lines, developing a POP production system. They hope eventually to do variable binding and instantiation and, at the same time, preserve the benefits of parallel dis- + +future work. These are: + +mitant analysis of network architectures. + +. The closer binding of PDP models with neuroscience. + +We discuss each of these developments below. + +. The application of parallel distributed processing to higher-level cognitive processes and sequential symbol processing. + +. Further development of mechanisms of learning and a concom- + +of these, suggested by Norman in Chapter 26, is the idea of a hybrid system- a PDP net or set of nets, coupled with a symbol processing controller . A similar approach is taken by Schneider (1985) in his recent model of controlled and automatic processes in attention . A slight variant of this approach is to embed calls to parallel modules + +inside a conventional sequential-processing system. + +We applaud this kind of approach since it strives to preserve the best of both worlds. It also captures the fact that the cognitive system is complex and consists of many parts- a point that no one would dispute. We do not take this road ourselves, in part because we see no reason to suppose that the mechanisms that control cognitive processing are not themsel ves constructed of the same underlying parallel hardware as the other aspects of the cognitive systems, and in part because we prefer to view the system not so much in terms of controlled and controlling + +modules, but in terms of more distributed forms of control . + +The final approach is to modify other computational frameworks so that they incorporate many of the features of PD P models. This approach is exemplified by John R. Anderson's (1983) production system implementation of our interactive activation model, and Thi - + +badeau, Just, and Carpenter's (1982) CAPS production system. + +These developments are signs that other researchers, coming from other computational viewpoints, have begun to appreciate many of the benefits of interactive parallel processing. By building parallel capabilities directly into production systems, however (that is, by effectively allowing large numbers of productions to partially match at the same time) , these models have some tendency of becoming top-heavy. It remains to be seen whether the direct computational benefits these models have (e.g., explicit , direct variable binding of many productions at the same time) will turn out to outweigh the extra computational overhead they introduce. Our own hope is that we can succeed in achieving models that capture the extent of human capabilities more naturally as emergent properties of parallel networks, but in the meantime , these massively parallel production systems provide another way to bring parallel distributed processing together with the sequential + +symbol-processing tradition in cognitive science. + +FUTURE DIRECTIONS 549 + +Language processing. We began our work on POP models with a strong interest in linguistic information processing. It was an attempt to deal with the problems we saw with more conventional accounts of language that contributed to our original attraction to POP models. Some of the basic directions of our account of language are indicated in Chapters 18 and 19. We see the fleshing out of these sketches as central to our understanding of language acquisition, syntactic processing, and the interaction between syntactic and semantic processing. + +550 CONCLUSION + +Although it is not yet represented directly in our work , we believe that our approach will offer new insight into the role of metaphor and analogy in language. Chapter 19 begins to indicate that the notion of literal meaning, like the notions of grammaticality in syntax and regularity in morphology, will turn out to be a matter of degree and will best be explained in terms of coalitions of units interacting to produce the observed regularities. The notions of figurative and literal meanings will best be seen as coarse categories describing the nature of the meanings synthesized by POP networks rather than fundamentally dif ferent meaning types arising from fundamentally different processes. Meanwhile, it is clear to everyone that language processing provides many challenges and many opportunities to test and elaborate our developing conception of how to build powerful processing machinery out of simple computational elements, while at the same time preserv- + +ing the beneficial aspects of parallel distributed processing. + +Learning and Architecture + +Learning has always been a key issue in the development of network models. One of the most appealing features of POP networks is that very simple, homogeneous learning procedures can be used to allow the networks to self-modify and adapt to their environments . Until very recently, these self-organizing systems have been of limited complexity . No multilayer learning algorithm has existed. Two such learning procedures have been developed in this book (Chapters 7 and 8) and others are under development elsewhere (cf. Barto & Anandan, 1985) . These learning schemes are already generating a large amount of activity . With the development of the error propagation learning procedure, for example (Chapter 8) , we can study the kinds of internal representations that evolve to support processing in particular problems and, in that way, come to understand better the problems under study as well as the nature of the networks required to solve them. Moreover, we can use these powerful learning procedures for genuine artifi cial intelligence- that is, as a tool for designing systems capable of dis- + +covering new ways of solving difficult problems. + +Neuroscience + +In spite of the fact that POP models exploit brain-style processing, our own work has not yet moved far toward making direct contact with neuroscience. We believe that the opportunity is there, however, and + +Neuropsychology. The study of cognitive deficits that arise from brain damage has focused on dissociations of function . If one patient shows one deficit , and another shows a different deficit , it is reasonable to infer that their different pathologies damaged different , separable components of the cognitive system. From this kind of data, one can try to characterize the separate components of the cognitive system and to identify the role each component plays in the functioning of the system as a whole. This approach has been successful in leading to several important insights about the macrostructure of the cognitive system. But there has been little work , until now, that focuses on the development of models that attempt to characterize the microstructure of the components in such as way as to provide an account of the way in which performance degrades with damage. Cognitive dysfunction is a matter of degree, so different patients can manifest widely different degrees of what appears to be a common deficit . Mild cases often show their deficits in subtle ways, and make rel'atively subtle errorsconfusing similar concepts but not confusing distinct concepts. Some pathologies that produce highly diffuse damage (e.g., Alzheimer 's disease) are progressive and increase gradually in severity as the disease + +process continues. + +PDP models hold out considerable promise of providing detailed accounts of the way in which cognitive function degrades with damage. This point has been made by J. A . Anderson (1977~ Anderson, Silverstein, Ritz, & Jones, 1977) and by Wood (1978) , and models of aspects of neuropsychological phenomena can be found in two places in this book (Chapters 3 and 25) . Much more can now be done, we think , to further the application of PDP models to neuropsychological phenomena. Equally important , neuropsychological data can, in some cases, help us make decisions about the macrostructure of the cognitive systems we construct out of PDP networks. Thus, there is hope that we will soon see real synergistic interactions between neuropsychology + +and parallel modeling. + +FUTURE DIRECTIONS 551 + +that the future will bring more and more models specifically designed with data from neuroscience in mind . There are two natural areas of application- the application to data from people with brain pathologies and the application of POP models to detailed modeling of neuro- + +physiological and neuroanatomical data. + +Physiology and anatomy. Our primary focus has been on "cognitive " data, but the language of PDP is, by design, well suited as a medium for actual neural modeling. We expect that as these theoretical tools become more familiar and better understood, they will prove more and more useful for organizing data from neuroscience. One clear example of this lies in the paper by Gluck and Thompson (in press) , in which POP modeling techniques are applied to an analysis of condition ing in the simple nervous system of Aplysia, :!s stLitiied by Kandel and his collaborators (Hawkins, Abrams, Carew, & Kandel, 1983~ Kandel & Schwartz, 1982) . Although we are a long way from connecting our more abstract networks with particular brain structures, we believe that the application of POP models to cognitive and neural modeling enterprises will serve to both clarify the specifically neuroscience questions and lead us to a better understanding of the actual neural substructure + +underlying cognitive processes in the brain. + +In addition to the neurophysiology of the brain, we expect that neuroanatomical facts will have an increasing impact on the way we build our POP models. We have learned that the major determiner of what a particular system learns is largely a function of the possible connections. 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( 1983b ) . Colour coding in the cerebral cortex : The responses of wavelength -selective and colour -coded cells in monkey visual cortex to + +changes in wavelen ~th composition . Neuroscience ~ 9~ 767-781 . + +Zipser , D . ( 1985) . A computational model of hippocampal place fields . + +Behavioral Neuroscience , 99 , 1006 - 1018 . + +Index + +Page numbers in roman type refer to Volume 1,. page numbers in + +italic type refer to Volume 2. + +Abeles , M ., 367 , 369 , 385 , 553 Abelson , R . P ., 18 , 19 , 574 Abrams , T . W ., 552 , 561 Abramson , A . S . , 94 , 560 Abstraction models of memory , + +199 -206 + +comparison of experimental and simulation results , 203 - 205 other findings on , 205 -206 summary of training and test + +stimuli , 202 -203 + +Whittlesea 's experiments on , 201 - + +202 + +Ackley , D . H ., 264 , 306 , 313 , 317 , 335 , 507 , 510 , 393 , 562 ACT \* model , 32 , 124 , 127 + +Activation functions examples of + +> gating activation function , 426 semilinear , 52 , 324 -328 quasi -linear , 425 quasi -multilinear , 426 squashing function , 425 + +unit , 425 logic of + +> conclusions on , 442 -443 description of , 363 examples of , 428 -429 main concepts of , 426 -428 as major aspect of POP models , + +51 - 52 + +results of , 429 , 439 -442 rules , examples of , 425 -426 three -dimensional plots , 429 , + +430 -438 (Figs.) views of , 423 -425 Activation rule . See Activation + +functions + +Activation vector of harmony theoretical model , 215 -216 Active representation in PDP + +models . See PDP models , active + +representation in + +Addition problem , simple binary , 341 -346 . See also Delta rule , + +generalized Albright , T . D ., 368 , 558 + +Algebra , linear . See Linear algebra Algebraic properties of inner products , 382-383 . See also + +Vectors + +Allman , J ., 347 , 374 , 375 , 553 , 554 Alternative activity patterns , 82-83 AM . See Monocular occlusion + +Amari , S. A ., 42 , 45 ~ 444 , 507 ~ 489 ~ + +495 , 553 Ambiguity + +> lexical , 302 - 304 structural , 304 -305 + +and shading of feature patterns , + +305 -306 + +Ambiguous characters , 8, 155-157 . See a/so Reading , programmable + +blackboard model of Amnesia . See also Memory , a distributed model of + +anterograde , 504 , 505 -506 , 512 -513 bitemporal , basic aspects of , 505 - + +506 + +conclusions on , 527 description of , 503 -505 + +neurochemistry of synaptic change , hypothetical account of , 507 -509 paradox of , resolution to , 506 -507 quantitative model , formulation of , + +509 + +relation to other accounts of , 510 - + +511 + +residual learning in , 518 -524 + +simulations , 511 - 518 + +anterograde amnesia , 512 -513 lost memories , recovery of , 515 - + +516 + +retrograde amnesia , 513-515 retrograde and anterograde amnesia , correlation of , 513 + +studies on , 516 -518 summary of , 518 + +spared learning in , 207 -208 , 518 , + +524 - 526 + +Anandan , P ., 322 , 508 , 550 , 554 AND function , 429 . See also Boolean function Anden , N . E ., 350 , 553 Andersen , P ., 336 , 553 + +Anderson , C . W ., 539 , 554 + +Anderson , J. A ., 33 , 42 , 56 , 62 , 66 , 68 , 80 , 82 , 101 , 406 , 409 , 410 , 418 , 507 , 510 , 511 , 8 , 173 , 183 , 200 , 226 , 277 , 311 , 380 , 389 , 394 , 399 , 432 , 551 , 553 , 554 , + +562 , 564 + +Anderson , J. R ., 32 , 124 , 127 , 251 , 461 , 507 , 173 ., 206 , 209 , 524 , + +549 , 554 , 558 Anlezark , G . M ., 477 , 554 + +Annealing , simulated . See Simulated + +annealing + +Aragon , C . R ., 235 , 508 Arbib , M . A ., 362 , 577 + +Arbitrary mapping , implementing , + +96 - 104 + +grapheme strings , 97-99 , 102 sememe units , 97 -98 , 99 , 101 - 102 three -layer network , 97-98. See also Boltzmann machines Arguments , missing , filling in , 301 - 302 . See also Case role assignment , model of + +Ary , M ., 477 , 564 Asanuma , H . , 357 , 554 Asynchronous update vs . synchronous update , 61 A TN . See Augmented transition + +network parsers + +Attention + +networks for focusing , 114- 118 shifting focus of , 147-151 Augmented transition network parsers (A TN ) , 119 + +Auto -associative paradigm . See a/so Memory , a distributed model of + +definition of , 55 , 161 modification of , 211 -212 + +Back -propagation simulator , description of , 328 -330 Bagley , W . C ., 58 , 98, 106, 554 + +Baht , L . R . , 293 , 508 Baker , J . F . , 347 , 554 Baker , R . G ., 24 , 515 + +Ballard , D . H . , 12 , 43 , 45 , 72 , 117 , 124 , 133 , 282 , 508 , 509 , 128 , + +Bitemporal amnesia . bitemporal Bixby , J. L ., 345 , 577 Blake , A ., 285 , 508 + +See Amnesia, + +Blakemore , C ., 11 , 508 , 475 , 489 , 490 , 491 , 497 , 500 , 555 , 571 , 577 + +Blanchard , H . E . , 161 , 568 Blank , M . A ., 79 , 111 , 559 Blasdel , G . G ., 487 , 490 , 555 Blends of memory traces , 208 . See also Memory , a distributed model + +of + +Bloom , F . E ., 364 , 385 , 569 Bloom , M . J., 385 , 560 Blumstein , S., 62 , 576 Bobillier , P ., 350 , 555 + +Bobrow , D . G ., 9 , 79 , 133 , 513 , 18 , + +19 , 536 , 555 , 570 Boltzmann machines + +damage , example of effects of , + +304 - 313 + +description of , 43 , 148- 149 hard learning , example of , 299-303 annealing schedule , 302 shifter network performance , + +302 - 303 + +training procedure , 300 learning algorithm , 294-303 , 209 conclusions on , 313 -314 derivation of (App .) , 315-317 failure of algorithm , 298-299 hardware , unreliable , achieving reliable computation with , 303- + +304 + +learning , easy and hard , 290-294 relaxation searches , use of to perform , 283 -290 research with , 264 + +second -order observables and , + +273 - 275 + +unlearning , 296 -298 Bond , Z . S . , 61 , 555 Bonds , A . B ., 476 , 478 , 560 + +Boolean function , 428 , 429 , 439 -442 activation function as extension of , + +373 , 381 , 554 , 559 Banerjee , S. P., 477 , 561 Barber , R . P ., 351 , 562 Bard , P ., 352 , 579 Barlow , H . B ., 373 , 554 Barnes , C . A . , 448 , 568 Barrow , H . G ., 63 , 554 + +Bartlett , F . C ., 81 , 508 , 17 , 19 , 554 Barto , A . G ., 43 , 53 , 57 , 321 - 322 , 444 , 508 , 515 , 383 , 539 , 550 , + +554 , 576 Barwise , J ., 195 , 508 Basket cells , 363 -364 + +Bates , E ., 217 , 273 , 274 , 554 , 567 Baumgartner , G ., 376 , 578 + +{J -coefficient constants , (App .) , 467 - 468 . See also {J-coefficient model {J -coefficient model , 460-466 . See also Place recognition and goal location , biologically plausible + +models of + +concept , network using , 461 -462 constants (App .) , 467 -468 description of , 460-461 + +issue in , 463 performance of , 464 programming , 463 simulation of , 469 -470 testing , 463 -464 + +BO . See Binocular deprivation + +Bear , M . F ., 477 , 554 Becker , J. T ., 435 , 554 Benoit , R ., 364 , 569 Bentivoglio , M ., 350 , 567 + +Berko , J ., 40 , 508 , 219 , 220 , 265 , + +555 + +Berman , N . , 475 , 478 , 558 Bernstein , J., 153 , 159 , 508 + +Best , P . , 435 , 571 + +Bever , T . G ., 274 , 555 , 559 Bienenstock , E . L ., 42 , 180 , 508 , 480 , 487 , 489 , 495 , 555 + +Binder , K ., 230 , 508 Binding problem , 88-90 of neurons , 377 -378 + +Boolean function (continued) linearly separable functions , 440 mapping from expressions , 439 neurons treated as devices , 424 -425 + +XOR function , 429 + +Bottom -up approach to analysis of information processing systems , + +123 + +Bottom -up presentation of harmony theory , 199, 213 -261 . See also + +Harmony theory + +Bottom -up processing system , 51 matrix representation of , 57-58 + +Boycott , B. B., 336 , 558 Brachman , R . J . , 313 , 555 + +Brain . See Cerebral cortex , anatomy and physiology of ~ Cerebral cortex , questions about computation in + +Brain damage . See also Amnesia ~ Damage , effects of on a network graceful degradation and , 29, 134 neuropsychological investigation of + +patients with , 134- 135 simulated effects of , 304 -313 Brain state in a box model (BSB) , + +66 -68 + +Branch , M ., 435 , 571 + +Brayton , R . K ., 381 , 382 , 575 Bresnan , J . , 274 , 559 , 564 Brightman , M . W ., 336 , 572 + +Broadbent , D . E ., 121 , 508 , 97 , 532 , + +555 + +Brock , L . G ., 367 , 555 Brodmann , K ., 345 , 346 , 555 Brodmann ' s areas of the neocortex , 345 -346 . See also Cerebral cortex , anatomy and physiology + +of + +Brooks , C . McC ., 336 , 553 Brooks , L . R . , 171 , 556 Brown , P., 295 + +Brown , R ., 219 , 241 , 556 Bruce , C . J . , 368 , 556 , 558 Brugge , J. F ., 356 , 563 + +BSB model . See Brain state in a box + +model + +f3 units , simulations of (App .) , 469 - 470 . See also {3-coefficient model + +Bunt , A . H . , 357 , 566 + +Bybee , J. L ., 221 , 24 7, 24 9, 250 , 251 , 254 , 255 , 256 , 556 + +CA . See Connection activation unit + +Caan , W ., 368 , 571 + +Cajal , S. Ramon y, 336 , 350 , 358 , 359 , 361 , 363 , 367 , 556 Caminiti , R ., 377 -378 , 560 Canonical feature detectors , 114 + +Caplan , C. J., 478 , 570 Carew , T . J ., 552 , 561 Carlson , M ., 275 , 573 Carman , J . B . , 350 , 556 Carnes , K . M ., 477 , 554 + +Carpenter , P. A ., 153, 161, 549 , 564 , + +577 + +Carroll , Lewis , 97 Cascade model , 42 + +Case role assignment , model of architecture of , 277 -289 + +> case role representation , 286 -288 semantic microfeatures , 278 -283 sentence processing and learning , + +details of , 288 -289 + +sentence - structure units , 283 - 286 + +descriptions of , 3-4 discussion of , 313 - 325 con text -sensi ti ve coding , + +iteration , and center embedding , + +323 - 325 + +fixed -length , 320 -322 limitation myths , 322 -323 meaning , representation of , 315 - + +316 + +model , basic features of , 314 -315 parsers , conventional interfacing + +with , 317 - 318 recursion , 318 -320 goals of , 276 -277 studies on , 277 + +multiple constraints on , 272 -275 studies on ~ 273 ~ 275 ~ 277 simulation experiments of , 289 -292 + +feature patterns ~ shading of ~ 305 - + +306 + +lexical ambiguity resolution ~ 302 - + +304 + +missing arguments, filling in~ + +301 - 302 + +novel words , generalization to , + +307 - 310 + +other creative errors ~ 306 -307 roles , distributed representation + +of , 312 -313 + +semantic and word - order cues , + +use of in , 293 -300 + +straightforward extensions , 310 - + +312 + +structural ambiguity of , 304 -305 verb -frame selection ~ 300 -301 + +Central module ~ 130 - 131 Cerebral cortex ~ anatomy and + +physiology of cortex inputs ~ 346 -356 + +irregularities within ~ 353 -356 topographic representation of , + +352 - 353 cortical areas of , 345 cortical outputs , 356 -357 feature detection of ~ 367 -371 firing , rates of , 366 -367 + +general organization of , 340 -345 + +main layers , 341 -345 general points on , 333 -335 group neuron behavior in , 365 -366 neocortical neurons , nature of cell types in , 358 -360 + +excitatory VS. inhibitory neurons , + +362 + +experimental methods , 357 -358 neurons without many spines , + +361 + +neurons with spines , 360 -361 special cell types , 362 neuron behavior in , 364 - 365 neuron ~ classical , 335 - 337 + +peptides , 339 + +synapses , types of , 338 -339 Cerebral cortex , questions about + +387 -389 + +neuronal plasticity in , 385 -387 neuronal processing in , 378 -382 nonlinear computations , 381 single-shot algorithms , 380-381 timing problem , 378 -380 representing information in , 373 - + +377 + +binding problem , 377 surround effects ~ 374 -377 temporal binding ~ 383 -385 + +Chace ~ P .~ 513 , 576 Chandelier cells ~ 362 -363 Changeux , J. -P., 387 ~ 556 Chapman ~ R . A .~ 485 , 556 Charniak , E .~ 324 , 556 Chase ~ W . G .~ 241 , 508 Chauvin , Y .~ 213 ~ 332 - 334 ~ + +Chomsky ~ N ., 24, 119~ 123, 246 , 508 + +Christen , W . G .~ 478 , 570 Christensen , R ., 227 ~ 508 CID . See Connection information distribution mechanism Clark ~ W . A ., 154 , 509 + +Class C' perceptron (Rosenblatt ) , + +155 - 156 + +Classification paradigm , 161 Coarse coding , 91-96 . See also Conjunctive encoding ~ Distributed representations + +limitations on , 92 -94 principle underlying , 94-96 Cognition and parallel distributed processing . See PDP approach , + +introduction to + +Cognition , microstructure of , 12- 13 Cognitive science . See PDP approach + +and cognitive science Cognitive theories , constraints on , + +129 - 130 + +Cohen ~ M . A . , 389 , 556 Cohen ~ M . M ., 81 , 86 , 568 Cohen ~ N . J ., 510 , 519 ') \_520 , 521 - 522 , 524 , 525 , 527 ') \_556 , 576 COHORT model (Marslen - Wilson ) , + +COHORT model (continued) resolution of , 101 - 106 Cole , K . S., 364 , 556 + +Cole , R . A ., 58 , 61 , 98 , 99 , 100 , + +107 , 111 , 556 , 557 Collins , A . M ., 85 , 508 + +Colonnier , M ., 348 , 361 , 557 , 571 Colon Osorio , F . C ., 424 , 510 Coltheart , M ., 102 , 508 Competence theorem , 226-229 Competitive inhibition , 21. See also Phoneme identification , factors + +influencing + +effect of at phoneme level , 89-90 + +Competitive learning + +architecture of competitive learning + +system , 162 - 166 + +basic components of , 151 - 152 characteristics of , 166 - 167 conclusions on , 190 definition of , 147 + +dipole experiments , results of , + +170 - 177 + +correlated teaching inputs , 182- + +183 + +letter similarity effects , 182 number of elements , effect of per serial position , 181- 182 position -specific letter detectors , + +180 - 181 + +word detection units , 181 word perception model , 177- 180 + +formal analysis of , 168- 170 geometric interpretation of , 164- + +166 + +history of , 152- 159 + +horizontal and vertical lines , experiments with , 184- 190 + +mechanism of , 159 + +neural -like processing systems , + +160 - 161 + +in P3 simulation system methods (App . B) , 504-506 plans for (App . A ) , 502-503 Completion task , example of , 206- + +cerebral cortex in , 387 - 389 Computational temperature ( 7) , 211 Computational viewpoint on POP + +models , 397 -398 Conel , J. LeRoy , 358 , 557 + +Confabulation , as a stable pattern , 81 Conjunctive encoding , 90-91 , 96 . See also Coarse coding ~ Distributed representations CONNECT statements for P3 system , 495 -496 . See also P3 + +system + +Connection activation system , 130 - + +134 + +Connection activation unit (CA ) . See also Connection information distribution mechanism definition of , 132 - 134 + +multiple pattern processing , 477 - + +478 + +requirements of , 474 -476 + +single pattern processing , 476 -477 summary of requirements , 480 -481 Connection information distribution (CID ) mechanism , 473 -486 , 129 - 134 , 137 , 139 - 140 benefits of , 164 - 166 + +central knowledge store in , 130-134 computer simulation of word recognition using , 134-136 extensions of , 167 - 168 + +resource requirements of , 473 -486 , + +166 - 167 + +Connectionist models , 72 Connolly , M ., 353 , 355 , 566 Connors , B . W ., 364 , 369 , 557 Constructor , as major component of P3 system , 489 . See also P3 + +system + +Content -addressable memory , 79 - 80 + +Continuity and uniqueness + +constraints in depth perception , + +19 -20 + +Cooling schedule , 244 -245 . See also Electricity problem -solving ~ + +in Boltzmann machines , 304 -313 + +Daniel , P . M . , 354 , 558 Daniels , J . D ., 477 , 554 Darien -Smith , J ., 480 , 574 Davis , E ., 432 , 558 + +Daw , N . W ., 497 , 500 , 558 , 577 Deacedo , B . S., 519 , 524 , 556 Decay process in increments to + +weights , 181 . See also Memory , a + +distributed model of Decision -making and freezing in + +harmony theory + +coherent interpretation , robustness + +of , 240 + +idealized task , 238 - 239 + +phase transitions , computational significance of , 236-237 symmetry breaking , 237-238 thermodynamic limit , 239 + +Deep dyslexia , 102 + +Degradation , effects of and benefits of redundancy , 472 . See also Standard pattern associators Deliberate conscious control (DCC ) , 543 -545 . See a/so PDP approach , + +reflections on + +Delta rule , 43 , 53 , 62 , 63 , 363 , 417 - + +418 + +Delta rule , analysis of . See also Delta rule , generalized and multiple linear regression , + +457 -458 + +in pattern -based coordinates , 447 - + +453 + +statistical learning and , 453 -457 + +summary of , 458 -459 in vector notation , 445 -447 Delta rule , generalized , 149 application of , 327 -328 conclusions on , 361 -362 general cases, 352 -361 recurrent nets , 354 -361 and gradient descent , 322 -324 + +problem of , 318-323 XOR problem , 319 -321 for semilinear activation functions in feedforward networks , 324 - 328 + +Cooper , L . N ., 42 , 180, 508 , 480 , 487 , 489 , 499 , 555 , 557 , 573 + +Corkin , S., 519 , 524 , 556 Cortical areas of the neocortex , Brodmann 's cortical parcellation + +scheme , 345 input systems , 346 + +irregularities within , 353-356 thalamus , as gateway to cerebral + +cortex , 349 - 352 + +topographic representation , 352 - + +353 + +output systems , 356 - 357 Cortical plasticity , processes that modulate , 476 - 478 Cotton , S., 99 , 105 , 557 + +Cottrell , G ., 165 , 277 , 311 , 314 , 557 + +Coulter , J . D ., 357 , 570 Cowan , J . D ., 381 , 389 , 578 Cowan , W . M ., 350 , 351 , 556 , 572 + +Cowey , A ., 363 , 576 Crain , S., 274 , 557 Crane , A . M ., 350 , 572 + +Crick , F . H . C ., 296 , 297 , 509 , 351 , + +384 , 387 , 557 + +Critical or sensitive period of plasticity , 473 -484 + +cortical plasticity , processes that + +modulate , 476 - 477 + +effect of environment on , 478 hypothesis for , 483-484 + +ocular dominance statistics , 474 - + +476 + +other examples of , 477 -478 Crosstalk , 139 - 142 . See also Reading , programmable blackboard model of Crow , T . J ., 476 , 477 , 554 , 557 Crowder , R . G ., 64 , 94 , 209 , 557 Cynader , M ., 475 , 476 , 478 , 492 , + +498 , 557 , 558 + +Dahlstrom , A . , 350 , 553 + +Damage , effects of on a network , 29, 134 , 472 . See also Amnesia ~ Boltzmann machines ~ Brain damage ~ Graceful degradation + +Delta rule , generalized (continued) simulation results , 328 -330 , 352 encoding problem , 335-339 negation problem , 346-347 + +parity , 334-335 + +simple binary addition problem , + +341 - 346 + +symmetry , 340 -341 T -C problem , 348-352 XOR problem . 330 - 334 use of to determine size and direction of changes in connections , 179 - 181 generalized , 209 DeMarzo , P . M . , 241 , 242 , 509 Dempster , A . P., 293 , 509 + +Dendrites , studies on , 381 -382 . See also Cerebral cortex , questions + +about computation in + +Denes , P ., 87 , 558 + +de Riboupierre , F ., 385 , 553 de Riboupierre , Y ., 385 , 553 Derthick , M ., 298 , 299 , 509 , 313 Desimone , R ., 368 , 374 , 556 , 558 Dipole experiments for competitive learning mechanisms , 170- 174 formal analysis of , 174- 177 homogeneous stimulus patterns , + +191 - 193 + +Distal landmarks for biologically plausible models of place + +recognition and goal location , 445 Distributed representations . See also Memory , a distributed model of ~ + +Schemata , concept of + +features of + +generalization effects , 82-85 + +memory , 79 -81 new concepts ~ 86 - 87 + +status of ~ 78 - 79 + +structure in representations and + +processes ~ 104 - 108 constituent structure ~ representing ~ 105- 106 sequential symbol processing ~ + +106 - 108 summary on ~ 108 - 109 technical details of ~ 87 - 104 arbitrary pairing , implementing , + +96 - 104 + +binding problem , 88-90 coarse coding , 91-96 conjunctive encoding , 90-91 Distributed view -field model for goal location , 449 - 460 . See a /so Place recognition and goal location , biologically plausible models of + +description of , 451 -453 network used in , 450 -451 P3 simulation of , 453 -454 + +Symbolics 3600 LISP machine , + +use of for , 454 -456 + +problems of , 451 properties of , 453 testing of , 453 Dobson , V ., 97 , 100 Dostrovsky , J., 435 , 571 Dowling , J. E., 336 , 558 , 578 Drager , U . C., 490 , 558 Dretske , F ., 195 , 509 Duckrow , R . B ., 477 , 561 Duda , R . 0 ., 380 , 558 Dukes , K ., 61 , 110 , 570 Durham , D ., 500 , 558 + +Dynamic functional system , 41 Dynamical systems , perspective of POP models as , 397 - 398 + +Eccles , J . C . , 336 , 367 , 370 , 553 , + +555 , 558 + +Edelman , G . M . , 387 , 558 Edmonds , D . , 153 , Ehrlich , S ., 163 , 573 + +Eichenbaum , H ., 385 , 519 , 524 , 556 , + +565 + +Eigenvalues . See Eigenvectors and + +eigenvalues + +Eigenvectors and eigenvalues , 399 - 403 . See also Matrices and linear + +systems + +Eimas , P . D . , 94 , 473 , 558 , 560 + +Eisen , M ., 456 , 509 Elbaum , C . , 499 , 573 + +on amount of , 159 - 161 . See also + +Reading , programmable blackboard model of + +Feedforward networks , delta rule for semilinear activation functions in , 324 -328 . See also Delta rule , + +generalized Feinstein , D . J., 296 , 511 Feirtag , M ., 334 , 342 , 570 + +Feldman , J . A ., 12 , 43 , 45 , 72 , 75 , 86 , 117 , 124 , 130 , 181 , 509 , 9, + +128 , 559 + +Feldman , M . L ., 363 , 377 , 559 Feldman and Ballard units , 72 conjunctive units , 72 relation to sigma -pi units , 72 Felleman , D . J ., 352 , 354 , 385 , 569 , + +570 + +Fennell , R . D ., 63 , 122 , 573 Feustel , T . C ., 197 , 198 , 559 , 574 + +Fillmore , C . J . , 273 , 559 Finlay , B. L ., 367 , 574 Firing , rates of in neocortical neurons , 366 - 367 . See also Neocortical neurons ~ nature of First formant onset frequency (FIOF ) , 84 , 85 . See also Phoneme identification , factors + +influencing + +Fixations . See also Reading , + +programmable blackboard model + +of + +sequences of , 161 - 164 single and multiple , 153- 155 Fodor , J . A ., 141 , 509 , 274 , 559 + +Foley , J. D ., 467 , 559 Ford , M ., 274 , 559 Foss , D . J . , 79 , 111 , 559 + +Fowler , C . A ., 60 , 73 , 77 , 95 , 118 , + +559 + +Fox , R . A ., 79 , 559 , 560 Frames , use of as knowledge + +structure , 9 . See also Schemata , + +concept of + +Elio , R ., 172 , 558 + +Elman , J . L ., 58 , 63 , 69 , 71 , 80 , 81 , + +119 , 558 , 559 , 568 EM . See Expectation and maximization method Empiricism vs . nativism , 139- 142 + +Emson , P . C ., 364 , 559 + +Encoding problem , 335-339 . See also + +Delta rule , generalized Equilibrium states of the competitive learning system , 168- 170 Erman , L . D ., 63 , 122 , 559 , 573 Error correction rule . See Delta rule Error propagation , learning internal representations by . See Delta + +rule, generalized Ervin , S., 219 , 220 , 254 , 559 Espinosa , I . E., 385 , 560 Evanczuk , S., 385 , 560 + +Exclusive or (XOR ) problem , 64-65 , 96 , 319 -321 , 330 - 334 . See also + +Delta rule , generalized Executive -driven processing , 134 Expectation and maximization (EM ) + +method , 293 + +Explicit inaccessible rule , 217 . See also Verbs , learning past tenses of Explicit rule formulation , tradition , + +32 + +Fahlman , S. E ., 85 , 86 , 264 , 509 + +Fairen , A . , 363 , 559 Famiglietti , E. V ., 336 , 559 Fan - in . See Fan - out + +Fan - out + +definition of , 51 + +limited , effects of , 468 -472 method for overcoming limitation , + +470 - 472 + +neural nets , biological limits on storage capacity of , 469 -470 Fanty , M ., 320 , 321 , 322 , 559 Farley , B. G ., 154, 509 + +Freezing and decision -making in harmony theory . See Oecision making and freezing in harmony + +theory + +Freund , T . F ., 363 , 576 Friedlander , M . J ., 351 , 560 + +Fry , O. B., 94, 560 Fuchs , A . F ., 357 , \_) 66 + +Fujimura , 0 ., 62 , 473 , 560 , 569 Fujisaki , H ., 77, 94~ 560 + +Fukushima , K ., 42 , 152 , 162 , 300 , + +313 , 350 , 509 + +Future directions for POP , 547 - 552 Fuxe , K ., 350 , 364 , 553 , 560 Fuzzy map theory , 432 - 433 . See also Place recognition and goal location , biologically plausible + +models of + +Gallistel ~ C . R ., 141 , 509 Gamma factor in bitemporal + +amnesia , 507 + +Ganong , W . F., 60, 78, 560 Garey , L . J., 348 , 497 , 500 , 555 , + +560 ~ 577 Garnes , S ., 61 , 555 Garrett , M . F ., 274 , 559 Garrud , P . , 434 , 466 , 569 Gary -Bobo , E., 476 , 478 , 556 + +Gati ~ I .~ 499 , \_560 + +Gating activation function , 426 . See + +also Activation functions Gee , J ., 60 , 63 , 107 , 115 , 561 Gelatt , C . D . , Jr ., 48 , 235 , 287 , 511 Geman , D ., 148 , 264 , 271 , 278 , 289 , + +509 + +Geman , S., 148 , 264 , 268 , 271 , 278 , + +289 , 509 + +Generalization , 30 , 85 . See also Memory , a distributed model of Georgopoulos , A . P., 377 -378 , 560 Gernsbacher , M . A ., 79 , 559 Gerstein , G . L ., 385 , 560 + +Gibbs sampler , research with , 264 + +Gibson , E . J . , 198 + +Gilbert , C . D ., 356 , 358 , 366 , 385 , 480 , 560 , 561 , 577 , 578 Ginsburg , H . P., 241 , 509 + +Glaser , E . M . , 366 , 577 Glass , L ., 494 , 571 Glorioso , R . M ., 424 , 510 Gluck , M . A ., 383 , 552 , 561 Glushko , R . J ., 43 , 510 , 171 , 561 Goal location . See Place recognition and goal location , biologically + +plausible models of Goldman - Rakic , P . S . , 350 , 572 Goodness -of -fit function , 14 - 16 , 31 , 32 -33 , 35 -36 . See also Schemata , + +concept of + +Graceful degradation , 29, 134. See also Damage , effects of on a + +network Gradient descent + +> and delta rule , 322 -324 use of to solve hard optimizing problems on conventional computers , 287 - 288 + +Grapheme strings , 97-99 , 102. See also Arbitrary mapping , + +implementing Gray , E. G ., 339 , 361 , 561 Green , D . M ., 466 , 510 , 225 , 561 + +Green , K ., 96 , 569 Greenberg , Z ., 254 Greenway , A . P., 477 , 554 Grinvald , A ., 385 , 561 + +Grosjean , F ., 60 , 63 , 99, 100, 105, 107 , 114 , 115 , 557 , 561 Gross , C . G ., 368 , 556 , 558 + +Grossberg , S., 42 , 53, 70, 116, 146, 152 , 162 , 164 , 167 , 418 , 510 , 90 , + +389 , 494 , 535 , 556 , 561 Grossberg 's models , 70-71 Guillery , R . W ., 351 , 561 Gutnick , M . J ., 364 , 369 , 557 + +Haggard , M ., 85 , 576 Hale , B . L . , 159 , 563 Halle , M ., 24 , 508 , 168 , 561 Halmos , P . R ., 422 , 510 Hamiltonian function (H) , 211 + +Hebbian learning rule , 36, 37, 38, + +53 , 69 - 70 , 297 Heggel und , P., 497 , 564 Heidmann ~ T ., 387 , 556 Hein , A ., 475 , 478 , 558 Heise ~ G .~ 63 ~ 569 + +Hendrickson , A . E ., 344 , 357 ~ 566 ~ + +572 + +Henneberg , R . ~ 341 , 561 Hewitt , C ., 132 , 510 + +Hidden units , augmenting memory with , 209 -214 . See a/so Memory ~ + +a distributed model of Hidden units , definition of ~ 48 Hierarchy , kinds of , 105- 106 + +Hinton ~ G . E .~ 17 , 20 , 33 , 42 , 80 , 82 ~ 83 , 84 , 96 , 107 , 114 ~ 115 , 127 , 133 ~ 264 , 272 , 282 ~ 283 , 289 , 297 ~ 302 ~ 306 , 313 , 317 ~ 335 , 350 ~ 507 ~ 508 ~ 510 , 511 ~ 515 , 8 , 23 ~ 24 , 63 , 68 ~ 128 ~ 129 ~ 151 , 173 , 175 ~ 209 , 210 , 277 , 278 , 312 , 313 , 314 ~ 318 , 322 , 373 , 377 , 381 , 389 , 393 ~ 394 , 533 , 539 ~ 548 ~ 554 , 562 , 575 ~ 577 Hinton 's scheme for mapping + +patterns , 114 - 115 , 117 ~ 118 . See a /so Attention , networks for + +focusing + +Hintzman , D ., 171 , 172 , 200 , 562 + +Hiorns , R . W ., 344 , 573 Hirst , G ., 321 , 575 Hoff , M . E ., 321 , 444 , 516 + +Hofstadter , D . R ., 43 , 132 , 202 , 213 , + +264 , 511 , 20 , 562 Hogg , T ., 313 , 511 , 389 , 562 H6kfelt , T ., 350 , 364 , 560 , 577 Homogeneous dipole stimulus patterns (App .) , 191- 193 Hopfield , J. J., 43 , 61 , 81 , 133, 148, 285 , 286 , 296 , 297 , 418 , 511 , 13 , + +14 , 389 , 394 , 562 + +Hopfield nets , applying simulated annealing to , 288 -289 . See also + +Simulated annealing Hopkins , W . F ., 477 , 562 Horizontal and vertical lines , experiments with , 184- 190 + +Harik , S. J., 477 , 561 Harmonium machine , 212 Harmony function (H) . See also + +Harmony theory + +basic requirements of , 220-223 cognitive systems and, 267-268 mathematic formulation of , 208 , + +211 + +retrieving information from , 269- + +272 + +terminology , 268-269 Harmony theory , 213-220 conclusions on , 261 - 262 + +decision -making and freezing , 236 - + +240 + +definition of , 148 + +electricity , problem -solving of , + +240 -250 goal of , 198-199 + +learning new representations , 258 - + +261 + +macrodescription , 251-258 mathematical results , description + +of , 226 - 236 + +competence theorem , 226 - 229 learnability theorem , 235-236 physics analogy , 229 -230 realizability theorem , 230-235 perceptual processing centrality , + +197 - 198 + +and probability , 220-226 research with , 264 + +schema theory and self -consistency + +of , 199 - 213 + +theorems on , formal presentation + +of , 264 - 281 + +top -down strategy pursued in , 196 + +Harris , K . S ., 92 , 576 Hart , P . E .~ 380 ~ 558 Hash coding , 80 Hawken , M . J ., 490 , 555 Hawkins , R . D ., 552 , 561 HEARSAY model of speech + +understanding , 43 , 119, 122- 123, + +associators ; Reading , + +programmable blackboard model of ; Standard pattern associators Interference of memories , 208 - 209 . See also Memory , a distributed + +model of + +Internal representations . See Delta rule , generalized ; Representation , + +learning of IS - A hierarchy , 105 Isenberg , D . , 7 , 511 + +Isomorphism hypothesis . See also POP models , neural and conceptual interpretation of of conceptual and neural levels , + +395 - 396 + +failure of in nonlinear models , + +422 - 424 + +levels and localized damage , 413 - + +416 + +levels , learning of connections and , + +416 - 418 + +in linear systems , 411 - 413 Iverson , L . L . , 340 , 563 + +Jackson , J . H . , 41 , 141 , 511 Jacoby , L . L . , 171 , 172 , 192 , 193 , + +556 , 563 + +Jakimik , J . , 61 , 98 , 99 , 100 , 107 , + +111 , 557 Jelinek , F . , 293 , 508 Jenkins , J . J . , 473 , 569 Jenkins , W . M . , 385 , 563 Johnson , D . S . , 235 , 508 Johnson , E . , 324 , 563 Johnston , D . , 477 , 562 + +Johnston , J . C . , 159 , 160 , 563 , 574 Jones , E . G . , 351 , 352 , 357 , 363 , + +563 , 564 + +Jones , R . S . , 56 , 406 , 409 , 410 , 418 , 507 , 173 , 226 , 311 , 551 , 554 + +Jouvet , M . , 350 , 555 Julesz , B . , 18 , 511 + +Just , M . A . , 153 , 161 , 549 , 564 , 577 + +Kaas , J . H . , 345 , 352 , 354 , 385 , 386 , + +Horizontally hierarchical networks , + +217 + +Houde , J ., 353 , 355 , 566 Houser , C . R ., 351 , 562 + +Hubel , D . H ., 340 , 353 , 356 , 367 , 373 , 474 , 475 , 483 , 497 , 500 , + +562 , 563 , 566 , 578 + +Huberman , B . A ., 313 , 511 , 389 , 562 Hughlings -Jackson , J., 41, 141- 142 Human information processing . See also PDP approach , reflections on + +essential properties of , 537 new understanding of , 545 -546 Human memory . See Memory , a distributed model of ; Memory ~ retrieving information from HummeJ , R . A ., 285 , 286 , 511 , 514 + +Hunt , S . P ., 364 , 559 + +Huppert ~ F . A .~ 516 ~ 517 ~ 563 - - . , , , 6-hydroxydopamine (6-0HDA ) , + +477 -496 + +Identity Irote combinations , 106. See also Case role assignment , model of ~ Distributed representations + +Imbert , M ., 476 , 478 , 556 Imig , T . J., 356 , 563 + +Implementational (physiological ) level of distributed memory , 121 Inner products . See also Vectors algebraic properties of , 382-383 in two -dimensional space , 380 - 382 + +Input units , definition of , 48 Interactive activation model of word perception , 43 , 71-72 , 177- 180, 216 - 217 , 125 - 129 , 137 -138 In teracti ve model of reading (Rumelhart ) , 43 , 122 + +Interactive models , representation of in matrix form , 57 , 59 -61 . See also Interactive activation model + +of word perception layered systems , 60 one -step system , 60 single -level , 60 three -level , 59 + +Kaiserman - Abramof , I . R ., 336 , 361 , + +365 , 571 + +Kalaska , J . P ., 378 , 560 + +Kandel , E . R ., 333 , 364 , 507 , 552 , + +561 , 564 , 576 Kanerva , P ., 76 , 465 , 511 Kant , E ., 17 , 19 , 564 + +Kaplan , R . M ., 119, 516 , 274 , 559 , + +564 + +Kasamatsu , T ., 476 , 477 , 492 , 497 , + +564 + +Kawamoto , A . H ., 101 , 511 , 277 , + +311 , 564 + +Kawashima , T ., 77 , 94 , 560 Keele , S. W ., 171 , 183 , 200 , 203 , + +572 + +Kelly , J. P., 480 , 560 Kewley -Port , D ., 85, 564 + +Kienker , P . K ., 302 , 350 , 511 , 515 Kinematics of the dynamical system , 398 -399 , 400 -403 . See a /so PDP models , neural and conceptual + +interpretation of + +Kirkpatrick , S., 148, 235 , 287 , 511 + +Kisvardy , Z . P., 363 , 576 Klatt , D . H ., 59 , 60 , 62 , 564 + +Kliegl , R ., 273 , 567 Knapp , A ., 173 , 200 , 564 Knowledge atoms definition of , 202 + +and electricity problem -solving , 242 Koch , C ., 365 , 381 , 383 , 564 , 565 Kohonen , T ., 42 , 45 , 62 , 63 , 152 , 406 , 409 , 418 , 422 , 424 , 425 , 444 , 446 , 455 , 461 , 511 , 222 , + +226 , 380 , 565 Konishi , M ., 473 , 565 Kratz , K . E ., 490 , 565 Krnjevic , K ., 339 , 565 + +Kubie , J . L ., 435 , 441 , 445 , 447 , + +565 , 570 + +Kucera , H ., 74 , 240 , 565 + +Kuczaj , S. A ., 219 , 220 , 221 , 253 , + +257 , 258 , 565 Kuffler , S. W ., 367 , 565 Kuipers , B., 433 , 565 Kullback , S., 294 , 511 Kuno , M ., 336 , 565 + +Kuperstein , M ., 385 , 565 Kupperman , B., 478 , 572 Kurtzman , H . S., 275 , 565 Kuypers , H . G . J. M ., 352 , 571 + +Laird , N . M ., 293 , 509 Lakoff , G ., 97 + +LaManna , J . C ., 477 , 561 Lamperti , J., 277 , 511 Lane , H . L ., 91 , 565 Lang , K ., 127, 510 Lang , M ., 511 + +Language acquisition device (LAD ) , 217 . See also Verbs , learning past + +tenses of Larkin , J . H ., 241 , 512 Larsson , K ., 350 , 553 Lashley , K . S., 41 , 512 + +Law of mass action , 509 -510 . See + +also Amnesia + +Layered systems in interactive + +models , 60 Lazarus , J. H ., 94 , 572 LC . See Locus coeruleus Leaky learning model , 179 + +Learnability theorem , 235-236 , 260 Learning . See also Boltzmann + +machines ~ Delta rule , generalized ~ Memory , a distributed model of ~ Neural plasticity and learning + +in Boltzmann machines easy and hard , 290 - 299 hard , example of , 299-303 learning algorithm , derivation of , + +315 - 318 + +establishing features through , 258- + +260 + +in symbolic and subsymbolic paradigms , 261-262 Learning machine (Minsky and Edmonds ) , 153- 154 Learning paradigms , 54-57 + +Learning rule , general form of , 52-53 + +Leavitt , R . Y ., 351 , 563 Le Cun , Y ., 322 , 512 Lehiste , I ., 61 , 565 + +Lenneberg , E . H ., 473 , 565 Lesser , U . R ., 63 , 559 + +Letter -perception model . See Interactive activation model of + +word perception + +LeVay , S., 350 , 353 , 355 , 361 , 374 , 497 ~ 500 ~ 563 ~ 565 . 566 Levels of analysis , 121- 129. See also Isomorphism hypothesis Marr ' s levels , 122 - 124 + +other notions of levels , 124 - 127 reductionism and emergent properties , 127- 129 Levin , J . A ., 43 , 85 , 512 , 90 , 566 Levin ' s proteus model , 43 Levine , R . D ., 227 , 512 Lewis , B ., 341 , 566 Lewis , C . H ., 251 , 512 LGN cells , 480 + +Liberman , A . M ., 61 , 62 , 73 , 92 , 94 , 95 , 473 , 560 , 566 , 569 , 573 , 576 + +Lichten , W ., 63 , 569 Licklider , J. C . R ., 106 , 566 Lieberman , F ., 489 , 557 Limited fan -out . See Fan -out , limited ~ Standard pattern + +associators + +Limited increment hypothesis , 520 . + +See also Amnesia Lin , C . S ., 351 , 560 Lindsay , P. H ., 8, 206 , 512 + +Linear algebra + +matrices and linear systems + +basis for vector space, change of , + +413 + +description of , 385 -386 eigenvectors and eigenvalues , + +399 -403 linearity , 393 matrices , 386 - 390 matrix inverses , 410 -413 matrix multiplication and multilayer systems , 395-399 one -layer POP system , 390 -393 POP systems , 2 examples , 406 - + +410 + +transposes and the outer product , + +403 - 405 + +nonlinear systems , 418 -420 + +vectors + +basic operations of , 367-370 concepts ~ use of in analysis of simple POP model , 383 -385 + +description of , 365 -366 inner products , 375 linear combinations and independence , 370-373 vector spaces , 374 - 375 Linear models , simple , 61-63 . See + +also Linear algebra auto -associator version of , 63 pattern associator , 63 simple linear associator , 62 + +weaknesses of , 63 + +Linear threshold units , 63 -66 , 425 , 224 . See also Activation + +functions perceptron , 65 XOR function , 64 -65 + +LISP programming language , 124 use of in P3 system , 492 , 496 -497 Llinas , R ., 364 , 370 , 558 , 566 Local representations , 77 , 85 , 96 Locus coeruleus (LC ) , 476-477 , 493 + +Loeb , G . E ., 383 , 566 + +Loftus , E . F ., 85 , 508 , 208 , 566 Logical computation , notion of . See + +Activation functions Logogen model , 43 , 192-193 Loomis , L . H ., 402 , 566 + +Lorente de No , R ., 344 , 358 , 566 + +Lovins , J . B ., 62 , 560 Luce , R . D ., 75 , 93 , 195 , 566 Luce choice rule , application of , 90- + +91 , 195 + +Lund , J . S ., 357 , 358 , 361 , 366 , 374 , + +566 , 573 + +Lund , R . D ., 336 , 357 , 566 Luria ~ A . R .~ 41 ~ 79 , 135 , 512 Luria 's dynamic functional system , + +41 + +Lynch , J. C ., 366 , 567 + +Ma , S . - K . , 388 , 567 Macchi , G ., 350 , 567 Macrodescription of harmony mechanism , 246 - 258 + +one -layer POP system , 390-393 transposes and outer product , 403 - + +405 + +Matrix inverses , 410 - 413 . See also Matrices and linear systems Matrix mapping , algebraic properties of , 389 - 390 . See also Matrices + +and linear systems + +Maunsell , J. H . R ., 345 , 352 , 353 , + +356 , 500 , 568 , 577 + +Maximum -likelihood model , 292 -294 + +McCarthy , J., 157- 158, 512 + +McClelland , J . L ., 20 , 22 , 24 , 27 , 28 , 42 , 43 , 71 , 79 , 85 , 120 , 121 , 133 , 177 , 199 , 202 , 216 , 321 , 512 , 514 , 8 , 58 , 59 , 63 , 69 , 71 , 75 , 77 , 80 , 90 , 119 , 123 , 126 , 127 , 130 , 131 , 135 , 138 , 140 , 141 , 142 , 170 , 172 , 195 , 217 , 370 , 380 , 381 , 383 , 394 , 532 , 558 , 559 , + +568 , 574 + +McClurkin , J . W ., 480 , 567 McConkie , G . W ., 161 , 163 , 568 , + +573 + +McCulloch , W . S ., 152 , 424 , 512 McDermott , D ., 432 , 568 McGeoch , L . A ., 235 , 508 McGill , J ., 145 , 575 + +McGuinness , E ., 374 , 375 , 553 McNaughton , B. L ., 448 , 568 MD . See Monocular deprivation Medin , D . L . , 171 , 181 , 200 , 205 , + +536 , 568 + +Meditch , J . S ., 456 , 512 + +Memory , a distributed model of . See also Distributed representations ~ Memory , retrieving information + +from + +conclusions on , 214 - 215 + +detailed assumptions of , 176- 182 experimental results of simulations repetition and familiarity effects , + +192 - 199 + +representation of general and specific information , 199-206 + +problem solving for , 246-247 productions and expertise , 251-253 + +schemata , 253 + +approximation , 256-258 for rooms ~ 255 -256 two -choice model , 253 -255 MacWhinney , B., 273 , 274 , 554 , 567 + +Macy , A ., 481 , 567 Magistretti , P. J., 364 , 569 Mann , V . A ., 95 , 118 , 567 + +Mapping from expressions , 439 . See + +also Boolean function Marcus , M . P . , 317 , 324 , 567 Marin , O . S . M ., 134 , 514 Marin -Padilla , M ., 363 , 567 Mark , R . F ., 490 , 555 + +Marr , D ., 18 , 19 , 20 , 42 , 113 , 116 , 117 , 121 - 122 , 123 , 196 , 283 , 512 , + +63 , 119 , 378 , 567 + +Marr 's levels of analysis , 122- 124. See also Levels of analysis Marrocco , R . T ., 480 , 567 Marshall , J. C ., 102 , 508 Marshall , W . H ., 352 , 579 + +Marslen - Wilson , W . D . , 43 , 512 , 63 , 77 , 79 , 80 , 97 , 98 , 99 , 275 , 567 Martin , K . A . C ., 363 , 567 , 576 Massaro , D . W ., 77 , 81 , 86 , 94 , 567 , + +568 , 571 Massey , T ., 378 , 560 + +Matrices and linear systems . See also + +Linear algebra + +basis for vector space, change of , + +413 - 418 + +descriptions of , 385-386 + +eigenvectors and eigenvalues , 399- + +403 + +examples of PDP systems , 406 -410 + +linearity , 393-395 matrices , 386 + +addition of , 387 -389 matrix mapping , algebraic properties of , 389 -390 scalars , multiplication by , 386 + +matrix inverses , 410 -413 multiplication and multilayer systems , 395 - 398 + +Memory , a distributed model of extensions of model (continued) interference and fan effects , 208 - + +209 + +memory blends , 208 regularities of behavior , emergence of , 207 + +semantic memory , emergence of from episodic traces , 206 general properties of , 173-175 modular structure , 174 - 175 pattern of activation , 175 hidden units , augmenting model + +with , 209 - 214 + +model ' s behavior , key aspects of , + +182 - 192 + +relation to basic concept in , 176 theories of , 2 -3 , 170 - 171 Memory , retrieving information from . See also Distributed representations , features of ~ Memory , a distributed model of content addressability , 25-29 default assignment , 29-30 graceful degradation , 29 + +spontaneous generalization , 30-31 + +Mercer , R . L ., 293 , 508 + +Merzenich , M . M ., 385 , 386 , 387 , + +563 , 569 + +Mesulam , M . M ., 350 , 569 Metropolis , N ., 230 , 277 , 513 Meyer , D . R ., 352 , 579 Michael , C . R ., 367 , 368 , 569 Micro - and macrolevels of harmony theory , 203-204 , 210 Microdescription , problem -solving of , 246 . See also Electricity + +problem -solving Microfeature , 80 - 81 + +Microfeatures , semantic . See Semantic microfeatures + +Microstructure of cognition , 12- 13 + +Miezin , J . , 374 , 375 , 553 Miller , D . T ., 536 , 564 + +Miller , G . A . , 63 , 106 , 323 , 566 , 569 + +Miller , W ., 254 + +Milner , B ., 504 , 506 , 510 , 514 , 569 + +Minciacchi , D ., 350 , 567 + +Minsky , M ., 65, 76, 96 , 111- 113, 153 , 154 , 157 - 158 , 160 , 233 , 291 , 319 , 321 , 334 , 348 , 354 , 361 , 424 , 513 , 18 , 19 , 535 , 569 Mitchell , D . E ., 475 , 558 + +Mitchinson , G ., 296 , 297 , 468 , 486 , + +509 + +Mitra , S. K ., 455 , 513 Miyuwaki , K ., 473 , 569 + +Models , similarities and differences + +between , 4 - 5 Modifications of patterns of + +interconnectivity in POP models , + +52-53. See also Learning Modular structure of memory , 79 , 174-175. See also Memory , a + +distributed model of Molinari ~ M . ~ 35 ~ 567 + +Monocular deprivation (MD ) , 474 , + +475 + +OD shift under , 487 rearing , 489 + +Monocular occlusion (AM ) , 474 Monotonicity concepts for activation functions , 427 -428 . See also + +Activation functions + +Monotonicity -in -context , 426 -428 + +Montero , V . M ., 351 , 569 Moran , J ., 374 , 558 Morrell , F . , 379 , 569 + +Morris , R . G . M . , 434 , 466 , 569 Morrison , J . H ., 364 , 569 + +Morton , J ., 43 , 513 , 97 , 106 , 192 , + +570 + +Moser , M . G ., 313 , 570 + +Motor control + +example of multiple constraints in , + +4 - 6 + +POP models f Of, examples of , 13- + +18 + +finger movements in skilled + +typing , 14- 16 + +Moussouris , J . , 289 , 513 Mower . G . D . . 478 . 570 + +groups of neurons behavior in cerebral cortex , 365 - 366 neurons without many spines , 361 neurons with spines , 360 -361 single -neuron behavior in cerebral + +cortex , 364 -365 special cell types , 362 -364 Network damage . See Damage , effects of on a network ~ Graceful + +degradation + +Neural and conceptual interpretation of PDP models . See PDP models , + +neural and conceptual interpretation of + +Neural -like processing systems , common learning paradigms in , + +160 - 161 Neural modeling , 130 + +Neural nets , biological limits on storage capacity of , 469 -470 . See + +a /so Fan - out , limited Neural or unit level of + +representation . See Pattern -based + +coordinates , delta rule in Neural plasticity in cerebral cortex , 385 - 387 . See also Cerebral cortex , questions about computation in Neural plasticity and learning critical period , effect of environment on , 478 critical period of , 473 -478 ocular dominance , measuring changes in , 474 -476 + +plasticity -modulating processes , + +476 - 478 + +discussion of , 471 -473 , 494 - 499 existing modification rules , state dependence and , 494 -496 global modulators as dynamic variables , 496 - 497 predictions for , 497-499 experimental data on , comparison + +with , 489 - 494 + +ocularity state and its effect on , + +, , , Mozer , M . C ., 68 , 127 , 507 , 513 , 125 , 139 , 140 , 142 , 570 Muller , R . U ., 435 , 441 , 445 , 447 , + +565 , 570 + +Multiple linear regression and the delta rule , 457 -458 . See also Delta rule , analysis of Multiple simultaneous constraints , 4 -9 , 58 , 124 , 272 -27 ~) mutual constraints , 7 operation of in syntax and semantics , 6 - 7 duplication of connection + +information , need for to exploit , + +124 + +role assignment , use of in , 272 -275 simultaneous mutual constraints in + +word recognition , 7-9 + +speech perception , role of in , 124 Munro , P . W ., 42 , 180 , 508 , 480 , 487 , 489 , 495 , 496 , 555 , 570 + +Murray , E. A ., 357 , 570 Mutt , V ., 364 , 560 + +Nadel , L ., 435 , 445 , 510 , 527 , 571 , + +576 + +Nakatani , L ., 61 , 110 , 570 Nathan , P . W ., 514 , 515 , 574 Nativism vs. empiricism , 139- 142 Nauta , W . J . H ., 334 , 342 , 570 NE . See Norepinephrine + +Necker cube , 11 , 13 , 16 , 28 . See a /so + +Schemata , concept of Neely , R . B., 63 , 122, 573 + +Negation problem , 346 -348 . See also + +Delta rule , generalized Neisser , U ., 81 , 113 , 116 , 212 , 513 , + +515 + +Nelson , R . J ., 352 , 354 , 385 , 477 , + +569 , 570 Nelson , S . B ., 477 , 554 Neocortical neurons , nature of cell types in , 358 -360 + +experimental methods , 357 -358 feature detection , 367 -371 firing , rates of , 366 -367 + +Neural plasticity and learning + +(continued) + +state dependencies of plasticity , + +484 - 489 + +POP models , learning rate as factor + +in , 472 + +single -unit learning , focus on , 472 + +summary of , 501 terminology , 473 + +visual cortex , ideas described with respect to ocular dominance in , + +499 - 501 + +Neural processing in cerebral cortex , 378 -382 . See also Cerebral cortex , questions about computation in + +Neural realism , lack of in POP models , 136 - 138 + +Neurons . See also Cerebral cortex , anatomy and physiology of ~ Neocortical neurons , nature of behavior in the cerebral cortex groups of neurons , 365 - 366 single neuron , 364 -365 classical description of , 335 -337 connections between , in brain , + +132 - 133 + +communication among , 132 continuous output of , 133 - 134 graceful degradation of , 134 + +neocortical , 358 - 365 number of , 131 speed of , 130 - 131 systems , 131 - 132 + +treated as devices , 424 -425 (see also Boolean function ) without many spines , 361 with spines , 360 -361 Newell , A ., 108 , 195 , 513 + +Newsome , w . T .~ 347 , 356 ~ 554 ~ 568 + +Newtonian mechanics , 125 Nicholson ~ C ., 364 , 566 Ninteman . F . W .. 493 . 572 Nonlinear systems . See also POP models , neural and conceptual + +isomorphism , failure of in , 422 -424 quasi -linear systems with , 418 -422 + +use of , 418 -421 + +limited dynamic range and , 420 - + +421 + +subthreshold summation , 420 Nonpyramidal cells , 358 -360 . See also Neocortical neurons , nature + +of + +Norepinephrine (NE ) , 476-477 , 478 , + +480 , 493 + +as potential modulator of neural plasticity , 476-477 , 492-494 , 497 + +Normal rearing (NR ) , 474 Norman , D . A ., 8 , 9 , 14 , 15 , 79 , 116 , 133 , 206 , 512 , 513 , 514 , 18 , 19 , ~) 37 , 539 , 540 , 543 , 545 , 555 , + +570 , 574 + +Norris , D . , 63 , 100 , 571 NR . See Normal rearing Nusbaum , H . C . , 120 , 571 + +Ochs , M . T ., 385 , 563 Ocular dominance (00 ) + +class , 484 + +histograms , 475 , 479 , 489 , 490 + +shift , under MD , 487 statistics , 474 - 476 + +Ocular dominance index , 481 -483 , + +484 , 490 + +vs. responsivity plot , 492 Ocularity plane , power of as tool in theoretical analyses of ocular dominance plasticity , 483 -484 Ocularity state and its effect on plasticity , 478-480 . See also Neural plasticity and learning + +ideal neuron , 479 - 480 ocularity plane , 480 -484 plasticity , state dependence of , + +484 - 489 + +00 . See Ocular dominance Oden , G . C ., 77 , 275 , 568 , 571 ODH . See Ocular dominance , + +histogram + +001 . See Ocular dominance index 6-0HDA . See 6-hydroxydopamine Ohzawa , I ., 481 , 492 , 560 , 567 + +system ) , 453 -454 + +competitive learning methods (App . + +B) , 504-506 + +description of , 364 , 488 -489 major components of , 489 -490 performance of , 500-501 + +plan for competitive learning , (App. + +A ) , 502-503 + +plan language of , 490 , 491 -497 simplified diagrams of , 454 -455 , + +464 + +simulation system , 497 - 500 typical plan for , 490 Parity networks , 159, 160 Parity problem , 334-335 See also Delta rule , generalized Parker , D . B ., 322 , 361 , 513 PARSIFAL (Marcus ) , 317 Parsing in PDP models , 317 -323 Part / whole hierarchy , 105 + +Past-tense acquisition , three stages of , 219 -221 . See also Verbs , learning past tenses of + +Patte , P ., 387 , 556 + +Pattern of activation , in distributed model of memory , 175 memory traces as change in + +weights , 176 mental state as , 176 + +prior , retrieval as reinstatement of , + +176 + +and response strength , 194- 195 Pattern association paradigm , definition of , 55 Pattern associators . See also + +Programmable pattern associators ~ Standard pattern associators ; Verbs , learning past tenses of basic properties of , 33-37, 226 -228 + +definition of , 161 + +learning regular and exceptional + +patterns in , 226 + +models , attractive properties of , 38 + +restrictions of , 228 -233 + +Oja , E., 489 , 557 + +O ' Keefe , J ., 434 , 435 , 445 , 448 , 466 , + +568 , 569 , 571 O' Kusky , J., 348 , 571 Olson , C . R ., 475 , 571 Olson , L ., 350 , 553 + +Olton , D . S., 435 , 522 , 554 , 571 One -layer POP systems , use of matrices in analyzing , 390 -393 . See also Matrices and linear + +systems + +One -layer perceptron , 111- 113 limitations of , 112 - 113 One -step system in interactive + +models , 60 + +Optimization problems , use of linear programming for , 284-286 Organization Qf Beha vior , 53, 152 + +Ortony , A ., 19, 32, 574 + +Output units definition of , 48 + +as major aspect of POP models , 46 , + +48 -49 + +P3 system . See Parallel process + +programmer + +PABLO . See Reading , programmable + +black board model of Palay , S. L ., 338 , 571 Palmer , R . G ., 296 , 511 , 513 Palmer , S. E ., 117 , 513 Pandemonium , 42 + +Pandya , D . N ., 352 , 571 , 573 Papert , So, 65, 76, 96 , 111- 113, 158, 160 , 233 , 291 , 319 , 321 , 334 , 348 , 354 , 361 , 424 , 513 , 535 , 569 + +Paradigms of learning associative , 54 - 55 regularity discovery , 55 Paradiso , M . A ., 477 , 554 + +Parallel distributed processing . See + +POP . + +Parallel Models ojAssociative Memory , + +Parallel network simulating system . See Parallel process programmer Parallel process programmer (P3 + +Pattern completion device , use of Boltzmann machine as , 289 - 290 . See also Boltzmann machines Pattern of connectivity as major aspect of POP models , 46 , 49 - 51 + +Patterson , K ., 102 , 508 + +POP approach and cognitive science + +conclusions on , 145 - 146 natural applications of , 144 + +objections to + +analysis , wrong level of , 121- 127 cognitive approach , lack of , 120- + +121 + +cognitive theories , constraints of , + +129 - 136 + +conscious knowledge and explicit + +reasoning , 143- 145 + +human vs . rat intelligence , 143 lack of neural realism in , 136 - 138 + +Marr ' s levels , 122 - 124 + +nativism vs . empiricism , 139- 142 other notions of levels , 124 - 127 reductionism and emergent properties , 127- 129 weaknesses of , 111 - 120 status of various models , 144 - 145 POP approach , introduction to active representation in , 31-40 as alternative to serial models , 12 - + +13 + +appeal of , 3-4, 10- 12 + +examples of + +memory retrieval , 25 - 31 motor control , 13 - 17 perception , 18-24 history of , 41-44 + +local vs . distributed representation , + +32 - 33 + +pattern associator models attractive properties of , 38 ensemble of patterns , extracting structure from , 39 -40 learning multiple patterns , 37-38 + +learning rules of , 36-37 workings of , 33-36 POP approach , reflections on computer metaphor and , 533-535 learning and consciousness , + +problems of , 543 -545 new directions in , 545 -546 strengths of , 535 -539 + +description , levels of , 538 -539 human information processing , essential properties of , 537 + +schema , 536 - 537 useful result of , 537 -538 weaknesses of , 539 -543 + +evaluative structure , need for , + +541 - 542 + +multiple systems , required for , + +542 -543 + +type -token problem , 539 -540 + +variables , 540 - 541 + +POP models , active representation + +in , 31 -40 , 175 - 176 local vs . distributed , 32 + +pattern associator models attractive + +properties of , 38 pattern associators , 33 - 37 + +structure of ensemble of patterns , + +extracting , 39-40 + +POP models and the brain . See also Cerebral cortex , anatomy and physiology of ~ Cerebral cortex , questions about computation in relationship between , 328 -330 models of neural mechanisms , + +330 -331 + +neurophysiology relevant to , 327 - + +328 + +POP models , future directions for , + +547 - 552 + +POP models , general framework for bottom -up processing , 57-59 conclusions on , 74 - 76 hierarchical organizations , 57 interactive models , 59 -60 learning paradigms , 54-57 major aspects of , 46-54 activation rule , 51 - 52 learning rule , 52-54 propagation rule , 51 sigma -pi units , 73-74 synchronous vs. asynchronous + +update , 61 + +top -down processing , 59 + +learning rule , 53, 154- 157 parallel reorganizing elements , + +158 - 159 + +Perceptual processing , centrality of , 197- 198. See also Harmony + +theory + +Perkel , D . H ., 381 , 571 Perkel , D . J ., 381 , 571 Perrett , D . 1., 368 , 571 Perry , J., 195, 508 Peterhans , E ., 376 , 578 + +Peters , A ., 336 , 338 , 361 , 363 , 365 , + +559 , 571 , 572 Petersen , S . E ., 347 , 554 Petitjean , F ., 350 , 555 + +Pettigrew , J. D ., 476 , 477 , 487 , 490 , + +492 , 555 , 564 + +Phase transitions , computational significance of , 236-237 + +Phillis , J . W . , 339 , 565 Phoneme identification , factors + +influencing + +categorical perception , 84 , 88-95 detectors , retuning of by context , + +95 - 97 + +lexical effects on , 77- 78 factors influencing , 78-80 simulations , summary of , 97 trading relations , 84-88 + +use of phonotactic rules in , 81-83 Phonemic restoration effect , 20 + +Piaget , J., 17, 19, 572 Piercy , M ., 516 , 517 , 563 Pillsbury , W . B., 20, 513 Pinker , S., 217 , 572 Pinto -Hamuy , T ., 352 , 579 Pisoni , D . B ., 60 , 77 , 92 , 94 , 100 , + +572 , 574 Pitts , W , 152 , 424 , 512 + +Place -field model . See also Place recognition and goal location , biologically plausible models of + +description of , 436 -441 goal location , 449 properties of , 439-440 + +scope of , 448 + +versions , specific + +brain state in a box model (BSB) , + +66 - 68 + +Feldman and Ballard ' s units , 72 Grossberg 's units , 70-71 interactive activation model , 71 linear threshold units , 63 -66 simple linear models , 61-63 thermodynamic models , 68-70 POP models , learning rate as factor in , 472 -473 . See also Neural plasticity and learning POP models , neural and conceptual + +interpretation of conclusions on , 429 -431 consideration of , 390 -391 distributed nonlinear models , natural competition in , 424 -429 as dynamical systems , 397 -398 interpretations , 391 -396 + +isomorphism hypothesis , failure of in nonlinear models , 422 -424 + +kinematics , 400 -403 + +kinematics and dynamics , 398 -399 + +learning connections and + +isomorphism of levels , 416 -418 linear systems , isomorphism of + +levels in , 411 - 413 + +localized damage and , 413 -416 nonlinearity , quasi -linear systems + +with , 418 - 422 + +pattern coordinates , 406 -411 vector space , structure of , 403 -406 + +Pearlmutter , B ., 298 Pearson , J . C ., 385 , 575 Peck , C . K ., 475 , 571 + +Peptides in the cerebral cortex , 340 + +Perez , R . , 494 , 571 + +Perception , examples of for POP + +models + +familiar patterns and , 20 - 23 novel patterns , completion of , 23- + +25 + +stereoscopic vision , 18-20 Perceptrons (Rosenblatt ) , 154- 158 convergence procedure , 41-42 , 65, + +Place recognition and goal location , biologically plausible models of .8 -coefficient constants (App .) , + +467 - 468 + +/3 -coefficient model , 460 -466 /3 units (App .) , 469 -470 conclusions on , 466 distal landmarks , 445 + +distributed view - field model , 449 - + +460 + +goal location , 449 + +location parameters , 441 -443 model , description of , 436-441 properties of , 439 -440 place - field location , 446 -448 place-field model , scope of , 448 place-field shape and size , 445 -446 + +place recognition , 434 -436 simulated experiments , 443-445 Plan language , as major component of P3 system , 489 , 490 , 491 -497 creating P3 plan for , 493 -497 + +features of , 490 functions of , 491 -493 Plasticity , neural . See Neural + +plasticity + +Podgorny , P., 501 , 575 + +Poggio , T ., 18, 19, 20, 42 , 117, 512 , 513 , 129 , 365 , 381 , 383 , 564 , + +565 , 572 Poincare , H . , 213 , 513 + +Pollack , J . B . , 277 , 278 , 311 , 314 , + +578 + +Porrino , L . J ., 350 , 572 Poschel , B . P . H ., 493 , 572 Posner , M . I ., 171 , 183 , 200 , 203 , + +572 + +Powell , T . P . S., 344 , 348 , 350 , 351 , 352 , 556 , 560 , 563 , 564 , 572 , 573 + +Prince , D . A ., 364 , 369 , 557 Principles ofNeurodynamics , 41-42 , + +154 + +Probability theory , 209-210 Processing units , set of for POP + +model , 46 -48 vs . one -unit -one -concept representational system , 47 Programmable blackboard model of reading . See Reading , programmable blackboard model + +Programmable pattern associators . See also Connection information + +distribution mechanism ~ Reading , programmable blackboard model + +CA units , requirements of , 474 - 476 CID networks , requirements of , + +473 - 474 + +conclusions on , 486 discussion of , 485 - 486 distributed representations , simultaneous access to , 483 - 485 multiple pattern processing , 477 - + +478 + +overlapping , 478 - 480 + +simultaneous access , cost of , 481 - + +482 + +single pattern processing , 476 - 477 summary of CA requirements , + +480 - 481 + +Proskauer , C . C . , 336 , 361 , 363 , 571 , + +exemplars , 189 - 192 + +learning from exemplars , 182 - 184 multiple , nonorthogonal , 184 - 188 Pyramidal cells , 358 - 360 . See also Neocortical neurons , nature of + +Quasi - linear activation function , 52 , + +425 . See also Activation + +functions + +Quasi - linear systems with + +nonlinearity , 418 - 422 . See also Nonlinear systems ~ POP models , + +interpretation of + +Quasi - local interpretations , 394 - 395 . See also POP models , neural and conceptual interpretation of Quasi - multilinear activation function , + +426 . See also Activation + +functions + +Quillan , M . R . , 85 , 513 + +conspiracies of , 157- 159 Realizability theorem , 230 -235 Receptor , cartoon of , 508 -509 . See + +also Amnesia + +Recurrent networks , 354 -360 . See also Delta rule , generalized performance of , 359 -360 + +sequence completion , learning of , + +358 - 359 + +shift register problem and , 357-358 + +Recursion , 119 - 120 , 318 -320 Reddy , O . R ., 63, 107, 122, 573 Reductionism , POP models as exercise in , 127 - 129 + +Redundancy , benefits of , 472 . See also Standard pattern associators + +Reese , T . S . , 336 , 572 + +Regularity detector paradigm , 161 + +Reich , P . A ., 323 , 573 Reilly , D . L ., 499 , 573 Reitboek , H . J . P . , 385 , 573 Relaxation searches , use of parallel networks to perform , 283-290 learning , difficult and easy, 290-292 maximum likelihood models , 292 - + +294 + +optimization problems and , 284- + +286 + +pattern completion , 289-290 probabilistic decisions , use of to escape from local minima , 287 - + +288 + +simulated annealing , application of to Hopfield nets , 288-289 Relaxation system , 135 - 136 Relearning , speed of in Boltzmann + +machines , 308 -310 + +Repetition and familiarity effects , + +192 - 199 + +alternative interpretation of , 193- + +194 + +pattern action and response strength , 194- 195 + +time -accuracy curves , effects of experimental variables on , 195- + +Rader , R . K ., 497 , 577 + +RaIl , W ., 336 , 381 , 382 , 569 , 572 , + +575 + +Ralston , H . J ., 336 , 572 Ramachandran , V . S ., 478 , 572 Ranck , J . B ., Jr ., 435 , 441 , 445 , 447 , + +565 , 570 + +Random -dot stereograms , 18 + +Rao , C . R ., 455 , 513 + +Rauschecker , J . P., 476 , 478 , 576 Rawlins , J . N . P., 434 , 466 , 569 Rayner , K ., 153, 161, 163, 164, 275 , + +560 , 572 , 573 + +Reading , programmable blackboard + +model of (PABLO ) + +ambiguous characters , 155-157 amount of feedback , effect of display length on , 159- 161 CID computer simulation , results + +of , 136 - 141 + +conclusions on , 168 - 169 connection information distribution , benefits of , 164 - 166 computer simulation of word recognition using , 134-136 + +cost of , 166 - 167 extensions of , 167 - 168 + +mechanism , details of , 129 - 136 (see also Programmable pattern + +associators ) description of , 2, 125 + +fixations , sequences of , 161 - 164 fixations , single and multiple , 153- + +155 + +interactive activation model , bottom - up activations of word units in CID version of , 137 - 138 interference and crosstalk , 139 - 141 + +PABLO simulation model coarse coding , 146- 147 details of , 151 - 153 feedback , 147 + +focus of attention , shifting , 147- + +151 + +Repp , B. H ., 95, 118, 567 , 573 Representation , distributed . See Distributed representation Representation of environment as major aspect of PDP models , 53- + +54 + +Representation vector of harmony + +theory , 213-214 Representational features of + +harmony theoretical model , 213- + +214 + +Representation , learning of . See Boltzmann machines ~ + +Competitive learning ~ Delta rule , + +generalized + +Representation , learning of new in + +harmony theory + +procedure and abstract features , + +258 - 260 + +in symbolic and subsymbolic + +paradigms , 261 + +Reproduction trials , 520 . See also + +Amnesia + +Residual learning skills in amnesia , + +518 -524 . + +Retinocentric feature detectors , 114 Retrograde amnesia , 505 -506 , 513 - + +515 + +Reverse learning , occurrence of , + +296 -298 + +Reverse suture (RS) , 474 , 487 -488 , + +489 + +Reverse suture paradigm , time course of , 489 -490 . See also Visual cortex , developmental + +models of Ribak , C . E ., 363 , 572 + +Riley , M . S., 241 , 264 , 514 , 515 Rinzel , J., 381 , 382 , 569 , 575 Ritz , S. A ., 56 , 406 , 409 , 410 , 418 , 507 , 173 , 226 , 311 , 399 , 551 , 554 + +Roberts , E ., 351 , 562 Rock , I ., 117 , 514 Rockel , A . J., 344 , 573 + +Rockland , K . S . , 352 , 366 , 374 , 573 Role -assignment model . See Case role assignment , model of Role -specific letter units , 145- 146. + +See also Reading , programmable + +blackboard model of Rolls , E . T ., 368 , 571 Rosch , E ., 171 , 573 Rose , J . E ., 345 , 573 Rosen , 1., 357 , 554 + +Rosenblatt , F ., 41 , 111 , 152 , 153 - 154 , 155 - 157 , 158 , 291 , 424 , 514 , + +226 , 289 , 535 , 573 + +Rosenbluth , A . W ., 230 , 277 , 513 Rosenbluth , M . N ., 230 , 277 , 513 + +Rosenfeld , A ., 285 , 514 Rosenthal , M ., 477 , 561 Ross , B . H ., 206 , 554 RS . See Reverse suture Rubin , O . S., 293 , 509 F.udnicky , A ., 58 , 557 + +Rule of propagation as major aspect of POP models , 46 , 51 Rumelhart , D . E ., 6 , 9 , 14 , 15 , 20 , 22 , 24 , 43 , 71 , 116 , 120 , 121 , 130 , 133 , 177 , 199 , 202 , 216 , 300 , 321 , 512 , 514 , 7, 18 , 19 , 31 , 59 , 71 , 75 , 77 , 90 , 170 , 195 , 217 , 316 , 380 , 394 , 532 , 539 , 540 , + +545 , 568 , 573 , 574 Russell , W . R . , 514 , 515 , 574 + +Ryder , J. M ., 7, 511 + +Sachs , M . B ., 383 , 574 Saffran , E . M ., 134 , 514 Said , S., 364 , 560 Sakaski , K ., 370 , 558 + +Salasoo , A . , 60 , 100 , 197 , 198 , 559 , + +574 + +Salvert , D . , 350 , 555 Samuel , A . G ., 95 , 160 , 574 Sanderson , K . J ., 480 , 574 Sayers , F . C ., 324 , 563 + +Scalars, multiplication by , 367 , 386 . See also Matrices and linear + +systems ~ Vectors Schacter , D ., 519 , 574 + +Schaffer , M . M ., 171 , 200 , 536 , 568 Schank , R . C ., 6 , 9 , 201 , 202 , 514 , + +18 , 19 , 324 , 574 Scheibel , A . B . , 351 , 574 Scheibel , M . E . , 351 , 574 + +Schein , S. J ., 374 , 558 + +Schemata , concept of , 9 , 78 -79 , 199 - 213 ~ 1~ 7-37 ~ 536 -537 account of mental processing , 38- + +53 + +consciousness , content of , 39 control , problem of , 39-40 conversations and , 42 -44 external representations and formal reasoning , 44-48 mental models and , 40 - 42 mental stimulation and practice , + +42 + +assumptions made about , 30-31 + +conclusions on , 53 - 57 + +constraint satisfaction and , 17 + +description of , 1, 7-8 example of , 22-25 + +examples of processing of , 25-31 goodness -of -fit landscapes of , 15 , 16 , 28 , 29 , 30 , 31 , 32 -33 , 35 in harmony theory , 199-213 completion task , 206 -208 construction of , 201 -203 formulation of , 209 -210 function of , 208 + +knowledge atoms , nature of in , + +205 -206 + +logical structure of , 199-200 mathematical properties of probability and , 211 -213 micro - and microlevels of , 203 - + +204 + +modified letter perception model , + +204 -205 history of , 17-19 + +important features of , 19-20 interpretation differences and , 21 + +POP models as constraint networks , 8 - 17 properties of + +active processes , 36 additional features , 36 -37 + +goodness -of - fit evaluation to data , + +variables , 33 -34 summary of , 31 , 48 + +thinking , goal direction in , 48 use of as knowledge structures , 9 + +Schermer , T . M ., 96 , 569 Schiller , P . H ., 367 , 574 Schmolze , J. G ., 313 , 555 Schneider , W ., 126 , 549 , 575 Schumacher , L . E ., 302 , 350 , 511 , + +515 + +Schwanenflugel, P. J., 181, 205, 568 Schwartz , J . H ., 333 , 507 , 552 , 564 + +Schwartz , M . F ., 134 , 514 Schwartz , M ., 477 , 554 Schweikert , J., 7 , 511 Sclar , G . , 492 , 560 Scott , G . L ., 351 , 569 Scott , J . P ., 473 , 575 Scripts , use of as knowledge + +structure , 9 Sears , T . A ., 336 , 553 Segev , I ., 381 , 382 , 575 Seguin , S., 350 , 555 + +Sejnowski , T . J., 118, 264 , 272 , 282 , 289 , 297 , 302 , 306 , 313 , 317 , 335 , 348 , 350 , 507 , 508 , 509 , 510 , 511 , 514 , 515 , 23 , 24 , 63 , 128 , 373 , 377 , 379 , 380 , 393 , + +554 , 562 , 575 + +Selfridge , O. G ., 8, 41 , 212 , 515 + +Selman , B . , 321 , 575 + +Semantic cues . See Word -order and semantic cues to role assignment Semantic memory , emergence of from episodic traces , 206 . See also Memory , a distributed model + +of + +Semantic microfeatures , 278 -283 . See also Case role assignment , + +model of + +Sememe unjts , 97 -98 , 99 , 101 - 102 , 305-310 . See also Arbitrary mapping ~ Damage , effects of on a + +network + +418 , 507 , 173 , 226 , 311 , 399 , + +551 , 554 + +Simon , H . A ., 241 ~ 508 + +Simple binary addition problem , 341 -346 . See also Delta rule , + +generalized + +Simulated annealing , 287 , 288 -289 , 313 . See also Cooling schedule ~ + +Harmony theory + +Simulation system environment , as major component of P3 system , + +489 , 497 - 500 + +,Singer , W ., 476 , 478 , 575 , 576 Single -level interactive model , 60 Single -shot algorithms , 380 . See also Cerebral cortex , questions about + +computation in + +Single -unit learning , focus on , 472 . See also Neural plasticity and + +learning Singley , 209 + +Skirboll , L . R ., 350 , 577 Slater , P . C . , 513 , 515 , 576 Slobin , D . I . ~ 221 , 247 , 249 , 250 , 251 , 254 , 255 , 256 , 556 Slowiaczek , L . M ., 120 , 571 Small , S . L ., 277 , 314 , 557 , 576 + +Smith , D . C ., 490 ~ 565 Smith , E ., 24 ~ 515 Smith , P . T . , 24 , 515 + +Smolensky , P., 125, 241 , 259 , 264 , 277 , 289 , 447 , 514 , 515 Sokolov , J . L ., 274 , 567 + +Somogyi , P., 362 , 363 , 567 ~ 576 Spared learning in amnesia , 518 -519 , 521 - 524 . See also Amnesia + +Spear ~ P. D .~ 490 , 565 + +Speech , fundamental aspects for development of TRACE model architecture for TRACE model ~ importance of , 63-64 + +context effects , left and right , 60 + +cues , sensitivity of , 62 lack of boundaries , 60 , 61 speech signal , noise and indeterminacy in , 62-63 + +stimulus , temporal nature of , 59-60 + +Sentence processing in POP networks . See Case role assignment , model of Sentence -structure (SS) + +representation , 283 -286 . See also Case role assignment , model of Sequential symbol processing , 106- + +108 + +Sequential thought processes in POP models . See also Recurrent networks ~ Sequential symbol processing ~ Seriality , emergent account of mental processing , development of , 38-39 conclusions on , 53 -57 + +consciousness , contents of ~ 39 control ~ problem of , 39-40 conversations ~ 42 -44 + +external representations and formal + +reasoning , 44-48 important aspects of , 47 role of language in , 47 mental models and , 40 - 42 + +mental simulations and practice , 42 + +summary of , 48 + +thinking , goal direction in ~ 48 tic -tac-toe example of ~ 48-53 , 54 Seriality , emergent ~ 24 7~ 249 . See also Electricity problem -solving + +Settlage ~ P. H ., 352 , 579 Shallice , T .~ 145 , 543 ~ 570 , 575 Shankweiler , 0 ., 92 , 94 , 566 Shannon , C . E ., 195 , 267 , 515 Sharma , V . K .~ 477 , 561 Shaw , G . L ., 385 , 575 + +Shepard , R . N ., 198 , 515 , 501 , 536 , + +575 + +Shepherd , G . M .~ 336 , 381 , 382 , + +572 , 575 + +Sherk , H . , 350 , 374 , 566 Sherman , S. M ., 351 , 560 + +Shiffrin ~ R . M ., 197 , 198 , 559 , 574 + +Shlaer , R ., 494 ~ 571 Sickels , E . R ., 324 , 563 Sigma -pi units , 72~ 73-74 , 426 generalized delta rule for , 353 Silverman , D . J . , 385 , 575 + +Spencer , W . A ., 364 , 576 Spoehr , K ., 24, 515 + +Spoken word recognition , study of , + +97 - 98 + +Spontaneous learning (Rosenblatt ) , + +155 - 156 + +Squashing function , 425 , 485 -489 . See also Activation functions ~ Ocularity state and its effect on + +plasticity + +Squire , L . R ., 505 , 510 , 513 , 515 , 516 , 517 , 525 , 527 , 556 , 576 Standard pattern associators . See also Programmable pattern associators + +conclusions on , 486 degradation , effects of , 472 limited fan -out , effects of , 468 -472 programmable nets , resource requirements , 465 -468 redundancy , benefits of , 472 resource requirements of , 460 , + +461 -465 + +computations of , 463 -465 Stanford , L . R ., 351 , 560 + +State of activation as major aspect of + +POP model , 46 , 48 + +State space (S) , 398 -399 . See also Kinematics of the dynamical + +system + +coordinate system for , 400 of general nonlinear activation + +model , 402 pattern view of , 406 + +unit coordinates for , 400 - 401 Statistical learning , analyzing case of , 453 - 457 . See also Delta rule , + +analysis of Steedman , M ., 274 , 557 Sternberger , J. P., 248 , 576 Sternberg , S., 133, 515 , 402 , 566 Stevens , K . N . , 62 , 168 , 561 , 576 Stimulus equivalence , problem of , + +113 - 114 + +Stochastic generative model , 293 - + +294 , 313 Stochastic units , 81 Strang , G ., 411 , 422 , 515 Strange , W ., 473 , 569 + +Structure in representations and processes , 104 - 108 constituent structure , 105 - 106 sequential symbol processing , 106- + +108 + +Studdert -Kennedy , M ., 92, 94, 566 , + +576 + +Subsymbolic and symbolic + +paradigms , learning in , 261-262 Subthreshold summation , 420 . See also Nonlinear systems , use of + +Summerfield , Q., 85 , 576 Sur , M . , 352 , 354 , 385 , 569 , 570 Surround effects in visual cortex , 374 - 377 . See also Cerebral cortex , Questions about computation in + +Sutton , R . S . , 43 , 53 , 57 , 444 , 508 , 515 , 383 , 539 , 554 , 576 Swanson , L . W ., 350 , 576 Swets , J . A ., 466 , 510 , 225 , 561 Swinney , D . A ., 109, 577 Symbolic and subsymbolic + +paradigms , learning in , 261-262 Symmetry problem , 340-341 . See also Delta rule , generalized Synapses in the cerebral cortex , + +basic types , 338 -339 + +Synaptic change , neurochemistry of , 507 - 509 . See also Amnesia Synchronous update vs. asynchronous update , 61 Syntactic processing in POP models , + +317 - 323 + +Szentagothai , J., 351 , 362 , 577 + +T -C problem ~ 348-352 . See also Delta rule ~ generalized Tabula rasa ~ 139 ~ 141 Takeuchi ~ A . ~ 489 ~ 495 ~ 553 Talbot ~ W . H . ~ 366 ~ 567 Tank ~ D .~ 389 ~ 562 Tash ~ J . ~ 92 ~ 572 + +Teitelbaum , P . ~ 142 ~ 515 Teller , A . H . , 230 ~ 277 ~ 513 Teller , E ., 230 ~ 277 , 513 Tenenbaum ~ J . M . ~ 63 , 554 + +57 - 59 + +Top -down theoretical strategy + +pursued in harmony theory , 196, + +199 - 213 + +Torre , V ., 117 , 513 , 129 , 365 , 381 , + +565 , 572 Touret , M ., 350 , 555 + +Touretzky , D ., 322 , 548 , 577 TRACE model of speech perception compared to Fanty 's parser , 321 - + +322 + +conclusions on , 120 - 121 deficiencies of , 119 - 120 description of , 2, 58-59 , 64-68 , 123 - 124 , 143 , 153 - 154 phoneme identification , factors + +influencing + +categorical perception , 84 , 88- 95 lexical effects of on , 77-81 phoneme detectors , retuning of + +by context , 95- 97 simulations , summary of , 97 trading relations , 84-88 + +use of phonotactic rules in , 81-83 phoneme units , context -sensitive + +tuning of , 68-69 + +programmable version of , 167- 168 speech , fundamental aspects for , + +59 - 63 + +spoken word recognition , study of , COHORT model , 98 - 101 , 102 , + +103 + +word segmentation , lexical basis + +of , 106 - 115 + +word segmentation simulations , summary of , 115 - 117 successes , summary of , 117 - 119 TRACE I model , 69 , 70 - 71 , 75 , 76 TRACE II model , 69 , 70 , 71 - 75 , + +76 , 102 , 110 Travis , A . M ., 352 , 579 Tribus , M ., 227 , 512 T ' so , D . Y ., 385 , 577 Turner , M . R ., 385 , 560 Tversky , A ., 499 , 560 Two -dimensional space , inner + +products in , 380 -382 . See also + +Terminal parameters , 491 . See also + +P3 system Terrace ~ H . S .~ 183 ~ 515 Theorems , harmony , (App.) + +Boltzmann machines , second -order observables and , 273 - 275 harmony function H , cognitive systems and , 267 - 268 terminology , 268-269 overview of definitions , 264 - 267 + +proofs of , 275-281 + +retrieving information from H , + +269 - 272 + +storing information in H , 272-273 Thermal equilibrium of network , + +290 - 291 , 313 Thermodynamic limit , 239 Thermodynamic models , 68-70 Boltzmann machines , 68 , 69 + +harmony theory , 68 Thibadeau , R . , 161 , 549 , 577 Thomas , G . B ., Jr ., 276 , 515 Thompson , H ., 60 , 63, 84, 107, 577 Thompson , R . F ., 383 , 552 , 561 Three -dimensional plots , 429 , 430 - 438 . See also Activation + +functions + +Three -layer network , 97-98. See also Arbitrary mapping , implementing Three -level interactive model , 59 Three -stage learning curve , 240 -245 . See also Verbs , learning past + +tenses of + +Threshold logic unit , 425 . See also + +Activation functions + +Tic -tac-toe , as example of sequential thought processes in POP models , + +48 - 53 , 54 Tigges , J., 348 , 577 Tigges , M ., 348 , 577 + +Timing + +problem of , 378 -380 + +of sensory stimulation , 383 -384 temporal binding , 383 -385 Timney , B. N ., 475 , 558 Tombol ~ T .~ 351 ~ 361 ~ 363 , 577 Top -down approach ~ 123 + +inner products , 375 -376 algebraic properties of inner product , 382 -383 angle , 377 -379 length , 376 -377 projections , 379 -380 two -dimensional space , inner products in , 380 -382 linear combinations and independence + +combinations of vectors , 370 -371 linear jndependence , 371 -373 + +vector spaces , 374 -375 structure of , 403 - 406 Venesky , R. L ., 24, 515 Verb -frame selection for role assignment models , 300 -301 Verbs , irregular , types of , 245 -246 , 247 -254 . See also Verbs , learning + +past tenses of + +Verbs , learning past tenses of binding networks for (App .) , 269 - + +271 + +conclusions on , 266 -268 + +example of model based on LAD + +approach , 217 -219 issue of , 3 , 216 -217 + +model of + +learning and , 225 -226 operation of , 223 -225 phonological patterns , featural representations of , 233 -239 simple pattern associator model , + +226 - 233 + +structure of , 221 -223 + +summary of structure of , 239 - 240 novel verbs , transfer to , 261 -266 simulations , main points of + +irregular verbs , types of , 245 -246 , + +247 - 254 + +regularization , types of , 257 -260 regular verbs , types of , 245 -246 , + +247 + +three -stage learning curve , 240 - + +245 + +vowel -change verbs , 254 -257 stages, sequence of in acquisition + +of use of , 219 - 221 + +Two - layer scheme in harmony + +theory , advantages of , 218 - 219 Tyler , L . K . , 97 , 98 , 99 , 104 , 275 , + +567 ~ 577 + +Type - token problem , as weakness of POP approach to cognition , 539 - + +Uchizono , K . , 339 , 577 Ungerleider , L . G . , 374 , 558 Ungerstredt , U . , 350 , 553 Uniform monotonicity , 426 - 428 Uniformly nondecreasing function , + +monotonic function , 427 + +Uniqueness and continuity constraints , 19 - 20 + +Unit parameters , 491 . See also P3 + +system + +UNIT TYPE statement for pattern generator in P3 , 493 - 494 Unlearning , 296 - 298 . See also Boltzmann machines + +Valverde ~ F . , 363 , 559 Van Dam , A . ~ 467 , 559 Van der Loos , H . ~ 366 , 577 Van Essen ~ D . C . ~ 352 , 353 ~ 355 , 356 , 368 , 500 ~ 566 , 568 ~ 577 Van Hoesen , G . W . , 350 , 569 + +van Santen ~ J . P . H . , 159 , 160 , 563 ~ + +Van Sluyters ~ R . C . , 489 , 490 , 491 , + +Variable translational mappings , 116 + +Vaughn ~ J . E . ~ 351 , 562 + +Vecchi , M . P . , 148 ~ 235 , 287 ~ 511 Vector notation , delta rule in . 445 - 447 . See also Delta rule , analysis + +basic operations of + +calculating averages , 369 scalars ., multiplication by , 367 vectors , addition of 368 - 369 concepts , use of to a \_nalyze simple POP model , 383 - 385 . description of , 365 - 366 + +Werblin , F . S., 336 , 578 Wessels , J ., 99 , 104 , 577 Westrum , L . E ., 336 , 578 + +Whitteridge , D ., 354 , 363 , 558 , 567 , + +576 + +Whittlesea , B . W . A ., 171 , 172 , 200 , 201 , 202 , 203 ~ 204 , 556 '1 578 Wickelfeature representation (Wickelgren ) blurring , 238 -239 details of , 234 - 239 + +Wickelgren , W . A ., 62 , 181, 233 , + +510 , 511 , 527 , 578 Wickelphones , 233 -234 , 236 -238 + +Widrow , G . , 321 , 516 + +Widrow - Hoff rule , 53 , 291 - 292 . See + +also Delta rule + +Wiener , 534 + +Wiesel , T . N . , 340 , 353 , 356 , 358 , 366 , 367 , 373 , 374 , 385 , 474 , 475 , 483 , 497 , 500 , 561 , 562 , + +563 , 566 , 577 , 578 Williams , R . J ., 425 , 516 + +Willshaw , D . J ., 42 , 97 , 100 , 460 , 461 , 465 -466 , 468 , 472 , 475 , 516 + +Willshaw nets , 461 - 465 + +comparison of to various kinds of local representation , 465 difficulties with , 465 -468 Wilson , H . R ., 381 , 389 , 578 Winston , P . H ., 32 , 516 , 524 , 578 + +Wise , R . A ., 493 , 578 Wise , S . P ., 357 , 564 Wolverton , G . S . , 161 , 568 Wood , C . C . , 102 , 516 , 551 , 578 Woods , W ., 119 , 516 , 322 ~ 5 78 Woolsey ~ C . N .~ 352 , 579 + +Woolsey ~ T . A .~ 355 , 500 ~ 558 ~ 579 Word identification simulations in TRACE , summary of , 115 - 117 Word -order and semantic cues to role assignment , 293 -300 . See also Case role assignment , model + +of + +Word perception model (McClelland & Rumelhart ) . See Interactive activation model of word + +Verbs , regular , 245 -246 , 247 , 254 - 257 , 258 -260 . See also Verbs , learning past tenses of Verbrugge , R ., 473 , 569 Vertical and horizontal lines , experiments with , 184- 190 Vertically hierarchical networks , 217 + +Videen , T . 0 ., 497 , 577 + +View -field model , distributed . See Distributed view -field model + +Vincent , S . R . , 350 , 577 + +Visual cortex , developmental models + +of , 489 - 494 + +alternating monocular occlusion , + +490 , 491 + +norepinephrine , role of , 492 -494 responsivity , relation of to connectivity , 490 , 492 reverse suture paradigm , time course of , 489 -490 Visual system , 282 - 283 . See also Boltzmann machines + +Vital - Durand , F ., 497 , 500 , 555 , 577 + +Voight , H . F ., 383 , 574 Volman , S. F ., 367 , 574 von der Heydt , R ., 376 , 578 von der Malsberg , C ., 42 , 147, 152, 162 , 164 , 516 , 384 , 489 , 494 , 578 Von Neumann architecture , 534 - 535 . See also POP approach , + +reflections on + +Von Neumann computer metaphor , + +195 + +Vygotsky , L . S., 43, 47 , 578 + +Walker , A . E . , 349 , 578 Walker , E . C . T ., 7 , 511 Walker , J . A ., 435 , 554 Wall , J . T ., 385 , 569 + +Waltz , D . L ., 277 , 278 , 311 , 314 , + +578 + +Warren , R . M ., 20 , 516 Webster , H . de F ., 338 , 571 Weight -decay , use of in Boltzmann + +Word segmentation, lexical basis of for TRACE~ 106-115 identification, word, 112-115 nonwords, end of, 111-112 short sentence xample, 115 word inputs, single and multiple, + +107-111 Wu, T. Y., 350, 577 Wyatt, H. J., 500, 558 + +XOR problem, 319-321, 330-334. See also Delta rule, generalized + +Yin, T. C. T., 366, 567 Young, E. D., 383, 574 + +Zadeh, L. A., 423, 516 + +Zeki, S. M., 368, 374, 577, 579 Zipser, D., 97, 300, 514, 432, 437, 438, 440, 442, 443, 444, 447, 579 + +Zola, D., 161, 568 + +Zucker, S. 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--git a/lit-marker2/edmund-husserl-logical-investigations-vol1/edmund-husserl-logical-investigations-vol1.md b/lit-marker2/edmund-husserl-logical-investigations-vol1/edmund-husserl-logical-investigations-vol1.md new file mode 100644 index 0000000000000000000000000000000000000000..e9988f7684a19780b1335e8936e4bcc6ecd0c4b5 --- /dev/null +++ b/lit-marker2/edmund-husserl-logical-investigations-vol1/edmund-husserl-logical-investigations-vol1.md @@ -0,0 +1,6041 @@ +**Logical Investigations** + +Volume I + +International Library of Philosophy + +Edited by Jose Bermudez, Tim Crane and Peter Sullivan + +Advisory Board: Jonathan Barnes, Fred Dretske, Frances Kamm, + +Brian Leiter, Huw Price and Sydney Shoemaker + +Recent titles in the ILP: + +**The Facts of Causation** + +*D.* H. *Mel/or* + +**The Conceptual Roots of Mathematics** + +J. R. *Lucas* + +**Stream of Consciousness** + +*Barry Dainton* + +**Knowledge and Reference in Empirical Science** + +*Jody Azzouni* + +**Reason without Freedom** + +*David Owens* + +**The Price of Doubt** N. *M.* L *Nathan* + +**Matters of Mind** *Scott Sturgeon* + +**Logic, Form and Grammar** + +*Peter Long* + +**The Metaphysicians of Meaning** + +*Gideon Makin* + +**Logical Investigations, Vols I & II** + +*Edmund Husserl* + +**Logical Investigations** + +**Edmund Husser!** + +Translated by J. N. Findlay + +from the Second German edition of *Logische Untersuchungen* + +with a new Preface by Michael Dummett + +and edited with a new Introduction by Dermot Moran + +**Volume I** + +**Prolegomena to pure logic** (Volume I of the German editions) + +**Expression and meaning** + +(Investigation I, Volume II of the German editions) + +**The ideal unity of the species and modern theories** + +**of abstraction** + +(Investigation II, Volume II of the German editions) + +I~ ~~~:!;~~~up LONDON AND NEW YORK + +First published in German as *Logische Untersuchungen* + +by M. Niemeyer. Halle 190011901 + +Second German edition. Vol. I and Vol. II. Part I. first published 1913 + +First published in English 1970 by Routledge & Kegan Paul Ltd Reprinted 1976. 1977. 1982 + +This paperback edition first published 200 I' + +by Routledge + +2 Park Square. Milton Park. Abingdon. Oxon OX 14 4RN Simultaneously published in the USA and Canada + +by Routledge + +270 Madison Ave. New York. NY 10016 Reprinted 2002. 2003. 2005. 2007. 2008 Transferred to Digital Printing 2008 + +*Routledge is an imprint* of *the Taylor* & *Francis Group, an informa business* + +Translation © 1970 J. N, Findlay Preface © 200 I Michael Dummett + +Introduction and editorial matter © 2001 Dermot Moran Typeset in Times by Graphicraft Ltd. Hong Kong + +Printed and bound in Great Britain by TJI Digital. Padstow. Cornwall + +All rights reserved. No part of this book may be reprinted or reproduced or utilised in any form or by any electronic. mechanical. or other means. now known or hereafter invented. including photocopying and recording. or in any information storage or retrieval system. without permission in + +writing from the publishers. + +*British Library Cataloguing in Publication Data* + +A catalogue record for this book is available from the British library + +*Library* of *Congress Cataloging in Publication Data* A catalog record for this book has been requested + +ISBN 978-0-415-241 *B9-2* (Vol. I) ISBN 978-0-415-24190-8 (Vol. II) + +Dedicated to Carl Stumpf with Honour and in Friendship **Contents** + +Preface by Michael Dummett Introduction by Dermot Moran + +Select bibliography + +Translator's Introduction (Abridged) + +Foreword to First German Edition, Volume I (1900) Foreword to Second German Edition, Volume I (1913) + +**PROLEGOMENA TO PURE LOGIC** + +xvii XXI lxxiii lxxvii + +> 1 3 + +**Volume I of the German Editions 9** + +INTRODUCTION I I + +§1 The controversy regarding the definition of logic and the + +essential content of its doctrines **11** §2 Necessity of a renewed discussion of questions of principle 12 §3 Disputed questions. The path to be entered 13 + +CHAPTER ONE + +*Logic as a normative and, in particular, as a practical discipline* I 5 §4 The theoretical incompleteness of the separate sciences 15 + +§5 The theoretical completion of the separate sciences by + +metaphysics and theory of science 16 §6 The possibility and justification of logic as theory of science 16 + +§7 Continuation. The three most noteworthy peculiarities of + +grounded validations 19 + +§8 The relation of these peculiarities to the possibility of science + +and the theory of science 21 + +§9 Methodical modes of procedure in the sciences are in part + +validatory, in part auxiliary devices towards validations 23 + +§1O The ideas of theory and science as problems of the theory of + +§11 Logic or theory of science as normative discipline and as + +technology + +§12 Relevant definitions of logic + +CHAPTER TWO + +*Theoretical disciplines as the foundation* of *normative disciplines* + +25 26 + +28 + +§13 The controversy regarding the practical character of logic 28 + +§14 The concept of a normative science. The basic standard or + +principle that gives it unity 33 §15 Normative disciplines and technologies 37 + +§16 Theoretical disciplines as the foundation of normative + +disciplines 38 + +CHAPTER THREE + +*Psychologism, its arguments and its attitude* to *the usual* + +*counter-arguments* + +§17 The disputed question as to whether the essential theoretical + +40 + +foundations of normative logic lie in psychology 40 §18 The line of proof of the psychologistic thinkers 41 + +§19 The usual arguments of the opposition and the psychologistic + +rejoinder 41 §20 A gap in the psychologistic line of proof 44 + +CHAPTER FOUR + +*Empiricistic consequences* of *psychologism* + +§21 Characterizing two empiricistic consequences of the psychologistic standpoint, and their refutation §22 The laws of thought as supposed laws of nature which operate in isolation as causes of rational thought §23 A third consequence of psychologism, and its refutation + +§24 Continuation + +CHAPTER FIVE + +*Psychological interpretations* of *basic logical principles* + +§25 The law of contradiction in the psycho logistic interpretation + +46 + +46 + +48 51 54 + +56 + +of Mill and Spencer 56 + +§26 Mill's psychological interpretation of the principle yields no + +law, but a wholly vague, and scientifically unproven, empirical + +proposition + +*Appendix to the last two sections:* On certain basic defects of + +58 + +§27 Analogous objections against remaining psychological interpretations of our logical principle. Ambiguities as + +sources of delusion 61 + +§28 The supposed two-sidedness of the principle of contradiction, in virtue of which it should be taken both as a natural law of + +thinking, and as a normal law for its logical regulation 64 §29 Continuation. Sigwart's doctrine 67 + +CHAPTER SIX + +*Syllogistic* inferences *psychologistically considered. Syllogistic and* + +*chemical formulae 70* §30 Attempts at interpreting syllogistic principles psychologically 70 §31 Syllogistic and chemical formulae 72 + +CHAPTER SEVEN + +*Psychologism as a sceptical relativism 75* + +§32 The ideal conditions for the possibility of a theory as such. + +The strict concept of scepticism 75 §33 Scepticism in the metaphysical sense 76 §34 The concept of relativism and its specific forms 77 §35 Critique of individual relativism 78 + +§36 Critique of specific relativism and, in particular, of + +anthropologism 78 + +§37 General observation. The concept of relativism in an + +extended sense 82 §38 Psychologism in all its forms is a relativism 82 §39 Anthropologism in Sigwart's Logic 83 §40 Anthropo1ogism in the Logic of B. Erdmann 90 + +CHAPTER EIGHT + +*The psychologistic prejudices* I 0 I §41 First prejudice 101 §42 Elucidations 103 + +§43 A look back at the opposed arguments of idealism. Their + +defects and their justified sense 106 §44 Second prejudice 108 + +§45 Refutation. Pure mathematics would likewise be made a + +branch of psychology 108 + +§46 The research domain of pure logic is, like that of mathematics, + +an ideal domain 109 + +§47 Confirmatory indications given by the basic notions of logic + +and the sense of logical laws 111 §48 The decisive differences 113 + +§49 Third prejudice. Logic as the theory of evidence 115 + +§50 Transformation of logical propositions into equivalent + +propositions about the ideal conditions for the evidence of + +judgement. The resultant propositions are not psychological 116 §51 The decisive points in this dispute 119 + +CHAPTER NINE + +*Logic and the principle* of *the economy* of *thought* **123** §52 Introductory 123 + +§53 The teleological character of the principle of Mach and A venarius and the scientific meaning of an 'economy of + +thought' *(Denkokonomik) 123* + +§54 Closer treatment of the justified ends of an 'economy of thought', in the sphere, mainly, of purely deductive + +methodology. Its relation to a logical technology 126 + +§55 The meaninglessness of an economy of thought for pure logic + +and epistemology, and its relation to psychology 129 + +§56 Continuation. The VcrTEpOV np6TEpov involved in any + +foundation of pure logic on an economy of thought 131 + +CHAPTER TEN + +*End* of *our critical treatments* **1 34** + +§57 Queries regarding readily formed misunderstandings of our + +logical endeavours 134 + +§58 Our links with great thinkers of the past and, in the first place, + +with Kant 135 §59 Links with Herbart and Lotze 136 §60 Links with Leibniz 138 + +§61 Need for special investigations to provide an epistemological + +justification and partial realization of the Idea of pure logic 140 *Appendix:* References to F. A. Lange and B. Bolzano 141 + +CHAPTER ELEVEN + +*The idea* of *Pure Logic 144* + +§62 The unity of science. The interconnection of things and the + +interconnection of truths 144 §63 Continuation. The unity of theory 146 + +§64 The essential and extra-essential principles that give science + +unity. Abstract, concrete and normative sciences 147 + +§65 The question as to the ideal conditions of the possibility of science or of theory in general. *A.* The question as it relates + +§66 *B.* The question as it relates to the content of knowledge 150 + +§67 The tasks of pure logic. First: the fixing of the pure categories of meaning, and pure categories of objects and their + +law-governed combinations 152 + +§68 Secondly: the laws and theories which have their grounds in + +these categories 154 + +§69 Thirdly: the theory of the possible forms of theories or the + +pure theory of manifolds 155 §70 Elucidation of the Idea of a pure theory of manifolds 156 + +§71 Division of labour. The achievement of the mathematicians + +and that of the philosophers 158 + +§72 Broadening of the Idea of pure logic. The pure theory of + +probability as a pure theory of empirical knowledge 160 + +**VOLUME II, PART I OF THE GERMAN EDITIONS 163** + +**INVESTIGATIONS IN PHENOMENOLOGY AND** + +**KNOWLEDGE PART I 163** + +INTRODUCTION **165** + +§ 1 The necessity of phenomenological investigations as a + +preliminary to the epistemological criticism and clarification + +of pure logic 165 §2 Elucidation of the aims of such investigations 166 §3 The difficulties of pure phenomenological analysis 170 + +§4 It is essential to keep in mind the grammatical side of our + +logical experiences 172 + +§5 Statement of the main aims of the following analytical + +investigations 173 §6 Additional Notes 174 + +§7 'Freedom from presuppositions' as a principle in + +epistemological investigations 177 + +**INVESTIGATION I** + +**EXPRESSION AND MEANING 181** + +CHAPTER ONE + +*Essential distinctions 183* §1 An ambiguity in the term 'sign' 183 §2 The essence of indication 183 §3 Two senses of 'demonstration' ('indication' and 'proof') 184 + +§4 Digression on the origin of indication in association 186 + +§5 Expressions as meaningful signs. Setting aside of a sense of + +'expression' not relevant for our purpose 187 + +§6 Questions as to the phenomenological and intentional + +distinctions which pertain to expressions as such 188 §7 Expressions as they function in communication 189 §8 Expressions in solitary life 190 §9 Phenomenological distinctions between the physical appearance + +of the expression, and the sense-giving and sense-fulfilling act 191 §1O The phenomenological unity of these acts 193 + +§ 11 The ideal distinctions between (1) expression and meaning as + +ideal unities 194 §12 Continuation: the expressed objectivity 196 §13 Connection between meaning and objective reference 198 + +§14 Content as object, content as fulfilling sense and content as + +sense or meaning simpliciter 199 + +§15 The equivocations in talk of meaning and meaninglessness + +connected with these distinctions 200 §16 Continuation: meaning and connotation 203 + +CHAPTER TWO + +*Towards a characterization* of *the acts which confer meaning 206* §17 Illustrative mental pictures as putative meanings 206 §18 Continuation of the above. Arguments and counter-arguments 207 §19 Understanding without intuition 209 + +§20 Thought without intuition and the 'surrogative function' of + +signs 210 + +§21 A difficulty regarding our necessary recourse to corresponding intuitions in order to clarify meanings or to know truths + +resting on them 211 §22 Varying marks of understanding and the 'quality of familiarity' 213 + +§23 Apperception as connected with expression and with intuitive + +presentations 213 + +CHAPTER THREE + +*Fluctuation in meaning and the ideality* of *unities* of *meaning* 216 §24 Introduction 216 + +§25 Relations of coincidence among the contents of intimation + +and naming 216 §26 Essentially occasional and objective expressions 217 §27 Other sorts of fluctuating expressions 221 §28 Variations in meanings as variations in the act of meaning 222 §29 Pure logic and ideal meanings 224 + +CHAPTER FOUR + +*The phenomenological and ideal content* of *the experiences* of *meaning* 228 + +§30 The content of the expressive experience taken in its + +psychological sense and in the sense of a unified meaning 228 §3l The act-character of meaning and the ideally unified meaning 229 §32 The ideality of meanings is no ideality in the normative sense 231 + +§33 The concepts meaning and concept (in the sense of species) do + +not coincide 231 + +§34 In the act of meaning we are not conscious of meaning as an + +object 232 §35 Meanings 'in themselves' and meanings expressed 233 + +**INVESTIGATION II** + +**THE IDEAL UNITY OF THE SPECIES AND** + +**MODERN THEORIES OF ABSTRACTION 235** + +Introduction 237 + +CHAPTER ONE + +*Universal objects and the consciousness* of *universality 239* + +§l We are conscious of universal objects in acts which differ + +essentially from those in which we are conscious of individual + +objects 239 §2 The indispensability of talk about universal objects 240 + +§3 Must the unity of the Species be regarded as a spurious unity? + +Identity and exact likeness 241 + +§4 Objections to the reduction of ideal unity to dispersed + +multiplicity 242 + +§5 Continuation. The controversy between John Stuart Mill and + +If. Spencer 244 §6 Transition to the following chapters 246 + +CHAPTER TWO + +*The psychological hypostatization* of *the universal 248* + +§7 The metaphysical and psychological hypostatization of the + +universal. Nominalism 248 §8 A deceptive line of thought 249 §9 Locke's doctrine of abstract ideas 250 § 10 Criticism 251 §1l Locke's universal triangle 254 §12 The doctrine of generic images 256 + +CHAPTER THREE + +*Abstraction and attention* + +§13 Nominalistic theories which regard abstraction as an + +**258** + +achievement of attention 258 + +§14 Objections to any and every form of nominalism. + +*(a)* The lack of a descriptive fixation of aims 260 + +§15 *(b)* The origin of modern nominalism as an exaggerated + +reaction to Locke's doctrine of general ideas. The essential character of this nominalism, and of the theory of abstraction + +in terms of attention 262 + +§16 *(c)* Generality of psychological function and generality as a meaning-form. Different senses of the relation of a universal + +to an extension 264 §17 *(d)* Application to the critique of nominalism 266 §18 The doctrine of attention as a generalizing power 266 + +§19 Objections. *(a)* Exclusive attention to one attributive aspect + +does not remove its individuality 268 §20 *(b)* Refutation of the argument from geometrical thought 270 + +§21 The difference between attending to a non-independent moment of an intuited object and attending to the + +corresponding attribute *in specie 271* + +§22 Fundamental deficiencies in the phenomenological analysis of + +attention 272 + +§23 Significant talk of attention embraces the whole sphere of + +thinking and not merely the sphere of intuition 274 + +CHAPTER FOUR + +*Abstraction and representation 277* §24 The general idea as a device for economizing thought 277 + +§25 Whether general representation can serve as an essential + +characteristic of our general presentations 278 + +§26 Continuation. The varying modifications of the consciousness + +of generality, and the sensuous intuition 280 §27 The justifiable sense of general representation 281 §28 Representation as substitution. Locke and Berkeley 282 §29 Critique of Berkeley's doctrine of representation 284 + +§30 Continuation. Berkeley's argument from geometrical + +demonstrations 285 §31 The main source of the errors that we have indicated 286 + +CHAPTER FIVE + +*Phenomenological study* of *Hume's theory* of *abstraction* **289** §32 Hume's dependence on Berkeley 289 + +§33 Hume's critique of abstract ideas and its supposed outcome. + +His ignoring of pivotal phenomenological issues 290 §34 Reduction of Hume's investigation to two questions 291 + +§35 The guiding principle and outcome of Hume's doctrine of + +abstraction and the main thoughts in which it is worked out 293 + +§36 Hume's doctrine of the *distinctio rationis* in its moderate and + +its radical interpretation + +§37 Objections to this doctrine in its radical interpretation + +Notes + +§38 Transference of our scepticism from abstract part-contents to + +294 295 299 + +all parts whatsoever 300 §39 The extreme limit of scepticism and its refutation 301 + +*Appendix:* Modern Humeanism + +CHAPTER SIX + +*Separation* of *varying concepts* of *abstraaion and abstraa* + +§40 Confusion of concepts of abstraction and abstract concerned with non-independent part-contents, on the one hand, and + +302 + +**308** + +Species on the other 308 + +§4l Separation of concepts grouped about the concept of the + +non-independent content 309 + +§42 Separation of the concepts that group themselves about the + +concept of the Species 311 + +Notes Index + +314 325 + +**Preface** + +Edmond Husserl's *Logical Investigations,* little known to English-speaking students of philosophy but well known to most students of the subject with a different mother tongue, is a work of the first importance in the history of philosophy. It was written at a turning point in Husserl's philosophical development, between his earlier book, *Philosophy of Arithmetic (1891),* deeply embedded in the psychologism so prevalent in German philosophy of the time, and the *Ideas towards a pure Phenomenology and phenomenological Philosophy* (1913) in which the notion of *noema* was first presented and the programme of phenomenology was first set out. In *Philosophy of Arithmetic* Husserl had criticised Gottlob Frege's *Foundations of Arithmetic* from a psychologistic standpoint. Psychologism attempts to explain concepts by reference to the inner mental operations supposedly involved in attaining them or grasping them; Frege had engaged in denouncing this methodology - the intrusion of psychological considerations into logic and the analysis of meaning - from the *Foundations of Arithmetic* onwards. Husserl, whose previous relations with Frege had been fairly cordial, was deeply affronted by his savage, and in certain respects unfair, review in 1894 of the *Philosophy of Arithmetic,* and had no further contact with him for the next twelve years. Frege's review was his most sustained attack on psychologism; and although it was resented by Husserl for its unkindness, it is widely believed to have influenced him profoundly, albeit some reject this conjecture. However this may be, Husserl had completely changed his attitude to psychologism by 1900. His arguments against it in the *Prolegomena* often coincided with those used by Frege, although he elaborated them in far more detail. Yet while Frege's objections to psychologism had made little impact, that of Husserl's assault on it was overwhelming: the *Prolegomena* came close to killing off the influence of psychologism within German philosophy, although Husserl's old + +teacher Brentano remained bewildered by this turn of events. + +Attention to Husserl's famous book may help to correct the impression of 'German philosophy' often given by those who declare their enthusiasm for what they describe as the German tradition in the subject. This they see as originating in the work of Hegel and the idealist school generally and + +descending to Heidegger. Heidegger indeed began as a pupil of Husserl's, though he diverged from him so markedly; but the false impression of what the German philosophical tradition has been may be corrected by reading Husserl's disparaging remarks about Hegel, and the accompanying encomium of Bolzano, in the Appendix to Chapter 10 of the *Prolegomena.* Frege did not see himself as the founder of a school, although he was highly conscious of his divergence from the approaches of other philosophers contemporary with him. Yet nowadays he is recognised by all analytical philosophers as the grandfather of their school of philosophy - with Bolzano, whom Husserl so greatly admired, as its great-grandfather. Husserl, on the other hand, set out to be the inaugurator of a new philosophical method; and no one could deny him the title of founder of phenomenology. They were thus progenitors of two philosophical schools that have diverged so widely from one another that communication between them has until recently been almost impossible. Yet, at the time when Husserl's *Logical Investigations* were published, no one who knew the work of both men would have thought of them as belonging to radically different schools of philosophy; they had somewhat different interests, and a markedly different literary style, but they did not then appear any great distance apart in philosophical outlook. The moment of the publication of the *Logical Investigations* was that at which the views of the founders of the rival philosophical + +schools approximated most closely to one another. + +They even had quite similar opinions about the nature of logic. Husserl denied that logic is an essentially normative discipline; he held that any normative discipline must rest on a theoretical science. Frege is often described as having held that logic *is* essentially normative in character, and he did indeed say as much in one of his unpublished writings. He did so because, when commenting on its description as embodying the 'laws of thought', he repeatedly observed that it did not lay down laws governing the way we do think, but promulgated laws concerning how we ought to think. In fact, however, his view was essentially the same as Husserl's. He frequently described logic as concerned with the laws of truth; and in the Introduction to his *Basic Laws of Arithmetic* he says that these are laws about what *is,* + +independently of our judgements. + +Any analytical philosopher interested in how philosophy arrived at its present state thus needs to study the *Logical Investigations* to discover how the philosophical traditions that stemmed from the work of these two innovators came to diverge so widely: one investigating intuitions of essences, the other analysing language (to which Frege himself had so ambivalent an attitude). Recent work within the analytical tradition, from the late Gareth Evans onwards, has tended to reverse the explanatory priority which that tradition has historically given to language over thought. This suggests the possibility of a *rapprochement;* at the same time it may seem to threaten a relapse into psychologism. That such a relapse has not occurred is due to + +the treatment of the structure of thoughts by adherents of this new tendency after the model of a Fregean semantic analysis of language. Do we have here a means of reconciling the two traditions? Or does the gulf between + +them remain to be bridged? + +MICHAEL DUMMETT + +*Oxford, April 2000* + +**Introduction** + +**The** *Logical Investigations (1900/1901)* + +Edmund HusserI (1859-1938) published his *Logische Untersuchungen (Logical Investigations)* in two volumes in 1900 and 1901. 1 The first volume, *Prolegomena zur reinen Logik (Prolegomena to Pure Logic)* appeared from the publisher Max Niemeyer in July 1900.2 The second volume, subtitled *Untersuchungen zur Phiinomenologie und Theorie der Erkenntnis* ('Investigations in Phenomenology and the Theory of Knowledge'), containing six long treatises or 'Investigations', appeared in two parts in 1901. This gargantuan work - which HusserI insisted was *not* a 'systematic exposition of logic' *(eine systematische Darstellung der Logik,* LI III, Findlay II: 3; Hua XIX/I: 228),3 but an effort at epistemological clarification and critique of the basic concepts of logical knowledge - consisted of a series of analytical inquiries *(analytische Untersuchungen)* into fundamental issues in epistemology and the philosophy of logic, and also extensive, intricate philosophical discussions of issues in semiotics, semantics, mereology (the study of wholes and parts), formal grammar (the *a priori* study of the parts of any language whatsoever in regard to their coherent combination into meaningful unities), and the nature of conscious acts, especially presentations and judgements. **In** fact it was these latter detailed descriptive psychological analyses of the essential structures of consciousness, in terms of intentional acts, their contents, objects and truth-grasping character, especially in the last two Investigations, which set the agenda for the emerging discipline HusserI fostered + +under the name *phenomenology.* + +The *Prolegomena4* appeared as a free-standing treatise dedicated to securing the true meaning of logic as a pure, *a priori,* science of ideal meanings and of the formal laws regulating them, entirely distinct from all psychological acts, contents and procedures. The *Prolegomena* offered the strongest possible refutation to the then dominant *psychologistic* interpretation of logic, propounded by John Stuart Mill and others, which HusserI viewed as leading to a sceptical relativism that threatened the very possibility of objective knowledge. Turning instead to an older tradition of logic stemming + +from Leibniz, Kant, Bolzano and Lotze, Husserl defends a vision of logic as a pure theory of science - in fact, the 'science of science', in the course of which he carefully elaborates the different senses in which this pure logic can be transformed into a normative science or developed into a practical + +discipline or 'technology' *(Kunstlehre).* + +The second volume of the *Investigations* (1901) was published in two parts: Part One contained the first Five Investigations and Part Two the long and dense Sixth Investigation, the writing of which had considerably delayed the appearance of the work as Husserl began to realise the depth of the phenomenological project he had uncovered. Whereas the *Prolegomena* was particularly influential in turning the tide against *psychologism* (Frege's efforts in the same direction being in relative obscurity at the time), it was the second volume of the *Investigations* in particular that had a major impact on philosophers interested in concrete analyses of problems of consciousness and meaning, leading to the development of phenomenology. Phenomenology, in line with a general turn away from idealism then current, was to be a science of 'concrete' issues. According to Husserl's Introduction, phenomenology aimed to avoid speculative constructions in philosophy (exemplified, in his view, by Hegel). The *Investigations* impressed its early readers as exemplifying a radically new way of doing philosophy, focusing directly on analysis of the things themselves - the matters at issue *(die Sachen selbst)* - without the usual detour through the history of philosophy, 'merely criticising traditional philosophemes' as Husserl put it (LI VI, Intro., Findlay II: 187; Hua XIX/2: 543), or making partisan declarations in favour of some philosophical system (such as empiricism, positivism, ration- + +alism, Hegelianism or Neo-Kantianism). + +Within a decade, as Husserl's ground-breaking efforts came to be recognised, the *Investigations* had established itself as the foundational text of the nascent 'phenomenological movement' (a term Husserl himself regularly invoked) in Germany. The *Investigations'* influence subsequently spread throughout Europe, from Russia and Poland to France and Spain, such that eventually, it is no exaggeration to say that this work took on a status in twentieth-century European philosophy analogous to that of another foundational text - this time in psychoanalysis - *Die Traumdeutung (Interpretation of Dreams)* ,5 published by Husserl's contemporary Sigmund Freud (1856-1939) in 1899. The *Investigations* continues to be a necessary startingpoint for anyone wanting to understand the development of European philosophy in the twentieth century, from Heidegger and Frege to Levinas, + +Gadamer, Sartre or Derrida. + +Given that the *Logical Investigations* is such a pivotal text in twentiethcentury philosophy, it remains something of a neglected masterpiece, remarkably little read, and where read, poorly understood. For some seventy years it remained untranslated into English. An American philosopher living in Europe, William B. Pitkin sought Husserl's permission to translate it into + +English in 1905, but he abandoned the effort when he could not get a publisher (see Hua XVIII: xxxvii; XIXI1: xxii). Seemingly, the philosopher William James, who was consulted on the project, advised the publisher not to proceed - suggesting that the last thing the world needed was another German textbook on logic, and so the project was abandoned, which grieved Husserl because he had been an admirer of James. 6 Marvin Farber, an American student of Husserl's, published a paraphrase of the *Investigations* in 1943,7 but it was not until 1970 that John N. Findlay produced the first and only complete English translation of the Second Edition. With the hundredth anniversary of the *Investigations'* publication now upon us, it is important to make Findlay's translation available once again in an accessible form for + +the English-speaking reader. + +**The emergence of phenomenology** + +In the first edition of 1901, Husserl adopted the existing term 'phenomenology' *(Phiinomenologie)* - a term already in currency since Lambert, Kant and Hegel, but given new vigour by Brentano and his students - in a somewhat less than fully systematic way to characterise his new approach to the conditions of the possibility of knowledge in general. Husserl wrote in his Introduction: + +*Pure* phenomenology represents a field of neutral researches, in which several sciences have their roots. It is, on the one hand, an ancillary to *psychology* conceived as an *empirical science.* Proceeding in purely intuitive fashion, it analyses and describes in their essential generality - in the specific guise of a phenomenology of thought and knowledge the experiences of presentation, judgement and knowledge, experiences which, treated as classes of real events in the natural context of zoological reality, receive a scientific probing at the hands of empirical psychology. Phenomenology, on the other hand, lays bare the 'sources' from which the basic concepts and ideal laws of *pure* logic 'flow', and back to which they must once more be traced, so as to give them all the 'clearness and distinctness' needed for an understanding, and for an + +epistemological critique, of pure logic. + +(LI, Findlay I: 166; Hua XIXI1: 6-7) + +The logician is not interested in mental acts as such, but only in objective meanings and their formal regulation, the phenomenologist on the other hand is concerned with the essential structures of cognition and their essential correlation to the things known. When Husserl says in this Introduction, 'we must go back to the things themselves' *(Wir wollen auf die 'Sachen selbst' zuriickgehen,* LI, Findlay I: 168; Hua XIXI1: 10), he means particularly that the task of phenomenology is to clarify the nature of logical + +Our great task is now *to bring the Ideas of logic, the logical concepts and laws (die logischen Ideen, Begriffe und Gesetze)*, *to epistemological clarity and definiteness.* Here *phenomenological analysis* must begin. + +(LI, Findlay I: 168; Hua XIXIl: 9) + +More broadly, Husserl wants to document all matters that present themselves to consciousness in their diverse modes of intuitive givenness (and not restricting the sources of intuition arbitrarily in advance, as empiricism and other theories traditionally had done). Husserl initially characterised phenomenology ambiguously as either a parallel discipline to *epistemology,* or as a more radical grounding of epistemology, that sought to *clarify* the essences of acts of cognition in their most general sense. In analysing knowledge, Husserl wanted to do justice both to the necessary *ideality* (that is: self-identity and independence of space and time) of the truths known in cognition, and at the same time properly recognise the essential contribution of the knowing acts of the subject. Thus, looking back in 1925, Husserl + +described the aim of the *Logical Investigations* as follows: + +In the year 1900-01 appeared my *Logical Investigations* which were the results of my ten year long efforts to clarify the Idea of pure Logic by going back to the sense-bestowing or cognitive achievements being effected in the complex of lived experiences of logical thinking. 8 + +Husserl's overall aim is to lay down what he describes as the 'phenomenological founding of logic' *(die phiinomenologische Fundierung der Logik,* LI, Findlay I: 175; Hua XIX 11 : 22), a clarification of the essential nature of logical knowledge as a preliminary to systematic formal logic and to science in genera1. 9 More narrowly, his 'phenomenology of the logical experiences' *(Phiinomenologie der logischen Erlebnisse,* LI, Findlay I: 168; Hua XIXIl: 10) aims to give descriptive understanding of the mental states and their 'indwelling senses' *(ihren einwohnenden Sinnes)*, with the aim of fixing the meanings of key logical concepts and operations, through elaborate and careful distinctions and clarifications. 'Phenomenology', in the First Edition, then, meant the efforts to inquire, radically and consistently, back from the categories of objectivities to the subjective acts, act-structures, experiential foundations in which the objectivities of the appropriate sorts come to be objects of consciousness and to evident self-givenness, working in the domain of pure intuition, rather than being a theoretical or hypothetical construction in the manner of naturalistic psychology. As Husserl put it in 1925, this 'regressive inquiry' brings a new world to light. 10 This is the domain of the + +*correlation* between objectivity and subjectivity. + +In particular, Husserl wants carefully to analyse the intentional subject matter of *expressive experiences (ausdriickliche Erlebnisse)* where 'expression' + +is understood as the articulating of meaning. His focus then is on the ideal sense of the objective intention *(ihr intentionaler Gehalt, der idea Ie Sinn ihrer gegenstandlichen Intention,* LI, Findlay I: 174; Hua XIX!1: 21). In giving an account of the idea of meaning or expression, Husserl takes concepts apart and elaborates extensively on their many meanings before moving on to discuss other related concepts. Thus, for example, he carefully distinguishes the number of different senses of the term 'presentation' *(Vorstellung),* separating out its various psychological, logical and epistemological meanings. Likewise, he embarks on conceptual analyses of key concepts such as 'content', 'judgement' and 'consciousness'. Thus he recognises the need to sort out the many meanings of the term 'content' *(lnhalt,* sometimes *Gehalt)*, a term particularly frequently invoked by logicians and psychologists of the day. In particular, the contrast between what Husserl terms in the First Edition *real (reell)* and *ideal* content, and later what he refers to as the distinction between *phenomenological* and *intentional* content (LI V §16). A typical example of the clarification Husserl is seeking is his differentiation in Sixth Investigation (§§30-5) of the kinds of unity and conflict of meaning contents that lay the basis for the logical laws of consistency and contradiction. It is these rigorous feats of analysis that won the admiration of early + +readers and, more recently, of analytic philosophers. + +While Husserl's own 'concrete' analyses were initially focused primarily on the foundations of arithmetic and logic, and the structures of knowledge, gradually he and his followers broadened phenomenology to address the *a priori* structures of consciousness in general, including affective, volitional, practical, evaluative, aesthetic, religious, legal, political and other forms of conscious awareness of meaning grasping and meaning articulating. Phenomenology was to be a science of essences and as such it was a pure, *a priori* discipline, attending to the nature of things as given in 'essential seeing' *(Wesensschau).* Phenomenology would broaden the sources of intuition further than previous philosophies had allowed, and clarify the fundamental + +relation of thought to truth. + +Quite early on, the *Investigations* attracted the attention of students of the Munich philosopher and psychologist Theodor Lipps (1851-1914), who himself had been criticised for psychologism in the *Prolegomena* and who, in consequence, altered his views to come largely into agreement with Husserl. Through Lipps's students, especially Johannes Daubert (1877-1947), the *Logical Investigations* became the leading philosophical text for a generation of German philosophers, including Alexander Pfander (1870-1941), whose prize-winning, *Habilitation* thesis, written under Lipps at Munich, *Phenomenology of Willing. A Psychological Analysis (Phiinomenologie des Wollens. Eine psychologische Analyse,* 1900), contained the word 'phenomenology' in the title, although the term does not occur elsewhere in the workY Subsequently, Max Scheler (1874-1928), Adolf Reinach (1883-1917), Edith Stein (1891-1942) and Roman Ingarden (1893-1970) were all drawn to this early + +conception of phenomenology with its strongly realist orientation and its + +promise of resolving philosophy's hitherto intractable disputes. + +**The role of the** *Investigations* **in Husserl's** + +**development** + +Husser! himself regarded his *Logical investigations* as a "'break-through", not an end but rather a beginning' *(ein Werk des Durchbruchs, und somit nicht ein Ende, sondern ein Anfang,* LI Findlay I: 3; Hua XVIII: 8).12 In it, Husser! abandoned his ear!ier approaches to logic and mathematics expressed in his first book, *Philosophie der Arithmetik (Philosophy of Arithmetic,* 1891),13 which had been judged psychologistic by its chief critic, Gottlob Frege (1848- 1925). Husser! discovered a much more fruitful way of doing philosophy in a rigorously scientific way through the clarification of the essences of our fundamental cognitive achievements, eventually leading to his later transformation of phenomenology into a comprehensive transcendental philosophical outlook. Ever a restless innovator, he constantly reinterpreted the significance of his own contribution, and thus the *investigations* played a singular role in his own philosophical development. Both in his lecture courses and in his private research manuscripts, he constantly reworked the ground covered in the *Logical investigations,* for example, in his Gottingen lectures on logic (1906-7), on meaning (1907-8), on logic (1910-11), in his Freiburg lectures on logic and in *Phenomenological Psychology* (1925), in the lectures that eventually evolved into *Formal and Transcendental Logic* (1929), and even in his *Crisis of European Sciences* (1936) and the posthumously published *Experience and Judgement* (1938). Husser!'s own 'breakthrough' seemed so surprising even to himself that it had to be constantly rethought. + +In later years, Husser! sought to distance himself from the common understanding of the work as solely an exercise in the philosophy of logic. He complained that he was being characterised rather limitedly as a logician, whereas he saw himself more broadly as a theorist of science in general, and as the founder of a new foundational science, first philosophy or *phenomenology,* which aimed at the careful description of all forms of making *meaning* and registering *meaningfulness* and hence the whole domain of subjectivity. He even claimed (in a letter to E. Spranger, 1918, quoted in Hua XVIII: xiii) that phenomenology had 'as little to do with logic as with ethics, aesthetics, and other parallel disciplines'. In other words, Husser! would later suggest that it was simply an accident of personal biography that he happened to come to phenomenology through *logical* researches; he could just as easily have entered the field from another direction entirely. In a letter to Georg Misch of 16 November 1930, Husser! said that he lost interest in formal logic and real ontology when he made his breakthrough to the transcendental, and later concentrated on founding a theory of transcendental subjectivity and intersubjectivity.14 Before analysing the *Investigations* in more + +detail, let us now turn, then, to a brief consideration of the author, Edmund + +Husserl. + +**Edmund Husserl (1859-1938): life and writings** + +Edmund Husserl was born in Prossnitz, Moravia (now Prostejov, Czech Republic), on 8 April 1859. He studied mathematics and physics at the universities of Leipzig and Berlin, where he was deeply influenced by the mathematician Carl Weierstrass (1815-97), before moving to the University of Vienna, where he completed his doctorate in mathematics in 1882. Following a brief period as Weierstrass' assistant and a term in the army, Husserl went back to Vienna to study philosophy with Franz Brentano from 1884 to 1886. On Brentano's recommendation, Husserl then went to the university of Halle to study with Brentano's most senior student, Carl Stumpf (1848- 1936), completing his *Habilitation* thesis, *On the Concept of Number. Psychological Analyses* with him in 1887. 15Husserl remained in Halle as a lowly, unsalaried *Privatdozent* from 1887 until 1901, the unhappiest years of his + +life, as he later confessed. + +Although Husserl wrote research notes and manuscripts continuously and obsessively, he published few books during his lifetime. 16 His first publication at Halle came in 1891 with the *Philosophy of Arithmetic,* whose opening chapters contained a revised version of his *Habilitation* thesis. The *Logical Investigations* took another ten years of difficult labour to write, during which Husserl sacrificed many of the routines of family life. Husserl always regarded its results as provisional. Nevertheless, writing the book 'cured' him, as he later said to Dorion Cairns. Its publication facilitated a move from Halle to a new salaried position at the university of Gottingen, a renowned centre of mathematics under David Hilbert (1862-1943). It was during his years at Gottingen that he began to attract both German and international students to pursue the practice and theory of phenomenology. However, Husserl still managed only two publications between 1901 and 1916: an important long essay, *Philosophie als strenge Wissenschaft* (,Philosophy as a Rigorous Science'), commissioned by Heinrich Rickert for his new journal *Logos* in 1910/1911,17 in which Husserl outlined his opposition to all forms of naturalism and historicism (as he understood Dilthey's *Weltanschauungsphilosophie* to be); and a major book, *Ideas Pertaining to a Pure Phenomenology and to a Phenomenological Philosophyl8* (hereafter *Ideas* I), published in 1913, which offered an entirely new way of entering + +into phenomenology. + +To the great shock of Husserl's earlier realist followers (such as Ingarden and Pfander), *Ideas* I quite deliberately espoused a form of transcendental idealism (involving a radicalisation of the projects of Kant and Descartes), an outlook Husserl would continue to maintain and develop throughout his career. Husserl himself, however, insisted that he really had this orientation + +in mind when he was developing phenomenology in the *Investigations.* **In** his Introduction to *Ideas* I, he said that readers of the *Logical Investigations* had misunderstood the work as an exercise in a kind of immanent psychology, whereas he had always intended a purer and more essential phenomenological + +approach: + +**In** supposed agreement with the *Logische Untersuchungen,* phenomenology has been conceived as a substratum of empirical psychology, as a sphere comprising 'immanental' descriptions of psychical mental processes, a sphere comprising descriptions that - so the immanence in question is understood - are strictly confined within the bounds of internal *experience.* It would seem that my protest against this concep- + +tion has been of little avail ... + +*(Ideas* I: xviii; Hua 11111: 2) + +**In** other words, HusserI would later claim that transcendental phenomenology as a science of pure essential possibilities was entirely distinct from psychology in all its forms, including descriptive psychology (which he now + +treats as a branch of empirical psychology). + +**In** 1916, HusserI was appointed to the chair of philosophy at the University of Freiburg, which he held until his retirement in 1928. Here, as he recorded in his 1920 Foreword to the revision of the Sixth Investigation (LI, Findlay 1970: 661; Hua XIX12: 533), he became deeply immersed in teaching and research, pursuing the ideal of a system of philosophy with phenomenology at its core, and published almost nothing, apart from an article on the renewal of philosophy in a Japanese journal *Kaizo,* a little article on Buddha, and a truncated version of his lectures on time, *On the Phenomenology of the Consciousness of Internal Time* (1928), edited by his successor to the Freiburg Chair, Martin Heidegger, more or less as a counterpoint to the latter's own *Being and Time* (1927).19 During the last decade of his life, however, HusserI was extremely active, giving lectures in Germany, Holland and France, and publishing *Formal and Transcendental Logic* in 1929,20 and the French version of his Paris lectures, *Meditations cartesiennes,* in 1931, translated by Gabrielle Peiffer and Emmanuel Levinas.21 **In** part, HusserI's intense activity was spurred by his desire to offer a corrective to Heidegger's version of phenomenological ontology, which HusserI felt distorted and + +betrayed his own mission for a transcendental phenomenology. + +Following the coming to power of the National Socialists in January 1933, HusserI and his family suffered under the increasingly severe anti-Semitic laws enacted in Germany, which led to the suspension of his emeritus rights and eventually (in 1935) to the withdrawal of German citizenship. While he continued to live in Freiburg, he was shunned by most of his former colleagues, apart from his assistant Eugen Fink (1905-75) and former student Ludwig Landgrebe (by then a professor in Prague). However, he set + +about the task of preparing his extensive research manuscripts for publication. Despite meeting with official opposition, Husserl continued to write with new vigour against the crisis of the age, producing work of astonishing scope and originality, e.g., the *Crisis of European Sciences,* developed in lectures in Vienna and Prague and published in Belgrade in 1936 (publication in Germany being denied him)Y After a period of illness, Husserl died in Freiburg in 1938. His last work, *Erfahrung und Urteil (Experience and Judgement)* appeared posthumously, with the extensive editorial involve- + +ment of Ludwig Landgrebe, in 1938.23 + +Through the intervention of a young Belgian philosophy graduate and priest, Fr Hermann Van Breda (1911-74), much of Husserl's *Nachlass,* including lecture notes and research manuscripts, amounting to some 45,000 pages of hand-written material, composed in an obsolete German shorthand, the Gabelsberger system, was smuggled out of Nazi Germany and is now preserved in manuscript form in the Husserl Archives in Leuven, Belgium. Here, in cooperation with the sister archives in Cologne and Freiburg, researchers are carefully editing these manuscripts for publication in the Husserliana *Gesammelte Werke* series of which more than 30 volumes have + +already appeared, with more scheduled. + +**The genesis of the** *Logical Investigations* + +On his own admission, the origin of Husserl's *Logical Investigations* lay in the studies in mathematics, logic and psychology, he had been pursuing, inspired by his teachers Weierstrass, Brentano and Stumpf. As he put it, the *Investigations* originally grew out of his desire to achieve 'a philosophical clarification *(eine philosophische Klarung)* of pure mathematics' (Findlay I: 1; Hua XVIII: 5). It worried Husserl that mathematicians could produce good results and yet employ diverse and even conflicting theories about the nature of numbers and other mathematical operations. Their intuitive procedures needed philosophical grounding. **In** search of this grounding for mathematics, Husserl was led to consider formal systems generally, and ultimately to a review of the whole nature of meaningful thought, its connection with linguistic assertion, and its achievement of truth in genuinely evident cognitions. Husserl suggested that the *Logical Investigations* was originally inspired by Brentano's attempts to reform traditional logic. As he put it in his + +'Phenomenological Psychology' lectures of 1925: + +... the *Logical Investigations* are fully influenced by Brentano's suggestions, as should be readily understandable in view of the fact that I was + +a direct pupil of Brentano.24 + +**In** lecture courses Husserl had attended, Brentano had proposed a reform of traditional Aristotelian syllogistic logic, restricting the range of significant + +logical forms, effectively reducing all forms of quantification to existential quantification, reformulating the structure of logical judgements and recasting sentences in new ways to highlight the underlying logical structure distinct from the grammatical form. Despite its promise, Husserl recognised that Brentano's project was destined to fail, since it lacked a proper clarification of the nature of meaning in general. Only a complete clarification of the 'essential phenomenological relations between expression and meaning, or between meaning-intention and meaning-fulfilment' (Findlay I: 173; Hua XIX/I: 19) could steer the proper course between grammatical analysis and + +meaning analysis *(Bedeutungsanalyse),* Husserl claimed. + +Brentano's failed reform of logic alerted Husserl's attention to serious deficiencies in current accounts of the nature of logic, in J. S. Mill, C. Sigwart, W. Hamilton, B. Erdmann, T. Lipps, and others. Husserl's familiarity with - and deep critique of - the logical and mathematical developments of the nineteenth century are evident in his several critical reviews of logical literature, published in 1894, 1897, 1903 and 1904.25 While he fully recognised the importance of logic understood as a calculus of classes being developed by George Boole (1815-64) and by his German contemporary, Ernst Schroder, and the attempts to interpret logical deduction as a mechanical process made by William Stanley Jevons (1835-82) and others, including Gottlob Frege, Husserl harboured worries about the limitations of formal mathematical logic, which he saw as a refinement of logical technique rather than as a genuine philosophy of logic. 26 In particular, Husserl saw a calculus purely as a formal device for mechanically transposing signs (or replacing them with equivalents) according to rules, and thus essentially different from proper logical deduction. Technical brilliance in mathematical logic still required critical theoretical insight in order to elevate it to + +SCIence. + +For a more positive view of logic, Husserl revived 'pure logic', a conception deriving from Leibniz and Kant, but expressed most clearly in the *Wissenschaftslehre* of the neglected Austrian logician Bernard Bolzano (1781- 1848),27 and his followers (especially Frege's teacher Rudolf Hermann Lotze, 1817-81), which saw logic as a purely formal 'science of science'. Husserl singled out Bolzano in particular as one of the greatest logicians and even as + +the unacknowledged forefather of modern mathematical logic: + +Logic as a science must ... be built upon Bolzano's work, and must learn from him its need for mathematical acuteness in distinctions, for mathematical exactness in theories. It will then reach a new standpoint for judging the mathematicizing theories of logic, which mathematicians, quite unperturbed by philosophic scorn, are so successfully constructing. These theories altogether conform to the spirit of Bolzano's + +logic, though Bolzano had no inkling of them. + +Hussed would also credit Hermann Lotze with opening his eyes to the true nature of the ideal objectivities which logic studied, helping him to understand the domain of the ideal while avoiding Platonic hypostasization. Of course, as Hussed set out to write the *Logical Investigations* many other philosophical issues pressed on him, leading him considerably beyond what might be considered to belong strictly to the task of laying the foundations of logic and into broader questions of epistemology, semantics and even ontology. Hussed was drawn to inquire into the conditions of meaningful utterance and expression generally, beginning with the nature of signification in general, linguistic expression, the relation between individual and species, the *a priori* laws governing the whole-part structures generally, the formal laws governing linguistic sense and non-sense, the puzzling nature of intentional content and reference, and, finally, the nature and structure of conscious acts as such, and specifically the nature and structure of judgements which aim at truth and which were traditionally considered to be the vehicles of logical thought. These themes make up the six Investigations of + +the second volume. + +**Husserl's struggle to rescue logic from psychology** + +As Hussed acknowledged in the Foreword to the *Investigations,* his philosophical career began from Brentano's assumption that logical issues could only be clarified by psychology. However, his initial attempts at laying a 'psychological foundation' *(psychologsiche Fundierung,* LI, Findlay I: 2; Hua XVIII: 6) for arithmetical and logical concepts and judgements quickly ran into problems. While psychology was undeniably useful for clarifying the practical procedures of human reasoning and in accounting for the origins of concepts, it failed completely to appreciate or handle the logical unity of the 'thought content' *(Denkinhalt,* Findlay I: 2; Hua XVIII: 6) involved, specifically, the complete independence of this content from all our psychical behaviour. The Pythagorean theorem stands as an independent valid truth whether anyone actually thinks it or not. Such thought contents possess an 'ideality' that allow them to be instantiated in different thought processes of the same individual (LI, Intro. §2, Findlay I: 167; Hua XIX/l: 8) or in diverse individuals' thoughts at different times. Psychological analysis could not accommodate this peculiar ideal unity of thought contents. Hussed therefore suspended his investigations into the philosophy of mathematics to grapple with the 'fundamental epistemological questions' *(die Grundfragen der Erkenntnistheorie,* Findlay I: 2; Hua XVIII: 7) thrown up by his recognition of the ideality of meanings. Mathematics and logic needed a thorough *epistemological* grounding; through a 'critique of knowledge' *(Erkenntniskritik)* to be carried out through the application of phenomeno- + +In the *Investigations,* then, Husserl aims at the very 'Idea *(Idee)* of meaning' and the 'Idea of knowledge' - the systematic conception of the essence of meaning and knowledge, which had been completely obscured in the psychologistic approach. He employed the term 'phenomenology' to express this kind of fundamental epistemological inquiry (see LI Intro. §7), which looked at the very structure of acts of thinking and knowing as well as at the + +objects of knowledge in terms of their essential meanings. + +Inspired by his intensive reading of Bolzano, Lotze and other logicians, and of contemporary Brentanians such as Kasimir Twardowski (1866-1938), Alois Hofler (1853-1922) and Alexius Meinong (1853-1920), Husserl came to question the idea of psychological grounding. Husserl came to reject the account in the *Philosophy of Arithmetic* of the genesis of arithmetic concepts as given which employed Brentanian descriptive psychology to trace the psychological genesis of numbers in acts of collecting and colligating. His much discussed interaction with the logician Gottlob Frege in the early 1890s may also have helped to accelerate the shift that was already occurring in his thinking.28 It is at least clear that both philosophers separately were developing sophisticated accounts of the difference between the 'sense' *(Sinn)* of an expression and its objective reference. In Husserl's case this distinction would deepen his understanding of the structure of the intentional relation leading ultimately to his 'breakthrough' recognition of the essential correlation between thinking and its object, which he says occurred + +around 1898.29 + +From the outset of his career, Husserl had regarded Brentano's rediscovery of intentionality (the 'aboutness' or 'directedness' of mental acts) as hugely significant for the analysis of cognitive acts and processes (which Husserl called *'Erlebnisse',* lived experiences or mental processes), but, during the 1890s, he came to reject as unsatisfactory Brentano's account, which seemed embedded in Cartesian immanentist assumptions about the nature of ideas, and which left dangling the issue of the status of intentional objects. Husserl was dissatisfied with Brentano's characterisation of the intentional object as 'inexistent' and as 'indwelling' in the act. This characterisation seemed to repeat the impasse of the modern representationalist account of knowledge in Locke and others, with its attendant problem of the ability of the mind to get beyond its own representations. Brentano had maintained that *every* presentation related to an object, but what about presentation that appeared to have no objects? Bolzano had discussed 'objectless presentations' and the problem of the status of thoughts that involved impossible or non-actual entities (round squares, golden mountains, and so on) had been bequeathed to Brentano's pupils, especially Twardowski and Meinong. Do all thoughts refer to objects, even thoughts of impossible objects? + +In a number of studies throughout the 1890s Husserl carefully clarified his own understanding of the relations between the intentional act, its content and object, in, for example, his fragments discussing the differences between + +'intuition' *(Anschauung)* and 'representation' *(Reprasentation)* in terms of the kind of 'fulfilment' *(Erfullung)* involved,30 in his draft review of Twardowski's book *On the Content and Object of Presentations,3l* and in the several drafts of his never completed study, *Intentionale Gegenstande* ('Intentional Objects'), probably written in 1894 and re-worked up to 1898.32 The results of these investigations found their way into the second volume of the *Investigations,* especially the First and Fifth Investigations and the Appendix to the Sixth Investigation, where the issue of intentionality and HusserI's distance from Brentano's conception of inner perception are treated at some length. Briefly, HusserI rejected Brentano's attempts to define psychical phenomena in distinction from physical phenomena and his account of 'immanent objectivity'. For HusserI, the main achievement of Brentano was that he identified the essential 'pointing-beyond-itself' *(uber-sich-hinausweisen)* of the mental act. Twardowski's attempt to distinguish between the sensuous immanent content of the act, the act's intentional object, and the real object referred to, also suffered from a 'false duplication' of the object.33 HusserI's answer was to distinguish between the immanent sensuous *'reelle'* contents of the mental act and the transcendent ideal meaning-content of the act, which guarantees we are speaking of the *same* meaning across repeated acts, and between these and the transcendent object of the act (and not as Twardowski considered it the *immanent* object).34 By the late 1890s HusserI had developed the main elements of his account of the relations between signs and things signified, between intentions and their intuitive fulfilments, but it seems likely that his crucial distinction between *sensuous* acts and acts of *categorial* intuition did not emerge until he began writing the six Investigations themselves. This notion of categorial intuition, a distinct intuition of complexes founded on sensory intuition, opened up the proper domain of + +phenomenological viewing as HusserI would develop it after 1901. + +The results of HusserI's intensive research during his most active decade of the 1890s were brought together in a remarkable way in the *Investigations.* Thus, for instance, his 1894 article, *Psychologische Studien zur elementaren Logik* ('Psychological Studies in the Elements of Logic')/5 sketched the distinction between dependent and independent contents that inaugurated the theory of parts and wholes later incorporated into the Third Investigation. But the first real start on writing the *Investigations* came in 1896 when HusserI delivered the lectures that formed the basis of the *Prolegomena* and in 1899 began to prepare the six Investigations themselves for the press. There is some evidence, chiefly his wife Malvine's account, that HusserI was still feverishly revising when the manuscript was wrested from his hands by Stumpf and sent to the publisher.36 Certainly, it is clear that HusserI was having difficulties containing the Sixth Investigation as it grew in length and complexity and forced him to rethink distinctions made in the earIier Investigations, including his account of the relation between demonstrative + +**The published revisions of the** *Logical Investigations* + +**(1913, 1921)** + +Almost as soon as the First Edition of the *Logical Investigations* appeared, HusserI began to express dissatisfaction with some of its formulations and began to revise. **In** his *1902/3* lectures on epistemology, he was already clarifying the distinction between phenomenology which he characterises as a 'pure theory of essences' *(reine Wesenslehre)* and descriptive psychology.37 But his first public opportunities came in 1903, with his reply to a critic named Melchior Palagyi38 - where he made clear that his concept of ideality was drawn from Hermann Lotze, and that he was not opposed to the psychological explanation of concepts but only to the founding of logic upon such an explanation - and with his *Bericht iiber deutsche Schriften zur Logik in den lahren* 1895-1899 ('Report on German Writings in Logic from the Years 1895-1899'), where he repudiated his initial characterisation of the work as a set of investigations in 'descriptive psychology'.39 From around 1905, as is evident from letters written to Scheler and others, HusserI clearly intended to publish a revised edition of the *Investigations* (see Hua XIX!1: xxiii). **In** subsequent lecture courses at Gottingen, e.g., in 1906-7,40 1907-8,41 and 1910-11,42 HusserI developed new conceptions oflogic, semiotics, and semantics (including the *theory of the forms of meanings* begun in the Fourth Investigation, but which needed to be revised in the light of the Sixth), offering essential revising of aspects of the earIier tentative formulations, and leading ultimately to an entirely new theory of *phenomenological meaning,* + +publicly announced as the doctrine of the *noema* in *Ideas* I. + +Also, from around 1905 and inspired by his reading of Kant and Descartes, HusserI was moving in a transcendental direction, embracing both Descartes' project of *prima philosophia,* first philosophy, and Kant's project of a 'critique of reason,.43 HusserI was revising his thoughts on the nature of the flow of consciousness and on the conception of the pure ego, which he had repudiated as an unnecessary postulate in the First Edition (where he was satisfied with the empirical ego). He gradually came to see the need for a fundamental *change of attitude (Einstellungsanderung)* away from the 'natural attitude' as a prerequisite for the proper phenomenological seeing of the essences of cognitive acts ('noetic' acts in general) and their objects understood as pure possibilities of any consciousness whatsoever. This reorientation shed new light on the *correlation* between the intentional act and its object, understood as what is intended in the manner in which it is intended, a conception that eventually would be named as the *noema,* which + +made its first published appearance in *Ideas* I. + +As HusserI engaged in this self-criticism and reorientation, the problem of relating these new concepts of phenomenology to his existing published work became evident. Around 1911, with the First Edition of the *Investigations* now out of print, and with misinterpretations gaining currency among + +his followers, Husser! began to think seriously about revising the whole work in the light of a new introduction to phenomenology and transcendental philosophy which he was planning, and which eventually appeared as *Ideas* I (1913).44 At first, Husser! harboured ambitious plans to offer a number of new expositions of phenomenology and phenomenological philosophy that would render the old *Investigations* obsolete (see his letter of 7 July 1912 to W. E. Hocking, quoted in Hua XIXIl: xxvi). However, since *Ideas* I was a deliberately programmatic work, to complement it Husser! saw the need for examples of concrete phenomenological analyses - 'attempts at genuinely executed fundamental work on the immediately envisaged and seized things themselves' *(Versuche wirklich ausfiihrender Fondamentalarbeit an der unmittelbar erschauten und ergriffenen Sachen,* Findlay I: 4; Hua XVIII: 9), as he puts it in the Foreword to the Second Edition. The six Investigations would remain the paradigm of these concrete phenomenological inquiries. Husser! began revising the text of the *Logical Investigations* in March 1911, but only made real progress in spring 1913 after *Ideas* I went to press. However, even his relatively modest planned revision, done in the light of his new understanding of phenomenology (as expressed in *Ideas* I), proved too demanding, and he produced only a partially revised Second Edition in 1913.45 This was Husser!'s 'middle course' *(Mittelweg),* as he put it in his Foreword to the Second Edition, where he articulated three 'maxims' that guided the revision (Findlay I: 4-5; Hua XVIII: 10-11): namely, to leave individual errors standing as representing steps in his own path of thinking; to improve what could be improved, without altering the course and style of the original; to lift the reader level by level to newer and deeper insights. In the revision the *Prolegomena,* which was written with a single purpose, was left largely unchanged; but those passages in the *Investigations* that specifically discussed the nature of phenomenology, and the kind of essential insight involved, were extensively altered and expanded. In general, the Second Edition highlights the central discovery of *phenomenology,* a concept that had received only tangential and incidental treatment in the First Edition, and gives surer indications about its nature. Thus, invoking his 1903 essay (quoted in Foreword to the Second Edition, Findlay I: 6; Hua XVIII: 13), Husserl claims that the chief error of the 1901 edition was to call phenomenology a 'descriptive psychology', whereas in fact, phenomenology knows nothing of personal experiences, of a self, or of others, similarly it neither sets itself questions, nor answers them, nor makes hypotheses. In 1903, Husser! had claimed that this purely immanent phenomenology was to be free of all suppositions about the nature of the psychological, and furthermore, it would actually provide a critique of knowledge that might then be used as a basis for empirical psychology or other sciences. But, in itself, phenomenology is not identical with descriptive psychology.46 This phenomenological approach brings to evidence the general essences of the concepts and laws of logic. While both descriptive psychology and + +phenomenology are *a priori* disciplines, phenomenology cuts all its ties with individual minds and real psychic processes, even those understood in the most exemplary manner (LI, Intro. §3, Findlay I: 171; Hua XIXIl: 16 - + +added in the Second Edition). + +Husserl is now more emphatic that this eidetic science relies entirely on the evidence of pure intuition, and operates within the 'sphere of immanence', bracketing all concerns with worldly existence and real psychological processes. Husserl thus imports into the text of the *Investigations* the notions of bracketing, *epoche,* and reduction, which had become central to his expositions of phenomenology only after 1905.47 Husserl now stresses the *remoteness* and *unnaturalness* of phenomenological reflection and expands the section (LI, Intro. §3) devoted to listing various difficulties that attach to how we move from naive to reflexive understanding. Pure phenomenological seeing *(Wesensschau)* must be purged of its inherent world-positing tendency and associated beliefs that belong to what Husserl calls 'the natural attitude' *(die naturliche Einstellung)* with its assumption of real existence *(empirisch-reales Dasein;* see LI V §2, Findlay ll: 82; Hua XIX/I: 357 - paragraph added in the Second Edition). It was this purification of epistemology from the distortions imposed by the natural attitude that led Husserl to see phenomenology as essentially distinct from any psychology, including descriptive psychology. Instead, phenomenology was to be the 'universal science of pure consciousness' .48 Husserl later stressed that the First Edition was already *de facto* 'analyses of essence', but that he gradually came to clearer self-consciousness regarding the purely eidetic nature of + +his inquiries.49 + +The revisions of the Second Edition constantly underscore the pure *a priori,* eidetic character of phenomenology. Consider the following typical revision to the Third Investigation. The original sentence in the First Edition, referring to the relations of dependence holding between quality and intensity of a tone, reads: 'And this is not a mere fact but a necessity'. The Second Edition reworks this sentence to read: 'Evidently this is no mere empirical fact, but an *a priori* necessity, grounded in pure essence' (LI III §4, Findlay II: 18; Hua XIX/I: 237). The pure *a priori* essential character of the laws uncovered by phenomenological insight is now sharply contrasted with the kind of empirical generalisation characteristic of the natural sciences. To clarify this further, Husserl replaced Section 12 of the Third Investigation (LI III §I2), which had dealt with dependence relations between temporally coexisting and successive parts, with a completely rewritten section in the Second Edition, which specifies more exactly the nature of the distinction between analytic and synthetic propositions, whereby analytic propositions are purely formal and are not determined by their content in any way, + +whereas *a priori* laws which relate to contents are *synthetic a priori.* + +Phenomenology focuses on the essential features of conscious states in general (akin to Kant's concern with knowledge in general, *Erkenntnis* + +*iiberhaupt* - a conception already elaborated in the First Edition) understood as pure possibilities rather than in terms of any empirical instantiation in animals, humans or other kinds of minds. In contrast with pure phenomenology, Husser! now more sharply characterises all psychology as empirical, as a causal science of physical organisms and their psychophysical states, e.g., 'as the empirical science of the mental attributes and states of animal realities' *(als Erfahrungswissenschaft von psychischen Eigenschaften und Zustanden animalischer Realitaten,* LI, Intro. §2, Findlay I: 169; Hua XIXIl: 12), the science which studies 'the real states of animal organisms in a real natural order' (LI Intro. §6, Findlay I: 176; Hua XIXIl: 23). Husser! distinguishes both empirical and its sub-branch descriptive psychology from pure phenomenology. While psychology is a valuable empirical science, the reduction of meanings to their psychological states, i.e., 'psychologism', is a natural, ever present temptation to the mind ('at first inevitable, since rooted in grounds of essence', LI, Intro. §2, Findlay I: 169; Hua XIXI1: 12), which can only be cured by phenomenological analysis. Only pure phenomenology, and not descriptive psychology, Husser! writes in the Second Edition, can overcome psychologism (LI, Intro. §2, Findlay I: 169; Hua XIXIl: 11-12). Furthermore, Husser! departs from Neo-Kantianism, by stressing that the grasp of the conditions for the possibility of knowledge comes from insight into the essence of knowledge, that is from phenomenological + +viewing. + +In keeping with his new transcendental orientation, Husser! has more appreciation in the Second Edition of 'the pure ego' *(das reine /ch,* LI V §§5, 8) of the Neo-Kantians (especially Natorp), which he had originally dismissed as an unnecessary postulate for the unification of consciousness (see LI V §8, Findlay II: 352; Hua XIXIl: 374). He also endeavours to improve his initial attempts at drawing a distinction between the quality and intentional matter of acts. In particular, he was unhappy with his original characterisation of the sensuous matter of the act and the manner in which it is taken up and interpreted in the act. His later account of the *noema* was offered as a + +corrective (see, e.g., LI V, §l6, Findlay II: 354; Hua XIX/I: 411). + +In the First Edition, Husser! had characterised phenomenology as expanding or as clarifying *epistemology* (e.g., LI Intro. § Findlay I: 166; §2, I: 168), in that it offered a kind of 'conceptual analysis' *(Begriffsanalyse),* concerned with differentiating and disambiguating the different senses of basic epistemological concepts (such as 'presentation', *Vorstellung).* In his Introduction to the Second Edition, Husser! is now more aware of a possible misunderstanding whereby this conceptual analysis would be misunderstood purely as an investigation of language, in short as *linguistic analysis,* whereas in fact Husser! is anxious to distinguish his 'analytical phenomenology' from linguistic analysis. Reliance on language can be misleading, Husser! believes, because linguistic terms have their home 'in the natural attitude' *(in der natiirlichen Einstellung)* and may mislead about the essential character + +of the concepts they express, whereas phenomenological thinking about consciousness takes place in the eidetic realm where all natural attitudes are bracketed. For Husserl, it is certainly true that the objects of logic - propositions or statements *(Siitze)* - are encountered only in their grammatical clothing, i.e., in linguistic assertions, and it is an obvious fact that the findings of science eventually take the form of linguistic utterances or sentences. Husserl, then, agrees with J. S. Mill that discussions of logic must begin with a consideration of language, though not issues of the nature of grammar or the historical evolution of language as such, but rather in relation to a theory of knowledge. Husserl is seeking a *'pure phenomenology of the experiences of thinking and knowing'* (Findlay I: 166; Hua XIXIl: 6), experiences not to be understood as empirical facts, but rather grasped in 'the pure generality of their essence' (ibid.). Linguistic analysis is not a substitute for a fundamental analysis of consciousness (see LI I §21). In this sense, phenomenology clarifies our linguistic practice and not the other way round. + +**Husserl's incomplete revisions of the Sixth** + +**Investigation** + +In 1913 Husserl intended to revise the Sixth Investigation in a radical fashion, but became bogged down (see his letter of 23 June 1913 to Daubert, quoted in Hua XIXIl: xxv), and eventually withheld it when he sent the revised five Investigations to press. Husserl now recognised that his original account of categorial intuition with its realist commitments did not fit comfortably with his new transcendental idealist framework. He made various attempts at a complete reworking of this Investigation in late 1913 and again in 1914, but lost enthusiasm for these revisions during the war years (1914-18), when exhaustion prevented research 'on behalf of the phenomenology of logic' *(fur die Phiinomenologie des Logischen,* Findlay II: 177; Hua XIX12: 533). As he recounted, he could only 'bear the war and the ensuing "peace'" by engaging in more general philosophical reflections, specifically the elaboration of his 'Idea of a phenomenological philosophy' *(Idee einer phiinomenologsiche Philosophie,* Findlay II: 177; Hua *XIX/2: 533).* Meanwhile, he gave the manuscripts to Edith Stein who attempted to order them into two articles for the *Jahrbuch,* but she could not get Husserl to + +look over her work and the project stalled. + +After the war, Husserl turned again to logic and eventually was prevailed upon to publish a limited revision of the Sixth Investigation in spring 1921. In his Foreword, dated Freiburg, October 1920, Husserl regrets that he was unable to produce the radically revised Sixth Investigation promised in 1913, and acknowledges that it was the pressure offriends (including, presumably, his new assistant, Martin Heidegger) that finally forced him to produce this new edition. In fact, Husserl was never satisfied with his revision and continued to work intermittently on a full revision of this crucial Investigation, + +leaving some drafts that remained unpublished at his death. 50 These drafts attempt a complete rethinking of the nature of signs involving a distinction between signitive and significative intentions in attempting to specify the achievement of abstract symbolic thought. 51 Husserl was also gradually coming to recognise the contextual aspect of meaning which would lead eventually to his discovery of 'genetic' phenomenology in the early 1920s. + +Husserl's 1920 Foreword is written in tones of exasperation and defensiveness regarding the many misunderstandings of his work then current. He details changes made, mainly in the second section of the Sixth Investigation, entitled *Sinnlichkeit und Verstand (Sensibility and Understanding),* where the concept of categorial intuition - originally introduced in the First Investigation - is treated at some length. Husserl maintains that his critics have misunderstood his talk of immediacy as relating to the immediacy of sensory intuition rather than to the nature of intuition generally. In particular he attacks the views of Friedrich Albert Moritz Schlick (1882-1936, founder of the Vienna Circle), as expressed in his *Allgemeine Erkenntnislehre (General Theory of Knowledge,* 1918)52 where he had argued that Husserl's *Ideas* I relied on a bizarre notion of non-physical intuition that required a peculiarly strenuous kind of study. Husserl replies that by 'strenuous study' he means no more than the application of a mathematician. Schlick's criticism typifies a more general unease in philosophical circles with Husserl's emphasis on intuition which was seen by many as promoting an irrational *intuitionism* that could not be corrected. The Neo-Kantians voiced similar criticisms of Husserl's concept of categorial intuition, as is evident from Fink's reply to Husserl's critics. 53 How could one have *intuition* of the categorial? Husserl, on the other hand, understood by intuition, cognitive experiences which are accompanied by adequate evidence. He wants always to emphasise that acts of knowing are essentially diverse and that their respective modes of intuitive + +fulfilment must be appreciated and appropriately distinguished. + +**In** his Foreword to the revision of the Sixth Investigation, Husserl also challenges an accusation - apparently widespread, but which he vehemently rejected - that he had rejected psychologism in the first volume of the *Investigations* only to fall back into it in the second (LI, Findlay **II:** 178; Hua *XIX/2:* 535).54 Husserl believes these critics have failed to appreciate the true sense of his phenomenology, and have misunderstood it as a kind of introspectionist psychology. In order completely to separate phenomenology from introspectionism, psychology and indeed all natural sciences, Husserl emphasises the need to undertake the *epoche* and the reduction. It was only by removing all traces of the natural attitude in regard to our cognitive achievements that their true essences can come into view in an undistorted manner. This claim integrates the *Logical Investigations* into Husserl's later transcendental idealism, whose treatment is beyond the scope of this introduction. Let us now turn to examine in more detail the philosophical con- + +**Husserl's** *Kampfschrift:* **the** *Prolegomena* + +In the Foreword to the Second Edition, Husserl records that the *Prolegomena* was a 'polemic on psychologism' *(Streit um den Psycho!ogismus,* Findlay I: 6; Hua XVIII: 12), and major figures such as Paul Natorp, Wilhelm Dilthey and Wilhelm Wundt recognised it as such, so that the *Prolegomena* took on a life of its own and had an independent impact in German philosophy for its criticism of psychologism. Husserl, however, liked to emphasise its coherence with the second volume and wrote to Meinong that the critique of psychologism was central to his phenomenology of knowledge in general (letter of 27 August 1900, quoted in Hua XVIII: xvii). Others, including Wundt, could not so easily see the connection between the two + +volumes. + +According to the Foreword, the first draft of the *Prolegomena* originated as two series of lectures delivered at Halle in the summer and autumn of 1896 (Findlay I: 5; Hua XVIII: 12) and written up in 1899. These 1896 lectures had already set out Husserl's conception of logic as a pure, formal, autonomous science of ideal meanings and the ideal laws which govern them, and offering a sharp differentiation of pure logic from the more traditional interpretation of logic as an 'art' or 'technique' *(Kunstlehre)* of thinking well. The Halle lectures, however, do not contain some of the more important parts of the *Prolegomena,* namely, the discussion of relativism *(Pro I.* §§32-7), and the detailed criticisms of Mill, Spencer, Sigwart and Erdmann, and the discussion of 'thought-economy' associated with Mach and Avinarius *(Pro!.* §§52-6). As the *Prolegomena* was written entirely in one cast of mind, Husserl did + +not feel the need to make major revisions in the Second Edition. + +Husserl's negative aim was to demonstrate that the psycho logistic inter- + +pretation of logic was a self-defeating, self-contradictory absurdity: + +the correctness of the theory presupposes the irrationality of its premises, + +the correctness of the premises the irrationality of the theory. + +*(Prol.* §26, Findlay I: 61; Hua XVIII: 95) + +Furthermore, whereas the study of traditional logic should have given a clear understanding of the 'rational essence of deductive science' and indeed be the 'science of science', in fact the logic of his time was not adequate to that task. Husserl's positive aim was to find out 'what makes science science' *(Pro!.* §62, Findlay I: 144; Hua XVIII: 230), but the unclarity and confusion surrounding logical concepts put the whole project of exact scientific knowl- + +edge at risk: + +In no field of knowledge is equivocation more fatal, in none have confused concepts so hindered the progress of knowledge, or so impeded + +insight into its true aims, as in the field of pure logic. + +In his 1900 *Selbstanzeige* ('Author's Report') to the *Prolegomena* HusserI announced that he was defending logic as a pure, *a priori,* independent, theoretical science, reviving the older Bolzanian idea of a pure logic against the prevailing psychologistic misinterpretation of logic that leads to contradictions and absurdities, and ultimately to sceptical relativism. HusserI argues that logical laws and concepts belong to the realm of the ideal, being purely formal, that is, applied in general to every kind of content. In the *Prolegomena* HusserI makes an important distinction between empirical *generalisation* and the kind of *formalisation* required for idealisation in science and mathematics. He contrasts this pure theoretical logic with applied logic, understood as an art of thinking *(Kunstlehre),* drawing an analogy with the contrast between pure geometry and the art ofland surveying *(Feldmesskunst).* + +Thus, in the *Selbstanzeige* HusserI defines pure logic as + +... the scientific system of ideal laws and theories which are purely grounded in the sense of the ideal categories of meaning; that is, in the fundamental concepts which are common to all sciences because they determine in the most universal way which makes sciences objective + +sciences at all: namely, unity of theory. 55 + +Science as such is for HusserI a regulated interconnection of ideal truths expressed in propositions. Logic deals with these propositions and their component meanings in their utmost generality, understood as pure categories. According to HusserI, following in the Kantian tradition, all logical distinctions are 'categorial' (LI II §l) and belong to 'the pure form of possible objectivities of consciousness as such' (LI II, Findlay I: 240; Hua XIX!1: 115). Furthermore, knowledge can be about many kinds of different things, there are multifarious objects of knowledge, not just real things, but ideal entities, relations, events, values. The conception of scientific knowledge must be sufficiently broad to accommodate this diversity of objects of knowledge. HusserI, then, wants a new account of logic as a pure *a priori* science, a *mathesis universalis* in the manner of Leibniz. It must be balanced with a new theory of the nature of objects in general, formal ontology, developed in the Third Investigation. In other words, pure logic has a counterpart, the + +pure theory of objects. + +**Husserl's encounter with Frege - the issue of** + +**psychologism** + +Since the rejection of psychologism and the defence of the ideal objectivity of logical laws is now more usually credited to Gottlob Frege rather than to HusserI, it is appropriate at this point to examine the relations between these two logicians. In fact, they corresponded with one another on various issues in mathematics and semantics in 1891 (and again in 1906). HusserI + +was one of the first philosophers in Germany to recognise Frege's work, and, although he had criticised Frege's account of the nature of identity in the *Philosophy of Arithmetic* in 1891, relations between the two were collegial and mutually respectful. But, in 1894, Frege published an acerbic review of Husser!'s *Philosophy of Arithmetic,* in which he accused Husser! of making a number of fundamental errors. 56 According to Frege, Husser! treated numbers naIvely as properties of things or of aggregates rather than as the extensions of concepts (the *extension* of a concept is the set of objects the concept picks out).57 Husser! had seen number as deriving from our intuition of groups or multiplicities and since neither one nor zero is a multiple, strictly speaking they were not positive numbers for Husserl. Frege criticised Husser!'s account of zero and one as negative answers to the question: 'how many?' Frege states that the answer to the question, 'How many moons has the earth?', is hardly a negative answer, as Husser! would have us believe. Furthermore, Frege believed, Husser! seemed to be confusing the numbers themselves with the *presentations* of number in consciousness, analogous to considering the moon as generated by our act of thinking about it. Crucially for Frege, in identifying the objective numbers with subjective acts of counting, Husser! was guilty of *psychologism,* the error of tracing the laws of logic to empirical psychological laws. If logic is defined as the study of the laws of thought, there is always the danger that this can be interpreted to mean the study of how people actually think or ought to think; understanding necessary entailment, for example, as that everyone is so constituted psychologically if he believes *p* and if he believes that *p* implies *q* then he cannot help believing that *q* is true. For Frege, Husser! has collapsed the logical nature of judgement into private psychological acts, + +collapsing together truth and judging something as true. + +According to the journal kept by W. R. Boyce-Gibson, who studied with Husser! in Freiburg in 1928, Husser! later acknowledged that Frege's criticisms had 'hit the nail on the head'. On the other hand, there is considerable evidence that Husser! was already moving away from his own ear!ier psychologism when Frege's review was published, especially in his critique of Schroder's *Algebra of Logic. 58*Husser! was already embracing Bolzano's *Wissenschaftslehre59* with its doctrine of 'states of affairs' and 'truths in themselves', whose precise nature he then came to understand through his reading of Hermann Lotze's account of the Platonic Ideas, as he had reported in his reply to Melchior Pahigyi in 1903. Given the supposedly crucial importance of Frege's review of Husser!, it is surprising that Frege receives only one mention in the *Prolegomena* in a footnote *(Pro I.* §45, Findlay I: 318; Hua XVIII: 172 n. \*\*) where Husser! writes: '1 need hardly say that I no longer approve of my own fundamental criticisms of Frege's antipsychologistic position set forth in my *Philosophy of Arithmetic'.* Husser! now cites both Frege's *Die Grundlagen der Arithmetik (Foundations of Arithmetic,* 1884) and the Preface to his *Grundgesetze der Arithmetik (Fundamental* + +*Laws of Arithmetic,* 1893) as anti-psychologistic statements of which Husser! + +can now approve. + +In fact, Husser! had abandoned the approach of the *Philosophy of Arithmetic* almost as soon as it was published in 1891. He realised that the cardinal numbers were not the basis of all numbers, and in particular that the psychological approach could not handle the more complex numbers (e.g., the imaginary numbers). In the *Prolegomena* Husser! explicitly denies that numbers themselves are to be understood in terms of acts of counting + +although they can only be accessed through acts of counting: + +The number Five is not my own or anyone else's counting of five, it is + +also not my presentation or anyone else's presentation of five. + +(U, *Pro I.* §46, Findlay I: 109; Hua XVIII: 173-4) + +While it is only by counting that we encounter numbers, numbers are not simply products of the mind. This would deny objective status to mathematics. The psychological origin of arithmetic concepts does not militate against the independent ideal existence of these concepts as species quite distinct from 'the contingency, temporality and transience of our mental acts' (LI, *Prol.* §46, Findlay I: 110; Hua XVIII: 175). Two apples can be eaten but not the number two, Husser! says in his 190617 lectures. For Husser!, logical concepts contain nothing of the process by which they are arrived at, any more than number has a connection with the psychological act of counting. Numbers and propositions, such as the Pythagorean theorem, are ideal 'objectivities' *(Gegenstandlichkeiten,* Findlay: 'objective correlates'), which are the substrates of judgements just as much as any real object is. In contrast to 'real' entities that bear some relation to time, if not to space, the pure identities of logic are 'irreal' or 'ideal'. Husserl characterised them as 'species' in the Aristotelian sense, along side other 'unities of meaning', for example the meaning of the word 'lion', a word which appears only once in the language despite its multiple instantiations in acts of speaking and writing. What is logically valid is *a priori* applicable to all worlds. In the *Prolegomena,* then, Husser!, holds a view similar to Wittgenstein in the *Tractatus* - logic says nothing about the real world, the world of facts. It is a purely formal *a priori* science. Husserl, however, integrates logic into a broader + +conception of the theory of science. + +Whereas Husserl had begun in 1887 with the assumption that psychology would ground all cognitive acts, he ends the Foreword to his *Investigations* by quoting Goethe to the effect that one is against nothing so much as errors one has recently abandoned, in order to explain his 'frank critique' *(die freimiitige Kritik)* of psychologism (U, Findlay I: 3; Hua XVIII: 7). While in agreement with Frege concerning the dangers of psychologism for logic, Husserl was not persuaded by Frege's project for mathematical logic as, in general, he was, as we have seen, suspicious of the purely formal turn + +to symbolic logic, exemplified in his day by the logical programmes of George Boole (see Hua XXIV: 162), William Stanley Jevons and Ernst Schroder, which for him contained theoretical flaws and confusions. That is not to say that HusserI thought of formalisation as unnecessary; in fact, he saw it as the only purely scientific way of advancing logic (LI, *Prol.* §71, Findlay I: 158-9; Hua XVIII: 254). Thus he praised the elegance with which mathematicians were expanding and transforming the domain of traditional logic, and he criticised those who refused to recognise the proper role of mathematics in these matters. However, HusserI believed that this mathematical tendency was manifesting itself as a kind of technical ability that had not reflected on the nature of its founding concepts. Philosophy must try to + +think through the essential meanings of logical procedures: + +The philosopher is not content with the fact that we find our way about in the worId, that we have legal formulae which enable us to predict the future course of things, or to reconstruct its past course: he wants to clarify the essence of a thing, an event, a cause, an effect, of space, of time, etc., as well as that wonderful affinity which this essence has with the essence of thought, which enables it to be thought, with the essence of knowledge, which makes it knowable, with meaning which make it + +capable of being meant etc. + +*(Prol.* §71, Findlay I: 159; Hua XVIII: 255) + +As HusserI put it in his *190617* lectures, 'Introduction to Logic and Theory of Knowledge', one must distinguish between mathematical logic and philosophical logic (Hua XXIV: 163). Towards the end of his life HusserI would repeat this criticism in *The Crisis of European Sciences,* where he would criticise this 'idolization of a logic which does not understand itself' and claim that a formal deductive system is not in itself an explanatory system *(Crisis,* §55, Carr: 189; Hua VI: 193). For HusserI, purely extensionalist logic or calculus could never be more than a brilliant technique. From the *Prolegomena* onwards, HusserI offered a complex account of the full nature of what he called 'formal logic' , utilising a much wider conception than is now current. In some respects his account of logic is quite traditional, being centred on the notion of judgement or assertion (Greek: *apophansis)* and hence is, following Aristotle, characterised as 'apophantic logic' (see LI, IV §14, Findlay II: 72; Hua XIXI1: 344). On the other hand, in *Formal and Transcendental Logic* (§§12-15) HusserI articulated this mature vision of this 'formal logic', which for him included formal grammar or what he called 'the pure theory of forms of meaning' that laid down the conditions of meaning combination as such; then a second level of 'consequence-logic' or the logic of validity which is concerned with inference; and finally a 'logic of truth', which recognised that logic aims not only at formal validity but seeks to articulate truth. In the *Prolegomena* HusserI also saw the need for a + +general 'theory of manifolds' or the theory of the possible forms of theories to complete his account of the nature of logic in general. We cannot deal with the complexities of Husserl's vision of logic here, except to note that in the *Investigations* Husserl was not pursuing an objectivist account of logic as his exclusive aim. Husserl recognised the essential 'two-sidedness' of the acts which are aimed at logical meanings, on the one hand there are the laws governing the meanings themselves, but there are also the judgings, inferrings, and other acts, which are oriented towards the subjective side, that need to be treated by phenomenology *(Formal and Transcendental Logic* §8). In other words, the aim of phenomenology is to study the essential *correlations* between acts of knowing and the objects known, something that became clearer + +to Husserl after he wrote the *Investigations.* + +**The structure of the six Investigations** + +While the *Prolegomena* was written with a single purpose and, by Husserl's standards, remains a relatively straightforward piece of writing, the six Investigations of the second volume at first sight seem much less unified and coherent, with most commentators testifying to their uneven, fragmentary and sprawling character. Husserl himself warned that the work could not be considered as a finished exposition of scientific results or as *'one* book or work in the literary sense' (LI, Findlay I: 5; Hua XVIII: 11), but rather should be seen as a 'systematically bound chain of investigations', 'a series of analytical investigations' *(eine Reihe analyticher Untersuchungen,* LI, Findlay I: 173; Hua XIX/1: 20), which would need further elaboration through 'resolute cooperation among a generation of research-workers' (LI, Findlay I: 171; Hua XIX/l: 16-17). It had to be seen as a living develop- + +ment of philosophical ideas, a journal of philosophical discovery. + +A recent commentator, Kit Fine, has remarked (referring specifically to the Third Investigation but applicable with justice to the whole): 'Such is the range of the work that it is with a growing sense of excitement that one discovers the riches that lie beneath its rough and seemingly impenetrable exterior'.60 David Bell has identified a threefold structure to the work, with the *Prolegomena* establishing the need for ideal unities in logic and knowledge generally, the first four Investigations clarifying issues of linguistics, semantics, formal ontology and formal grammar, while the final two Investigations were properly phenomenological, studying the nature of conscious acts and their claim to knowledge and truth. 61 The *Investigations,* then, is more united than its outward appearance suggests, and rich in sophisticated philosophical insights, albeit embedded in Husserl's wordy and labyrinthine presentation. In part, the progressive structure of the work is obscured by Husserl's tendency to enter into exhaustive critiques of other positions in order to arrive at his own view in circuitous manner, and then set out again + +circumspectly and tentatively, warning always of the need for further analyses and distinctions to be borne in mind. 62 One always has the sense of philosophising in progress rather than of a completed system, of listening to a great mind communing with itself. According to the author, the *Investigations* proceed by lifting the reader from lower to higher levels, moving in a 'zig-zag' manner *(im Zickzack,* LI, Findlay I: 175; Hua XIX 11 : 22), forced to employ concepts that would be clarified later in a reflective 'turning back' *(zuruckkehren).* Indeed, HusserI's whole approach has the character of such + +'backward questioning' *(Ruckfragen).* + +The six lengthy Investigations of the second volume are concerned with analysing elements of the form of knowledge, such notions as meaning, concept, proposition, truth (LI *Prol.* §71, Findlay I: 159-60; Hua XVIII: 236-7). HusserI begins with the general structure of signs and meaningful expressions; then moves to analyse the status of universals (which he calls *species)* and the nature of abstraction; followed by a treatise on the laws governing the relations of dependence between parts and wholes; another mini-treatise on the relation between logic and grammar as *a priori* disciplines; the nature of consciousness, including the meaning of intentionality and the ambiguities surrounding the associated notions of content, object, presentation, and finally the nature of the identifying syntheses involved in judgement and its relation to truth. Along the way, he offers sharp criticisms of prevailing views, including a critique of 1. S. Mill's account of connotation and denotation, a refutation of sensationalism, a rebuttal of empiricist theories of abstraction (Locke, Berkeley, Hume, Mill), a sharpened definition of the *a priori* including a new distinction between the formal (analytic) and material (synthetic) *a priori* which claims to be an advance on Kant, and careful discussions of Bolzano, Mill, Brentano and others, in terms of their views on logic, psychology and the nature of judgements and their + +contents. + +A basic assumption of HusserI's understanding of knowledge is that knowledge is essentially understood and communicated in the form of expressive statements, where a statement is a unified whole with a single, possibly complex, meaning, that says something *about* something. It refers to an object (whether an individual thing or a state of affairs) through a 'sense' or 'meaning' (HusserI employs both *Sinn* and *Bedeutung* for 'meaning'). Of course, in the *Logical Investigations,* and indeed since 1891, HusserI was fully aware of Frege's distinction between *Sinn* ('sense') and *Bedeutung* (,reference' or 'meaning'), but he does not observe it since it is at variance with ordinary German usage. HusserI prefers to use the terms *Sinn, Bedeutung* and also *Meinung* more or less as equivalent notions (see LI II §2, Findlay I: 240; Hua XIXIl: 115) although later, in *Ideas* I §124, he will restrict *'Bedeutung'* to linguistic meaning only and use *'Sinn'* more broadly to include all meanings, including non-conceptual contents (e.g., perceptual sense). Both Frege and HusserI agree that the *sense* of a statement is an ideal unity + +not affected by the psychic act grasping it, nor by the psychic stuff (mental imagery, feelings, and so on) that accompanies the psychological episode. Logic (and mathematics and the other formal sciences) is concerned to process the laws governing these abstract ideal unities which Husserl characterises as having 'being in itself' *(An-sich-sein,* translated by Findlay as 'intrinsic being') as unities in manifolds (Findlay I: 169; Hua XIX!1: 12) as well as a 'being for' *(Fur-sich-sein)* the thinker. In themselves, they are pure identities, remaining unchanged irrespective of their being counted, judged, or otherwise apprehended in psychic acts. As Husserl says in the *Prolegomena,* truths are what they are irrespective of whether humans grasp them at all *(Pro I.* §65, Findlay **I:** 150; Hua XVIII: 240). Despite the fact that the objects of logic are ideal and transtemporal, nevertheless, they must also be accessible and graspable by the human mind, as Husserllater explains: + +... it is unthinkable that such ideal objects could not be apprehended in + +appropriate subjective psychic acts and experiences.63 + +We can imagine any such ideal meaning or *Sinn* being entertained or judged or considered in some way by a mind. It is simply a fact that these ideal meanings *(Sinne)* present themselves to us as something that is subjectively grasped: ' ... ideal objects confront us as subjectively produced formations in the lived experiencing and doing of the forming'.64 This is their 'beingfor'. They are always truths *for* some possible mind, subjective acts are 'constituting acts' for these ideal objectivities. The question then becomes: how are these hidden psychic experiences *correlated* to the 'idealities'? Frege had answered in a naive manner: our minds simply *grasp* ideal thoughts. But Husserl wants to give an account that does justice to the essential twosidedness of our cognitive achievements by analysing the structure of this + +expressing and grasping of meaning. + +For Husserl, the primary interest of what he calls 'phenomenology' in the second volume of the *Investigations* does not lie in identifying the ideal nature of the idealities (numbers, logical entities, pure meanings) that are the focus of mathematics, logic, semantics and other sciences. Rather, Husserl is primarily interested in the mental acts *correlated* with these ideal objectivities and the laws governing these essential intentional correlations (see Hua XXIV: 172). Initially, he tended to understand these acts as psychological realities which instantiate pure essences in a kind of token! type relation. To get at their essential natures he initially thought he could use Brentanian descriptive psychology. After 1901 Husserl realised he was mistaken to characterise in psychological terms what were the essences of cognitive acts and their correlative objects. Psychic acts, like physical objects, are parts of the natural world and are governed by temporal relations, and other features of our contingent universe. The essential structures of acts of cognition, on the other hand, were not parts of the world, and hence could + +not be treated by psychology. Thus it was some four years after the *Investigations,* as Husserl recalled in the *Crisis* §70 (Carr: 243; Hua VI: 246), that he arrived at self-consciousness regarding the true nature of the phenomenological method uncovered in 1901. He then realised that pure or transcendental phenomenology has essentially to replace descriptive psychology and that real/ideal distinction had to be replaced by a purely essential study of the noetic/noematic structure of intentional experiences. Husserl thinks the intentional acts themselves can be isolated as true for all possible consciousnesses. Phenomenology does not discuss states of animals, but rather perceptions *as such,* willings *as such,* just as pure arithmetic deals with pure number and geometry deals with pure shapes, and not actual shapes as encountered in nature. For Husserl, it was the task of phenomenology to delineate in advance the possible forms of each intentional act and its limits. This is why phenomenology despite its descriptive rigour is actually an *a* + +*priori* science, not an empirical one. + +Husserl is aware that one cannot just assume one has a grasp of the *concepts* just because one understands the *meanings* of the words that express the concepts. There are concealed ambiguities in the linguistic expressions, and so it is necessary to fix our concepts through clear self-sustaining intuitions: + +We desire to render self-evident in fully-fledged intuitions that what is here given in actually performed abstractions is what the word-meanings in + +our expression of the law really and truly stand for. + +(LI, Findlay I: 168; Hua XIX/I: 10) + +The aim is to achieve clarity and distinctness in concepts by making whatever appropriate disambiguations as can be brought to intuitive clarity. For Husserl, questions concerning the relation of the objective to the subjective acts of the mind, questions of the meaning of the so-called *adequatio rei ad intel/ectus,* cannot be separated from issues in pure logic. Such questions as how these ideal objectivities come to be presented to the mind and grasped by it and so end up becoming something subjective must be + +addressed: + +How can the ideality of the universal *qua* concept or law enter the flux of real mental states and become an epistemic possession of the think- + +ing person? + +(LI, Intro. §2, Findlay I: 169; Hua XIX/I: 13) + +How is there an *adequatio rei et intel/ectus* in the case of the relation between ideal concepts and human psychical acts? We have to pass over from a naIve performance of acts to an *attitude of reflection (Einstellung der Reflexion).* Husserl wants to discover the *a priori* relations between meaning and its expression, and he sets out the basis of this in the First Investigation. + +**The First Investigation: the nature of** + +**meaningful expression** + +Although, at first glance, the First Investigation appears to be an essay on *signs (Zeichen),* clearly influenced by Mill's *Logic* (LI I §16), and by linguistic studies by Brentanists such as Twardowski and Anton Marty, in fact Husserl intended it to have a 'merely preparatory character' (LI, Findlay I: 6-7; Hua XVIII: 13), aiming correctly to identify the elements of the meaning function *(Bedeutungsfunktion)* in conscious life. Although it contains discussions of proper names, common names, collective terms, demonstratives, speech acts, and so on, Husserl's interest was not in philosophy of language as such, but rather in specifying the structure of meaningful assertion, separating out the acts which go to make up the intentional expression and fulfilment of meaning. In this First Investigation (§9) Husserl develops his crucial distinction (held from early in his career) between meaning-intending and meaning-fulfilling acts and the 'unity of coincidence' or 'covering' *(Deckungseinheit)* between meant and fulfilled senses in those situations where a concrete intuition fills out the intending sense. As Husserl's conception of signification became more nuanced, this Investigation was + +considerably reworked in the Second Edition. + +Husserl begins from Mill's claim that, since all thought is expressed in language, a study of linguistic forms is a prerequisite to the clarification of logical forms. He departs from Mill, however, in his account of the manner in which proper names (,Schulze', 'Socrates') signify their referents. Drawing on and refining some traditional distinctions in then current semantics (e.g., Marty), Husserl distinguishes between the function of an expression to *intimate (die kundgebende Funktion)* something to someone, and its expression of an ideal *sense* or *meaning (Sinn* or *Bedeutung)* which is the same in different performances of the assertion or in acts of understanding it. Moreover, normally an act of expressing is directed *beyond* its meaning to its associated object or objectivity *(zugehorige Gegenstdndlichkeit),* through a specific manner of intentional reference *(intentionale Beziehung).* Finally, Husserl has a brief introductory discussion of the different kinds of 'objectivities' to which things can be directed, distinguishing between simple and categorial objectivities (LI I § 12) - the focus of the Sixth Investigation. Husserl begins by distinguishing between signs functioning as *indications (Anzeichen),* which operate through linking one *extant* thing with another without a mediating meaning, e.g., smoke indicating fire, flag is a sign of a nation, a brand that marks a slave, chalk that marks out a house, and *expressions (die Ausdriicke),* in his specific sense, that require the mediation of a meaning or sense and refer to some object regardless of its existential status. As Husserl says: 'It is part of the notion of an expression to have a meaning' (LI I §lS). A meaningless expression, e.g., 'abracadabra', would not be an expression at all. This is not meant to be an exhaustive treatment + +of signs and signification, but merely a distinction between different *Junctions* of signs. Husser! is interested in the mental act of meaningful *expression,* irrespective of whether it is uttered, written, or simply thought to oneself. His account is a semantics of speaker intention. Communication is not Husser!'s concern, because, for him, logic is concerned only with the *expression* of ideal meanings. The pragmatics of communication or reception of meaning is a secondary matter, a concern for the philosopher of language. An expression may have a set of physical sounds or written marks or merely imagined utterance, but what makes it an *expression* (and not just a reproduction of sounds like a parrot) is the mental state (or act) that 'enlivens' or 'ensouls' it. Normally, in any expressive act, the inner fused unity *(eine innig verschmolzene Einheit,* LI I §IO) of sign and thing signified, of word and object, is experienced. Our interest usually focuses on the object intended and not on either the meaning or any associated verbal chain (unless our interest is, let us say, in assonance or in grammar, e.g., if someone says, 'I done that', the speaker's attention may be directed at confirming having done something and not towards the poor grammatical form). This is not to say that the thought exists apart from its expression. Thoughts + +*come to Jorm* in a linguistic way. + +There are many other features entwined with the act of expression. Husser! further distinguishes between what expression 'shows forth', conveys, or *intimates (kundgibt)* and what it *means,* and between what it *means* and what *object* it names (LI I §6). Typically, Husser! recognises the inherent complexities (even if he here does not focus on them), for instance, in communication, an expression both expresses a meaning and indicates something to the hearer. An expression functions as an indication when, for example, it indicates to the hearer the meaning intentions of the speaker (LI I §7). Through this intimating function other aspects of the communicative situation may be picked up, e.g., that the speaker is angry or is making a judgement. Expressions, then, have a communicative function in relation to others. A speaker endows a certain word-chain with a sense that can be understood by a hearer, with certain 'sense-giving acts' *(sinnverleihende Akte,* LI I §7). This, Husser! says, makes mental commerce *(geistige Verkehr)* possible. But besides their function in communication with others, expressions playa role in our individual, solitary, mental life, where communicating has no role, and therefore the act of meaning *(Akt des Bedeutens)* must be strictly distinguished from its 'intimation achievement' *(die kundgebende Leistung,* LI I §8). When an expression is articulated it normally directs interest away from itself towards what it intends to convey, but this directing away is not a form of indicating (§8). In silent soliloquy we may use imagined words rather than spoken words, we may even imagine the sounds of the words. Here we express our meanings although we do not intimate them to others. The expression of meaning, therefore, remains an issue even for the solitary + +Husserl distinguishes between expressions which function solely to *name (nennen)* and other more complicated forms, which Husserl calls 'predicatively formed complexes' which are essentially predicates. Husserl thinks that the referential power of proper names has been misunderstood by Mill, who views a proper name as non-connotative and directly *denoting* its 'subject' (in Mill's terminology) without the mediation of an abstract meaning (or 'attribute').65 Names do pick out their objects directly, but not through *indication,* rather they have an expressive function that allows the name to + +*mean* the object in different sentential formations. + +According to Husserl's fundamental distinction between meaning intentions and meaning fulfilments, 'meaning intentions' *(Bedeutungsintentionen)* or 'meaning-conferring acts' *(die bedeutungsverleihenden Akte)* include all those acts involved in *confirming, corroborating, illustrating (erfullen, bestiitigen, bekriiftigen, illustrieren,* LI I §9). An expression has to be consciously endowed with meaning to be a vehicle of meaning. The content or meaning of the thought expressed is furthermore an ideal unity, e.g., 'three perpendiculars of a triangle intersect in a point' (LI I §ll). This meaning is something identical *(das Identische),* whose precise identity is preserved in repetition *(Wiederholung)* of the expression. In assertion, we are asserting that state of affairs 'holds' or 'obtains'. We commit ourselves to the 'objective validity' of the state of affairs, even though the state of affairs is what it is, whether we maintain its validity or not. It is a 'validity-unity in itself' *(eine Geltungseinheit an sich).* We judge that the state of affairs obtains because we see it to be so. Every expression says something 'of' or 'about' *(uber)* something (LI I §11), but the object does not usually coincide with the meaning. Different names, e.g., 'victor of Jena', 'vanquished at Waterloo', or 'London', 'Londres', can refer to the same object (Napoleon, the city of London). Expressions may have different meanings but the same objective reference. Similarly, expressions with the same meaning may have different objective references, e.g., the expression 'horse' as applied to different horses, to both the individual 'Bucephalus' and to the type, the carthorse (§12). Proper names are 'equivocal' for Husserl in that they can name something different only if they mean something different, they have multiple senses (§15). On the other hand, general names, words like 'horse' can have many different values but have the one meaning (§15). In general, Husserl wants to distinguish between the *meaning (Bedeutung)* of an expression and its power to *name,* that is, to direct itself to something objective *(ein Gegenstiindliches).* An expres- + +sion names its object *through (mittels)* its meaning (LI I §13). + +In the First Investigation, Husserl distinguishes between objective expressions and those 'subjective' expressions whose meaning shifts with the occasion. This broad category, which includes pronouns ('I', 'you'), demonstratives ('this', 'that'), temporal adverbs like 'now', he terms 'essentially occasional expressions' *(wesentlich okkasionelle Ausdrucke,* LI I §26). These depend on the context for their specific meaning and yet also seem to have a fixed sense + +of their own. 'Now' means 'the present time'; 'I' means 'the person who is currently speaking'. But Husserl recognises that one cannot simply replace the word 'I' with 'the person who is currently speaking' in all contexts and preserve meaning (LI I §26). The term, however, is not wholly equivocal, but has layered elements, one of which depends on the context in which it is used (the 'indicated meaning'), and the other meaning which shows an act of indicating or pointing is being performed (the 'indicative meaning', LI I §26; Findlay I: 219; Hua XIXI1: 89).66 In the First Edition, indexicals are treated as non-normal or derivative forms of meaning (unlike words like 'lion'), which could, at least in theory, be replaced by non-indexical expressions (LI I §28), although Husserl recognises this may be practically impossible. Husserl saw the need to broaden this account in the Sixth Investigation (LI VI §5), so that indexicals stand at the basis of all empirical predication, a change of mind Husserl notes in the Second Edition (LI, Findlay I: 7; Hua XVIII: 13). In a sense, every statement must be located in a context before its precise meaning can be understood (e.g., referring to the 'birth of Christ', or 'the sun' requires a certain *deixis;* see Husserl's notes, Hua XIX/2: 817). In 1929, in *Formal and Transcendental Logic* (§80; Hua XVII: 207), Husserl says that in the First Edition of the *Investigations* he had not understood the 'horizonal intentionality' at work whereby the understanding of a statement requires attention to its horizoning context. A formal system needs the sup- + +port of context-relative elements. + +Husserl also discusses another kind of expression where the mental act the speaker is performing is announced in the expression itself, for example, in speech acts where the speaker promises, wishes, and so on. Husserl here identifies the class of speech acts, subsequently studied by his student, Adolf Reinach. Interest in speech acts was revived by John Austin and system- + +atised by John Searle.67 + +An important part of the discussion in the First Investigation concerns Husserl's vigorous attempts to distinguish between the meaning of an expression and the various accompanying images, feelings and illustrations that intertwine with it. Husserl's aim is to distinguish the logical content of meaning from all accompanying psychological content (he remarks that even Descartes had distinguished the imaginative representation of a chiliagon from its conceptual meaning, LI I §18). A central issue of this Investigation is the distinction between expressions based on intuition and those which function through some kind of symbolisation. Seeing something in the case of perceiving an object and seeing it symbolically are different act functions for Husserl (LI I §20). Husserl was not satisfied with his account of expression in this Investigation and his advances in the Sixth Investigation forced him to rethink the very basis of his account in the years after 1901. His 1908 lectures on meaning, for example, offer the basis for a revised account, which has a more sophisticated treatment of the relation between expressive act, meaning and empty or filled intention. In later years, Husserl would + +constantly return to the essential nature of meaning intending in its various + +forms. + +**The Second Investigation: abstraction and the** + +**grasp of universals** + +The Second Investigation treats of the nature of universal meanings or *species (Spezies)* as Husser! calls them. Understanding the true nature of abstraction is important for the foundations of logic, since logic utilises the crucial distinction between *individual* and *general* or *universal* objects *(allgemeine Gegenstiinde).* Husser! wants to develop empiricism by defending the need to recognise universal objects also, a view which is best understood as a kind of Aristotelianism. Some critics, however, accused Husser! of Platonism. In a remark added in the Second Edition, he concedes that his view may be termed *idealism* (LI II, Findlay I: 238; Hua XIX/I: 112), understood as a purely epistemological doctrine, which recognises the proper domain of the ideal *(das Ideale)* against psychologism. Husser! in fact thinks that the 'excesses of extreme conceptual realism' *(Begriffsrealismus,* LI II §2) have led philosophers to challenge not just the reality of general concepts + +but also their 'objectivity'. + +In this Investigation Husser! offers primarily a historical critique of Locke, Berkeley, Hume and of abstractionist representationalism in general, with the overall aim of understanding the relation between meaning as an ideal unity and the *act* of meaning *(das Bedeuten)* expressing it. In the *Prolegomena* Husser! had already established that meanings are ideal unities, now he wants to specify the relation between this ideal unity of meaning and the expression which 'means' it, the significant or 'meaning consciousness' *(Bedeutungsbewusstsein).* Husser!'s claim (developed from Lotze) in the First Edition is that this relation is the same as that between species and individuals. Indeed, for Husser!, meaning is a kind of 'species' *(Spezies)* which is instantiated in a particular act. The traditional account says that we intend the species (e.g., 'horse' as opposed to an individual horse) by abstraction from the individual, but there are different accounts of the nature of this abstraction. One view he rejects is that abstraction is a kind of selective attention on one aspect of an object. In opposition to this view, Husser! wants to develop a proper concept of abstraction, freed from the distortions of the modern philosophical and psychological tradition. He calls this 'ideation' but revises his views in the Second Edition since, in *Ideas* I, Husser! had developed a new account of ideation now understood as essential seeing + +or essence inspection *(Wesenserschauung, Ideas* I §3). + +For Husser!, the difference between an act that intends an individual and one that intends the species becomes clear in reflecting on the manner in which evidence is fulfilled for such presentations (LI II §l). Husser! insists that intending the species is essentially different in kind from intending + +the individual *qua* individual. In both acts, the same concrete object *(dcis Konkretum)* may be given, with the same sense contents interpreted in exactly the same way (LI II §l), but we *mean* 'red' not 'red house', the species not the individual. In the act of individual reference, we intend this thing or property or part of the thing, whereas in the specific act we intend the species, that is, we intend not the thing or a property understood in the here and now, but rather the 'content' *(lnhalt),* the 'idea' *(die Idee),* that is 'red' as opposed to the individual 'red-moment' (LI II §l). As Husser! adds in the Second Edition (referring forward to the Sixth Investigation), this specific act is a *founded (fundierte)* act, involving a new 'mode of apprehension' *(AujJassungsweise),* which sets the species before us as a general object. When we mean the species we perform a distinct act which is oriented towards the + +species as such and not towards the individual thing or part. + +Husser! understands this relation between general and individual as that between *species* and individual *instance (EinzelJall* §1), between 'red' in general and this red 'moment' of an object. Husser! goes on to insist (§2) on an important difference between individual singular items, *Einzelheiten* (things of experience) and *specific singulars* (e.g., the number 2). He makes a parallel distinction between individual and specific universals, whereby individual universal judgements, e.g., 'all men are mortal', are distinguished from specific universal judgements, e.g., 'all propositions of logic are *a priori'.* + +Husser! offers deep criticisms of the prevailing empiricist and nominalist accounts of the process by which universals are distinguished in our knowledge. Husser! ends by introducing his notions of abstract, dependent parts and concrete, independent parts, as a way of beginning to understand the true nature of abstraction in a phenomenological manner. This leads him to + +the theory of parts and wholes. + +**The Third Logical Investigation - parts and wholes** + +Husser! himself stressed the importance of the Third Investigation as offering the proper way into his thought, and, in his 1913 revision, was already lamenting its neglect. This Investigation sketches a 'pure theory of wholes and parts', called, in the Second Edition, 'formal ontology' (LI III, Findlay II: 3; Hua XIXJl: 228), inaugurating a discipline now known as *mereology.* With the specific view of clarifying the relations holding between the parts of meaningful acts of *expression* (in the Fifth and Sixth Investigations), Husser! here attempts to specify the *a priori* possibilities inherent in partwhole relations in general, i.e., the precise forms part-whole relations can + +take in advance of all empirical instances (LI **III** §l). + +Husser! is interested in the different ways in which something can be a part, and the laws governing the relation of parts to the whole, and of parts to other parts. Every object either is or can be a part. Wholes can be parts of larger wholes, and parts can have parts. Not all parts can be + +wholes however. Wholes and parts stand in various relations of *dependency (Unselbststandigkeit)* such that one part is *founded* on another. Hussed gives a strict sense to foundation (a notion already present in Meinong): when part A cannot be presented without a part **B,** A is said to be founded on B + +(LI III §14). + +Hussed's account recapitulates his studies of the eady 1890s. His starting point (LI III §3) is his mentor Cad Stumpf's work on the relations between parts and wholes in psychological acts, specifically in relation to sensory concepts such as colour and extension, or the quality and intensity of sounds. Stumpf situated his discussion of part/whole relations specifically in relation to *psychology,* whereas Hussed wants to formalise to a pure theory of wholes and parts in the most general sense. Stumpf was influenced by Brentano's reflections on the subject in his lectures on *Descriptive Psychology,68* and Hussed also acknowledges the independent investigations of Christian von Ehrenfels on 'form qualities' *(Gestaltqualitaten,* LI III §4), where items are grouped in specific ways, e.g., flocks, points seen against a background, and so on. 69 Hussed even discovers whole/part analysis in the 'phenomenology of inner experience' of George Berkeley in his critique of Locke (LI III §2). Hussed begins somewhat misleadingly by discussing the different ways parts are presented and are differentiated in *experience,* but in fact wants a formal analysis of the manner in which parts and wholes of any *objects* whatsoever cohere or co-exist together. Anything that can be distinguished in an object is a *part (Teil).* Parts may be divided into 'independent' *(selbststandig)* and 'dependent' *(unselbtstandig),* according as they can stand on their own or whether they require inherence in the whole of which they are a part. A part may be independently presented, e.g., head of a horse, and these Hussed terms 'pieces' *(Stucke,* LI III §2), e.g., the segments of an orange which can stand apart from one another and from the whole. But some parts are inseparable *(untrennbar),* e.g., colour and extension, and these Hussed calls 'moments' and which he sometimes characterises as 'abstract' parts in that they can only appear in the context of a larger whole. A *dependent* moment is one that *depends,* or, in Hussed's language, is *founded* on another whole or part. Thus, to give an example, Hussed will constantly repeat, the act-quality of a conscious experience is an abstract moment of the act (LI III §20), unthinkable detached from all matter. Of course, one can isolate parts within parts, so that the whole notions of dependence and independence are relativised (LI III §13). Hussed goes on to lay down six laws concerning parts and wholes (LI III §14), which have since been modified and expanded in a whole formal mereological theory. These laws include, for example, the law that: if a is dependent part of a whole W then it is also a dependent part of any other whole that has W as a part. In later writings (e.g., *Experience and Judgement* and *Formal and Transcendental Logic),* Hussed returns to part-whole relations in a somewhat different analysis but his part-whole analysis always remains central to his philosophy. + +**The Fourth Investigation: formal grammar** + +The Fourth Investigation, extensively revised and expanded in the Second Edition, is a study of what Husserl terms 'pure grammar' (Second Edition: 'pure logical grammar'), i.e., of the formal laws governing the combining or binding of meanings *(Bedeutungen)* into a senseful unity rather than simply yielding a nonsensical string of words, and is, generally speaking, an application of his part-whole theory to the field of semantics. He speaks of the 'pure theory of forms of meanings' *(die reine Formenlehre der Bedeutungen,* LI IV §14). The aim is to provide a pure morphology of meaning that lays the basis by providing possible forms of logical judgements, whose objective validity is the focus of formal logic proper. Husserl is explicitly reviving the old idea of an *a priori* grammar against both the psychological interpretations of grammar dominant in his day and the empirical theorists who were imprisoned in a false paradigm (e.g., assuming Latin grammar as the para- + +digm, LI IV §14). + +Just as simple objects can be combined to produce complex objects, *simple* meanings combine to produce *complex* meanings (LI IV §2). Moreover, meaning-parts need not mirror parts of the object, and vice versa. Meaning has its own parts and wholes. Husserl maintains that all combinations are governed by laws; his aim is to find the least number of independent elementary laws (LI IV §13). It must be possible to identify the rules of all such possible valid combinations *a priori,* combinations that produce well-formed expressions as opposed to nonsense (such as 'This careless is green', LI IV §lO). Husserl famously distinguished (LI I §l5 and LI IV §12) between *nonsense (Unsinn)* and *countersense* or absurdity *(Widersinn).* The concept of 'square circle' is not senseless or non-sensical, but constitutes an absurdity, a contradiction in terms, a 'counter-sense' that cannot be realised. Formal grammar, on Husserl's account, can eliminate only nonsense not absurdity and is therefore not yet formal logic in the sense of specifying what can be objectively valid. 70 In later writings, notably the *Formal and Transcendental Logic* and *Experience and Judgment,* Husserl continued to maintain that formal grammar provided the bedrock rules for meaningfulness which made possible formal logic, and is the basis for both the logic of inference *(Konsequenzlogik)* and what Husserl calls the 'logic of truth'. He is more careful in later writings to emphasise that he is dealing with formal combinations of meanings (e.g., 'A and B not if') rather than material combinations of meanings (e.g., 'round square'), whereas in the Fourth Investigation he tends misleadingly to employ examples drawn from the material sphere. 71The laws of formal meaning are purely analytic laws as opposed to synthetic *a priori* laws which govern such areas as geometry or mechanics. The core of Husserl's analysis is his use of a traditional distinction (but specifically developed by Anton Marty) between *syncategorematic* words (e.g., words like 'but', 'and', 'to', 'if'), and *categorematic* words, e.g., nouns, verbs (but not complete + +expressions) and his analysis of these in terms of independence and dependence relations. Husser! treats *syncategorematic* expressions as meaningful but dependent, incomplete parts of wholes, which in this case are well-formed expressions which are complete or 'closed' *(geschlossen).* Verbal parts can be distinguished in terms of those that are separately meaningful (like particles, e.g., 'bi-' as in 'bi-sexual') or meaningless ('bi' as in 'bite'). Husser! focuses on proper names and the manner in which they name the object in a 'single ray'. The formal theory of meanings will lay down the formal laws that regulate how adjectives can become substantives, how a subject can shift to the predicate position and so on, and other rules of combination and 'modification' (a concept drawn from Twardowski, who studied the manner certain adjectives modify the noun, e.g., a *false friend* is not a *friend* at all. This Investigation had a profound influence on the work of the linguist Roman lakobson (1896-1982), especially on his notion of phonemes as complex unities.72It also influenced the Polish logician Stanislaw Lesniewski (1886-1939) in his account of categorial grammar, and indeed finds echoes in Noam Chomsky's project of a 'universal grammar' (a term Husser! himself invokes with approval, LI IV §14). For Husser!, however, the meaningfulness of linguistic combinations is distinct from the structural laws governing conscious acts and their contents, to which he turns in the Fifth Investigation. + +**The Fifth Investigation: intentional experiences and** + +**their contents** + +The Fifth Logical Investigation, subtitled 'International Experiences and Their "Contents'" is Husser!'s attempt to sort out ambiguities in Brentano's descriptive psychological analysis of conscious acts, their contents and objects (in the Second Edition, these are restricted to 'pure immanence'). Husser! begins by specifying what he means by 'consciousness', bracketing discussion of the relation of conscious acts to an ego, and focusing exclusively on the intentional character of conscious experiences deriving from Brentano's rediscovery of intentionality. However, Husserl regards Brentano's characterisation of intentionality as misleading and inadequate, trapped inside the old Cartesian dualism of subject and object and with all the problems inherent in that representationalist account. Under the notion of 'objectifying act' he offers a more precise account of what Brentano called 'presentation', and goes on to address what he calls 'cardinal problem of phenomenology', namely, the doctrine of judgement (LI, Findlay I: 7; Hua XVIII: 14), which is further treated in the Sixth Investigation. Husser! is especially critical of the many unresolved ambiguities in Brentano's foundational concept of 'presentation' *(Vorstellung)* and carefully differentiates between the many senses of the term (LI V §44) , stressing however that logic must decide which meaning of 'presentation' is most appropriate for its own needs. Logic does not follow linguistic usage as logical definition is a kind of artifice (LI IV §3). + +In *Psychology from an Empirical Standpoint* (1874), Brentano had held + +that all psychic acts are characterised by 'directedness' or 'aboutness': + +Every mental phenomenon is characterized by what the Scholastics of the Middle Ages called the intentional (or mental) inexistence of an object, and what we might call, though not wholly unambiguously, reference to a content, direction towards an object (which is not to be understood + +here as meaning a thing), or immanent objectivity.73 + +In a general sense, every psychic act intends an object, though not necessarily something existent. Husserl paraphrases: 'in perception something is perceived, in imagination, something imagined, in a statement something stated, in love something loved, in hate hated, in desire desired etc.' (LI V §1O, Findlay II: 95; Hua XIXI1: 380). Brentano himself came to realise that his expression 'intentional inexistence', which he claimed he had used to express the concept of inherence or *in esse* of the Scholastics, had been misunderstood as a special kind of subsistence. In his later writings, he claimed he never intended to say that the intentional object is merely some kind of object in our minds, some purely immanent thing. Husserl rejects Brentano's attempt to distinguish between 'psychical' and 'physical' phenomena, but sees his discovery of intentionality as having independent value (LI V §9). Husserl is cautious about using Brentano's term 'act' without qualification, but, above all, wants to avoid misleading talk of 'immanent' objectivity. He insists that all objects of thought - including the objects of fantasy and memory - are *mind-transcendent.* Even when I am imagining something non-existent, e.g., if I am thinking of the mythical god Jupiter the God Jupiter is not *inside* my thought in any sense, it is not a real element or real part of the experience (LI V §ll). Rather, even fictional objects are *transcendent* above our mental experiences; intentional experience always transcends itself towards the object, its character is a 'pointing beyond itself + +towards' *(uber sich hinausweisen)* something. + +Drawing on the older logical tradition, Husserl offers a new global distinction between the *matter* and the *quality* of intentional acts. Acts of different quality (judgings, wishings, questionings) may have the same matter. Not all our experiences are intentional in the sense of presenting something to our attention. According to Husserl, *sensations* in themselves are not intentional, they are not the object which we intend, rather they accompany the intentional act and fill it out. Sensations belong to the 'matter' (and are grasped as such only in reflection), whereas the act quality provides the form of the act. With an eye to distinctions made by Brentano's followers, especially Kasirnir Twardowski, Husserl goes on to develop the differences between the contents of experience and the properties of the mind-transcendent object. When I see an object, I only ever see it from one side, in a certain kind of light, from a certain angle and so on. As I walk around the box for example, I see different + +'profiles' *(Abschattungen)* or 'aspects' of the box, and yet I know I am getting glimpses of the same object in the different perceptual acts. The same object is presenting itself to me in different modes. Husserl's distinction in the Fifth Investigation (LI V §17) between the object which is intended and the particular mode under which it is intended forms the basis for his later distinction between *noesis* and *noema* in *Ideas* I. Furthermore, Husserl regards it as an *a priori* law that physical objects are displayed in *Abschattungen.* Whereas Brentano recognised only three basic classes of psychical acts (namely, *presentations, judgements,* and what he called *'phenomena of love and hate'),* Husserl recognises myriad forms of intentional structure. He more carefully differentiates the fundamental structure of *judgements* in a manner opposed to Brentano, who had challenged the traditional notion of judgement as a synthesis of subject and predicate, and had interpreted the judgement 'the cat is black' as an asserting or positing of 'black cat'. Husserl denies that judgements can be treated as nominal acts, as simply *naming* complex states of affairs (LI V §17). We can, of course, turn a judgement into a nominal act, by nominalising the content of the judgement. This belongs as an *a priori* essential possibility to judgements (LI V §36). So, to the judgement 'the cat is black' corresponds the nominalisation 'the cat's being black' which can then function as the basis for further judgements. But this internal relation between judging and nominalising does not mean that they are essentially the same kind of act. Husserl, following Bolzano, declares judgements to be essentially different from presentations. Judgements *assert* something to be the case (LI V §33). A judgement *articulates* and specifies in a 'many-rayed act' the parts of the situation that a nominalising act presents in a 'single-rayed act', as Husserl puts it. 74 The relation between + +presentation and judgement is not as described by Brentano. + +Rather than operating with Brentano's simple and rather naive distinction between the presenting act and presented content of an intention, or even using the broader notion of a 'nominal act', Husserl suggests that we ought to speak more generally of 'objectivating acts' (LI V §37) which include both the nominal and the judgemental act. Husserl thinks that the claim that all acts either are or are founded on objectifying acts is a more accurate reformulation of Brentano's basic law that all psychic acts are either presentations or founded on presentations. Husserl's clarification of the nature of presentation and judgement leads to his discussion of the manner in which these acts find intuitive fulfilment in the Sixth Investigation. + +**The Sixth Logical Investigation: towards the** + +**phenomenology of knowledge** + +The Sixth Investigation - by far the longest and most difficult - attempts to connect the previous analyses of the act of meaning to the notion of truth through a deeper exploration of the relations between the acts that intend + +meaning and the various levels of possible fulfilment, as they feature in different kinds of conscious act, e.g., perceptions, imaginings, and acts of what HusserI calls 'signitive intention' where meanings are handled in a purely symbolic way without intuitive fullness. HusserI's target is knowledge and the connection with truth. In earIier Investigations HusserI had recognised a new class of categorial acts or acts of categorial intuition, founded on sensuous acts but with essentially different objects. The Sixth Investigation is the first full analysis of the nature of these categorial acts, including reviewing the relation of sensory matter to the content of the act as a whole. HusserI wants a 'phenomenology of the varying degrees of knowledge' (LI VI, Findlay II: 184; Hua XIX12: 539), carefully discriminating between the many different senses in which something can be realised or fulfilled for us in an act of perception or imagination, the relation between concept and + +intuition, e.g., in the act of seeing a blackbird. + +HusserI sees the paradigm case of a successful intentional act as an act where the meaning is fulfilled by the *presence* in intuition of the intended object with full 'bodily presence' *(Leibhaftigkeit).* Thus, when I actually see something before my eyes, I have a fulfilled intuition. Later, I can relive this intuition but it is now a memory, still oriented to the object, but not presented with the same presence or immediacy. In memory or in other forms of 'calling to mind' or 're-presenting' *(Vergegenwiirtigung)* we still may have a full intuition of the object, but now no longer with the distinctive bodily presence that characterises perception. There are other forms of intending which are merely 'empty' *(Leermeinen),* e.g., when I use words in a casual way without really thinking about what I am saying, when I talk about something without really thinking about it and so on. Empty or 'signitive' intendings, of course, constitute the largest class of our conscious acts, and, from the beginning of his career, HusserI had been fascinated as to how + +these kinds of intentions can function as knowledge. + +HusserI's interest in the manner in which meaning is expressed in different acts leads him to revise the account of meaning as species which was employed in the earIier Investigations. I can utter different sentences with different senses or meanings based on the same act of perceiving (LI VI §4). Furthermore, a listener can understand the meaning with enacting the act of perception or indeed re-enacting it in imagination. The listener can understand it as a *report* of my act of perceiving, i.e., 'he says that he sees a blackbird'. In the expression 'I see a blackbird' the sense or meaning of that expression is not carried by the perceptual act alone. For HusserI the *sense* of the statement can survive the elimination of the act of perception, in other words, I do not have actually to enact the act of seeing to grasp the meaning of the statement. The act of perception somehow anchors the meaning but does not embody it completely. This leads HusserI to revise his earlier discussion of 'essentially occasional expressions' (§5), recognising that meaning is not simply instantiated in an act, but that the act has its own specific form of + +intending where the meaning appears with its own mode of givenness which + +the instantiation model did not adequately handle. + +According to Kant, our experience has two components: a receptive element of sensory intuition and an element of reflective conceptuality (which Kant called 'spontaneity'). But Kant explicitly denied that humans had the capacity to *intuit* concepts. HusserI agrees with Kant concerning the sensory matter of most of our concepts, but holds that in higher order intuitions we do have the capacity to intuit ideal 'categorial' entities, from the 'mixed category' of the concept of colour, to pure categories, and at the highest level, logical categories such as unity, plurality and existence. HusserI treats 'categorial intuition' *(kategoriale Anschauung)* as akin to a kind of perception. The first attempt to express it comes in the second section of the Sixth Investigation entitled 'Sense and Understanding' (§§40-66). Categorial intuition involves a broadening of the concepts of perception and intuition. According to HusserI my intuition of a 'state of affairs' *(Sachverhalt),* e.g., 'I see *that* the paper is white', involves categorial intuition, a complex intuition that something is the case. In a judgement of this kind I intuit *what is going on,* as it were. How is this 'being the case' intuited? HusserI agrees with Kant that being is not a predicate, that is, that the existing situation is not a property of the individual object (the white paper). Saying that something *is* does not give us an intuition of a new property in a manner similar to learning 'something is red'. But this shows for HusserI that assertion of the category of being does not involve grasping a property or the object itself. Nor does it emerge from reflecting on the act of consciousness as some had thought, rather the categorial structure belongs to the ideal structure of the object, to the objectivity as such. Categorial acts yield up the grasp of the pure categorial concepts, 'if ... then', 'and', 'or' and so on, which have no correlates in the objects of the perceptual acts themselves. For HusserI, moreover, categorial acts are *founded* on the sensory acts of perceiving, but do not *reduce* to them. For HusserI, categorial acts grasp states of affairs and in fact constitute them in the very categorial act. Thus it is not the case that I grasp sensuously the components of the judgement and synthesise them using some kind of subjective rules of the understanding as Kant suggests (according to HusserI's interpretation), rather we apprehend the state of affairs of which the non-sensuous categorial elements are necessary constituents. In the course of this complex investigation HusserI outlines a new conception of truth, re-thinking the classical correspondence account. It was this discussion of truth which attracted the interest of Heidegger and others (e.g., Ernst Tugendhat), but unfortunately we cannot treat it further here. + +**The influence of the** *Logical Investigations* + +Although, as the young Heidegger recognised, the *Logical Investigations* did not have an immediate impact on mainstream philosophy in Germany, within + +a decade it was recognised as a major philosophical achievement by leading figures such as Paul Natorp, Wilhelm Dilthey, Wilhelm Wundt and Heinrich Rickert.75 Husserl suspected that much of Meinong's work after 1901 owed a direct - but unacknowledged - debt to the *Investigations,* but Brentano + +ignored the work. + +In particular, the *Prolegomena* was credited with refuting psychologism. In a 1905 study, the elder statesman of German philosophy, Wilhelm Dilthey praised Husserl's *Investigations* as 'epoch-making' for its use of description in epistemology.76 The psychologist Wilhelm Wundt, too, accepted the *Prolegomena's* arguments against psychologism, but criticised Husserl's second volume as proposing an extreme 'logicism' and demanding a complete reform of psychology. Husserl rejected Wundt's criticism as a complete misunderstanding of the work, saying he neither advocated logicism (in Wundt's sense), nor said a word about the reform of psychology.77 In line with the Neo-Kantian tradition in general, Paul Natorp had been an early critic of psychologism. Indeed, Husserl had written to Natorp in 1897 announcing that he was working on a book to dispel the 'subjective-psychologising tendency' from logic. Natorp reviewed the *Prolegomena* favourably in *Kant Studien* in 1901, portraying Husserl as broadening the essentially Kantian inquiry into the necessary conditions of the possibility of experience. 78 Natorp predicted that Husserl would move towards Kant as he came to overcome his naIve opposition between the empirical psychological realm and the realm of abstract idealities.79 Husserl, however, always kept his distance from Neo-Kantianism, claiming that phenomenology was more radical. As we have seen, in his Gottingen years (1901-16), Husserl attracted many brilliant students, e.g., Johannes Daubert (1877-1947), Moritz Geiger (1880-1937), Adolf Reinach (1883-1917), Max Scheler (1874-1928), Hedwig Conrad-Martius (1888-1966), Roman Ingarden and Edith Stein, all drawn to Husserl's new way of approaching logical and epistemological problems which broke with the tradition. Around 1909, the young Freiburg seminarian Martin Heidegger encountered the *Logical Investigations* and poured over the work without being certain what it was that fascinated him.80 He + +later recalled: + +... both volumes of Husserl's *Logical Investigations* lay on my desk in the theological seminary ever since my first semester there ... I had learned from many references in philosophical periodicals that Husserl's thought was determined by Franz Brentano ... From Husserl's *Logical Investigations,* I expected a decisive aid in the questions stimulated by + +Brentano's dissertation.81 + +Heidegger himself initially began reading Husserl to understand Brentano's account of the nature of being and was drawn especially to the Fifth and Sixth Investigations, especially Husserl's original accounts of categorial + +intuition and of truth. Heidegger saw in Husserl's account of categorial intuition not only a method for articulating the nature of the existential judgement but also the basis of a new way of thinking about the notion of truth and the meaning of being. Heidegger went on to read the *Investigations* in the seminars of Heinrich Rickert and Emil Lask, a young scholar who also worked on categorial intuition. Heidegger discussed the *Logical Investigations* in one of his first publications, a review of recent logical research published in 1912, where he recognises that Husserl had drawn out the theoretic incoherence of psychologism and its relativistic consequences. For Heidegger, Husserl had not only enlarged the scope of logic, but had made central the problematics of judgement and the nature of evidence. 82 Indeed, it was Heidegger who, as Husserl's assistant at Freiburg from 1919, repeatedly urged Husserl to reprint the Sixth Investigation, to which Husserl + +finally agreed in 1920. + +News of the *Logical Investigations* spread outside Germany also, being translated into Russian as early as 1909, which version had a major influence on Roman Jacobson's conception of a formal science of language. Through Roman Ingarden, who reviewed it in Polish, the *Investigations* played an important role in Polish philosophy, influencing Stanislaw Lesniewski's development of mereology, for instance. It was translated into Spanish in 1929. A French translation of the Second Edition appeared in three volumes between 1959 and 1963,83 but Husserl's influence on French philosophy had begun much earlier through the efforts of his earlier G6ttingen students, Jean Hering and later through the writings of Emmanuel Levinas, Jean-Paul Sartre, Maurice Merleau-Ponty, Paul Ricoeur and Jacques Derrida, all of whom began their philosophical careers with critical studies of Husser!' Derrida, for instance, has acknowledged that his whole philosophical impetus arises out of his studies on Husserl, e.g., his study of Husserl's concept of genesis, written as a part of his doctoral research project in 1953-4. 84 Since the publication of Derrida's influential interpretations and critique of Husserl's account of signs in the First Investigation, an argument has raged as to whether Derrida has misinterpreted - even wilfully + +distorted - Husserl's account. 85 + +During his Freiburg years (1916-38), Husserl became a philosopher of international renown, in contact with prominent philosophers of his day, including Ernst Cassirer, Bertrand Russell, Rudolf Carnap, Charles Hartshorne and William Kneale, among others. Among his own brilliant Freiburg students were Oskar Becker (1889-1964) and Fritz Kaufmann (1891-1958). Husserl's phenomenology also had a stimulating influence on philosophers who later came to be associated with the Frankfurt School, including Herbert Marcuse, Hannah Arendt, Theodor Adorno and Max Horkheimer (the latter of whom both wrote dissertations on Husserl). Husserl of course has been a major influence on both Ernst Tugendhat's and Karl-Otto Apel's philosophies of language, and his work in the *Investigations* + +has been compared with the equally original breakthroughs of Ludwig + +Wittgenstein. + +**In** contrast to the situation in continental Europe, the *Logical Investigations* was somewhat slower to gain recognition in the English-speaking world. Bertrand Russell wrote to Husserl on 19 April 1920 saying that he had taken a copy of his *Logical Investigations* with him to jail, with the intent of reviewing it for *Mind,* but the review never appeared. However, in 1924, Russell recognised the *Logical Investigations* as a 'monumental work', listing it alongside his own *Principles of Mathematics* (1903) and works by William James, Frege and G. E. Moore (who, incidentally, also admired Husserl's book),86 for their efforts in the refutation of German idealism.87 Indeed, as Findlay noted, the *Logical Investigations* have much in common with the practice of philosophy as understood by Bertrand Russell. Richard Rorty in his *Philosophy and the Mirror of Nature* has remarked: 'Russell joined Husserl in denouncing the psychologism which had infected the philosophy of mathematics, and announced that logic was the essence of philosophy.'88 Indeed, one can find many themes in the *Logical Investigations* which are also treated in analytic philosophy, e.g., Husserl offers his own version of a solution to the problem of definite descriptions, famously + +treated by Russell. 89 + +Husserl himself visited England in 1922 intent on establishing relations with English philosophers (Husserl being the first German philosopher to visit England since the Great War). He delivered a number of lectures which were attended by Gilbert Ryle among others, but the lectures were not a success, despite his meeting well-known figures such as Broad, Stout and G. Dawes Hicks. The *Logical Investigations* has been discussed in relation to the history of analytic philosophy by Michael Dummett, David Bell and others.90 The logician Kurt Godel studied the *Logical Investigations* after 1959 and was especially impressed by the treatment of categorial intuition in + +the Sixth Investigation which he recommended to other 10gicians.91 + +**The contemporary relevance of the** + +*Logical Investigations* + +The six Investigations stand as a vast resource of philosophical ideas, some tentatively sketched, others more confidently laid out. Of primary significance are Husserl's discussions of the meanings of key philosophical terms. He carefully differentiates between logical and psychological content, empty and filled intuitions, the difference between generalisation and formalisation, the meanings of signification and reference, the nature of nominal and + +categorial acts, and so on. + +Husserl's *Prologemena* is still of interest for its original conception of the nature and scope of pure logic and its discussion of the self-refuting character of psycho log ism, relativism (including 'anthropologism'). Husserl's critique of psychologism later expanded to a wide-ranging critique of natu- + +ralism, specifically the 'naturalisation of consciousness', in his 1911 essay 'Philosophy as a Rigorous Science', and these anti-naturalist arguments are still relevant to the contemporary debate between naturalists (e.g., Quine, Dennett, Churchland) and anti-naturalists (e.g., Hilary Putnam, John McDowell, Robert Brandom). Indeed, Putnam regularly cites Husserl's critique of naturalism, especially as formulated in the *Crisis,* but which has + +its origins in the *Investigations.* + +The *Investigations* are an important resource for discussions of consciousness and other issues discussed in contemporary philosophy of mind. In particular, Husserl's account of intentionality in the Fifth Investigation has been hugely influential, but his views on the nature of perceptual content are also important and relevant to the work of Peacocke and others. Husserl has been seen as a strong defender of the subjective point of view and the ineliminability of consciousness from any full account of the nature of knowledge, themes which have more recently been treated by John Searle, Colin McGinn, Thomas Nagel and others. 92 Indeed, John Searle's account of intentionality strongly resembles Husserl's, although Searle himself denies any direct influence. Other contemporary philosophers, e.g., Peter Simons, Barry Smith, Kevin Mulligan, are interested in developing morely precisely the + +formal ontology or descriptive metaphysics of the *Investigations.* + +The *Investigations* are also of crucial interest as a source text for anyone wishing to understand the nature of phenomenology as it was developed both by Husserl and by his followers. Heidegger's phenomenological writings of the period between 1919 and 1928 would not be comprehensible without a thorough understanding of Husserl's breakthrough work. As the meaning of the phenomenological tradition comes once more to be interrogated, a return to the *Investigations* to attempt to understand the precise nature of the phenomenology that appeared therein seems inevitable. + +**John N. Findlay's translation** + +Finally some words on the present translation. The publication of J. N. Findlay's translation of the *Investigations* helped to correct a view of Husserl which, up to 1970, had been based primarily on the availability of Gibson's translation of *Ideas* 1. Findlay has produced a powerful and much admired translation, based on the Second Edition. In keeping with the nature of that edition, he does not usually indicate where the text departs from the First Edition. It is important to bear in mind that this (and subsequent editions up to the fourth) were the ones Husserl himself authorised and a critical edition did not appear in the Husserliana series until 1984, and thus was not + +available to Findlay.93 + +Inevitably, given both the size of the book and the need to find suitable English terms to render Husserl's many technical distinctions and innovations, Findlay's translation has its limitations. There is some sloppiness, with words, phrases, and even whole sentences being omitted. Some footnotes have been + +66 See K. Mulligan and B. Smith, 'A Husserlian Theory of Indexicality', *Grazer Philosophische Studien* 28 (1996), 133-63. See also K. Schuhmann, 'Husserl's Theories of Indexicals', in F. M. Kirkland and D. P. Chattopadhyaya (eds), *Phenomenology* - *East and West* (Dordrecht: Kluwer, 1993), pp. 111-27. 67 John R. Searle, *Speech Acts: An Essay in the Philosophy of Language* (Cambridge: Cambridge University Press, 1969). On Reinach, see K. Mulligan (ed.), *Speech Act and Sachverhalt. Reinach and the Foundations of Realist Phenomenology* + +(Dordrecht: Martinus Nijhoff, 1987). + +68 F. Brentano, *Descriptive Psychology,* trans. B. Miiller (London: Routledge, 1995). In the background also is Bolzano's discussion of parts and wholes in his + +*Wissenschaftslehre.* + +69 See Barry Smith and K. Mulligan, 'Husserl's Third Logical Investigation: The Formal Ontology of the Part-Whole Relation', in B. Smith and K. Mulligan (eds), *Parts and Moments. Studies in Logic and Formal Ontology* (Munich: Philo- + +sophia Verlag, 1992), pp. 35-45. + +70 A similar point is made by Rudolf Carnap, who may have been directly influenced by Husserl whose seminars he attended in 1924. See Y. Bar-Hillel, 'Remarks on Carnap's Logical Syntax of Language', in Paul Schilpp (ed.), *The Philosophy* + +*of Rudolf Carnap* (La Salle, IL: Open Court, 1963), pp. 519-43. + +71 See Suzanne Bachelard, *A Study of Husserl's Formal and Transcendental Logic,* trans. Lester Embree (Evanston, IL: Northwestern University Press, 1968), p. 7. 72 Roman Jakobson acknowledges the importance of Husserl's work for linguistics in his essays, 'Zur Struktur des Phonems' (1939) and in his *Main Trends in the Science of Language* (London: Allen & Unwin, 1973), pp. 13-16. See Elmar Holenstein, 'Jakobson's Contribution to Phenomenology', in *Roman Jakobson: Echoes of His Scholarship,* ed. David Armstrong and C. H. Van Schooneveld + +(Lisse: Peter De Ridder Press, 1977), pp. 145-62. + +73 F. Brentano, *Psychology from an Empirical Standpoint,* trans. A. C. Rancurello, D. B. Terrell and L. L. McAlister, 2nd edn with new Introduction by Peter + +Simons (London: Routledge, 1995), p. 88. + +74 Nominalisation makes possible the shift from formal apophantics to formal + +ontology. + +75 For an account of some of the immediate reactions to Husserl's *Investigations* in Germany, see Farber, *The Foundation of Phenomenology, op. cit.,* pp. 147-69. 76 Wilhelm Dilthey, *Studien zur Grundlegung der Geisteswissenschaften,* Gesammelte Schriften VII (Stuttgart: B. G. Teubner, 1968), p. 14n: 'Suche ich nun hier diese meine Grundlegung einer realistisch oder kritisch objektiv gerichteten Erkenntnistheorie fortzubilden, so muss ich ein fUr allemal im ganzen darauf hinweisen, wie vieles ich den in der Verwertung der Deskription fUr die Erkenntnistheorie epochemachenden "Logische Untersuchungen" von Husserl (1900.1901) verdanke.' [If I am now seeking to develop further my foundation of a theory of knowledge with a realistically or critically objective orientation, I must first and foremost and in general mention how much lowe to the *Logical Investigations* of Husserl, which are epoch-making in the use of description for + +the theory of knowledge.] + +77 See W. Wundt, 'Psychologismus und Logizismus', in *Kleine Schriften,* Vol. 1 (Leipzig, 1910) and Husserl's reply in his draft Preface of 1913 (in the new edition of Ullrich Melle), 'Zwei Fragmente zum Entwurf einer Vorrede zur zweiten Auflage der *Logischen Untersuchungen',* to appear in Husserliana series. Husserl is very critical of Wundt's misreading: exclaiming at one point: 'One cannot read + +the *Logical Investigations* like a newspaper'. + +78 Paul Natorp, 'Zur Frage der logischen Methode. Mit Beziehung auf Edmund Husserls Prolegomena zur reinen Logik', *Kant Studien* 6 (1901), 270ff., reprinted **Select bibliography** + +**Primary Sources** + +Husser!, Edmund (1956- ) *Gesammelte Werke.* Husser!iana. Dordrecht: K1uwer. + +Husser!, Edmund (1996) *Gesammelte Schriften.* Hamburg: Meiner. + +Husser!, Edmund (1999) *Erfahrung und Urteil: Untersuchungen der Genealogie der* + +*Logik,* hrsg. L. Landgrebe. Hamburg: Meiner. + +**Husserl in Translation** + +HusserI, Edmund (1964) *Philosophy as a Rigorous Science,* 1911, in Quentin Lauer, *Edmund Husser!' Phenomenology and the Crisis of Philosophy,* New + +York: Harper & Row. + +HusserI, Edmund (1967) *Cartesian Meditations,* trans. Dorion Cairns, The Hague: + +Martinus Nijhoff. + +HusserI, Edmund (1969) *Formal and Transcendental Logic,* trans. Dorion Cairns, + +The Hague: Martinus Nijhoff. + +Husser!, Edmund (1970) *The Crisis of European Sciences and Transcendental Phenomenology. An Introduction to Phenomenological Philosophy,* trans. David + +Carr, Evanston, **IL:** Northwestern University Press. + +HusserI, Edmund (1973) *Experience and Judgment: Investigations in a Genealogy of Logic,* trans. J. S. Churchill and Karl Ameriks, Evanston, **IL:** Northwestern + +University Press. + +Husserl, Edmund (1975) *Introduction to the Logical Investigations. Draft of a Preface to the Logical Investigations,* ed. E. Fink, trans. P. J. Bossert and + +C. H. Peters, The Hague: Martinus Nijhoff. + +Husserl, Edmund (1977) *Phenomenological Psychology. Lectures, Summer Semes-* + +*ter* 1925, trans. J. Scanlon, The Hague: Martinus Nijhoff. + +Husserl, Edmund (1981) *Husser!' Shorter Works,* trans. and ed. Frederick Elliston and Peter McCormick, Notre Dame: University of Notre Dame Press. Husserl, Edmund (1983) *Ideas pertaining to a Pure Phenomenology and to a Phenomenological Philosophy, First Book,* trans. F. Kersten, Dordrecht: + +Kluwer. + +HusserI, Edmund (1989) *Ideas pertaining to a Pure Phenomenology and to a Phenomenological Philosophy, Second Book,* trans. R. Rojcewicz and A. Schuwer, + +Dordrecht: Kluwer. + +Husser!, Edmund (1990) *On the Phenomenology of the Consciousness of Internal Time,* trans. J.B. Brough, Collected Works IV, Dordrecht: Kluwer. Husser!, Edmund (1994) *Early Writings in the Philosophy of Logic and Mathematics,* trans. Dallas Willard, Collected Works V, Dordrecht: Kluwer. Husser!, Edmund (1997) *Thing and Space: Lectures of 1907,* trans. R. Rojcewicz, + +Collected Works VII, Dordrecht: Kluwer. + +Husser!, Edmund (1999) *The Idea of Phenomenology,* trans. Lee Hardy. + +Dordrecht: Kluwer. + +Husser!, Edmund (1999) *The Essential Husserl,* ed. Donn Welton, Bloomington, + +IN: Indiana University Press. + +**Further Reading** + +Bell, David (1990) *Husserl,* London: Routledge. + +Bernet, Rudolf, Iso Kern and Eduard Marbach (1993) *An Introduction to Husserlian* + +*Phenomenology.* Evanston, IL: Northwestern University Press. + +DeBoer, Theodor (1978) *The Development of Husserl's Thought.* The Hague: Martinus + +Nijhoff. + +Derrida, Jacques (1973) *Speech and Phenomena and Other Essays on Husserl's Theory of Signs,* ed. and trans. David Allison, Evanston, IL: Northwestern University + +Press. + +Dreyfus, Hubert L. (ed.) (1982) *Husserl, Intentionality and Cognitive Science,* Cam- + +bridge, MA: MIT Press. + +Dummett, Michael (1991) *Frege: Philosophy of Mathematics,* London: Duckworth. Dummett, Michael (1991) *Frege and Other Philosophers,* Oxford: Oxford University + +Press. + +Dummett, Michael (1993) *Origins of Analytic Philosophy,* London: Duckworth. Elveton, R. O. (ed.) (2000) *The Phenomenology of Husserl. Selected Critical Read-* + +*ings,* 2nd edn, Seattle: Noesis Press. + +Farber, Marvin (1943) *The Foundation of Phenomenology,* Albany, NY: State Uni- + +versity of New York Press. + +Levinas, Emmanuel (1973) *The Theory of Intuition in Husserl's Phenomenology,* trans. + +A. Orianne, Evanston, IL: Northwestern University Press. + +Mohanty, J. N. (ed.) (1977) *Readings on Husserl's Logical Investigations,* The Hague: + +Martinus Nijhoff. + +Mohanty, J. N. (1982) *Husserl and Frege,* Bloomington, IN: Indiana University + +Press. + +Moran, Dermot (2000) *Introduction to Phenomenology.* London and New York: + +Routledge. + +Moran, Dermot (2000) 'Heidegger's Critique of Husserl's and Brentano's Accounts + +of Intentionality', *Inquiry* 43: 39-66. + +Mulligan, Kevin and Smith, Barry (1986) 'Husserl's Logical Investigations', *Grazer* + +*Philosophische Studien* 27: 199-207. + +Ricoeur, Paul (1967) *Husserl. An Analysis of his Philosophy,* Evanston, IL: North- + +western University Press. + +Scherer, Rene (1967) *La Phl:nomenologie des 'Recherches Logiques' de Husserl,* Paris: + +Presses Universitaires de France. + +Schuhmann, Karl (1977) *Husserl-Chronik. Denk- und Lebensweg Edmund Husserls,* + +Husserliana Dokumente 1, The Hague: Martinus Nijhoff. + +Sepp, Hans Rainer (ed.) (1988) *Edmund Husserl und die phiinomenologische Bewegung.* + +*Zeugnisse in Text und BUd,* FreiburgiMunich: Karl Alber Verlag. + +Smith, Barry and Woodruff Smith, David (eds) (1995) *The Cambridge Companion to* + +*Husser!,* Cambridge: Cambridge University Press. + +Sokolowski, Robert (1971) The Structure and Content of Husserl's *Logical Inves-* + +*tigations', Inquiry* 14: 318-50. + +Sokolowski, Robert (2000) *Introduction to Phenomenology,* Cambridge: Cambridge + +Univesity Press. + +Spiegelberg, Herbert (1994) *The Phenomenological Movement. A Historical Introduction,* 3rd revised and enlarged edition with the assistance of Karl Schuhmann, + +Dordrecht: Kluwer. + +Straker, Elizabeth (1993) *Husserl's Transcendental Phenomenology.* Stanford, CA: + +Stanford University Press. + +Taminiaux, Jacques (1985) 'Heidegger and Husserl's *Logical Investigations',* in *Dia-* + +*lectic and Difference,* New Jersey: Humanities Press, 91-114. + +**Translator's Introduction** + +**(Abridged)** + +The *Logical Investigations* which is here translated is the work through which Edmund Husserl first established his reputation: it is also, in the opinion of many, including this translator, his greatest and most important philosophical work. First published in 1900~1, when Husserl was teaching at Halle, it was preceded by his *Philosophy of Arithmetic* (Volume I alone published, Halle, 1891), a surpassingly excellent but almost entirely forgotten work on the foundation of mathematics, and succeeded by a long series of brilliant works, some only published since Husserl's death in the series known as *Husserliana* (Nijhoff, The Hague), which expound a systematic position known as 'phenomenology', and of which the best known is the *Ideas towards a pure Phenomenology and phenomenological Philosophy,* first published in 19l3, and translated into English by W. Boyce-Gibson (Muirhead Library, Allen and Unwin). The *Logical Investigations* occupies a position midway between the *Philosophy of Arithmetic* and the later, full-blown phenomenology, and while the word 'phenomenology' quite often occurs in its text, it is used in a somewhat different, simpler sense than that of the later system. It means only 'descriptive psychology': the study of what enters into the 'description', the clarificatory analysis, of conscious experience and its various sub-species, rather than what may be involved in the actuality of consciousness in the world, and its causal and other relations to the body + +and to mundane existences generally. + +The text of the *Logical Investigations* underwent a few excisions, modifications and additions in the Second Edition of 19l3 (The Prolegomena and Investigations I~V) and 1921 (Investigation VI), and they were mainly such as to bring it more into line with the later phenomenology. Fatigue and change of interest, however, prevented Husserl from carrying out the thorough revision of the text that he contemplated, and the Second and Third Editions of the *Logical Investigations* are not importantly different from the First. It was only in works like *Formal and transcendental Logic (1929)* that Husserl substantially developed the treatments of Logic which occur in the *Logical Investigations.* We may be glad that this is so. For the *Logical Investigations* has merits quite independent of its interesting relations to + +the phenomenological system, or to the subsequent development of German philosophy. It is, despite much that is dated, and much that is drearily detailed and technical, a surpassingly good piece of philosophical work, and one that has a permanent interest for Anglo-Saxon philosophers, owing to its close relations, at many points, to traditional British empiricism, and to the analytic concerns which perturbed Russell and Moore. But it may also claim, particularly in its last two studies, 'On Intentional Experiences and their "Contents'" and 'Elements of a phenomenological Elucidation of Knowledge', to have reached an Aristotelian level of many-sided profundity, and to have sketched the basic grammar of conscious experience in a manner never before or since surpassed, or even equalled. Brentano may have led up to this remarkable consummation, and Husserl's later phenomenological writings may have developed it richly and variously, but it is here in its least controversial, best-argued form, free from the extraneous trappings of a 'system', and its dubious methodological and covertly metaphysical pretensions, and simply one of the prime achievements of philosophy. Husserl, a Jew or of Jewish origin, died dishonoured in 1938, forbidden to enter the university where he had taught, and forbidden entry (no doubt owing to political exigencies) by his own most famous pupil. It will not, however, be doubtful to anyone who carefully reads the *Logical Investigations* and many of the later works, that we have in him one of the small number of supreme contributors to philosophy, not unworthy of being spoken of in the same breath with Kant and Hegel, or with Plato + +and Aristotle. + +It is because I have found the writings of Husserl so superlatively valuable, and so deeply stimulating even when I rejected their detail, and because I so deeply regretted his inadequate accessibility in English ~ particularly when infinitely less important works were both translated and much discussed ~ that I undertook the present translation, which has occupied me during spells of reduced academic pressure over many years. It has proved very difficult, since I was determined that the result should be English, even if inevitably it had to be a somewhat heavy, Teutonic English, such as Husserl himself might have written, had he felt himself, authentically if extraneously, into the world of Anglo-Saxon culture. The task of teasing Husserl's richly redundant, serpentine style, with its multitude of higher-order expressions having no equivalent in our own linguistic stock-in-trade, into something that would flow, and have conciseness and clarity of form, even when its content was very difficult, has agitated me immensely, and I have no doubt that I have fallen short of perfect faithfulness or perfect English at many points. I do not, however, regard a translation, however good, as a substitute for the original, and believe that the attempt to make it such a substitute makes it less good as a translation than it could be. If I have made Husserl accessible to many who will make a profitable use of his ideas, instead of ranging them in a dreary chronological museum, leading up to a + +final show-case which enshrines pure Nothingness or pure Being - it scarcely + +matters which - I shall have achieved my purpose. + +Personal explanations and panegyric should not, however, extend beyond the first paragraphs of an Introduction. I must try to say, in general terms, why I think Husserl's *Logical Investigations* such an important work. It is important not because it can now count as a valuable contribution to the logical syntax of our language, but because it uses its investigations of logic to illuminate much more fundamental topics: the nature of meaning, the ontology which meaningful discourse presupposes, and, infinitely most important, the nature of those conscious acts in virtue of which alone our words point beyond themselves to things in the world, and in virtue of which alone there *is* a world for us and any fellows with whom we can communicate. Husserl's polemics in favour of an adequate theory of meaning, of an 'objective' view of logical categories and of an 'intentional' analysis of consciousness, are directed against the contemporary idols of the theatre, the naturalisms and psychologisms of the time, which he thoroughly demolishes. They could, however, with equal point, have been directed against our own more elaborate naturalisms, which, intoxicated with new-found behaviouristic categories, and employing a sophistry of models rather than a sophistry of arguments - my reference here is to certain famous 'languagegames' - manage to divert attention from that central conscious subjectivity, and from its varied 'constitutive' activities, which not only *can* be rendered intelligible, whether in ourselves or in others, but in ignorance of which + +nothing whatever can be rendered intelligible at all. + +As regards Husserl's view of meaning, he is the first to attempt a study of its phenomenology, of the queer manner in which words, whether spoken or written or heard or seen, and so 'given in intuition', yet bow themselves off the stage as prime terms of our references, and merely serve to introduce, or to help introduce, objects and connections other than themselves. And he is also the first to stress how words so used seem to *clothe* the objects to which they make reference possible, how they are phenomenologically inscribed upon the whole world around us and to what an extent knowing or cognizing an object consists in putting the right name to it, seeing it as *called* this or that. All this has many points of affinity with recent linguistic philosophy, but it is also profoundly different. For recent linguistic philosophy is a third-person, observer's analysis, which sees meaning only in the varied use made of words and combinations of words in many natural and social situations. This observer's analysis is of course both valuable and necessary, for the phenomenology of meaning would not be complete without a study of its behavioural working out, and its detailed exhibition in the conduct of persons in their environment. A life of meaningful references that had no 'fulfilment' in responsiveness to what environs the person, would, in fact, be not merely not actual, but intrinsically impossible. But this does not affect the fact that a personal appropriation of meaning, a lived-through + +understanding of what it is that words are naming or communicating, is a central feature of the meaningful use of words, and that, in default of it, there could be no more genuine semiosis than there is in the case of a computer or a tape-recorder. Beings who faultlessly used the right words in the right circumstances, and who got about the world and helped other similar beings to get about it, but to whom the rationale, the sense of their proceedings was never a lived experience, totally embraced in each present and not spread out over tracts of time, nor referred hypothetically to the future - we shall not say that such a sense must *always* be so experienced would not deserve to be called speakers or users of a language at all. Of them it would be right to say: Words they are moved by, but they hear not, words they utter, but they speak not, neither do they understand. The phenomenology of meaning has, of course, been carried much further than we find it in Husserl, particularly by phenomenologists like Roman Ingarden, + +but the all-important beginnings are there. + +As regards Husserl's contributions to ontology, the *Logical Investigations* introduces us to a richness of categorical distinctions such as we find in Aristotle, and such as only his great contemporary Meinong carried further. We have none of the misplaced economy, suitable in natural science, where it is all-important to have only a few explanatory ultimates or laws, carried over into the realm of thought-distinctions, where it encourages one to massacre some valuable concept, or to warp the expression of some wellunderstood principle, in order to satisfy the exigencies of a cheese-paring behest not to multiply entities, and which so fears the 'jungle' of ramifying things of reason that it is prepared to sink into the Serbonian bog of enforced simplification. Obviously one does not lose, but gain, by noting all the iridescent variety which confronts one even at the categoriallevel, and which is indefeasibly part of the world as we deal with it through word and thought. There is the distinction between the thing and its parts, and between its separable parts and its inseparable 'sides' or 'moments', there is the distinction between the patterns instantiated in things and the detached patterns which they exemplify, there is the distinction between things and states of affairs concerning things, and among the many varied sorts of such states of affairs, and there is the distinction between the forms of things and states of affairs and the matter, the items bound together by those forms. A philosopher sensitive enough to point to the semantic and ontological difference between the passing postman and the fact that the postman is passing, is obviously sensitive to differences which a training of the economizing, reductive sort only serves to blunt. In the *Logical Investigations* one sees the beginnings of the doctrine that all the categorial distinctions recognized by logic extend beyond the limits of language and symbolism and are implicit in our unverbalized experience. This was afterwards to be carried further in such works as *Erfahrung und Urteil,* where a whole world of pre-predicative negations, modalities etc., was recognized in the primitive texture of human, + +and even of animal experience. The heresy of 'pre-linguistic meanings', so much condemned by certain linguistic philosophers, is thus made the basis of an illuminating analysis. Husserl's ontology, further, is not uniformist and monolithic, as in those modern ontologies where *any* case of quantification commits one to a whole range of 'entities', which all, however, have being in precisely the same sense and manner. Like Aristotle, Husserl too has his analogy of being, where some things are there in a more foundational, primitive sense, while other entities have an essentially 'founded', secondary, derivative status. The developments of Husserl's ontology, and the changes induced in it by the idealistic positions of the later phenomenology, are not, + +however, matters that can be further discussed here. + +In Husserl's phenomenology, understood as a purely descriptive, internal analysis of consciousness and its varieties, we have, however, the supreme contribution of the *Logical Investigations,* as of the later, specifically sostyled, phenomenological writings. What Husserl clearly saw, and what later analysts of language have failed to see, is that the interpretation of speech always proceeds in two necessarily correlated, but in many respects deeply different, and often disparate dimensions: the interpretation of speech as referring to entities and situations in the world, or to ideal abstractions from these latter, and the interpretation of speech as revealing the 'references' that it thus embodies, the so-called 'acts' or 'conscious appearances' in which such entities and situations display themselves before us, are given separately or together, as making up or at least 'framing' our world, whether as possibilities or as limiting impossibilities. To talk of objects 'our there', and their actual or possible predicates and relations, may not be to talk of our conscious awareness of such matters, but it is always to imply it, and to imply it in no vague, general fashion, but in one precisely proportioned and accommodated to the objective matters of which we are talking. There is nothing mysterious, puzzling in all this, or in the regular, natural swing-over from an external to an internal reference, in the passage from a situation as we think of it or perceive it, to the situation of our thought or perception of it: we are not suddenly translated from a world of limpid natural objects to the murky contents of the 'queer medium of the mind'. We have merely passed from the obverse to the reverse side of the same coin, and any limpidity which attaches to the objects and situations referred to, attaches also to our conscious, significant references to them. People are wont to speak as if there were some close-wrapped mystery about the inner, private side of things which does not apply to their outer, public side, as if one could be wholly clear about the latter and deeply confused or in doubt about the former. This is not the case at all. To perceive that the soap in one's bathroom is exhausted, or to understand what it is for one's bathroom soap to be exhausted, is to be able to perceive or understand what one's own perception or understanding of the exhaustion of one's bathroom soap is like, and to understand, further, what *anyone's* understanding of the same matter + +must be like. We are not unclear as to what happens in a man's experience when he knows his bathroom soap to be exhausted, at least not in the respects in which that experience is directed to the domestic situation in question. There are of course *other* respects in which our understanding of the 'inner' situation presents difficulties which our understanding of the 'outer' situation does not, difficulties which we perfectly understand in the light of the fact that it *is* an inner situation. There are mental pictures and feelings and attenuations of mental pictures and feelings, which have to be approached, if at all, through people's hesitant, analogical accounts of what they picture and feel, and it is clear that there are difficulties, if not ones of principle, in our access to such things. There are also philosophical puzzles connected with the manner into which our experience packs or reduces to unity what can only be spelt out or unpacked in a lengthy exegesis, difficulties which have led certain philosophers to explain our packed inner state as one of *readiness* to say or do certain things, or of readiness to behave in certain ways, all explanations which reduce the packed concentration of conscious life to the content or process of its unpacking. All such solutions spring from a peculiar inability to see that consciousness just is, or at least is, the bringing into a focus of indivisible contemporaneity of what, from another point of view may be successive and dispersed, and that a world in which, perhaps per impossible, there were only mutually external happenings in space and time, would be a world of which we could not be conscious, in which there could be no such thing as conscious experience at all. There are, therefore, and must be, corresponding to any well-formed, articulate tract of fully significant speech - and speech is of course not always fully significant - mental stances or appearances complete and consummated in the moment, and only spread over time in the sense of lasting and changing throughout that time, in which objects and situations are set before us in various definite or indefinite lights, which change and develop as we consider those objects and situations. It is to the analysis and classification and law-governed interconnection of these mental stances or appearances that phenomenology must be directed, and through which it must illuminate the mind and language and the world. The use of a language of *acts,* of things done, is in this context traditional, but Husserl makes clear, like Brentano and Meinong, that his use of the term has no special connection with *activity.* The mere *presence* of something to mind, its entry into consciousness in whatever unheralded manner, its mere turning up or appearance or *Erscheinung,* constitutes an 'act' in the sense relevant to Husserl's analysis. What it then becomes important to note are the wide variety of alternative species into which the one invariant thing, consciousness, differentiates itself, and in fact only *is* the one invariant thing consciousness because it can be thus differentiated. Of these differences of manner, the most fundamental is the difference between the *empty* manner in which things can be there for mere thought, for meaning-intention, and the *fulfilled* or *seeing* manner in + +which they can be there for illustrative intuition *(Anschauung).* Husserl is infinitely skilled in showing the vast number of differing manners and proportions in which the intuitive and emptily cogitative can be combined, and in stressing the fact that, except in the ideal limit, they are always so combined in our perception of physical objects, a physical object being always something that could be further and more richly seen and explored, however much of it is or has been present to our senses. Husserl also dwells by analogy on the intuitive grasp, the full givenness of ideal characters and states of affairs, as opposed to their imperfect presence to mind by way of symbols whose meaning or valid combination is only partially felt. And he stresses the case of 'fulfilment' by way of internal images and by way of external physical models or diagrams or pictures, which is only a surrogate for the more complete fulfilment when what we have before us is given as 'the thing itself'. Nowhere in the literature of philosophy are these matters more subtly treated and more full of an evident clearness and rightness: it is only a pity that they have been so infrequently and so superficially studied. Husserl's analysis of consciousness derives, of course, from Brentano's concept of intentionality, but is in several respects superior. Husserl we may say was the first to stress a property of intentional reference which Brentano also stated in the first appendix to the 1911 edition of his *Psychology,* that conscious reference is not strictly speaking a real relation, since the object or state of affairs referred to need not exist at all. The God Jupiter, Husser! says in chapter 2 of the Fifth Investigation, is not a real constituent, is not really present, in my conscious reference to him: to think that he need be, or could be, is to misunderstand the nature of conscious reference altogether. This point was never understood by Meinong, who had to give a certain *Vorhandenheit* even to non-existent or absurd objects. It is not unlikely that Brentano got the first idea for his 1911 Appendix from the 1901 discussion of the God Jupiter in the *Logische Untersuchungen,* together, of course, with much that also infuriated him: certainly the example of the God Jupiter is + +cited by Kraus in his exposition of Brentano's doctrine. + +Husserl, however, did not fall into the prime error of making the possible non-existence of a thought-object the criterion of mentality, a mistake persisted in by Chisholm. For he is clearly aware, in the second place, that references that fail of a target imply the existence of references where the target is in the nature of things hit, is itself intuited or given - the meaning of intuition is simply that of an ultimate, perfect self-givenness - and given as it in itself is. Unless there was this limiting form of intentionality, there would be no meaning in saying that certain intentions fail of their mark, that they present their objects in an inadequate or distorted light, and not as they are, or not as they wholly are. Consciousness can only give sense to its inadequacies by contrasting them with an ultimate, inerrant adequacy or self-givenness. The notion of the self-evident or inwardly evident which in Brentano is no more than an internal index of our title to judge or believe + +something, is therefore for Husserl no more than the limiting state where doubt becomes senseless, irrelevant, since the standard of self-givenness has been reached. For Husserl therefore it is part of the notion of intentionality that there is a limiting state (ideal in the case of physical objects) in which the object as it is thought of or given simply fades out in, or achieves coincidence with, the object as it in and for itself is. The difficulties of this account of self-evidence, the many cases of seeming self-evidence which later require revision, is finely dealt with in the 1929 *Formal and transcendental Logic* which must certainly be studied if we are fully to evaluate the *Logical* + +*Investigations.* + +It is to be regretted that Husserl did not allow the implications of his own views on self-givenness to guide him away from the methodological ETIOxi] or suspension of conviction which is preached in the later *Ideas* (§§31, 32 *et seq.).* For there is arguably no clear sense to be given to a total suspension of belief in the entire world: it is only in the context of a limiting, if unattainable, complete givenness of all sides of physical realities that the notion of their doubtful, distorted, merely intended presence to consciousness can be significantly entertained, a point since made by many analytic philosophers. Husserl sees that we cannot accord a merely phenomenal, intentional status to the *acts* of consciousness in which physical objects are given, a point clear to Descartes as it was not clear to Kant, and he is also unwilling to accord a merely intended status to the experiences of others: he thinks, however, that he can significantly 'bracket' the reality of all natural things, and even passes on from this to the idealistic conviction that physical things have, despite their transcendent status for consciousness, no more than a merely intended, phenomenal being, while consciousness itself exists in an 'absolute' manner *(Ideas,* §§41-6). To the extent that Husserl makes this move, he transforms his brilliant, original analysis of consciousness into one of those ordinary subjectivisms which comfort the shattered ego by assuring it, quite baselessly, that in some secret manner it has manufactured its own shattering world. Of this form of subjectivism, respectable only on a theistic background like Berkeley's, there is not a trace in the *Logical Investigations.* The examination of consciousness, and of how things are given to consciousness, goes with no implication that such things have no being other than their givenness to consciousness: the contrary implication is in fact without reservation taken to be part and parcel of consciousness itself. Room is of course left for metaphysical reversals, but a proper suspension of conviction and assertion is maintained on such possibilities. It is only in the *Ideas,* with its pretended methodological suspension of all conviction, + +that such a suspension is, in fact, not truly practised. + +A third respect in which Husserl's treatment of consciousness is greatly superior, lies in its acknowledgement of lived-through experiences or livedthrough moments of experience which are not intentional at all, which present nothing to consciousness, not even themselves. Our sensations, treated as + +modifications of our own interior selfhood, are experienced moments of this type, and they are utterly to be distinguished from the properties of physical objects which appear in corresponding perceptions. There is, Husserl thinks, as Meinong does also, a red wise mode of interior experience which corresponds to the redness we perceive, whether validly or illusorily, out there in objects: this redwiseness we feel rather than perceive (in normal experience), but *in* feeling we can also pass to perceiving the objective redness which is as it were its 'other side'. This use of interior experience to mediate objective reference is misleadingly described in a language of *beseelende Auffassungen,* animating conceptions or interpretations, which suggests the traditional theory, infinitely repugnant to Husserl, of causal inferences from immediate sense-data to unperceived physical objects. For Husserl the sensation (though sometimes called a 'datum') is not normally given at all, and its *Auffassung* or interpretation is a primary act of mind's self-transcendence and not therefore, properly speaking, an interpretation or an inference at all. What it reveals is also not any remote function of physics but the redness that is authentically perceived. The theory of 'inner felt sides' to the sensible properties of things has of course been adversely criticized by the few who have understood it properly, among whom G. E. Moore is to be reckoned: it is arguable that, though dubious on a first analysis, it becomes ever more acceptable on further examination. Husserl uses the same notion of representing contents which are not themselves presented, in his theory of categorial intuition. Through the mind's various acts of synthetic combination it can come to set before itself various forms of *objective* synthesis, e.g. the synthesis of properties in a thing, of items in a group, of identity in varying contexts etc. It is a pity that there have been so few people to understand + +and discuss these interesting doctrines. + +It is not possible, in an Introduction of this length, to do more than touch on some of the many questions of interpretation raised by Husserl's *Logical Investigations.* And it is not at all possible to trace the relations of the position of that work to those of the later phenomenology. The interpretation, criticism and evaluation of Husserl's vast, immensely hard, supremely rewarding corpus of writings is barely in its beginnings. What remains for me to do, however, is to give some account as to how I have rendered some of the key-terms of Husserl, an account which the use of the Index will improve. I have been largely, but not absolutely uniform, in my translation of these key-terms, since my aim has been to render their sense, which demands adaptation to their German or English context, rather than to provide a code from which the German can be uniformly inferred from the English. The German text is, after all, again available, even if, regrettably it was long out of print. And Husserl, despite his prolixity and technicality, + +conforms to the Keynesian description of a Cambridge philosopher as 'a prose writer, hoping to be understood'; he is not a hierophant, requiring a word-for-word translation of his dark locutions in the hope that some of their doubtful sense will be preserved. I have translated *Vorstellung* almost uniformly by 'presentation', recognizing that the latter is not really an English word: the concept expressed by Husserl's (and Brentano's) term is not an English concept either. 'Idea' is required for other purposes, and is in any case ambiguous, and 'representation', if anyone can tolerate it, is required for the cases where Husserl uses *Repriisentation, Darstellung* etc. *Anschauung (anschaulich* etc.) I have rendered by 'intuition' ('intuitive' etc.) since this is the traditional rendering of the term in translations of Kant, and since the word has no proper equivalent in English. I have occasionally varied this use by substituting or adding such terms as 'envisage', 'illustrate', 'picture', 'see', and their derivatives. *Einsicht* etc., which more properly means 'intuition' as understood in English, I have translated by 'insight' etc., though sometimes I have talked of 'perspicuity' etc. I have translated *Idee* by 'Idea' and *Spezies* by 'Species', capitalizing both terms where ideal entities are in question. I have sometimes capitalized terms, e.g. 'Perception', where ideal notions were intended, but in general I have been inconsistently sparing with capitals, as I believe that they readily become tyrannous and obfuscate sense. I have translated *Erlebnis (erleben* etc.) by 'experience', though I have sometimes substituted 'lived experience', 'live through' etc.; I have not devised a separate word for *Erfahrung,* since Husserl often uses the words interchangeably, and since the English word is used in two ways, clear in the context, and is in fact practically two words. 'Having an experience' and 'learning by experience' obviously involve two distinct, though cognate, uses of the word 'experience'. I have translated *psychisch* by 'mental' in informal contexts like the Prolegomena where 'psychical' would be strained, but I have used 'psychical' where Brentano's technical use, and its contrast with *physisch,* was in question. I have indicated the difference between *real* and *reel!* (meaning 'in the world of natural things' and 'actually part of' respectively) by putting the German word in brackets after an English use of 'real'. I am not convinced that Husserl meant much by his solemn distinction of these two terms, and I regret the necessity of translating *wirklich* by 'actual', when 'real' is often more suitable. It is curious that Husserl should have used the word *real* of a thing-like status which need not involve 'reality' in the sense of genuine existence, and which he came afterwards to hold *never* involved 'reality' in the English sense. I have translated *schlicht* by 'straightforward', and *eigentlich* (in technical contexts) by 'authentic', and I have translated *unselbstiindig* by 'non-independent', since the English word 'dependent' has less negativity and more relativity than *unselbstiindig.* Sometimes I have also had traffic with 'self-sufficient' for *selbstiindig,* instead of 'independent'. *Inhalt* I have, of course, translated by 'content', but this makes difficulties in the case of other words for which 'content' alone seems + +suitable: *Gehalt,* e.g. has been badly translated by 'substance'. *Fundieren, fundierte* etc., are of course 'found', 'founded' (though sometimes I have yielded to the charms of 'basing', 'based' etc.) but *fundierend* has varied from 'foundational' to 'underlying' according to context or euphony. *Moment* I have usually translated as 'moment', but sometimes, in less technical contexts, as 'side' or 'aspect'. *Bedeutung* in the sense of significant content I have translated by 'meaning', less commonly by 'sense': Husserl does not follow Frege in keeping the two words distinct, and neither ever means the *object* of a reference. The word *bedeuten* I have translated by 'act of meaning' or simply by the verb 'to mean', though I have sometimes used 'refer', 'reference' as an equivalent. Husserl in the main tends to say that we mean *objects, not meanings, by way of* the meanings which words *have* rather than *mean,* and I have followed his usage in English, with which it on the whole agrees, rather than trying to introduce distinctions into my translation which have only recently been thought necessary. *Wahrnehmen, Wahrnehmung* etc., I have translated by 'perceive', 'perception', the established equivalents, though when a *Wahrnehmung* means an individual act, I have, for the sake of shortness, translated it by 'percept'. *Innere Wahrnehmung* has been translated by 'inner', 'inward' or 'internal perception' quite without principle, and the same holds *mutatis mutandis* of *aiissere Wahrnehmung. Erkennen, Erkenntnis* I have generally translated by 'know', 'knowledge', though there are contexts, particularly in the Sixth Investigation where 'cognize', 'cognition', 'recognize', 'recognition' seemed more suitable. *Evidenz* and its derivatives I have rendered by 'self-evidence', 'inward evidence' according to context: there are cases of *Evidenz,* e.g. those of *innere Wahrnehmung,* which have no *self-evidence* in the English sense. The adjective *evident* I have sometimes translated by 'evident', but in general I have found that the forensic and documentary associations of the English word 'evidence' are fatal to understanding. Many students are permanently bewildered by these associations. That a similar thing holds of 'reflection', 'reflective' etc., used to translate the German word where it has to do with introspection, and not with 'reflection' as we ordinarily understand it, has not led me to depart from the use in question. After all, Locke's similar use of 'reflection' has misled, and always will mislead, countless incautious and forgetful students. I have translated *begriinden, Begriindung* etc., by 'grounding' etc., also by 'prove' ('proof'), 'demonstrate' (,demonstration'), 'validate' (,validation'). It expresses a reversed view of argument more usual to Continental than to British intellectuals. With these explanations, it is to be hoped that Husserl + +can speak for himself. + +J. N. FINDLAY + +*Yale University* + +(First Edition) + +The logical Investigations whose publication begins with these *Prolegomena,* have arisen out of unavoidable problems which have constantly hindered, and finally interrupted, the progress of my efforts, spread over many years, at achieving a philosophical clarification of pure mathematics. Together with questions regarding the origin of the basic concepts and insights of mathematics, these efforts were especially concerned with difficult questions of mathematical theory and method. The expositions of the traditional logic, so often reformulated, should have succeeded in providing us with an intelligible and perspicuous account of the rational essence of deductive science, with its formal unity and symbolic methodology. A study of the actually given deductive sciences, however, left all these things problematic and obscure. The deeper that my analyses penetrated, the more conscious I became that the logic of our time was not adequate to that actual science + +which it was none the less its function to elucidate. + +I was plunged into peculiar difficulties by my logical researches into formal arithmetic and the theory of manifolds, a discipline and method which stretches far beyond all peculiarities of the special forms of number and extension. They forced me into discussions of a very general sort, which lifted me above the narrow sphere of mathematics, and pushed me towards a universal theory of formal deductive systems. There were many sets of problems that then bore down upon me, of which I shall here mention only + +a single one. + +There were evidently possibilities of generalizing (transforming) formal arithmetic, so that, without essential alteration of its theoretical character and methods of calculation, it could be taken beyond the field of quantity, and this made me see that quantity did not at all belong to the most universal essence of the mathematical or the 'formal', or to the method of calculation which has its roots in this essence. I then came to see in 'mathematicizing logic' a mathematics which was indeed free from quantity, while remaining none the less an indefeasible discipline having mathematical form and method, + +which in part dealt with the old syllogisms, in part with new forms of inference quite alien to tradition. Important problems then loomed before me regarding the universal essence of the mathematical as such, and the natural connection, or the possible boundaries, between systems of quantitative and non-quantitative mathematics, and especially, e.g., regarding arithmetical and logical formality. Naturally, I also had to go on from this point to more fundamental questions regarding the essence of the form of knowledge in contradistinction to its matter, and the sense of the distinction between + +formal (pure) and material properties, truths and laws. + +But in another quite different direction I also found myself involved in problems of general logic and epistemology. I began work on the prevailing assumption that psychology was the science from which logic in general, and the logic of the deductive sciences, had to hope for philosophical clarification. For this reason psychological researches occupy a very large place in the first (the only published) volume of my *Philosophy of Arithmetic.* There were, however, connections in which such a psychological foundation never came to satisfy me. Where one was concerned with questions as to the origin of mathematical presentations, or with the elaboration of those practical methods which are indeed psychologically determined, psychological analyses seemed to me to promote clearness and instruction. But once one had passed from the psychological connections of thinking, to the logical unity of the thought-content (the unity of theory), no true continuity and unity could be established. I became more and more disquieted by doubts of principle, as to how to reconcile the objectivity of mathematics, and of all science in general, with a psychological foundation for logic. In this manner my whole method, which I had taken over from the convictions of the reigning logic, that sought to illuminate the given science through psychological analyses, became shaken, and I felt myself more and more pushed towards general critical reflections on the essence of logic, and on the relationship, in particular, between the subjectivity of knowing and the objectivity of the content known. Logic left me in the lurch wherever I hoped it would give me definite answers to the definite questions I put to it, and I was eventually compelled to lay aside my philosophical-mathematical investigations, until I had succeeded in reaching a certain clearness on the basic questions of epistemology and in the critical understanding of logic as a + +SCIence. + +If I now publish these essays, the product of many years of work, *on a new foundation of pure logic and epistemology,* I do so in the conviction that I shall not be misunderstood for independently choosing a path remote from that of prevailing logical trends, in view of the grave, factually based motives that have inspired me. The course of my development has led to my drawing apart, as regards basic logical convictions, from men and writings to whom lowe most of my philosophical education, and to my drawing rather closer to a group of thinkers whose writings I was not able to estimate + +rightly, and whom I consulted all too little in the course of my labours. I have had, however, unfortunately to abstain from any subsequent insertion of comprehensive literary and critical references to researches having an affinity with my own. As regards my frank critique of the psycho logistic logic and epistemology, I have but to recall Goethe's saying: There is nothing to which one is more severe than the errors that one has just abandoned. + +E. HUSSERL + +*Halle a. d.* S. *May 21st 1900* + +(Second Edition) + +The question as to the form in which I should undertake to republish the present work, out of print for some years, has caused me no little concern. My *Logical Investigations* were my 'break-through', not an end but rather a beginning. When the work had been printed, my studies continued forthwith. I tried to give a fuller account of the meaning, the method and the philosophical scope of phenomenology, to pursue the woven threads of my problems further in every direction, and to track down and tackle parallel problems in all ontic and phenomenological fields. Understandably, as the horizon of my research widened, and as I became better acquainted with the intentional 'modifications' so perplexingly built on one another, with the multiply interlacing structures of consciousness, there came a shift in many of the conceptions formed in my first penetration of the new territory. Remaining obscurities were cleared up, ambiguities removed, isolated observations to which at the start no special importance could be given, gained fundamental meaning as one passed over into larger contexts. Everywhere, in brief, there were not merely supplementations but transvaluations in one's original field of research, and from the point of view of one's widened, deepened knowledge, even the arrangement of one's treatments no longer seemed quite adequate. The sense and the extent of these forward steps, and their widening effect on one's field of research comes out in the recently published First Book of my *Ideas towards a pure Phenomenology and Phenomenological Philosophy,* printed in the first volume of the *fahrbuch fur Philosophie und phiinomenologische Forschung* (1913), and the publication of the two remaining Books, which will follow immediately, will show this still better. + +I originally cherished the hope that, after discovering and exploring the radical problems of pure phenomenology and phenomenological philosophy, I should be able to present a series of systematic expositions that would render a reprinting of the old work unnecessary, in so far as its content, not at all jettisoned, but purged and divided according to subject, would come into its own in association with the new work. But when execution began, a + +serious objection at once raised itself. Many years would be needed for the carrying out of the extensive, difficult task of imposing literary unity on our Investigations: though they stood there complete and concrete, they would have for the most part to be expounded anew and to have their difficulties ironed out. I therefore decided first of all to plan my *Ideas.* They were to give a universal, yet contentful presentation of the new phenomenology, based throughout on actually executed work, a presentation of its method, of its systematic field of problems, of its function in making possible a strictly scientific philosophy, as well as a reduction to rational theory of empirical psychology. After all this, the *Logical Investigations* would be republished, and that in a better form, adapted to the standpoint of the *Ideas,* and so helping to introduce the reader to the nature of genuinely phenomenological and epistemological *work.* For if these Investigations are to prove helpful to those interested in phenomenology, this will be because they do not offer us a mere programme (certainly not one of the high-flying sort which so encumber philosophy) but that they are attempts at genuinely executed fundamental work on the immediately envisaged and seized things themselves. Even where they proceed critically, they do not lose themselves in discussions of standpoint, but rather leave the last word to the things themselves, and to one's work upon such things. The *Ideas* ought in effect to rest on the work of the *Logical Investigations.* If, through the latter, the reader has been brought openly to investigate and concern himself with a group of fundamental questions, then the *Ideas,* with their policy of illuminating method from ultimate sources by putting a sketch of the main structures of pure consciousness before one, by systematically locating one's work-problems in + +the latter, could assist him to a further, independent advance. + +The carrying out of the first part of my plan was relatively easy, though the unexpected length of the first two Books of the *Ideas,* essential for my purposes and undertaken by me in one piece, forced me to divide their publication, so that the First Book alone had to suffice provisionally. But the fulfilment of my second aim was far harder. Anyone who knows the old work, will see the impossibility of lifting it entirely on to the level of the *Ideas.* That would mean a complete recasting of the work, and a postponement to the Greek kalends. It seemed to me, on the other hand, to be a comfortable rather than a conscientious decision, in view of the aims justifying a new edition, to abandon all revision and merely reprint the work mechanically. Was I entitled to mislead the reader once more, through all my omissions, waverings and self-misunderstandings, which, however unavoidable and pardonable in the first edition of such a work, would yet put unnecessary + +difficulties in the way of a clear grasp of essentials? + +All that remained possible was to attempt a middle course, and in a manner to let myself go in attempting it. It meant leaving untouched certain unclarities, and even errors, which were part and parcel of the unified style + +1. To allow nothing into the new edition regarding which I was not fully persuaded that it deserved thorough study. In this respect single errors could be left standing, since I could allow them to count as natural steps towards a truth that would transform their good intentions. I could say to myself in all this: Readers who stem from general philosophical drifts of the present which are in essence the same as those in the decade of this work's origin can, like the work's author, only at first gain access to what are mere steps towards certain phenomenological (logical) positions. Only when they have gained sure mastery over the style of phenomenological research, do they see the fundamental meaning of certain distinctions which appeared pre- + +viously to be insignificant nuances. + +2. To improve all that could be improved, without altering the course and style of the old work, and, above all, to bring to most definite expression the new thought-motives that had their 'break-through' in the old work, but which had, in the first edition, been at times sharply stressed, at times blurred, + +by the hesitant and timid author. + +3. To lift the reader gradually, in the course of the expositions, to a relatively rising total level of insight, following in this the original peculiarity of the work. We must here voice the reminder that the work was a systematically bound *chain of investigations* but not, properly speaking, *one* book or work in a literary sense. There is in it a regular ascent from a lower to a higher level, and a working of oneself into ever new logical and phenomenological insights, which never leave the previously achieved ones quite untouched. Ever new phenomenological strata swim into our view and add determination to our conceptions of the earlier ones. This character of the old work made a kind of revision seem possible, which consciously leads the reader onward and upward, in such a way that, in the final Investigation, the level of the *Ideas* is in essentials reached, so that the previous unclearnesses and half-truths, that we had to put up with, appear perspicuously clarified. I went ahead in the sense of these maxims, and have the impression as regards both provisionally published pieces (the Prolegomena and the first part of the Second Volume) that the big efforts I made have not been wasted. I have naturally had to add here, and strike out there, at times to rewrite single sentences, and at times whole paragraphs and chapters. The thoughtcontent has become more packed and full in extent: the total extent of the work, more specifically that of the Second Volume, has grown unavoidably, despite all suppression of critical supplementation, so that this volume has + +had to be divided. + +Regarding the individual Investigations and their reconstructed form, the following should be said. The *Prolegomena to Pure Logic* is, in its essential content, a mere reworking of two complementary series of lectures given at Halle in the summer and autumn of 1896. To this the greater liveliness of the exposition is due, which has assisted its influence. The piece is, moreover, written in one cast of thought, and I therefore thought I ought not to revise + +it radically. But I found I could, on the other hand, from about the middle on, carry out many quite large improvements in presentation, could expunge slips and put main points into sharper light. Some very essential, if partial, insufficiencies - such as the concept of a 'truth in itself' which is too onesidedly oriented to *verites de raison* - had to be left, since they were part of the unified level of the piece. The Sixth Investigation (now the Second Part of the Second Volume) brings in necessary clarification in this respect. To burden the polemic on psychologism with new criticisms and countercriticisms (which would not have introduced the least new thought-motive) did not seem very appropriate to me. I must emphasize the relation of this piece to 1899, the precise date at which I merely rewrote it. (The printing of the *Prolegomena,* minus the Foreword, was already complete in November 1899. See my self-reference in the *Vierteljahrschr. f wiss. Philosophie, 1900,* p. 512 *f)* Since its appearance, some authors that I looked on as representing logical psychologism have essentially changed their position. Th. Lipps, e.g., in his extremely significant, original writings, has since 1902 not at all been the man that is here quoted. Other authors have, in the meantime, sought different foundations for their psychologistic position, a point not to + +be ignored, since my presentation takes no account of it. + +As regards the Second Volume of the new edition, the hesitant Introduction, so little true to the essential sense and method of the actually written Investigations, was radically revised. I felt its defects immediately after its appearance, and also found immediate occasion (in a review in the *Archiv f system. Phi/os.* XI (1903), p. 397 *ff)* to object to my misleading account of phenomenology as descriptive psychology. Some of the main points of principle are there briefly but sharply characterized. The psychological description performed in inner experience appears as put on a level with the description of external events in nature performed in external description, but it is, on the other hand *opposed* to phenomenological description, from which all transcendent interpretations of immanent data, even those of psychical acts and states of a real ego, are entirely excluded. The descriptions of phenomenology are said (p. 399) 'to deal neither with lived experiences nor classes of lived experiences of empirical persons ... phenomenology knows nothing of persons, of my experiences or those of others, and surmises nothing regarding them: it raises no questions in regard to such matters, attempts no determinations, constructs no hypotheses'. The complete reflective clarity that I had achieved in these and following years regarding the essence of phenomenology, which led gradually to the systematic doctrine of 'phenomenological reduction' (cf. *Ideas,* 1, Section 2), was of use in the rewriting of this Introduction, and also in the text of all the following Investigations, thereby raising the whole work to an essentially higher level of + +clarity. + +Of the five Investigations which occupy the First Part of the Second Volume, the first, *Expression and Meaning,* retains its merely preparatory + +character in the new edition. It stimulates thought, it directs the gaze of the phenomenological beginner to the initial, already most difficult problems of the consciousness of meaning, without doing full justice to them. The manner in which it deals with occasional meanings (to which, however, in strictness, all empirical predications belong) is an act of violence - the enforced consequence of the imperfect conception of the essence of 'truth in itself' in the + +*Prolegomena.* + +As a further defect of this Investigation, only understood and corrected at the end of the volume, we must note that it has no regard to the distinction and parallelism between the 'noetic' and the 'noematic': the fundamental role of this distinction in *all* fields of consciousness is first fully laid bare in the *Ideas,* but comes through in many individual arguments in the last Investigation of the old work. For this reason, the essential ambiguity of 'meaning' as an Idea is not emphasized. The noetic concept of meaning is one-sidedly stressed, though in many important passages the noematic con- + +cept is principally dealt with. + +The Second Investigation concerning *The Ideal Unity of the Species and Modern Theories of Abstraction,* had a style and limitation of theme, a certain completeness, which made a few detailed amendments, but no thoroughgoing reconstructions, desirable. As before, there is no discussion of the various types of Ideas, with their demand for a deep separation of essence, to which naturally Ideations, as deeply and essentially separate, correspond. All that this Investigation is concerned with, is the fact that one can learn to see Ideas, represented, e.g. by the Idea Red, and that one can become clear + +as to the essence of such 'seeing'. + +The Third Investigation *On the Doctrine of Wholes and Parts* has undergone very thorough revision, though in its case no unsatisfactory compromises needed to be made, and no subsequent corrections or deepenings were necessary. All that was here needed was to assist the inner sense of the Investigation, and what I thought were its important results, to better operation and to remove numerous imperfections of statement. I have the impression that this Investigation is all too little read. I myself derived great help from it: it is also an essential presupposition for the full understanding + +of the Investigations which follow. + +The position of the Fourth Investigation, *On the Distinction between independent and non-independent Meanings and the Idea of Pure Grammar,* is similar to that of the Third. My position in this case is also unaltered. I not only amended, but also in many places enriched, the content of the text, changes which point to future publications from my lectures on logic. + +The Fifth Investigation, *On intentional Experiences and their 'Contents',* had to undergo deep-going revision. In it cardinal problems of phenomenology (those in particular of the phenomenological doctrine of judgement) were tackled: in these it was possible to achieve a considerably higher level of clarity and insight without needing to alter the structure and essential + +content of the Investigation. I no longer approve of the rejection of the pure ego, but left the arguments in question in a shortened and formally improved form, as being the basis of P. Natorp's interesting polemic in his new *Allgemeine Psychologie,* volume 1, 1912. I have completely excised the much cited, very unclear, and, in the context, quite dispensable §7, 'Reciprocal Demarcation of Psychology and Natural Science'. I was perhaps all too conservative in retaining the quite unsuitable term 'nominal presentation': I was afraid in general of tampering with the terminology of the old work. The revised version of the Sixth Investigation, now in the press, is designed as the Second Part of the Second Volume: it is the most important Investigation from a phenomenological point of view. In this case I soon persuaded myself that it would not be enough to revise the old content, following the original content paragraph by paragraph. Its fund of problems still were my pace-setter, but I had advanced considerably in regard to them, and the sense of my 'maxims' would not permit a further use of compromises in regard to them. I accordingly went along quite freely, and, in order to give scientific treatment to the great themes so imperfectly dealt with in the first edition, I added whole series of new chapters, which increased + +the bulk of this Investigation very considerably. + +As in the *Prolegomena* I did not, in my second volume (my Fourth Investigation made a small exception) go into the many criticisms which rest, I am sorry to say, almost exclusively on misunderstandings of the *sense* of my positions. I therefore thought it more useful to discuss in universal form, and in their historical position, the *typical* misunderstandings of my philosophical endeavours, and that at the end of the Second Volume, in an epilogue, so to say. It will be a good thing if the reader has a look at this Appendix immediately after reading the *Prolegomena,* so as to guard him- + +self in time against such apparently natural misunderstandings. + +A full index will be added to the work, prepared with great care by my doctoral candidate Rudolf Clemens. I must express my heartfelt thanks for much friendly assistance, and, in the first place, to the Privatdozent Dr Adolf Reinach, who helped me with his zeal and knowledge when, two years ago, I first went thoroughly into deliberations concerning the possibilities of revision. The labours of correction were greatly lightened by the help of + +Dr Hans Lipps and by the doctoral candidate Jean Hering. + +E. HUSSERL + +*Gottingen October 1913* + +Prolegomena to + +Pure Logic + +Volume I of the German Editions + +**Introduction** + +§ **I The controversy regarding the definition of logic** + +**and the essential content of its doctrines** + +'There is accordingly as much difference of opinion in regard to the definition of logic as there is in the treatment of the science itself. This was only to be expected in the case of a subject, in regard to which most writers have only employed the same words to express different thoughts' (John Stuart Mill, *Logic,* Introduction, §l). Many decades have passed since John Stuart Mill introduced his valuable work on logic with these sentences, and important thinkers here and beyond the Channel have devoted their best powers to logic and have enriched its literature with ever new presentations. But even today these sentences could serve as a suitable expression of the state of logical science, even today we are very far from complete agreement as to the definition of logic and the content of its essential doctrines. Contemporary logic, of course, wears quite a different face from the logic of the mid-century. Owing particularly to the influence of the distinguished thinker just mentioned, the first of the three main tendencies that we find in logic, the psychological, has definitely come to prevail over the formal and the metaphysical tendencies, both as regards the number and the importance of its exponents. But the other two tendencies are still carried on, and the disputed questions of principle, reflected in different definitions of logic, are still disputed, while it is still true, and perhaps more true than ever, that different writers merely employ the same words to express different thoughts. This is not merely true of expositions stemming from different philosophical 'camps'. The side on which most life is to be found, that of psychological logic, manifests unity of conviction only in regard to the demarcation of the discipline, its essential aims and methods. But one could scarcely be blamed for exaggerating if one applied the phrase *bellum omnium contra omnes* to the doctrines put forth, and, in particular, to the opposed interpretations of traditional formulae and doctrines. It would be vain to seek to delimit a sum total of substantial propositions or theories in which one might see the hard core of our epoch's + +**§2 Necessity of a renewed discussion of questions** + +**of principle** + +In this state of the science, which does not permit one to separate individual conviction from universally binding truth, a reversion to questions of principle remains a task that must ever be tackled anew. This holds particularly as regards the questions which play a decisive role in the dispute among logical 'tendencies' and, together with this, in the dispute as to the correct demarcation of the science. The interest in just these questions has certainly cooled off in the last decades. After Mill's brilliant attacks on the logic of Hamilton, and the no less famous, but not so fruitful, logical investigations of Trendelenburg, these questions seemed to have been fully dealt with. But with the great resurgence of psychological studies, the psychologistic tendency in logic also gained dominance, and all effort centred in the systematic building up of the discipline upon principles presumed valid. The fact, however, that so many attempts made by such important thinkers to put logic on the sure path of a science, have not led to any shattering success, suggests that the ends in view have perhaps not been sufficiently clarified to + +allow successful investigation. + +One's conception of the aims of a science find expression in its definition. We naturally do not think that successful work on a discipline demands a prior conceptual demarcation of its field. The definitions of a science mirror the stages of that science's development; knowledge of the conceptual character of a science's objects, of the boundaries and place of its field, follow the science and progress with it. None the less, the degree of adequacy of such definitions, or of the views of the field they express, react on the progress of the science itself, and, according to the direction in which such definitions depart from truth, such a reaction can have a slight, or a very important influence on the development of the science. The field of a science is an objectively closed unity: we cannot arbitrarily delimit fields where and as we like. The realm of truth is objectively articulated into fields: researches must orient themselves to these objective unities and must assemble themselves into sciences. There is a science of numbers, a science of spatial figures, of animal species etc., but there are no special sciences of prime numbers, of trapezia, or of lions, nor of all three taken together. Where a group of discoveries and problems impresses us as 'belonging together', and leads to the setting up of a science, inadequate demarcation can consist merely in the fact that the field-concept is at first too narrow for what is given, and that concatenations of grounding connections stretch beyond the delimited field, and only draw together in a closed unity over a much wider field. Such limitations of horizon need not be prejudicial to the flourishing progress of the science. It may be that theoretical interest finds its first satisfaction in the narrower field, and that work that can be done without regard to deeper and wider logical ramifications, is what is needed in the first instance. + +There is another, much more dangerous fault in field-delimitation: the confusion of fields, the mixture of heterogeneous things in a putative field-unity, especially when this rests on a complete misreading of the objects whose investigation is to be the essential aim of the proposed science. Such an unnoticed IJET6:!3acnS Els 0"-"-0 YEVOs can have the most damaging consequences: the setting up of invalid aims, the employment of methods wrong in principle, not commensurate with the discipline's true objects, the confounding oflogical levels so that the genuinely basic propositions and theories are shoved, often in extraordinary disguises, among wholly alien lines of thought, and appear as side-issues or incidental consequences etc. These dangers are considerable in the philosophical sciences. Questions as to range and boundaries have, therefore, much more importance in the fruitful building up of these sciences than in the much favoured sciences of external nature, where the course of our experiences forces territorial separations upon us, within which successful research can at least be provisionally established. It was Kant who uttered the famous special words on logic which we here make our own: 'We do not augment, but rather subvert the sciences, if we allow their boundaries to run together.' The following Investigation hopes to make plain that all previous logic, and our contemporary, psychologically based logic in particular, is subject, almost without exception, to the above-mentioned dangers: through its misinterpretation of theoretical principles, and the consequent confusion + +of fields, progress in logical knowledge has been gravely hindered. + +**§3 Disputed questions. The path to be entered** + +The traditionally disputed questions which concern the demarcation of logic + +are the following: + +1. Is logic a theoretical or a practical discipline (a 'technology')? + +2. Is it independent of other sciences, and, in particular, of psychology + +and metaphysics? + +3. Is it a formal discipline? Has it merely to do as usually conceived, with + +the 'form of knowledge', or should it also take account of its matter? + +4. Has it the character of an *a priori,* a demonstrative discipline or of an + +empirical, inductive one? + +All these disputed questions are so intimately bound up together, that to take up a stance on one of them, is to some extent at least to be determined, or factually influenced, in the stance one takes up on the others. There are really only two parties. Logic is a theoretical discipline, formal and demonstrative, and independent of psychology: that is one view. For the other it counts as a technology dependent on psychology, which of course excludes the possibility of its being a formal, demonstrative discipline like the other + +side's paradigm arithmetic. + +Since we do not really mean to become involved in these traditional disputes, but rather to clarify the differences of principle at work in them, and + +to work towards a clarification of the essential aims of a pure logic, we shall proceed as follows: we shall start from the almost universally accepted contemporary treatment of logic as a technology, and shall pin down its sense and its justification. This will naturally lead on to the question of the theoretical foundations of this discipline, and of its relations, in particular, to psychology. This question coincides in essence, in the main if not entirely, with the cardinal question of epistemology, that of the objectivity of knowledge. The outcome of our investigation of this point will be the delineation of a new, purely theoretical science, the all-important foundation for any technology of scientific knowledge, and itself having the character of an *a priori,* purely demonstrative science. This is the science intended by Kant and the other proponents of a 'formal' or 'pure' logic, but not rightly conceived and defined by them as regards its content and scope. The final outcome of these discussions is a clearly circumscribed idea of the disputed discipline's essential content, through which a clear position in regard to the + +previous mentioned controversies will have been gained. + +**Logic as a normative and, in** + +**particular, as a practical discipline** + +**§4 The theoretical incompleteness of the** + +**separate sciences** + +It is a common experience that the excellence of an artist's mastery over his material, and the decisive certainty with which he judges and assesses works in his art, is only quite exceptionally based on a theoretical knowledge of the rules which prescribe direction and order to his practice, and determine the standards of value on which the perfection or imperfection of the complete work must be assessed. Normally the practising artist is not the man who can who can inform us rightly regarding the principles of his art. He follows principles neither in his creation nor his evaluation. In his creation he follows the inner activity of his harmoniously trained powers, in his judgement his finely formed artistic taste and feeling. This is not merely so in the case of fine art, of which one may first have thought, but in that of the arts generally, in the widest sense of the word. It therefore holds for the activities of scientific creation and the theoretical evaluation of their results, for the scientific demonstrations of facts, laws, theories. Even the mathematician, the physicist and the astronomer need not understand the ultimate grounds of their activities in order to carry through even the most important scientific performances. Although their results have a power of rational persuasion for themselves and others, yet they cannot claim to have demonstrated all the last premisses in their syllogisms, nor to have explored the principles on which the success of their methods reposes. The incomplete state of all sciences depends on this fact. We do not here mean the mere incompleteness with which the truths in a field have been charted, but the lack of inner clarity and rationality, which is a need independently of the expansion of the science. Even mathematics, the most advanced of all sciences, can in this respect claim no special position. Though often still treated as the ideal of all science as such, how little it really is such is shown by the old, yet never finally composed disputes as to the foundations of geometry, or as to the justification of the method of imaginaries. The same thinkers who sustain marvellous mathematical methods with such incomparable mastery, and + +who add new methods to them, often show themselves incapable of accounting satisfactorily for their logical validity and for the limits of their right use. Though the sciences have grown great despite these defects, and have helped us to a formerly undreamt of mastery over nature, they cannot satisfy us theoretically. They are, as theories, not crystal-clear: the function of all their concepts and propositions is not fully intelligible, not all of their presuppositions have been exactly analysed, they are not in their entirety + +raised above all theoretical doubt. + +**§5 The theoretical completion of the separate sciences by metaphysics and theory of science** + +To reach this theoretical goal we first need, as is fairly generally admitted, a + +type of investigation which belongs to the metaphysical realm. + +Its task is to pin down and to test the untested, for the most part not even noticed, yet very significant metaphysical presuppositions that underlie at least all those sciences that are concerned with actual reality. Such presuppositions are, e.g., that an external world exists, that it is spread out in space and time, its space being, as regards its mathematical character, threedimensional and Euclidean, and its time a one-dimensional rectilinear manifold; that all process is subject to the causal principle etc. These presuppositions, all to be found in the framework of Aristotle's First Philosophy, are at present ranked under the quite unsuitable rubric of 'epistemology'. + +Such a metaphysical foundation is not, however, sufficient to provide the desired theoretical completion of the separate sciences. It concerns, moreover, only such sciences as have to do with actual reality, which does not include all sciences, certainly not the purely mathematical sciences whose objects are numbers, manifolds etc., things thought of as mere bearers of ideal properties independent of real being or non-being. The case is different in regard to another class of investigations whose theoretical completion is plainly an indispensable postulate in our quest for knowledge, investigations which concern all sciences equally, since they concern, in brief, whatever makes sciences into sciences. This names the field of a new, and, as we shall see, complex discipline, whose peculiarity it is to be the science of science, and which could therefore be + +most pointedly called theory of science *(Wissenschaftslehre).* + +**§6 The possibility and justification of logic as** + +**theory of science** + +The possibility and justification of such a discipline - a normative and practical discipline relating to the Idea of science - can be shown by the + +following considerations. + +Science is concerned, as its name indicates, with knowing, but this does not mean that it itself consists of a sum or tissue of acts of knowing. Science + +exists objectively only in its literature, only in written work has it a rich relational being limited to men and their intellectual activities: in this form it is propagated down the millennia, and survives individuals, generations and nations. It therefore represents a set of external arrangements, which, just as they arose out of the knowledge-acts of many individuals, can again pass over into just such acts of countless individuals, in a readily understandable manner, whose exact description would require much circumlocution. For us it is here sufficient that science provides, or should provide, certain more immediate preconditions of acts of knowing, real possibilities of knowing, whose realization by the 'normal' or 'suitably endowed' individual in wellknown, 'normal' circumstances can be looked on as an attainable goal of his + +endeavour. In this sense, therefore, science aims at knowledge. + +In knowledge, however, we possess truth. In actual knowledge, to which we see ourselves ultimately referred back, we possess truth as the object of a correct judgement. But this alone is not enough, since not every correct judgement, every affirmation or rejection of a state of affairs that accords with truth, represents *knowledge* of the being or non-being of this state of affairs. Rather we may say that, if it is to be called 'knowledge' in the narrowest, strictest sense, it requires to be evident, to have the luminous certainty that what we have acknowledged is, that what we have rejected is *not,* a certainty distinguished in familiar fashion from blind belief, from vague opining, however firm and decided, if we are not to be shattered on the rocks of extreme scepticism. Common talk does not, however, stay put in this strict concept. We also speak, e.g. of an act of knowing where the judgement we pass is associated with a clear memory that we previously passed a judgement of precisely the same content accompanied with inner evidence. This happens particularly where our memory also concerns a demonstrative thought-process out of which this inner evidence grew, and that we are sure we can reproduce *with* such evidence. ('I know that the Pythagorean theorem is true - I can prove it': instead of the second half, one + +can of course also say 'but I have forgotten the proof'.) + +We therefore conceive 'knowledge' in a wider, but not wholly loose sense: we separate it off from baseless opinion, by pointing to some 'mark' of the presumed state of affairs or for the correctness of the judgement passed by us. The most perfect 'mark' of correctness is inward evidence, it counts as an immediate intimation of truth itself. In the vast majority of cases we lack such absolute knowledge of truth, in whose place we make use - one need *only* think how memory functions in the above examples - of the inner evidence for a higher or lower degree of probability for our state of affairs, with which, if probability-levels become high enough, a firm judgement is usually associated. The inward evidence of the probability of a state of affairs *A* will not serve to ground the inward evidence of its truth, but it will serve to ground those comparative, inwardly evident value-assessments, through which, in accordance with positive or negative probability-values, + +we can distinguish the reasonable from the unreasonable, the better-founded from the worse-founded assumptions, opinions and surmises. Ultimately, therefore, all genuine, and, in particular, all scientific knowledge, rests on inner evidence: as far as such evidence extends, the concept of knowledge + +extends also. + +There is none the less a remaining duality in the concept of knowing or knowledge. Knowledge in the narrowest sense of the word is the being inwardly evident that a certain state of affairs is or is not, e.g. that S is *P* or that it is not *P.* If it is evident that a certain state of affairs is probable to this or that degree, then we have knowledge in the strictest sense of such a probability, but, in regard to the being of the state of affairs itself, and not of its probability, we only have knowledge in a wider, modified sense. It is in this latter sense, with an eye to degrees of probability, that one speaks of a greater or lesser degree of knowledge. Knowledge in the pregnant sense - its being quite evident that S is *P* - then counts as the absolutely fixed, ideal limit which the graded probabilities for the being-P of S approach + +asymptotically. + +But the concept and task of science covers more than mere knowledge. If we live through and recognize the presence of inner percepts, singly or in groups, we have knowledge, but are far removed from science: the same applies generally to all incoherent groups of acts of knowing. A group of isolated bits of chemical knowledge would certainly not justify talk of a science of chemistry. More is plainly required, i.e. *systematic coherence in the theoretical sense,* which means finding grounds for one's knowing, and + +suitably combining and arranging the sequence of such groundings. + +The essence of science therefore involves unity of the foundational connections: not only isolated pieces of knowledge, but their grounded validations themselves, and together with these, the higher interweavings of such validations that we call theories, must achieve systematic unity. The aim is not merely to arrive at knowledge, but knowledge in such degree and form as would correspond to our highest theoretical aims as perfectly as + +possible. + +That we look upon, and practically strive after, systematic form as the purest embodiment of the Idea of science, does not evince some merely aesthetic trait in our nature. Science neither wishes nor dares to become a field for architectonic play. The system peculiar to science, i.e. to true and correct science, is not our own invention, but is present in things, where we simply find or discover it. Science seeks to be a means towards the greatest possible conquest of the realm of truth by our knowledge. The realm of truth is, however, no disordered chaos, but is dominated and unified by law. The investigation and setting forth of truths must, therefore, likewise be systematic, it must reflect the systematic connections of those truths, and must use the latter as a ladder to progress and penetrate from the knowledge given to, or already gained by us to ever higher regions of the realm of truth. + +Science can never do without this helpful ladder. The inward evidence on which all knowledge ultimately reposes, is no gift of nature, appearing together with the mere idea of states of affairs without any methodically artful set-up. People would otherwise never have thought of building up sciences. The longueurs of method would lose their sense if to intend meant to succeed. Why should one search into relations of entailment or construct proofs, if one shared in truth through immediate intimation? The inward evidence, moreover, which stamps one presented state of affairs as having real being, or the absurdity which stamps it as having no being at all (and the same, likewise, in regard to probability and improbability) is, in fact, only immediately felt in the case of a relatively quite limited group of primitive facts. Countless true propositions are only grasped by us as true when we methodically validate them. In their case, a mere regard to our propositional thought, will not induce inward evidence, even if it does induce judgemental decision. Both are, however, induced, certain circumstances being normal, where we set forth from certain known truths, and tread a certain path in thought to our intended proposition. There may be many ways of establishing the same proposition, starting from these or those bits of knowledge. It is, however, a characteristic and essential circumstance that there are infinitely many truths which could never be transformed into knowledge without + +such methodical procedures. + +That this is the case, that we need grounded validations in order to pass beyond what, in knowledge, is immediately and therefore trivially evident, not only makes the sciences possible and necessary, but with these also a *theory of science,* a *logic.* All sciences proceed methodically in the pursuit of truth, employ more or less artificial aids in order to bring to knowledge truths or probabilities that would otherwise remain hidden, and in order to use the obvious or the already established as a lever for achieving what is remote and only mediately attainable. The comparative treatment of these methodical aids, in which the insights and experiences of countless generations of thinkers are stored up, should provide the means for setting up general norms for such procedures and likewise rules for their inventive + +construction in various classes of cases. + +**§7 Continuation. The three most noteworthy** + +**peculiarities of grounded validations** + +Let us penetrate somewhat more deeply into this matter, and reflect on the most noteworthy peculiarities of the remarkable thought-sequences called + +by us 'validations'. + +They have in the *first* place the character of a fixed structure in relation to their content. We cannot, in order to reach a given piece of knowledge, that, e.g. of the Pythagorean theorem, choose our starting point at random among the pieces of knowledge immediately given to us, nor can we add or subtract + +any thought-items at will, if the evidence of the proposition to be validated is to burst forth genuinely, the validation to be a genuine validation. + +A *second* point is at once evident. It might seem thinkable *a priori,* i.e. before we glance at, and compare instances of validation streaming in on us abundantly from every quarter that each validation should be unique both in content and in form. A whim of nature - this might at first seem a tenable thought - might have framed our psychic constitution so wantonly that our familiar talk of a multiplicity of modes of validating matters might have lacked all sense. The only thing that could be pronounced common to any validations that we might compare would be that a proposition S, itself lacking inner evidence, achieves an evident character if it appears in combination with certain known truths *P], P2*•.• truths whose relevance to it is a non-recurrent matter not subject to a rational rule. This is not how the matter stands, however. A blind caprice has not bundled any set of truths *P], P2 •* •• S together and then so instituted the human mind that it must necessarily (or in 'normal' circumstances) connect the knowledge of S with the knowledge of *P], P2 •* •• In no single case is this so. Connections of validation are not governed by caprice or chance, but by reason and order, i.e. by regulative laws. We hardly need an example to illuminate the point. If in a mathematical problem relating to a certain triangle *ABC,* we apply the proposition *An equilateral triangle is equiangular,* we carry out a validation which, made explicit, runs: Every equilateral triangle is equiangular; the triangle *ABC* is equilateral, and is therefore equiangular. If we set beside this the arithmetical argument: Every decimal number with an even last digit is an even number, 364 is a decimal number with an even last digit, and is therefore an even number, we note at once that the 'establishments' have something in common, an inner constitution of like type, which is intelligibly expressed in the syllogistic form 'Every *A* is *B, Xis A,* so Xis *B'.* Not only have these two arguments this same form, but countless others have it as well. Our syllogistic form further represents a class-concept, under which falls an infinite multitude of sentence-combinations all with the constitution that this form pointedly expresses. There is also an *a priori* law, making any putative validation that follows this form, also actually a correct one, pro- + +vided, that is, that it proceeds from correct premisses. + +This holds in general. Wherever we ascend by an establishing argument from given pieces of knowledge to new ones, a certain form resides in our modes of validation, which is common to countless other validating arguments, and which stands in a certain relation to a general law that allows us to justify all these single validations at one 'go'. No validating procedure - such is the quite remarkable fact - stands in isolation. None ties bits of knowledge up with other bits of knowledge, unless in their external mode of association, or in this together with the inner structure of the separate propositions, a definite type is brought out, a type which, if conceptually generalized, at once leads to a general law applying to an infinity of possible cases of validation. + +A *third* remarkable feature deserves emphasis. *A priori,* i.e. before one compares validating arguments in *different* sciences, one might think it a possible thought that forms of validation should be bound up with territories of knowledge. Though the appropriate validations do not vary with types of object, it might still be the case that they divide sharply along certain highly general class-lines, the lines perhaps that demarcate varying scientific fields. Is it not the case that there is no pattern of validation common to two sciences, to mathematics, e.g. and chemistry? But this too is plainly not so, as our above example shows. There is no science where laws are not applicable to individual cases, where we do not therefore have syllogisms of the form illustrated above. The same holds of many other types of syllogism. We may in fact say of all other types of syllogism that they may be so generalized, so purely conceived, as to be free of all essential + +relation to some conceivably limited field of knowledge. + +**§8 The relation of these peculiarities to the possibility of science and the theory of science** + +These peculiarities of our validations, whose remarkable character escapes us since we are all too little disposed to turn everyday matters into problems, are visibly related to the *possibility of a science* and, further, of *a theory of* + +*science.* + +That there are validating arguments is not in this connection enough. If they were formless and lawless, if it were not a fundamental truth that all validating arguments have certain indwelling 'forms', not peculiar to the simple or indefinitely complex arguments set before us here and now, but typical of a whole class of arguments, and that the correctness of this whole class of arguments is guaranteed just by their form - if the contrary of all this were true, there would be no science. Talk about a method, about a systematically regulated progress from one bit of knowledge to another, would be senseless, and all progress would be fortuitous. The propositions *P], Pz* ... which were fitted to confer evident truth on the proposition S, might fortuitously come up together in our consciousness, and this evident truth would then become duly luminous. It would no longer be possible to learn anything at all from a validating argument for future use on new validating arguments with novel material. No validating argument could serve as a paradigm for any other, none could embody a type, and no set of judgements, conceived as a system of premisses, could have anything typical about it which could (without conceptual high-lighting or recourse to explicit 'inference-forms') crop up, on the occasion of a new case with quite novel materials, and help us on to a fresh gain in knowledge. It would be senseless to look for a proof of a given proposition. How indeed could one attempt it? Should one tryout all possible sets of propositions to see if they could be employed as premisses for the proposition in question? + +The cleverest man would here have no advantage over the stupidest, and it may be questioned whether he would have any essential advantage over him at all. A rich imagination, a comprehensive memory, a capacity for close attention etc., are fine things, but they have intellectual meaning only in the case of a *thinking* being, whose validation and invention falls under laws + +and forms. + +It is generally true, in fact, that in all mental compounding, combinatory forms as well as mere elements have their associative or reproductive effect. The form, therefore, of our theoretical thoughts and thought-combinations may well prove useful. As, e.g., the form of certain premisses makes the emergence of appropriate conclusions much easier, since former inferences of like form have succeeded, so the form of some proposition to be proved may recall certain validating forms that have formerly yielded conclusions of the same form. If this is no clear, genuine case of memory, it is none the less analogous to the latter, and to some extent latent memory, an 'unconscious excitation' (in the sense of B. Erdmann). It is in any case something that greatly promotes proofs (and this not only in fields like mathematics that are dominated by arguments in form). The trained thinker finds proofs more readily than the untrained one. Why is this so? Because types of proof have been ever more deeply engraved on his mind through a varied experience, and so must operate more readily for him and determine the direction of his thought. To a certain extent any sort of scientific thought gives us practice in scientific thinking, but it is true also that to a peculiar degree and extent mathematical thought predisposes to what is mathematical, physical thought to what is physical etc. The former rests on the existence of typical forms common to all sciences, the latter on the existence of other forms, perhaps to be characterized as peculiarly structured complexes of the former - which are peculiarly related to what is peculiar to the separate sciences. The unique features of scientific flair, of anticipatory intuition and divination, hang together with this. We speak of a philological, of a mathematical flair and eye etc., and who possesses them? The trained philologist, mathematician etc., with his many years of practice. **In** the general nature of the objects of each realm certain forms of factual connection are rooted; these in their turn determine typical peculiarities of forms of validation that predominate in this realm. Herein we have the foundation for the pioneering hunches of science. All testing, invention and discovery therefore rests on + +regularities of form. + +If all this shows that it is *regular form* that makes possible the existence of sciences, so, on the other hand, it is the wide degree of *independence of form from afield of knowledge* that makes possible a *theory of science.* Were there no such independence, there would only be coordinated logics separately corresponding to the separate sciences, but no general logic. **In** fact both are needed: investigations into the theory of science concerning all sciences equally, and, supplementary to these, particular investigations concerning + +the theory and method of the separate sciences which endeavour to search + +into what is peculiar to them. + +To stress the peculiarities revealed by the comparative treatment of validating arguments, is not therefore without use in casting light on our discipline + +itself, on logic in the sense of a theory of science. + +**§9 Methodical modes of procedure in the sciences are in part validatory, in part auxiliary devices** + +**towards validations** + +Certain points must still be added, first in regard to the restriction of our treatment to validations, which plainly do not exhaust the notion of methodical procedure. Validations have, however, a central significance that will + +justify our provisional restriction. + +One can in fact say that all scientific methods which do not themselves have the character of actual validating arguments (whether simple or of any degree of complexity) are, on the one hand, *abbreviations* and *substitutes* for such validating arguments, used to economize thought, since, having themselves once and for all received sense and value from such validation, their application now in practice does the work of validation without its charge of cogitative insight. They may, on the other hand, represent more or less complex *auxiliary devices,* which serve to prepare for, to facilitate, to ensure or to render possible future processes of validation without themselves being able to claim a significance which is of like value with, or + +independent of, these basic scientific processes. + +To take up the latter group of methods, it is, e.g. an important prerequisite for securing one's validations that one's thoughts are adequately expressed by readily distinguishable, unambiguous signs. Language offers the investigator a widely applicable sign-system to express his thoughts, but, though no one can do without it, it represents a most imperfect aid towards strict research. The pernicious influences of ambiguities on the validity of syllogistic inferences are familiar. The careful thinker will not therefore use language without artificial precautions; to the extent that the terms he uses are not unambiguous and lack sharp meaning, he must define them. The definition of names we therefore see as a methodical auxiliary procedure towards ensuring validations, the latter being one's primary, truly theoreti- + +cal procedures. + +The same is true of *nomenclature.* Brief, characteristic symbols for the more important, recurrent concepts are - to mention only one point - indispensable wherever the expression of such concepts, by means of one's original stock of defined expressions would be unduly circumstantial. Involved expressions with such inbuilt Chinese-box complexity impede validatory + +operations or render them unperformable. + +Examples of the first group of methods are provided by the extraordinarily fruitful *algorithmic methods,* whose peculiar function is to save us as much genuine deductive mental work as possible by artificially arranged mechanical operations on sensible signs. Whatever marvels these methods may achieve, their sense and justification depends on validatory thought. Here also belong what are literally mechanical methods - one may think of the apparatus for mechanical integration, calculating machines etc. - as well as the methodical procedures for establishing objectively valid empirical judgements, such as the various methods of determining the position of a star, electrical resistance, inert mass, refractive index, the gravitational constant etc. Each such method represents a set of provisions whose choice and arrangement is fixed by a validatory context, which shows, in general, that such a procedure, even when blindly performed, must necessarily lead to an objec- + +tively valid individual judgement. + +But enough of examples. It is plain that each actual advance in science is performed in an act of validation: to this all those methodical precautions and devices relate, which logic considers in addition to processes of validation. To this relation their typical character is likewise due, which is essentially involved in the Idea of method. On account of this typical character they + +too have a place in the discussions of the previous paragraph. + +§ I **0 The ideas of theory and science as problems of** + +**the theory of science** + +Something more must be added. The theory of science, as here shown up, is not merely concerned to investigate the forms and laws of isolated validations, and the auxiliary devices which go with these. Isolated validations also occur beyond the boundaries of science: clearly, therefore, isolated validations - and loosely piled heaps of such validations - do not make up science. Science requires, as said above, a certain unity of validatory interconnection, a certain unity in the stepwise ascent of its validatory arguments, and this form of unity has itself a lofty teleological meaning in the attainment of the highest goal of knowledge for which all science strives: to advance as far as possible in the research into truth, i.e. not in the research into separate + +truths, but into the realm of truth or its natural provinces. + +The task of the theory of science will therefore also be to deal with the sciences as *systematic unities of this or that sort* in other words, with the formal features that stamp them as sciences, with the features that determine their mutual boundaries and their inner articulation into fields, into relatively closed theories, with the features which fix their essentially different species + +or forms etc. + +This systematic tissue of validatory arguments can in fact be subordinated to the concept of method, so that science's task is not merely to deal with the methods of knowledge in the sciences, but also with such methods as are + +themselves styled sciences. Its task is not merely to separate off valid from invalid demonstrations, but also valid from invalid theories and sciences. The task thus assigned it is plainly not independent of the one previously mentioned, but to a considerable extent presupposes a prior carrying out of the former. Research into the sciences as systematic unities is unthinkable without prior research into their validatory procedures. Both at least enter + +into the notion of a science of science as such. + +§ I **I Logic or theory of science as normative discipline** + +**and as technology** + +From our discussions up to this point logic - in the sense of the theory of science here in question - emerges as a *normative discipline.* Sciences are creations of the spirit which are directed to a certain end, and which are for that reason to be judged in accordance with that end. The same holds of theories, validations and in short of everything that we call a 'method'. Whether a science is truly a science, or a method a method, depends on whether it accords with the aims that it strives for. Logic seeks to search into what pertains to genuine, valid science as such, what constitutes the Idea of Science, so as to be able to use the latter to measure the empirically given sciences as to their agreement with their Idea, the degree to which they approach it, and where they offend against it. In this logic shows itself to be a normative science, and separates itself off from the comparative mode of treatment which tries to conceive of the sciences, according to their *typical* communities and peculiarities, as concrete cultural products of their era, and to explain them through the relationships which obtain in their time. For it is of the essence of a normative science that it establishes general propositions in which, with an eye to a normative standard, an Idea or highest goal, certain features are mentioned whose possession guarantees conformity to that standard, or sets forth an indispensable condition of the latter. A normative science also establishes cognate propositions in which the case of non-conformity is considered or the absence of such states of affairs is pronounced. Not as if one had to state general marks in order to say what an object should be to conform to its basic norm: a normative discipline never sets forth universal criteria, any more than a therapy states universal symptoms. Special criteria are what the theory of science particularly gives us, and what it alone can give us. If it maintains that, having regard to the supreme aim of the sciences and the human mind's actual constitution, and whatever else may be invoked, such and such methods Mj, *M2* ... arise, it states general propositions of the form: 'Every group of mental activities of the sorts *AB* ... which realize the combinatory form *M j* (or *M2* ... ) yield a case of correct method', or, what amounts to the same 'Every (soi-disant) methodical procedure of the form *M j*(or *M 2 •* •• ) is a correct one.' If one could really formulate all intrinsically possible valid + +propositions of this and like sort, our normative science would certainly possess a measuring rod for every pretended method, but then also only in + +the form of special criteria. + +Where the basic norm is an end or can become an end, the normative discipline by a ready extension of its task gives rise to a technology. This occurs in this case too. If the theory of science sets itself the further task of investigating such conditions as are subject to our power, on which the realization of valid methods depends, and if it draws up rules for our procedure in the methodical tracking down of truth, in the valid demarcation and construction of the sciences, in the discovery and use, in particular, of the many methods that advance such sciences, and in the avoidance of errors in all of these concerns, then it has become a *technology of science.* This last plainly includes the whole normative theory of science, and it is therefore wholly appropriate, in view of the unquestionable value of such a technology, that the concept of logic should be correspondingly widened, + +and should be defined in its sense. + +**§ 12 Relevant definitions of logic** + +The definition of logic as a technology was much favoured by tradition, but closer determinations of it left much to be desired. Definitions such as 'technology of judgement, of reasoning, of knowing, of thinking' *(I'art de penser)* are misleading, and in any case too narrow. Ifwe restrict the vague meaning of the word 'thinking' in the last-mentioned definition (in use to this day) to the concept of correct judgement, our definition reads: 'the technology of correct judgement'. But that this definition is too narrow is plain from the fact that the aim of scientific knowledge does not follow from it. If one says that 'the aim of thinking is first perfectly fulfilled in science', this is without doubt right, but it concedes that not thought or knowledge is really the end of the technology in question, but that towards which thought itself is a + +means. + +Other definitions are open to similar objections. They are open to the objection recently revived by Bergmann that the technology of an activity, e.g. painting, singing, riding, would be expected above all 'to show what one must do to perform the relevant activity correctly, e.g. how one must hold and wield the brush in painting, how one must use the chest, throat and mouth in singing, how one must pull and relax the reins in riding and press with one's legs'. This would admit into the field of logic doctrines wholly + +alien to it. 1 + +Schleiermacher's definition of logic as the technology of scientific knowledge certainly comes closer to the truth. For obviously in a discipline so defined one would have to consider only what is peculiar to scientific knowledge, and to probe its possible demands: the further preconditions which in general favour the emergence of knowledge would be left to pedagogy, + +hygiene etc. But Schleiermacher's definition does not plainly say that this technology should also set up rules for the demarcation and construction of the sciences, whereas this aim, on the other hand, includes the aim of scientific knowledge. Excellent thoughts towards the circumscription of our discipline are to be found in Bolzano's *Wissenschaftslehre,* but rather in his preliminary critical searchings than in the definition he himself espouses. This last sounds oddly enough: the theory of science (or logic) is 'the science which shows us how to present the sciences in convenient textbooks'.2 + +**Theoretical disciplines as the** + +**foundation of normative disciplines** + +**§ 13 The controversy regarding the practical** + +**character of logic** + +Our last discussions have given so obvious a justification to the view of logic as a technology, that it might seem remarkable that there should ever have been controversy on this point. A practically oriented logic is an indispensable postulate of all the sciences, and this corresponds to the historical fact that logic arose out of practical motives connected with the business of science. This we know happened in those thought-stirring times when the young, budding science of the Greeks was in danger of succumbing to the attacks of sophists and subjectivists, when all its future success depended on finding objective criteria of truth, which might destroy the cheating illusions + +of the sophistical dialectic. + +In modern times, mainly under the influence of Kant, there have been repeated denials that logic is a technology, though such a characterization has, on the other hand, been held to have some value: this dispute cannot have turned on the mere question whether it is possible to give logic practical aims, and so to conceive of it as a practical discipline. Kant himself spoke of an applied logic which should have as its task the regulation of the use of the understanding 'under the contingent conditions of the subject, which might hinder or assist it' *(Critique of Pure Reason:* Intro. to Trans. Logic, I, last paragraph *A54/B78-9),* and from which we might learn 'what promotes the correct use of the understanding, what assists it and what cures it from logical mistakes and errors' (Kant's *Logik,* Introduction II, Hartenstein's edition 1867, VIII, p. 18). Though he is not willing to let it rank, with *pure* logic, as an authentic science, though he even thinks that 'it should not properly be called logic' *(Critique of Pure Reason,* Werke, ed. Hartenstein, III, p. 83), everyone is none the less at liberty to extend the aim of logic so as to include applied, practical logic.' It may in any case be disputed, as has in fact frequently happened, whether great gain can be hoped for from logic as a practical theory of science, whether, e.g. one could really hope for such great revolutions and advances from an extension of the old logic (which could only serve to test given knowledge) into an *ars* + +*inventiva,* a 'logic of discovery', as Leibniz is known to have believed etc. This dispute, however, concerns no point important in principle, and it is settled by the clear maxim that even the moderate probability of a future advance in the sciences justifies us in working on a normative discipline pledged to this end, without regard to the fact that the rules we deduce + +represent a valuable enrichment of knowledge. + +The genuinely disputed question of important principle, to which neither side has given precision, lies in quite a different direction: whether the definition of logic as a technology really touches its *essential character.* We ask, in other words, if it is only a practical standpoint that establishes the right of logic to count as a peculiar scientific discipline, while, from a theoretical standpoint, all the findings accumulated by logic consist, on the one hand, in purely theoretical propositions having their original home in otherwise known theoretical sciences, and mainly in psychology, and, on the other + +hand in rules based on these theoretical propositions. + +The essence of Kant's conception of logic does not, in fact, lie in the fact that he disputes the practical character of logic, but that he believes in the possibility and the epistemologically basic character of a certain delimitation or restriction of logic, which would make of it a wholly independent science, one which, in comparison with otherwise known sciences, is wholly new and entirely theoretical, and which, like mathematics, stands outside of any thought of possible application, in being an *a priori,* purely demonstrative + +discipline. + +The restriction of logic to its theoretic knowledge-content leads, on the prevailing form of the doctrine opposed to Kant's, to psychological and perhaps also grammatical and other propositions, i.e. to small excerpts from otherwise delimited, and, let us add, empirical sciences. Whereas, on Kant's view, we rather dig down to an internally closed, independent and, let us + +add, *a priori* field of theoretical knowledge, to pure logic. + +It is apparent that other weighty oppositions are at work in these doctrines; whether logic should count as an *a priori* or an empirical science, as an independent or dependent science, as a demonstrative or non-demonstrative science. If we drop these questions as remote from our immediate interests, only the above mentioned point of dispute remains: on one side we abstract the assertion that under every logic thought of as a technology lies a *peculiar* theoretical discipline, a pure logic, whereas, on the other view, all theoretical doctrines admitted into the logical technology are held to be classifiable in + +otherwise known theoretical sciences. + +The second point of view was stoutly defended by Beneke,2 and J. Stuart Mill stated it clearly in his *Logic* which has also been influential in this respect. 3 Sigwart's *Logik,* the leading contribution to recent logical work in Germany, also stands on similar ground. Clearly and decisively it is there said: 'The highest task of logic, and the one which constitutes its real essence, is + +On the other side we have, in addition to Kant, principally Herbart, and + +a large number of their disciples. + +How easily the most extreme empiricism accords in *this* respect with Kant's conception is seen from Bain's *Logic* which, constructed as a technology, expressly acknowledges, and claims to include, a logic which is a peculiar, abstract, theoretical discipline - a science of the same sort as mathematics. This theoretical discipline is held by Bain to rest on psychology; it is not thought of, as by Kant, to precede all other sciences as an absolutely independent science. But it remains a science on its *own* account: it is not, as Mill would have it, a mere assemblage of psychological chapters, offered + +with the intention to regulate knowledge practically.s + +In the many treatments which logic has received this century, the point of difference here in question has hardly ever been clearly emphasized and carefully considered. Since the practical treatment of logic accords with either standpoint, and is generally admitted to be useful on either, the whole dispute as to the essentially practical or theoretical character of logic has seemed meaningless to many. They have never in fact been clear as to how + +the standpoints differ. + +We are not required by our purposes to go critically into the disputes of older logicians as to whether logic is an art or a science or both, and whether, in the second case, it is a practical or speculative science or both. On these questions, and on the value of these questions, Sir William Hamilton has + +pronounced as follows: + +The controversy ... is perhaps one of the most futile in the history of speculation. In so far as Logic is concerned, the decision of the question is not of the very smallest import. It was not in consequence of any diversity of opinion in regard to the scope and nature of this doctrine, that philosophers disputed by what name it should be called. The controversy was, in fact, only about what was properly an art, and what was properly a science; and as men attached one meaning or another to these terms, so did they affirm Logic to be an art, or a science, or both, or neither. + +*(Lectures on Logic,* ed. III, vol. I (1884), pp. 9-10) + +One must note, however, that Hamilton himself did not dig very deeply into the content and value of the distinctions and controversies in question. If there were appropriate agreement as to the way to treat logic, and the content of the doctrines to be attributed to it, the question if and how the concepts *art* and *science* entered into its definition, would be of minor importance, though by no means a mere question of labelling. But the dispute over the definition (as we have already maintained) is really a dispute regarding the science itself, and one not regarding the completed science but the provisionally pretended one, the one still in progress, whose methods, doctrines, in short everything, are still in doubt. Even in Hamilton's day, + +and long before, men differed considerably as to the essential content, the scope and the manner of treatment of logic. One need only compare the works of Hamilton, Bolzano, Mill and Beneke. And how the differences have grown since then. Put together Erdmann and Drobisch, Wundt and Bermann, Schuppe and Brentano, Sigwart and Uberweg, and ask whether one then has a single science, or only a single name. One might settle for the latter, if there were not occasionally some more comprehensive groups of common themes, though in respect of the doctrine, and even the problems, no two logicians reach a tolerable understanding among themselves. If we associate with this the point stressed in the Introduction, that definitions of logic merely express beliefs as to its essential tasks and methodical character, and that errors and prejudices on these points can help to mislead so retarded a science on to wrong paths of research. We shall certainly not agree with Hamilton in saying that 'the decision of the question is not of the very + +smallest import'. + +Confusion has not a little been promoted by the fact that even distinguished protagonists of the autonomy of a *pure* logic, such as Drobisch and Bergmann, have put the normative character of the discipline among the features essential to its notion. Their opponents saw in this a patent inconsequence, even a contradiction. Has not the concept of normativity got an inherent relation to a guiding aim, and to activities devoted to it? Does not + +a normative science mean exactly the same as a technology? + +The manner in which Drobisch introduces and conceives his determinations merely confirms these impressions. In his ever valuable *Logic* we read: ·'There are two angles from which thought can be made the object of a scientific investigation: as an activity of mind whose conditions and laws may be looked into, and as a tool for acquiring mediate knowledge, permitting both of a correct and a faulty use, and leading in the one case to true, in the other to false results. There are therefore both *natural* and *normal laws* for thinking, and the latter are *prescriptions* (norms) to which one must *direct* oneself to reach these results. The investigation of the natural laws of thinking is a task for psychology, whereas the establishment of its normal rules is the task of logic' *(Neue Darstellung der Logik,* §2, p. 3). And to this the further more than sufficient explanation is added: 'Normal rules always regulate an + +activity in conformity with a certain end.' + +On the other hand one might say: here nothing is said to which Beneke or Mill could not subscribe, and which they could not adapt to their own advantage. If we grant the identity of the concepts 'normative discipline' and 'technology', it is obvious that, as in the case of technologies in general, it is not the mutual connectedness of matters but our guiding aim which serves to bind and unite logical truths into a discipline. It is then plainly wrong to set logic bounds as narrow as those of the traditional Aristotelian logic, since 'pure' logic certainly goes beyond these. It is absurd to set logic a goal, and then to exclude from it classes of norms and normative investigations + +that pertain to this goal. The exponents of pure logic still live under the spell of tradition; the marvellous magic distilled by the hollow formularies hawked about by the school logic down the ages, still works powerfully in them. Such is the list of obvious objections likely to turn modern interest from a closer discussion of the objective reasons which have weighed with great, independent thinkers in favour of an autonomous science of pure logic, and which still call for serious probing. The worthy Drobisch may have gone wrong in his statement, but this does not prove that his position, or that of his master Herbart, or that ultimately of his prime inspirer Kant,6 was in essence misguided. It does not even rule out the possibility that a valuable thought, that has not achieved conceptually clear expression, may lie hidden under his imperfect statement. Let us dwell on the coordination of logic with pure mathematics, of which the champions of pure logic are so fond. The mathematical disciplines also yield a basis for technologies. To arithmetic corresponds the practical art of calculation, to geometry the art of landsurveying. Technologies are similarly connected, though somewhat differently, with the abstract theoretical natural sciences, physical technologies with physics, chemical technologies with chemistry. This readily suggests the view that it is the true sense of our supposed pure logic to be an abstract theoretical discipline providing a basis for a technology just as the previously mentioned disciplines do, its technology being logic in the ordinary, practical sense. And just as technologies sometimes have one main, basic, theoretical discipline from which their norms flow, sometimes several such basic disciplines, so logic, taken as a technology, might depend on a plurality of such disciplines, and have pure logic merely as one, though perhaps the most important one, of its basic disciplines. Possibly it could be further shown that logical laws and forms, in the pregnant sense of these words, belong to a theoretically closed round of abstract truth, that cannot in any way be fitted into previously delimited theoretical disciplines and so must themselves be regarded as the pure logic in question. We should then be led to suppose that defects in the conceptual definition of this discipline, and the inability to present it in its purity, and clearly state its relation to logic as a technology, have favoured its confusion with this technology, and have made possible the dispute as to whether logic should be defined as being essentially a theoretical or a practical discipline. While the one party trained its sights on purely theoretical propositions that were logical in the pregnant sense, the other party stuck to the vulnerable *definitions* of the pretended theoretical science, and the manner in which it was actually carried out. To object that we are attempting to restore the Aristotelian-scholastic logic, on whose worthlessness history has pronounced judgement, will not perturb us. Possibly it may yet appear that the discipline in question is by no means so narrow in scope, and so poor in profound problems, as it is here reproached with being. Possibly traditional logic was merely a highly imperfect, distorted realization of the Idea of Pure Logic, but none the less sound + +and respectable as a first onslaught and initiative. One may also ask whether our scorn for the traditional logic is not perhaps an unjustifiable after-effect of renaissance attitudes, whose motives no longer touch us. It is understandable that the historically justified, but in reality often foolish battle, against scholastic science, should be above all directed against its logic, its characteristic doctrine of method. But that formal logic should, in the hands of scholasticism, particularly decadent scholasticism, have taken on the character of a false methodology, perhaps only shows the lack of a correct philosophical understanding of logical theory, as so far developed. The practical use of this logic therefore entered mistaken pathways, and methodological achievements were attributed to it for which it is in essence unqualified. **In** the same way, number-mysticism proves nothing against arithmetic. The logical polemics of the renaissance are well known to have been void of substance or effect: they are the utterances of passion, not of insight. Why should we still yield ourselves to the guidance of such scornful utterances? A theoretically creative mind like Leibniz, in whom the enthusiastic reformatory zeal of the renaissance went together with a sober, scientific, modern spirit, would hear nothing of a baiting or harrying of scholasticism. With warm words he took the despised Aristotelian logic to his bosom, however much he thought it needed extension and improvement. We can in any case quietly leave aside the reproach that pure logic represents a revival of 'hollow, formal, scholastic truck', while we have not yet become clear as to the sense and content of the discipline in question, nor as to the justification + +of the surmises that have suggested themselves to us. + +**In** order to test these surmises, we do not intend to assemble and to subject to a critical analysis any and every argument historically advanced for this or that conception of logic. This would not be a way to give new interest to an old dispute. The oppositions of principle which were not properly sorted out in this dispute, have, however, their own interest, and this interest rises above the empirical limitations of the disputants. It is these oppositions + +that we have to track down. + +**§ 14 The concept of a normative science. The basic** + +**standard or principle that gives it unity** + +We begin by concentrating on a proposition that is of decisive importance for our further investigation: that every normative and likewise every practical discipline rests on one or more theoretical disciplines, inasmuch as its rules must have a theoretical content separable from the notion of normativity (of the 'shall' or 'should'), whose scientific investigation is the duty of + +these theoretical disciplines. + +To clear up this point, let us first discuss the concept of a normative science in its relation to that of a theoretical science. The laws of the former tell us (it is usually held) what shall or should be, though perhaps, under the actual + +circumstances, it neither is nor can be. The laws of the latter, contrariwise, merely tell us what is. We must now ask what is meant by such a 'shall be' + +or 'should be' as opposed to what is. + +The original sense of 'shall' or 'should', which relates to a certain wish or will, a certain demand or command, is plainly too narrow, e.g. You shall listen to me, *X* shall come to me. As we speak in a wider sense of a demand, where there is no one who demands, and perhaps no one on whom demand is made, so we frequently speak of a 'shall' or a 'should' which is independent of anyone's wishing or willing. If we say 'A soldier should be brave', this does not mean that we or anyone else are wishing or willing, commanding or requiring this. One might rather suppose that a corresponding wishing and requiring would be generally justified, i.e. in relation to every soldier, though even this is not quite right, since it is surely not necessary that we should here be really evaluating a wish or a demand. 'A soldier should be brave' rather means that only a brave soldier is a 'good' soldier, which implies (since the predicates 'good' and 'bad' divide up the extension of the concept 'soldier') that a soldier who is not brave is a 'bad' soldier. *Since* this value-judgement holds, everyone is entitled to demand of a soldier that he should be brave, the same ground ensures that it is desirable, praiseworthy etc., that he should be brave. The same holds in other instances. 'A man should practise neighbourly love', i.e. one who omits this is no longer a 'good' man, and therefore *eo ipso* is (in this respect) a 'bad' man. 'A drama should not break up into episodes' - otherwise it is not a 'good' drama, not a 'true' work of art. In all these cases we make our positive evaluation, the attribution of a positive value-predicate, depend on a condition to be fulfilled, whose non-fulfilment entails the corresponding negative predicate. We may in general, take as identical or at least as equivalent the forms 'An *A* should be *B'* and 'An *A* that is not *B* is a bad *A',* or 'Only an *A* which + +is a *B* is a good *A'.* + +The term 'good' naturally functions in the widest sense of what is in any way valuable: in the concrete propositions ranged under our formula it is to be understood in the specific sense of the valuations it presupposes, e.g. as useful, beautiful, moral etc. There are as many ways of speaking of a 'should' as there are different species of valuations, as there are, in consequence, + +actual or presumed values. + +Negative statements of what should not be are not to be taken as negations of the corresponding affirmative statements, as, too, in the ordinary sense, the denial of a demand does not amount to a prohibition. 'A soldier should not be cowardly' does not mean that it is false that a soldier should be cowardly, but that a cowardly soldier also is a bad one. The following forms are therefore equivalent: 'An *A* should not be *B',* and 'An *A* which is *B* is in + +general a bad *A'* or 'Only an *A* which is not *B* is a good *A'.* + +That 'should' and 'should not' are mutually exclusive follows formally from their interpretations, and the same holds of the proposition that + +judgements regarding what should be entail no assertion regarding what + +correspondingly is. + +The just clarified judgements of normative form are plainly not the only ones that one would allow to count as such, even if the word 'should' or 'shall' does not occur in their expression. It is inessential if, instead of saying *'A* should (or should not) be *B'* we also are able to say *'A* must (or may not) be *B'.* We touch more substance if we point to the two new formulae *'A* need not be *B'* and *'A* may be *B',* which are in contradictory opposition to the above forms. 'May not' is therefore the negation of 'should', or, what is the same, of 'must'; 'may' the negation of 'should not' or, what is the same, of 'may not', as can readily be seen from the interpreting value-judgements: 'An *A* need not be *B'* = 'An *A* that is not *B* is not therefore a bad *A';* 'An *A* + +may be *B'* = 'An *A* that is *B* is not therefore a bad *A'.* + +There are yet other propositions that must be reckoned with here, e.g. 'For an *A* to be a good *A* it suffices (or does not suffice) that it is *B'.* Whereas our former propositions are about certain *necessary* conditions for attributing or denying positive or negative value-predicates, our concern in the present proposition is with *sufficient* conditions. Other further propositions aim at stating what are at once necessary and sufficient conditions. We have thus run through the essential forms of general normative propositions. To them of course correspond forms of particular and singular value-judgement which contribute nothing of importance to our analysis, and of which the latter at least do not count for our purposes. They have always a nearer or remoter relation to certain normative generalities: in abstract normative disciplines, they can only occur in relation to their governing generalities. Such disciplines are as such located beyond all individual existence, their generalities are 'purely conceptual', they have a lawlike + +character in the strict sense of the word 'law'. + +We see from these analyses that each normative proposition presupposes a certain sort of valuation or approval through which the concept of a 'good' or 'bad' (a value or a disvalue) arises in connection with a certain class of objects: in conformity with this, objects divide into good and bad ones. To be able to pass the normative judgement 'A soldier should be brave', I must have some conception of a 'good' soldier, and this concept cannot be founded on an arbitrary nominal definition, but on a general valuation, which permits us to value soldiers as good or bad according to these or those properties. Whether or not this valuation is in any sense 'objectively valid', whether we can draw any distinction between the subjectively and objectively 'good', does not enter into our determination of the sense of should-propositions. It is sufficient that something is held valuable, that an *intention* is effected + +having the content that something is valuable or good. + +If, conversely, a pair of value-predicates has been laid down for an appropriate class, following upon a certain general valuation, then the possibility of normative judgements is given: all forms of normative proposition have + +then definite sense. Every constitutive property *B* of the 'good' *A* yields, e.g. a proposition of the form 'An *A* should be *B',* every property incompatible + +with *B,* a proposition 'An *A* may not (should not) be *B'* etc. + +Finally, as regards the *concept of the normative judgement* we can, following our analysis, describe it as follows: In relation to a general underlying valuation, and the content of the corresponding pair of value-predicates determined by it, every proposition is said to be 'normative' that states a necessary, or a sufficient, or a necessary and sufficient condition for having such a predicate. If we have once drawn a distinction between 'good' and 'bad' in our valuations in a particular sense, and so in a particular sphere, we are naturally concerned to decide the circumstances, the inner or outer properties that are or are not guarantees that a thing is good or bad in this sense: what properties may not be lacking if an object from that sphere is to + +be accorded the value of 'good'. + +Where we speak of good and bad, we also usually make comparative valuational distinctions between *better* and best or between *worse* and worst. If pleasure is our good, then the more intense, and again the more enduring, pleasure is better. If knowledge counts as our good, not every piece of knowledge will therefore count as 'equally good'. We value the knowledge of laws more highly than the knowledge of singular facts: the knowledge of more general laws, e.g. 'Every equation of the nth degree has *n* roots', more highly than the knowledge of the special laws that fall under them ~ 'Every equation of the fourth degree has four roots'. There are therefore normative questions relating to relative value-predicates just as there are in the case of absolute value-predicates. If the constitutive content of what is to be esteemed good or bad is fixed, one must ask what, in comparative valuation, will count constitutively as better or worse, and, further, what are the nearer and the more remote, the necessary and the sufficient conditions for the relative predicates, laying down the content of the better and worse, and ultimately of the relatively best. The constitutive contents of positive and relative value-predicates are, so to say, the metric units in terms of which + +objects of the relevant sphere are measured. + +The sum total of these norms plainly forms a closed group, determined by our fundamental valuation. The normative proposition which demands generally of the objects of a sphere that they should measure up to the constitutive features of the positive value-predicate to the greatest extent possible, has a central place in each group of mutually coherent norms, and can be called their *basic norm.* This role is, e.g., played by the categorical imperative in the group of normative propositions which make up Kant's Ethics, as by the principle of the 'greatest possible happiness of the greatest + +possible number' in the Ethics of the Utilitarians. + +The basic norm is the correlate of the definition of 'good' and 'bad' in the sense in question. It tells us on what basic standard or basic value all normativization must be conducted, and does not therefore represent a + +normative proposition in the strict sense. The relationship of the basic norm to what are, properly speaking, normative propositions, is like the relation between so-called definitions of the number-series and the arithmetical theorems about the relations of numbers which are always referred back to these. The basic norm could also be called a 'definition' of the standard conception of good ~ e.g. of the morally good ~ but this would mean departing + +from the ordinary logical concept of definition. + +If, in relation to such a 'definition', or fundamental and universal valuation, we make it our aim to conduct scientific researches into a sum total of mutually relevant normative propositions, we come upon the Idea of a Normative Discipline. Each such discipline is therefore unambiguously characterized by its basic norm, or by the definition of what shall count as 'good' in such a discipline. If, e.g. the production, maintenance, increase and intensification of pleasure counts as our good, we shall ask by what objects, or in what subjective and objective circumstances, pleasure is excited. We shall enquire generally into the necessary and sufficient conditions for the emergence, maintenance, increase etc., of pleasure. These questions taken as targets for our scientific discipline yield a *hedonic:* this hedonic is normative ethics in the sense of the hedonists. The valuation directed to the arousal of pleasure yields the basic norm which determines the unity of the discipline and distinguishes it from every other normative discipline. Every normative discipline therefore has its own basic norm which is in each case its unifying principle. *Theoretical disciplines* do not have this central reference of all researches to a fundamental valuation as the source of a dominant normative interest. The unity of their researches, and the coordination of what they know, is determined exclusively by a theoretical interest directed to investigating matters that really belong together theoretically, in virtue of the inner laws of things, and which must therefore be investigated together + +in their mutual coherence. + +§ **IS Normative disciplines and technologies** + +A normative interest is naturally dominant in the case of *real (realen)* objects, as the objects of *practical* valuations. Hence the undeniable tendency to identify the notion of a normative discipline with that of a practical discipline or a *technology.* It is easy to see, however, that such an identification cannot be sustained. Schopenhauer, e.g., who is led by his doctrine of inborn character to reject in principle all practical moralizing, has an ethics in the sense of a normative science, which he himself works out. For he does not at all abandon distinctions in moral value. A technology represents a particular case of a normative discipline which arises when the basic norm consists in achieving a universal practical aim. Plainly, therefore, every technology includes in itself an entire normative discipline, which is not itself a practical discipline. For its task presupposes that, altogether apart from + +everything relating to practical attainment, the narrower task of fixing norms has first been carried out, norms by which we can assess the adequacy to the general notion of the end to be achieved, or the possession of the properties characteristic of the class of values in question. Every normative discipline, conversely, whose fundamental valuation is transformed into a correspond- + +ing teleological prescription, widens out into a technology. + +**§ 16 Theoretical disciplines as the foundation of** + +**normative disciplines** + +It is now easy to see that each normative, and, *a fortiori,* each practical discipline, presupposes one or more theoretical disciplines as its foundations, in the sense, namely, that it must have a theoretical content free from all normativity, which as such has its natural location in certain theoretical sciences, whether these are already marked off or yet to be constituted. The basic norm (or basic value, or ultimate end) determines, we saw, the unity of the discipline: it also is what imports the thought of normativity into all its normative propositions. But alongside of this general thought of measurement in terms of a basic norm, these propositions have their own theoretical content, which differs from one case to another. Each expresses the thought of a measuring relation between norm and what it is a norm for, but this relation is itself objectively characterized - if we abstract from valuational interest - as a relation between condition and conditioned, which relation is set down as existent or non-existent in the relevant normative propositions. Every normative proposition of, e.g., the form 'An *A* should be *B'* implies the theoretical proposition 'Only an *A* which is *B* has the properties C', in which 'C' serves to indicate the constitutive content of the standard-setting predicate 'good' (e.g. pleasure, knowledge, whatever, in short, is marked down as good by the valuation fundamental to our given sphere). The new proposition is purely theoretical: it contains no trace of the thought of normativity. If, conversely, a proposition of the latter form is true, and thereupon a novel valuation of a C as such emerges, and makes a normative relation to the proposition seem requisite, the theoretical proposition assumes the normative form 'Only an *A* which is *B* is a good *A',* i.e. 'An *A* should be *B'.* Normative propositions can therefore make an appearance even in theoretical contexts: our theoretical interest in such contexts attaches value to the being of a state of affairs of a sort - to the equilateral form, e.g., of a triangle about to be determined - and then assesses other states of affairs, e.g. one of equiangularity, in relation to this: If the triangle is *to be* equilateral, it must be equiangular. Such a modification is, however, merely passing and secondary in theoretical sciences, since our last intention is here directed to the theoretical coherence of the things themselves. Enduring results are not therefore stated in normative form, but in the forms of this objective coherence, in the form, that is, of a general proposition. + +It is now clear that the theoretical relations which our discussion has shown to lie hidden in the propositions of normative sciences, must have their logical place in certain theoretical sciences. If the normative science is to deserve its name, if it is to do scientific work on the relations of the facts to be normatively considered to their basic norms, it must study the content of the theoretical nucleus of these relations, and this means entering the spheres of the relevant theoretical sciences. In other words: Every normative discipline demands that we know certain non-normative truths: these it takes from certain theoretical sciences, or gets by applying propositions so taken to the constellation of cases determined by its normative interest. This naturally holds, likewise, in the more special case of a technology, and plainly to a greater extent. The theoretical knowledge is there added which will + +provide a basis for a fruitful realization of ends and means. + +One point should be noted in the interest of what follows. Naturally these theoretical sciences may share in very different degrees in the scientific foundation and elaboration of the normative discipline in question. Their significance for it can also be greater or less. It may become plain that, to satisfy the interests of a normative discipline, the knowledge of certain sorts of theoretical connection has a prime urgency, and that the development and bringing closer of the theoretical field of knowledge to which they belong therefore plays a decisive part in making such a normative discipline possible. In building up such a discipline, it may be that certain sorts of theoretical knowledge playa useful and perhaps very weighty role, but none the less are of secondary significance, since their removal would only narrow, but not wholly destroy, the field of the discipline. One may think, e.g., of the relation between merely normative and practical ethics (see above, §15). All the propositions which have to do with making practical realization possible, do not effect the sphere of the pure norms of ethical valuation. If these norms, or the theoretical knowledge underlying them, were to fall away, ethics would vanish altogether. If the former propositions were to drop out, there would be no possibility of ethical practice (or no possibility of a technology + +of ethical conduct). + +It is in relation to such distinctions that talk of the *essential* foundations of a normative science must be understood. We mean thereby the theoretical sciences that are absolutely essential to its construction, perhaps also the relevant groups of theoretical propositions which are of decisive importance + +in making the normative discipline possible. + +**Psychologism, its arguments and its attitude to the usual** + +**counter-arguments** + +**§ 17 The disputed question as to whether the essential** + +**theoretical foundations of normative logic lie in** + +**psychology** + +If we now apply the general results arrived at in the last chapter to logic as a normative discipline, a first, very weighty question arises: Which theoretical sciences provide the essential foundations of the theory of science? And to this we forthwith add the further question: Is it correct that the theoretical truths we find dealt with in the framework of traditional and modem logic, and above all those belonging to its essential foundations, have their theoretical place in the sciences that have been already marked off and independently developed? Here we encounter the disputed question as to the relation between psychology and logic, since one dominant tendency of our time has a ready answer to the questions raised: The essential theoretical foundations of logic lie in psychology, in whose field those propositions belong - as far as their theoretical content is concerned - which give logic its characteristic pattern. Logic is related to psychology just as any branch of chemical technology is related to chemistry, as land-surveying is to geometry etc. This tendency sees no need to mark off a new theoretical discipline, and, in particular, not one that would deserve the name of logic in a narrower and more pointed sense. Often people talk as if psychology provided the sole, sufficient, theoretical foundation for logical technology. So we read in Mill's polemic against Hamilton: 'Logic is not a science separate from and coordinate with psychology. To the extent that it is a science at all, it is a part or branch of psychology, distinguished from it on the one hand as the part is from the whole, and on the other hand as the art is from the science. It owes all its theoretical foundations to psychology, and includes as much of that science as is necessary to establish the rules of the art' *(An Examination of Sir William Hamilton's Philosophy,* p. 461). According to Lipps it even seems that logic is to be ranked as a mere constituent of psychology for he says: 'The fact that logic is a specific discipline of psychology distinguishes them satisfactorily from one another' (Lipps, *Grundzuge der Logik* (1893), §3). + +**§ 18 The line of proof of the psychologistic thinkersl** + +If we ask for the justification of such views, a most plausible line of argument is offered, which seems to cut off all further dispute *ab initio.* However one may define logic as a technology - as a technology of thinking, judging, inferring, knowing, proving, of the courses followed by the understanding in the pursuit of truth, in the evaluation of grounds of proof etc. - we find invariably that mental activities or products are the objects of practical regulation. And just as, in general, the artificial working over of a material presupposes the knowledge of its properties, so this will be the case here too, where we are specially concerned with psychological material. The scientific investigation of the rules according to which this stuff should be worked over, naturally leads back to the scientific investigation of these properties. Psychology therefore provides the theoretical basis for constructing a logical + +technology, and, more particularly, the psychology of cognition. 2 + +Any glance at the contents of logical literature will confirm this. What is being talked of throughout? Concepts, judgements, syllogisms, deductions, inductions, definitions, classifications etc. - all psychology, except that they are selected and arranged from normative and practical points of view. Draw the bounds of pure logic as tightly as one likes, it will not be possible to keep out what is psychological. This is implicit in the concepts constitutive for logical laws: truth and falsehood, affirmation and negation, universality + +and particularity, ground and consequent etc. + +**§ 19 The usual arguments of the opposition and the** + +psycho logistic **rejoinder** + +Remarkably enough, the opposition believes that it can base a sharp separation of the two disciplines on precisely the normative character of logic. Psychology, it is said, deals with thinking as it is, logic with thinking as it should be. The former has to do with the natural laws, the latter with the normative laws of thinking. It reads in this sense in Jiische's version of Kant's Lectures on Logic: 'Some logicians presuppose psychological principles for logic, but to introduce such principles into logic, is as absurd as to derive morality from Life. If we take principles from psychology, i.e. from observations of our understanding, we shall only see how thought proceeds, and what happens under manifold subjective hindrances and conditions. Those would only lead to a knowledge of merely *contingent* laws. Logic does not however ask after *contingent,* but after *necessary* laws - not how we think but how we ought to think. The rules of logic must therefore be taken, not from the *contingent,* but from the *necessary* use of reason, which one finds in oneself apart from all psychology. In logic we do not wish to know what the understanding is like and how it thinks, nor how it has hitherto proceeded in its thinking, but how it ought to proceed in its thinking. + +It should teach us the correct use of the understanding, the use in which it is consistent with itself' (Introduction, I. Concept of Logic. Kant's *Werke,* ed. Hartenstein, 1867, VIII, p. 14). Herbart takes up a similar position when he objects to the logic of his time and 'the would be psychological stories about understanding and reason with which it starts', by saying that this is as badly in error as a moral theory which tried to begin with the natural history of human tendencies, urges and weaknesses, and by pointing to the normative character of logic as of ethics (Herb art, *Psychologie als* + +*Wissenschaft,* II, §119, original ed. II, p. 173). + +Such arguments do not dismay the psycho logistic logicians. They answer: A necessary use of the understanding is none the less a use of the understanding, and belongs, with the understanding itself, to psychology. Thinking as it should be, is merely a special case of thinking as it is. Psychology must certainly investigate the natural laws of thinking, the laws which hold for all judgements whatever, whether correct or false. It would, however, be absurd to interpret this proposition as if such laws only were psychological as applied with the most embracing generality to *all* judgements whatever, whereas special laws of judgement, like the laws of correct judgement, were shut out from its purview. (Cf., e.g. Mill, *An Examination,* p. 459 *f)* Or does one hold a different opinion? Can one deny that the normative laws of thinking have the character of such special laws? This also will not do. Normative laws of thought, it is said, only try to say how one must proceed *provided* one wants to think *correctly.* 'We think correctly, in the material sense, when we think of things as they are. But for us to say, certainly and indubitably, that things are like this or like that, means that the nature of our mind prevents us from thinking of them otherwise. For one need not repeat what has been so often uttered, that one can obviously not think of a thing as it is, without regard to the way in which one must think of it, nor can one make of it so isolated an object of knowledge. The man, therefore, who compares his thought of things with the things themselves can in fact only measure his contingent thinking, influenced by custom, tradition, inclination and aversion, against a thinking that is free from such influences, and + +that heeds no voice but that of its own inherent lawfulness.' + +'The rules, therefore, on which one must proceed in order to think rightly are merely rules on which one must proceed in order to think as the nature of thought, its specific lawfulness, demands. They are, in short, identical with the natural laws of thinking itself. Logic is a physics of thinking or it is nothing at all.' (Lipps, 'Die Aufgabe der Erkenntnistheorie', *Phi/os. Monat-* + +*she/te,* XVI (1880), p. 530 *f)* + +It may perhaps be said from the antipsychologistic side:3 Of course the various kinds of presentations, judgements, syllogisms etc., also have a place in psychology as mental phenomena and dispositions, but psychology has a different task in regard to them than logic. Both investigate the laws of these activities, but 'law' means something quite different in the two cases. + +The task of psychology is to investigate the laws governing the real connections of mental events with one another, as well as with related mental dispositions and corresponding events in the bodily organism. 'Law' here means a comprehensive formula covering coexistent and successive connections that are without exception and necessary. Such connections are causal. The task oflogic is quite different. It does not enquire into the causal origins or consequences of intellectual activities, but into their truth-content: it enquires what such activities *should* be like, or how they *should* proceed, in order that the resultant judgements should be true. Correct judgements and false ones, evident ones and blind ones, come and go according to natural laws, they have causal antecedents and consequences like all mental phenomena. Such natural connections do not, however, interest the logician; he looks rather for ideal connections that he does not always find realized, in fact only exceptionally finds realized in the actual course of thoughts. He aims not at a physics, but an ethics of thinking. Sigwart therefore rightly stresses the point that, in the psychological treatment of thought, 'the opposition of true and false has as little part to playas the opposition of + +good or bad in human conduct is a psychological matter'.4 + +We cannot be content ~ such will be the psychologistic rejoinder ~ with such half-truths. The task of logic is of course quite different from that of psychology: who would deny it? It is a technology of knowledge, but how could such a technology ignore questions of causal connection, how could it look for ideal connections without studying natural ones? 'As if every "ought" did not rest on an "is", every ethics did not also have to show itself a physics.' (Lipps, 'Die Aufgabe der Erkenntnistheorie', *op. cit.* p. 529.) 'A question as to what should be done always reduces to a question as to what must be done if a definite goal is to be reached, and this question in its turn is equivalent to a question as to how this goal is *in fact reached'* (Lipps, *Grundziige der Logik,* §l). That psychology, as distinct from logic, does not deal with the opposition of true and false 'does not mean that psychology treats these different mental conditions on a like footing, but that it renders both intelligible in a like manner' (Lipps, *op. cit.* §3, p. 2). Theoretically regarded, Logic therefore is related to psychology as a part to a whole. Its main aim is, in particular, to set up propositions of the form: Our intellectual activities must, either generally, or in specifically characterized circumstances, have such and such a form, such and such an arrangement, such and such combinations and no others, if the resultant judgements are to have the character of evidence, are to achieve knowledge in the pointed sense of the word. Here we have an obvious causal relation. The psychological character of evidence is a causal consequence of certain antecedents. + +What sort of antecedents? This is just what we have to explore.s + +The following often repeated argument is no more successful in shaking the psychologistic ranks: Logic, it is said, can as little rest on psychology as on any other science; since each science is only a science in virtue of its + +hannony with logical rules, it presupposes the validity of these rules. It would therefore be circular to try to give logic a first foundation in psychology.6 The opposition will reply: That this argument cannot be right, is shown by the fact that it would prove the impossibility of all logic. Since logic itself must proceed logically, it would itself commit the same circle, would itself + +have to establish the validity of rules that it presupposes. + +Let us, however, consider more closely what such a circle could consist in. Could it mean that psychology presupposes the validity of logical laws? Here one must notice the equivocation in the notion of 'presupposing'. That a science presupposes the validity of certain rules may mean that they serve as premisses in its proofs: it may also mean that they are rules in accordance with which the science must proceed in order to be a science at all. Both are confounded in our argument for which reasoning *according* to logical rules, and reasoning *from* logical rules, count as identical. There would only be a circle if the reasoning were *from* such rules. But, as many an artist creates beautiful works without the slightest knowledge of aesthetics, so an investigation may construct proofs without ever having recourse to logic. Logical laws cannot therefore have been premisses in such proofs. And what is true + +of single proofs is likewise true of whole sciences. + +**§20 A gap in the psychologistic line of proof** + +In these and similar arguments the anti-psychologistic party seem undoubtedly to have got the worst of it. Many think the battle quite at an end, they regard the rejoinders of the psychologistic party as completely victorious. One thing only might arouse our philosophical wonder, that there was and is such a battle at all, that the same arguments have repeatedly been adduced while their refutations have not been acknowledged as cogent. If everything really were so plain and clear as the psychologistic trend assures us, the matter would not be readily understandable, since there are unprejudiced, serious and penetrating thinkers on the opposite side as well. Is this not again a case where the truth lies in the middle? Has each of the parties not recognized a valid portion of the truth, and only shown incapacity for its sharp conceptual circumscription, and not even seen that they only had part of the whole? Is there not perhaps an unresolved residuum in the arguments of the anti-psychologists - despite much unclearness and error in detail which has made refutation easy; are they not informed by a true power, which always re-emerges in unbiased discussion? I for my part would answer 'Yes'. It seems to me that the greater weight of truth lies on the anti-psychologistic side, but that its key-thoughts have not been properly worked out, and are + +blemished by many mistakes. + +Let us go back to the question we raised above regarding the essential foundations of nonnative logic. Have the arguments of psychologistic thinkers really settled this? Here a weak point at once appears. The argument only + +proves one thing, that psychology *helps* in the foundation of logic, not that it has the only or the main part in this, not that it provides logic's *essential foundation* in the sense above defined (§16). The possibility remains open that another science contributes to its foundation, perhaps in a much more important fashion. Here may be the place for the 'pure logic' which on the other party's view, has an existence independent of all psychology, and is a naturally bounded, internally closed-off science. We readily grant that what Kantians and Herbartians have produced under this rubric does not quite accord with the character that our suggested supposition would give it. For they always talk of normative laws of thinking and particularly of conceptformation, judgement-framing etc. Proof enough, one might say, that their subject-matter is neither theoretical nor wholly unpsychological. But this objection would lose weight if closer investigation confirmed the surmise suggested to us above in §13, that these schools were unlucky in defining and building up the intended discipline, yet none the less approached it closely, in so far as they discerned an abundance of interconnected theoretical truths in traditional logic, which did not fit into psychology, nor into any other separate science, and so permitted one to divine the existence of a peculiar realm of truth. And if these were the truths to which all logical regulation in the last resort related, truths mainly to be thought of when 'logical truths' were in question, one could readily come to see in them what was essential to the whole of logic, and to give the name of 'pure logic' to their theoretical unity. That this hits off the true state of things I hope + +actually to prove. + +**Empiricistic consequences of** + +**psychologism** + +**§21 Characterizing two empiricistic consequences of the psychologistic standpoint, and their refutation** + +Let us place ourselves for the moment on the ground of the psychologistic logic, and let us assume therefore that the essential theoretical foundations of the prescriptions of logic lie in psychology. However the latter discipline may be defined - as the science of psychic phenomena, of the facts of consciousness, of the facts of internal experience, of experiences in their dependence on the experiencing individual, or whatever - it is universally agreed that psychology is a factual and therefore an empirical science. We shall also not be controverted if we add that psychology has so far lacked genuine and therefore exact laws, and that the propositions in it which are dignified with the name of laws, are merely vague,l even if valuable, generalizations from experience. They are statements about approximate regularities of coexistence and succession, which make no claim to determine, with infallible, unambiguous definiteness, what will go together or will follow in exactly described relationships. One may look to the laws of the association of ideas, to which association-psychology wished to accord the position and importance of basic psychological laws. As soon as one takes the trouble adequately to formulate their empirically justified sense, they at once lose the pretended character of laws. This being granted, most serious con- + +sequences arise for the psychologistic logicians. + +The first is that only vague rules could be based on vague theoretical foundations. If psychological laws lack exactness, the same must be true of the prescriptions of logic. It cannot be doubted that many of these prescriptions are infected with empirical vaguenesses. But precisely the laws which are pointedly called 'logical', which as laws of proof make up the real core of all logic - the logical 'principles', the laws of syllogism, the laws of many other kinds of inference, as, e.g. equational inferences, the Bernoullian argument from *n* to *n* + 1, the principles of probability-inferences etc. - are of absolute exactness. Every interpretation that would base them on empirical indefinitenesses, make them depend for their validity on vague 'circumstances', + +would fundamentally alter their true sense. Plainly they are genuine laws, + +and not 'merely empirical', i.e. approximate, laws. + +If, as Lotze thought, pure mathematics is merely an independently developed branch of logic, the above-mentioned sphere of exact logical laws will also cover the inexhaustible wealth of the laws of pure mathematics. **In** all further objections we must keep our eye on the sphere of pure mathematics + +together with our sphere of logic. + +**In** the second place, were one to seek to counter our first objection by denying the thoroughgoing inexactness of psychological laws, and try to found norms of the above-mentioned type on supposedly exact natural laws, + +little would have been gained. + +No natural laws can be known *a priori,* nor established by sheer insight. The only way in which a natural law can be established and justified, is by induction from the singular facts of experience. Induction does not establish the holding of the law, only the greater or lesser probability of its holding; the probability, and not the law, is justified by insight. Logical laws must, accordingly, without exception, rank as mere probabilities. Nothing, however, seems plainer than that the laws of 'pure logic' all have *a priori* validity. They are established and justified, not by induction, but by apodeictic inner evidence. Insight justifies no mere probabilities of their holding, but + +their holding or truth itself. + +The Law of Contradiction does not tell us that one must *surmise* that one of two contradictory judgements is true, one false, the mood *Barbara* does not tell us that when two propositions of the form 'All *A's* are *B's'* and 'All *B's* are *C's'* are true, it is to be *surmised* that a corresponding proposition of the form 'All *A's* are *C's'* is true. And so generally, and in the field of mathematics as well. Otherwise we should have to treat it as an open *possibility* that such a surmise would fail to be confirmed by an extension of our ever limited horizon of experience. Perhaps our logical laws are mere 'approximations' to genuinely valid laws of thought that are beyond our reach. Such possibilities are seriously and rightly weighed in the case of natural laws. Though the law of gravitation is recommended by the most comprehensive inductions and verifications, no investigator of nature would now look on it as an absolutely valid law. New gravitational formulae are occasionally tried out: it was shown, e.g. that Weber's basic law for electrical phenomena could quite well function as the basic law of gravity. The differentiating factor in both formulae conditions differences in calculated values not exceeding the field of unavoidable observational error. Innumerable factors of this sort are, however, thinkable; hence we know *a priori* that endlessly many laws could and must do the same work as the Newtonian law of gravitation, recommended only by its peculiar simplicity. We know that, in view of in eli minable observational imprecision, it would be foolish to look for a uniquely true law. Such is the situation in the exact factual sciences, but by no means in logic. The justified possibility of the former becomes the open absurdity of the latter. + +We have insight into, not merely the probability, but the truth of the logical laws. We see the truth of the principles of the syllogism, of Bernoullian induction, of arguments in probability, of general arithmetic etc. We grasp their very truth, so that talk of zones of inexactness, of mere approximations etc., loses all possible sense. But if what follows from a demand for a psychological validation of logic is absurd, this validation is itself absurd. Against the truth that is itself grasped with insight, the strongest psychologistic argument cannot avail: probability cannot wrestle with truth, nor surmise with insight. If anyone likes to stay in a sphere of general discussions, he may allow the psychologistic arguments to deceive him. But a mere glance at any logical principle, at its real meaning and the full insight with + +which it is seen as true in itself, must abolish such deceit. + +How plausible the ready suggestions of psychologistic reflection sound. Logical laws are laws for validations, proofs, What are validations but peculiar human trains of thought, in which, in normal circumstances, the finally emergent judgements seem endowed with a necessarily consequential character. This character is itself a mental one, a peculiar mode of mindedness and no more. And, obviously, none of these mental phenomena is isolated, but is a single thread in the tangled web of mental phenomena, of mental disposition and organic process, called human life. How could anything beyond empirical generalities result in such circumstances? Where has psy- + +chology yielded more? + +We reply: Psychology certainly does not yield more, and cannot for this reason yield the apodeictically evident, and so metempirical and absolutely + +exact laws which form the core of all logic. + +**§22 The laws of thought as supposed laws of nature which operate in isolation as causes of rational thought** Here is also the place to take up an attitude towards a widely held conception of logical law, which characterizes correct thought by its conformity with certain laws of thought (however we may formulate them), but is disposed at the same time to interpret such conformity in the following psychologistic manner: The laws of thought count as natural laws characterizing the peculiarity of our mind *qua* thinking, and the essence of the conformity, as definitory of correct thinking, lies in the *pure* operation of these laws, their non-disturbance by alien mental influences (such as custom, inclination, tradition). (Cf. the citations above in §19 from Lipps' article on + +the task of epistemology.) + +We need only instance one of the grave consequences of this doctrine. Laws of thought, as causal laws governing acts of knowledge in their mental interweaving, could only be stated in the form of probabilities. On this basis, no assertion could be *certainly* judged correct, since probabilities, taken as the standard of all certainty, must impress a merely probabilistic + +stamp on all knowledge. We should stand confronted by the most extreme probabilism. Even the assertion that all knowledge was merely probable would itself only hold probably: this would hold of this latter assertion, and so on *in infinitum.* Since each successive step reduces the probability level of the previous one a bit, we should become gravely concerned about the worth of all knowledge. One may hope, however, that, with some luck, the probability-levels of these infinite series may always have the character of a Cantorian 'fundamental series', of such a sort that the final limiting value or the probability of the knowledge to be judged is a real number> o. Sceptical awkwardnesses would of course vanish if one looked on the laws of thought as matters of direct insight. But how should one have insight into causal laws? Even if this difficulty were removed, we could still ask: Where on earth is the proof that the pure operation of these laws (or any other laws) would yield correct laws of thinking? Where are the descriptive and genetic analyses which entitle us to explain the phenomena of thought by two sorts of natural law, one exclusively determining such causal sequences as allow logical thought to emerge, whereas others help to determine alogical thought? Does the assessment of thoughts by logical laws amount to a proof of their + +causal origin in these same laws as laws of nature? + +It seems that certain ready confusions have here opened the way to psychologistic errors. Logical laws have first been confused with the judgements, in the sense of acts of judgement, in which we may know them: the laws, as *'contents of judgement'* have been confused with the *judgements themselves.* The latter are real events, having causes and effects. Judgements whose contents are laws are, in particular, frequently operative as *thoughtmotives,* directing the course of our thought-experience, as those contents, the laws of thinking, prescribe. In such cases the real order and connection of our thought-experiences conforms to that which we think generally in our governing knowledge of the law: it is a concrete individual instance of that general law. If, however, the law is confused with the judgement or knowledge of the law, the ideal with the real, the law appears as a *governing power* in our train of thought. With understandable ease a second confusion is added to the first: we confuse a law as a *term in causation with a law as the rule of causation.* In other fields, too, we familiarly employ mythic talk of natural laws as presiding powers in natural events - as if the rules of causal connection could themselves once more significantly function as causes, i.e. as terms in just such connections. The serious confusion of things so essentially dissimilar has plainly been favoured in the case before us by the previous confusion of a law with the knowledge of a law. Logical laws already appeared as motive powers in thinking. They presided causally, it was imagined, over the course of our thoughts - they were accordingly causal laws of thinking. They expressed how we must think in consequence of the nature of *our* mind, they characterized the human mind as a thinking mind in the pointed sense. If at times we think otherwise than these laws + +require, we are not, properly speaking, 'thinking' at all, we are not judging as the natural laws of thinking, or the *nature of our mind qua* thinking, requires, but as other laws determine (once more causally). We are follow- + +ing the disturbing leads of custom, passion etc. + +Other motives of course may have suggested the same conception. The empirical fact that persons performing normally in a given sphere, e.g. scientists in their fields, usually judge in a logically correct manner, seems to demand, as a natural explanation, that the logical laws by means of which the correctness of thinking is assessed, also determine the course of thinking, in the manner of causal laws, while isolated deviations from the norm may readily be put to the account of the troubling influences stemming from + +other psychological sources. + +Against this the following argument should suffice. Let us imagine an ideal person, in whom *all* thinking proceeds as logical laws require. Naturally the fact that this occurs must have its explanatory ground in certain psychological laws, which govern the course of the mental experiences of this being, starting from certain initial 'collocations'. I now ask: Would the natural laws and the logical laws in this assumed situation be one and the same? Obviously the answer is 'No'. Causal laws, according to which thought must proceed in a manner which the ideal norms of logic might justify, are by no means identical with those norms. If a being were so constituted as never to be able to frame contradictory judgements in a unified train of thought, as never to be able to perform inferences which defy the syllogistic moods, this would not mean that the law of contradiction, the *Modus Barbara* etc., were laws of nature explanatory of this being's constitution. The example of a computer makes the difference quite clear. The arrangement and connection of the figures which spring forth is regulated by natural laws which accord with the demands of the arithmetical propositions which fix their meanings. No one, however, who wants to give a physical explanation of the machine's procedures, will appeal to arithmetical instead of mechanical laws. The machine is no thought-machine, it understands neither itself nor the meaning of its performances. But our own thought-machine might very well function similarly, except that the real course of one kind of thought would always have to be recognized as correct by the insight brought forward in another. This latter thinking could be the product of the same or other thought-machines, but ideal evaluation and causal explanation would none the less remain disparate. The 'initial collocations' should also not be forgotten: indispensable in causal explanation, they are senseless for ideal + +evaluation. + +The psychologistic logicians ignore the fundamental, essential, never-tobe-bridged gulf between ideal and real laws, between normative and causal regulation, between logical and real necessity, between logical and real grounds. No conceivable gradation could mediate between the ideal and the real. It is characteristic of the low state of logical insights in our time, that a + +thinker of Sigwart's stature should dare, in connection with the fiction of an intellectually ideal being like that discussed above, to maintain that, for such a being, 'logical necessity would also be a real necessity that engenders real thinking', or that he should make use of the concept of thoughtcompulsion to elucidate the notion of 'logical ground' (Sigwart, *Logik, I,* p. 259 f). The same holds of Wundt when he sees in the law of sufficient reason the 'basic law of the dependence of our thought-acts on one another' (Wundt, *Logik,* I, p. 573). That one is really concerned in these connections with basic errors in logic will, one hopes, become a certainty, even to the + +prejudiced, in the course of further investigations. + +**§23 A third consequence of psychologism,** + +**and its refutation** + +A third consequence (see §21 above) for the psychologistic logician is that, if the laws of logic have their epistemological source in psychological matter of fact, if, e.g., as our opponents generally say, they are normative transformations of such facts, they must themselves be psychological in content, both by being laws for mental states, and also by presupposing or implying the existence of such states. This is palpably false. No logical law implies a 'matter of fact', not even the existence of presentations or judgements or other phenomena of knowledge. No logical law, properly understood, is a law for the facticities of mental life, and so not a law for presentations (as experiences), nor for judgements (experiences of judging), nor for our other + +mental experiences. + +Most psychologistic thinkers are too deeply enthralled by their general prejudice even to try to verify it in the case of the definitely acknowledged logical laws. If such laws *must* be psychological, why try to show in detail that they really are so? No one sees that a consistent psychologism would force one to interpret logical laws in a manner quite alien to their true sense. One fails to see that these laws, naturally understood, presuppose nothing mental, no facts of psychic life, whether in their establishment or their content. They do so no more than the laws of pure mathematics do so. + +If psychologism were on the right track, one should, in treating of syllogisms, expect only rules of the following type: It is an empirical fact that, in circumstances *X,* conclusions of the form C, stamped with apodeictically necessary consequence, attend upon premisses of the form *P.* To syllogize 'correctly', i.e. to achieve judgements of this distinctive stamp through syllogizing, one must proceed in this manner, one must see that the circumstances really are *X,* and the premisses *P.* Mental matters of fact would then be the matters regulated, the existence of such matters would be presupposed in the grounding of such laws, and would be part of their content. But no single syllogistic rule is of such a type. What, e.g., does the mood *Barbara* tell us? Only this: that, if in the case of any class-terms *A, B,* C all *A's* are *B's* + +and all *B's* C's, then all *A's* will be C's. The *Modus Ponens,* likewise, written out in full, reads: It is a valid law for any propositions *P,* Q, that if *P* is the case, and it also is the case that if *P* is the case Q is so, then Q also is the case. These and all similar laws are as little psychological as they are empirical. They were of course set up by traditional logic to serve as norms for our judging activities. But do they implicitly say anything about a single actual judgement, or about any other mental phenomenon? If anyone thinks they do let him prove it. Whatever a proposition implicitly asserts can be inferred from it in a valid syllogism. But what forms of syllogism permit us + +to deduce facts from a pure law? + +It is irrelevant to object that talk of logical laws never could have arisen had we not actually experienced presentations and judgements, and abstracted the relevant, basic logical concepts from them, or that, wherever we understand and assert such laws, the existence of presentations and judgements is implied, and can therefore be inferred. We need hardly observe that this does not follow from our law, but from the fact that we understand and assert such a law, and that a like consequence could be inferred from every assertion. One ought not, further, to confuse the psychological presuppositions or components of the *assertion* of a law, with the logical 'moments' of its *content.* 'Empirical laws' have, *eo ipso,* a factual content. Not being true laws, they merely say, roughly speaking, that certain coexistences or successions obtain generally in certain circumstances, or may be expected, with varying probability, in varying circumstances. But even the strict laws of the natural sciences are not without factual content. They do not merely concern facts, + +but also imply their existence. + +We must, however, be more precise. Exact laws, as normally formulated, are pure laws: they exclude all factual content. But, if we consider the proofs to which they owe their scientific justification, it is at once clear that we cannot justify them as pure laws, in their normal formulation. The law of gravitation, as formulated in astronomy, has never really been proved. What has been proved is a proposition of the form: Our knowledge up to date serves to found a probability of the highest theoretical dignity to the effect that, in so far as experience yields to the instruments on hand, either Newton's law, or one of the endlessly many conceivable mathematical laws whose differences from Newton's law lie within the limits of unavoidable experimental error is true. This truth carries its big load of factual content, and is not at all a law in the strict sense of the word. It also plainly includes + +several vaguely delimited concepts. + +All laws of fact in the exact sciences are accordingly genuine laws, but, epistemologically considered, no more than idealizing fictions with a *fundamentum in reo* They fulfil the task of rendering those theoretical sciences possible, which bring the ideal of science as near as may be to actuality, and so realize, to the extent that this can be within the unsurmountable limits of human knowledge, the ideal of explanatory theory, of law-governed unity, + +the highest theoretical aim of all scientific research into facts. Instead of the absolute knowledge that is denied us, we use our insight on individual and general facts of experience, and from these first work out those apodeictic probabilities (so to speak) in which all attainable knowledge of the real is comprehended. We then reduce these probabilities to certain exact thoughts having the genuine form of laws, and so succeed in building up formally perfect systems of explanatory theory. Such systems as theoretical mechanics, theoretical acoustics, theoretical optics, theoretical astronomy etc., really only hold as ideal possibilities with *afundamentum in re;* they do not exclude countless other possibilities, but even include these within limits. This, however, concerns us no further, nor are we concerned to discuss the practical functions in knowledge of these ideal theories, their feats of successfully predicting future facts or reconstructing past ones, and their technical feats of enabling us to master nature practically. We return to the case we were + +considering. + +If, as we have shown, pure law remains a mere ideal in the realm of factual knowledge, it is realized in the realm of 'purely conceptual' knowledge. In this sphere our purely logical laws belong, as well as the laws of *mathesis pura.* Their origin, or, rather, their justifying proof, is not an inductive one, and so they are free from that existential content which attaches to all probabilities as such, even to such as are the highest and most valuable. What they say has entire validity: they themselves in their absolute exactness are evident and proven, and not, in their stead, certain other assertions of probability of obviously vague constitution. The law we have is not one of countless theoretical possibilities within a certain factually delimited sphere. It is the single, sole truth which excludes all other possibilities and which, being established by *insight,* is kept pure from fact in its content and mode of + +proof. + +The above considerations show how intimately the two halves of the psycho logistic case hang together: that logical laws do not merely entail existential assertions of mental facts, but are also laws *for* such facts. We have just refuted the first half of their case. But the following argument suggests that our refutation also covers the second half. For just as each law established empirically and inductively from singular facts, is a law *for* such facts, so, conversely, each law *for* facts is a law established empirically and inductively, and from such a law, as has been shown, assertions with exis- + +tential content are inseparable. + +We ought of course to exclude from factual laws such general assertions as merely apply pure conceptual propositions - which state universally valid relations on a basis of pure concepts - to matters of fact. If 3 > 2, then the three books on this table also exceed the two books in this cupboard, and so for any things whatever. But our pure proposition of number does not refer to things, but to numbers in their pure generality - it is *the* number 3 that is greater than *the* number 2 - and it applies not merely to individual, but to + +'general' objects, e.g. to species of colour or sound, to types of geometrical + +figure and to suchlike timeless generalities. + +If all this is admitted, it is of course impossible to regard logical laws (considered in their purity) as the laws either of mental activities or of + +mental products. + +**§24 Continuation** + +Many would perhaps try to evade our conclusion by objecting: Not every law for facts has an empirico-inductive origin. We should rather draw a distinction. All knowledge of law rests on experience, but not all such knowledge arises out of experience inductively, by the well-known logical process which goes from singular facts, or empirical generalities of lower level, to general laws. The laws of logic are, in particular, empirical, but not inductive laws. The basic notions of logic are abstracted from psychological experience together with the purely conceptual relations given with them. What we find true in the individual case, we recognize at a glance to be true universally, since based upon abstracted contents. Experience accordingly yields an immediate awareness of the law-governed character of our mind. And since we have no need of induction, our conclusion is likewise free from inductive imperfection: it has no mere character of probability, but one of apodeictic certainty. It is not vague, but precise in sense, it in no way + +includes assertions having existential content. + +What is here objected will not, however, do. Undoubtedly our knowledge of logical laws, considered as an act of mind, presupposes an experience of individuals, has its basis in concrete intuition. But one should not confuse the *psychological* 'presuppositions' and 'bases' of the *knowledge* of a law, with the *logical* presuppositions, the grounds and premisses, of that *law: we* should also, therefore, not confuse psychological dependence (e.g. dependence of origin) with logical demonstration and justification. The latter conforms to an insight into the objective relation of ground and consequence, whereas the former relates to mental links of coexistence and succession. No one can seriously hold that the concrete singular cases before us, on which our insight into a law is 'grounded', really function as logical grounds or premisses, as if the mere existence of such singulars entailed the universality of law. Our intuitive grasp of the law may require two psychological steps: one glance at the singulars of intuition, and a related insight into law. Logically, however, only one step is required. The content of our insight is not + +inferred from singulars. + +All knowledge 'begins with experience', but it does not therefore 'arise' from experience. What we assert is that each law for facts arises *from* experience, which means that it can only be inductively based on individual experiences. If there are laws known by insight, these cannot (immediately) be laws for facts. Where in the past immediate self-evidence has been claimed + +for factual laws, it is clear that men have been confusing genuine factual laws, i.e. laws of coexistence and succession, with ideal laws to which a reference to definite times is alien, or that they have been confusing the lively persuasive force of familiar empirical generalities, with the insight + +only found in the realm of pure concepts. + +Should such an argument not seem decisive, it can none the less serve to strengthen other arguments. Another such argument will be here added. Hardly anyone would deny that all laws of pure logic are of one and the same character. If we can show, in the case of some of them, that they cannot possibly be regarded as laws for facts, the same must hold for all of them. Among logical laws there are, however, some which concern truths, which have truths as their regular 'objects'. It is the case, e.g., that for every truth *A,* its contradictory opposite is no truth. It is the case, for each pair of truths *A, B,* that their conjunctions and disjunctions2 are truths, and that if three truths *A, B,* C are so related that *A* is a ground for *B, B* for C, that *A* is also a ground for C. It is, however, absurd to treat laws which hold for truths as such, as laws for facts. No truth is a fact, i.e. something determined as to time. A truth can indeed have as its meaning that something is, that a state exists, that a change is going on etc. The truth itself is, however, raised above time: i.e. it makes no sense to attribute temporal being to it, nor to say that it arises or perishes. This absurdity is clearest in the case of the laws of truth themselves. If they were 'real' laws, they would be rules for the coexistence and succession of facts, i.e. of such facts as are truths, and to these facts, which they govern, they themselves as truths would belong. A law would therefore ascribe a 'coming and going' to certain facts called truths, among which, as one among others, the law would itself be found. The law would arise and perish in conformity with the law, a patent absurdity. The case is similar if we treat the law of truth as a law of coexistence, as temporally singular and yet fixing a general rule for each and every existence in time. Such absurdities3 are unavoidable if the fundamental distinction between ideal and real objects, and the corresponding distinction between ideal and real laws, is disregarded or misunderstood. We shall see repeatedly how this distinction settles the disputes which divide psychologistic logic + +from pure logic. + +**Psychological interpretations of** + +**basic logical principles** + +**§25 The law of contradiction in the psychologistic** + +**interpretation of Mill and Spencer** + +We have said above that a consistent carrying out of the notion oflogicallaws as laws which concern mental facts, must lead to essential misinterpretations of these laws. The logic which at present prevails has, however, generally been afraid of consistency, on this point as on all others. One might almost say that it is only inconsistency that keeps psychologism alive: to think it out to the end, is already to have given it up, unless extreme empiricism affords an example of the greatly superior strength of ingrained prejudices to the most certain deliverances of insight. What we have said in objection to this logical position ~ that on it logical truths must lose their *a priori* guarantee, and their wholly exact, purely conceptual character, and must become more or less vague probabilities resting on experience and induction, concerned with matters of fact in the mental life of man ~ all this, if we ignore its emphasis on vagueness, is what empiricism expressly teaches. We cannot attempt an exhaustive criticism of such an epistemological trend. But we have a special interest in the psychological interpretation of logical laws which this school has fostered, and whose bemusement has also spread beyond its borders.l John Stuart MilV it is well known, held the principle of contradiction to be 'one of our earliest and most familiar generalizations from experience'. Its original foundation is taken by Mill to be the fact 'that belief and disbelief are two different mental states' which exclude one another. This we know ~ we follow him *verbatim* ~ by the simplest observation of our own minds. And if we carry our observation outwards, we find that here too light and darkness, sound and silence, equality and inequality, precedence and subsequence, succession and simultaneity, any positive phenomenon, in short, and its negation, are distinct phenomena, in a relation of extreme contrariety, and that one of them is always absent when the other is present. 'I consider the axiom in question', he remarks, 'to be a generalization from all these facts.' Where the fundamental principles of his empiricistic prejudices are at stake, all the gods seem to abandon Mill's otherwise keen intelligence. Only + +one thing is hard to understand: how such a doctrine could have seemed persuasive. It is obviously false to say that the principle that two contradictory propositions cannot both be true, and in this sense exclude one another, is a generalization from the 'facts' cited, that light and darkness, sound and silence etc., exclude one another, since these are not contradictory propositions at all. It is quite unintelligible how Mill thinks he can connect these supposed facts of experience with the logical law. In vain one looks for light among Mill's parallel statements in his polemic against Hamilton. Here he approvingly quotes 'the absolutely constant law' on which the like-minded Spencer bases the logical principle in question, i.e. 'that the appearance of any positive mode of consciousness cannot occur without excluding a correlative negative mode: and that the negative mode cannot occur without excluding the correlative positive mode'.3 Who can fail to see that this law is a pure tautology, since mutual exclusion enters into the *definition* of the correlative terms 'positive and negative phenomenon'? The law of contradiction, on the other hand, is by no means tautologous. We do not *define* contradictory propositions by saying that they are mutually exclusive, and, even if the principle in question makes them so, the converse does not hold: not every pair of mutually exclusive propositions is a contradictory pair - proof enough that one should not confuse our principle with the above tautology. Mill himself does not want it to be taken as a tautology, + +since he locates its original source in an induction from experience. + +The empirical sense of the principle is not illuminated by Mill's barely intelligible references to non-coexistences among the data of outer experience: more light is shed by other statements where Mill asks if the three basic logical laws should be treated as 'inherent necessities of thought', 'an original part of our mental constitution', 'laws of our thoughts by the native structure of our minds', or if they are not perhaps laws of thought merely 'because we perceive them to be universally true of observed phenomena', an issue on which Mill does not, however, care to pronounce positively. We + +read in regard to these laws: + +They mayor may not be capable of alteration by experience, but the conditions of our existence deny to us the experience which would be required to alter them. Any assertion, therefore, which conflicts with one of these laws, any proposition, for instance, which asserts a contradiction, though it were on a subject wholly removed from the sphere of our experience, is to us unbelievable. The belief in such a proposition is, in the present constitution of nature, impossible as a mental fact. 4 + +We conclude from this passage that the inconsistency expressed in the law of contradiction, the impossibility of the joint truth of contradictory propositions, is seen by Mill as an incompatibility of such propositions in our belief. In other words, he substitutes for the impossibility that the + +propositions should *both be true,* the *real incompatibility* of the corresponding *acts of judgement.* This also fits in with Mill's repeated assertion that acts of belief are the only things that can properly be called true and false. The principle must be interpreted as saying: *Two contradictorily opposed acts of* + +*belief cannot coexist.* + +**§26 Mill's psychological interpretation of the principle yields no law, but a wholly vague, and scientifically** + +**unproven, empirical proposition** + +All sorts of difficulties now rise up. The expression of the principle is certainly incomplete. What are the circumstances, we should have to ask, in which opposed acts of belief cannot coexist? Opposed judgements can very well coexist in different individuals. We ought therefore to be more precise, and at the same time to set forth the sense of real coexistence, by saying that in the same individual, or rather in the same consciousness, contradictory acts of belief are incapable of lasting for any time, however short. But is this really a *law?* Can we really utter it with such boundless generality? What are the psychological inductions which justify its acceptance? May there not have been people, and may there not still be people who, deceived by fallacies, contrive at times to believe contradictories together? Has the occurrence of contradictions, even quite obvious ones, been scientifically investigated in the case of the insane? What happens in hypnotic states, in + +delirium tremens etc.? Does this law also hold for animals? + +Possibly the empiricist will escape these objections by suitably qualifying his law, e.g. by saying that it only applies to normal individuals of the *genus homo,* having a normal mental constitution. It is sufficient to raise the insidious question of the exact definition of the concepts 'normal individual', and 'normal mental constitution' to see how imprecise and complex the content + +of the law, as now stated, has become. + +We need not carry our discussions further, though the law's reference to time might, e.g., provide occasion to do so: they a're enough to leave us with the amazing result that our familiar principle of contradiction, which has always counted as a wholly exact, self-evident, exceptionless law, is the very paradigm of a grossly imprecise, unscientific proposition, that can only be raised to the status of a plausible surmise after its seemingly exact content has been rendered quite vague by numerous corrections. This must indeed be the truth if empiricism is right in regarding the incompatibility mentioned in the principle, as the real non-coexistence of contradictory acts of judgement, if the principle is itself to be treated as a generalization of empirical psychology. Mill's brand of empiricism does not even think of scientifically delimiting and proving his extraordinarily imprecise proposition, the immediate outcome of his psychological interpretation: it takes it in all its native imprecision, as being 'one of the earliest and most familiar + +generalizations from experience', i.e. as being what a rough generalization from pre-scientific experience might be expected to be. At the very point where the last foundations of all science are in question, we have recourse to this naIve empiricism with its blind mechanism of association. Persuasions begotten without insight, through psychological mechanisms, and with no better justification than widespread prejudices, whose origin rules out all fixed, tenable delimitation, and which, taken literally, include manifest falsehood - these are to be the last grounds on which all strictly scientific knowl- + +edge is to be justified. + +The matter need not be pursued further. It is, however, important to touch on the basic mistake in the doctrines we are attacking, by asking whether our proposition about acts of belief can, in any formulation, be the proposition we make use of in logic. It tells us: In certain subjective circumstances *X* (unfortunately not further investigated nor capable of being completely specified) two acts of belief having a Yes-No opposition cannot coexist in the same consciousness. Is this what logicians really mean when they say that two contradictory propositions cannot both be true? We need only look at the cases where our law serves to regulate our activities of judging to see that it means something quite different. In its normative form it plainly says one thing and one thing only: Whatever pairs of opposed acts of belief we may select, whether belonging to one or to several individuals, whether coexisting in the same time-stretch or separated by time-stretches, it holds strictly, and absolutely, and without exception, that not both members of each such pair are correct, or in accordance with truth. I do not think that even an empiricist could question the validity of this norm. Logic at all events, when it speaks of 'laws of thought', is concerned only with these second, *logical* laws, not with our former vague 'laws' of psychology, whose content is totally different, and has not even yet been formulated. + +**Appendix to the last two sections** + +**On certain basic defects of** *empiricism* + +Since empiricism and psychologism are intimately linked, we may perhaps permit ourselves a small digression to expose the basic errors of empiricism. Extreme empiricism is as absurd a theory of knowledge as extreme scepticism. *It destroys the possibility of the rational justification of mediate knowledge,* and so destroys *its own possibility* as a scientifically proven theory.s It admits that there is mediate knowledge, the product of various validating connections, and it does not reject principles of validation. It not only admits that there is a logic, but itself helps to construct it. If, however, all proof rests on principles governing its procedure, and if its final justification involves an appeal to such principles, then we should either be involved in a *circle* or in an infinite *regress* if the principles of proof themselves required + +further proof, in a circle if the principles of proof used to justify the principles of proof were the same as the latter, in a regress if both sets of principles were repeatedly different. Plainly, therefore, the demand for a fundamental justification of all mediate knowledge can only have a sense if we can both see and know certain ultimate principles on which all proof in the last instance rests. All principles which justify possible proofs must therefore be deductively inferrible from certain last, immediately evident principles, so that even the principles of the deduction in question all themselves occur + +among such principles. + +Extreme empiricism, therefore, since it only basically puts full trust in singular judgements of experience - a quite uncritical trust since it ignores the difficulties which so richly attend upon such singular judgements - *eo ipso* abandons all hope of rationally justifying mediate knowledge. It will not acknowledge as immediate insights, and as given truths, the ultimate principles on which the justification of mediate knowledge depends; it thinks it can do better by deriving them from experience and induction, i.e. by justifying them mediately. But if one asks what principles justify such a derivation, empiricism, forbidden to appeal to immediately evident universal principles, appeals rather to naive, uncritical, everyday experience, which it thinks to dignify more highly by explaining it psychologically in Humean fashion. It therefore fails to see that, having no insightful justification for our mediate assumptions, no justification, therefore, for the relevant proofprocedures from the immediately evident general principles that they follow, its whole psychological theory, its whole mediately known doctrine of empiricism, is without rational foundation, is, in fact, a mere assumption, + +no more than a common prejudice. + +It is extraordinary that empiricism should give a readier credence to a theory so loaded with absurdities than to the fundamental trivialities of logic and arithmetic. As a genuine psychologism, it tends always to confuse the psychological origin of certain general judgements in experience, on account of some supposed 'naturalness', with a justification of the same + +judgements. + +It is worth noting that it goes no better with Hume's moderate empiricism which, despite bouts of psycho logistic confusion, still tries to keep for the pure spheres of logic and mathematics, an *a priori* justification, and only surrenders the factual sciences to experience. Such an epistemological standpoint can likewise be shown up as untenable, even absurd, for a reason similar to that brought by us against extreme empiricism. Mediate judgements of fact - we may compress the sense of Hume's theory into this phrase - *never permit of rational justification, only of psychological explanation.* One need then but ask how this applies to the rational justification of the psychological judgements (about custom, association of ideas etc.) on which the theory itself rests, and the factual arguments that it itself employs. One then at once sees the self-evident conflict between the sense of the + +proposition that the theory seeks to prove, and the sense of the deductions that it employs to prove it. The psychological premisses of the theory are themselves mediate judgements of fact, and therefore lack all rational justification in the sense of the thesis to be established. In other words: the correctness of the theory presupposes the irrationality of its premisses, the correctness of the premisses the irrationality of the theory (or thesis). (Hume's doctrine is on this showing also a *sceptical* one, in the pointed sense to be + +defined in chapter VII.) + +**§27 Analogous objections against remaining** + +**psychological interpretations of our logical principle.** + +**Ambiguities as sources of delusion** + +It is easy to see that objections like those raised in our last section must touch every psychological misinterpretation of the so-called laws of thought, and all laws which depend on them. There is no route of escape from the demand for definition and proof by an appeal to the 'self-confidence of reason', or to the self-evidence which these laws have in logical thinking. Our insight into the *logical* laws is assured. But in so far as their thoughtcontent is seen as psychological, their original sense, to which our insight into them attaches, has been wholly altered. Exact laws have, as we saw, been turned into vague, empirical generalities: if their range of indefiniteness is duly noted, they may claim validity, but they are quite removed from selfevidence. Following their natural thought-trends, though without a clear consciousness of them, psychological theorists of knowledge no doubt *at first* understand the laws in question in an objective sense - before, that is, their arts of philosophical interpretation are brought into play. They then make the mistake of thinking that they can appeal to the self-evidence attaching to the properly interpreted formulae, a self-evidence guaranteeing their absolute validity, even when subsequent reflection has imposed wholly new senses on the logical formulae in question. If there is any case where one can justifiably speak of an insight through which truth itself is directly perceived, the statement that of two contradictory statements not both are true, is a case in point, but, if we are to deny justification to such talk, we may plainly do so in regard to all psychologizing reinterpretations of the same (or of its equivalents), e.g. 'that affirmation and negation exclude one another in our thought', 'that judgements recognized to be contradictory cannot coexist in a single consciousness', 6 'that it is impossible for us to believe an explicit contradiction' / that no one can take something to be and + +not to be at the same time, and so forth. + +Let us dwell for a while, to leave no residual unclarity, on all these shimmering wordings. Regarded more closely, they at once reveal the misleading influence of *ambiguities,* as a result of which the true law, or its equivalent normative transformation, is confused with psychological assertions. Affirmation + +and denial exclude one another in *thought.* The term 'thought', which in its wider sense covers all intellectual activities, is in the usage of certain logicians by preference applied to rational, 'logical' thought, to correct judgement. That in *correct* judgement, Yes and No exclude one another, is plain, but this is merely an equivalent of the logical law, and not at all a psychological proposition. It tells us that no judgement is correct in which the same state of affairs is at once affirmed and denied: it says nothing regarding a possible coexistence of contradictory acts of judgement, whether in *one* consciousness, or in several. (Even Hofler and Meinong's *Logic,* 1890, p. 133, inadvertently substitutes the thought of non-coexistence for our logical principle.) + +The second formula - 'that judgements recognized as contradictory cannot coexist in a single consciousness' - is likewise excluded if consciousness is interpreted as 'consciousness as such', as a timeless, *normal* consciousness. A primitive logical principle can of course not presuppose a notion like 'normality', since this cannot even be formulated without regard to such a principle. It is plain, further, that if our proposition is thus misunderstood, and is kept free from all metaphysical hypostatization, it is merely an equivalent rewriting of our logical principle, and has nothing whatever to do with + +psychology. + +An ambiguity similar to that in our first formulation occurs in our third and fourth. No one *can* believe in a contradiction, no one *can* take something both to be and not to be - no one, that is, who is rational, to add an obvious qualification. The impossibility concerns anyone who wishes to judge rightly and no one else. It does not therefore express a psychological compulsion, but our insight that contradictory propositions are not both true, that the states of affairs corresponding to them cannot both coexist, so that, if anyone claims to judge rightly, i.e. to treat the true as the true, and the false as the false, he must judge as this law prescribes. Actual judgements may be quite different: no psychological law drives the judging subject under the yoke of logical laws. We therefore again have before us an equivalent restatement of the logical law, infinitely far from the thought of psychological laws which govern judgement-phenomena. But this thought forms the essential kernel of the psychological interpretation. This last arises when 'cannot believe' etc. is taken to mean a non-coexistence of judgements instead of the incompatibility of the corresponding propositions, i.e. a neces- + +sary non-realization of their joint truth. + +The proposition: No 'reasonable' (or merely 'responsible') individual *can* believe a contradiction, permits of yet another interpretation. We call a man 'reasonable', if we credit him with an habitual tendency to judge rightly, in his own sphere, of course, and in a normal frame of mind. A man regularly capable, when normal, of hitting off 'the obvious', what 'lies to hand', is a 'responsible thinker' in the sense here in question. The avoidance of explicit contradiction is naturally included in the (quite vague) range of the 'obvious'. If we carry out this subsumption, the statement 'No responsible, reasonable + +person can believe in contradictions', does no more than trivially apply a general principle to a particular case. We should of course not *call* a thinker 'responsible', if the case were otherwise. Here again there is no reference to + +a psychological law. + +But we have not reached the end of possible interpretations. There is a grave ambiguity in the word 'impossibility', which not only points to *a union excluded by objective law,* but also to a *subjective incapacity* to unify factors: this ambiguity serves to reinforce our psychologistic tendencies. I *cannot believe* that contradictories coexist: try as hard as I will, my attempt shivers itself upon an unconquerable, felt resistance. This incapacity for belief is arguably an inwardly evident experience: I see belief in contradictories to be impossible for me, as for any being that I must think of by analogy with myself. I therefore have evident insight into a psychological law of which + +the principle of contradiction is the expression. + +To limit ourselves to the new errors in this argument, we may answer as follows: Experience shows that, once we have passed judgement on an issue, the attempt to give up the conviction now flooding us, and to embrace some opposed alternative, is vain, even if new thought-motives come up, retrospective doubts arise, old convictions at variance with our present ones haunt us, we are often assailed by an obscure 'feeling' of upsurging, embattled thought-masses. The 'vain attempt', the 'felt resistance' etc., are individual experiences, limited as to person and time, bound up with definite, if not exactly specifiable circumstances. How could they provide inner evidence for a universal *law* which transcends persons and times? One ought not to confuse the assertoric inner evidence for the existence of a single experience, with the apodeictic inner evidence for the holding of a general law. Can the evidence for the existence of a feeling which we interpreted as one of incapacity, provide the insight that what we now in fact do not bring off will be for ever denied us by law? One should note how impossible it is to specify the circumstances which play so essential a role in the situation. Often enough we make mistakes on the matter, though deep conviction as to the reality of a fact *A* pushes us to say: It is unthinkable that anyone should judge *not-A.* It is in this same sense that we are able to say: 'It is unthinkable that anyone should not accept the law of contradiction' (of which we are most firmly convinced), or 'No one can manage to believe in two contradictory propositions at the same time'. It may be that multiplied testing by examples has engendered a lively empirical judgement to this effect, but the inner evidence + +that this always and necessarily happens we do not possess at all. + +The true situation can be set forth thus: we have apodeictic inner evidence, insight in the pointed sense, in regard to the not-both-being-true of contradictory *propositions* or the not-both-being-the-case of opposed states of affairs. This law of incompatibility is the true principle of contradiction. Apodeictic inner evidence then extends itself to a useful psychological application: we can also see that two *judgements* of contradictory content, both + +merely setting forth in judgement what their intuitive foundations offer, cannot coexist. We can also see that pairs of contradictory judgements having either assertoric inner evidence, or apodeictic inner evidence, can coexist neither in a single consciousness, nor dispersed among several consciousnesses. All this merely tells us that states of affairs which, as contradictory, are objectively incompatible, can also in fact never be *thought together* in the sphere of anyone's intuition or insight - which does not at all mean that he cannot *hold* them to be coexistent. We have, on the other hand, no apodeictic inner evidence in regard to contradictory judgements in general: we only *empirically* know that, within the limits of practically familiar classes of cases, sufficiently defined for practical purposes, contradictory acts of judgement + +in fact exclude one another. + +**§28 The supposed** two-sided ness **of the principle of contradiction, in virtue of which it should be taken both as a natural law of thinking, and as a normal law** + +**for its logical regulation** + +In our psychologically obsessed age, few logicians have been quite able to steer clear of psychological misinterpretations of logical principles, even if they have stood out against attempts to found logic on psychology, and even if they would, on other grounds, resent the charge of 'psychologism'. What is not psychological is not accessible to psychological illumination, and each well-meant attempt to use psychological researches to throw light on the essence of 'laws of thinking', presupposes a psychological reinterpretation of those laws. If one reflects on these truths, one will have to count all German logicians who have followed the lead of Sigwart among such psychological reinterpreters, even if they have been far from expressly formulating, or characterizing, logical laws as psychological, and even if they have strongly opposed them to other psychological laws. If such conceptual shifts are not expressed in the chosen formulations of the laws, they more certainly appear in the accompanying elucidations, or in the whole expository context. Very remarkable attempts have been made to give the principle of contradiction a *double status,* in virtue of which it is, on the one hand, a *natural law* which determines our actual judging, while, on the other hand, it is a *normal law,* serving as a foundation to all logical rules. This conception is most attractively presented by F. A. Lange in his *Logische Studien,* a brilliant work whose aim is not to contribute to a psychologistic logic a la Mill, but to lay 'new foundations for formal logic' . But if one looks more closely at these 'new foundations', one reads that the truths of logic, like those of mathematics, derive from our intuition of space *(op. cit.* (1877), p. 130), and that, 'since the simple foundations of these sciences guarantee the strict correctness of all knowledge whatsoever', they are 'the foundations of our intellectual organization', and that the 'lawfulness we admire in them, *springs* + +*from ourselves .* .. from our own unconscious foundations' *(op. cit.* p. 148). When we read this, we cannot fail to classify Lange's view as a psychologism, even if of another sort, to which Kant's formal idealism - on the prevailing interpretation - as well as all other forms of the doctrine of innate faculties + +and innate sources of knowledge, belong. 8 Lange writes on this point as follows: + +The law of contradiction is the point at which the natural laws of thought come into touch with the normative laws. The ever-active psychological conditions of our idea-formation bring forth truth and error in ever burgeoning abundance in our natural, unregulated thinking, but they are supplemented, restricted, and employed towards a definite end, by the fact that we cannot combine contradictory elements in our thought, when once they have been made (as it were) to coincide. The mind swallows the grossest contradictions as long as the contradictory elements can be kept apart in different thought-compartments. Only when a statement and its contradictory relate to the same object, do we lose our power to combine them: we either become quite unsure of ourselves or one of the two assertions has to yield. Psychologically such an elimination of contradiction may be temporary, since the immediate coincidence of the contradictions is temporary. What has deep roots in different departments of thought cannot simply be destroyed, if mere inferences have shown it to be contradictory. At the point where the consequences of the two propositions are brought to immediate coincidence, this result certainly follows, but it does not filter back through the whole deductive chain to the seat of the original conflict. Doubt as to the validity of this deductive chain or as to the identity of its object often serve to protect error. And even when such error is disturbed for the moment, it springs once more from the familiar round of associated ideas, and lives on for as long as repeated assaults do not finally lay + +it low. + +Despite this toughness of error, the psychological law which rules out the union of immediate contradictions must continue to exert great influence on our thought. It is the sharp edge by which, in the course of experience, untenable combinations of ideas are destroyed while the more tenable combinations survive. It is the destructive principle in the natural progress of human thought, which, like the progress of organisms, depends on the fact that ever new combinations of ideas are being produced, of which the main mass are continually destroyed, while the + +better ones survive and have further effects. + +This *psychological* law of contradiction is given immediately by our organism, and operates prior to all experience, as a condition of all experience. Its mode of action is objective, and it need not first be + +If we now wish to conceive of the same law as the foundation of logic, if we wish to acknowledge it as the *normative law* of all thought, as it also has been operative as a law of nature without our acknowledgement, then we certainly have need of typical intuitions to convince + +us, as in the case of all other axioms. + +*(op. cit.* p. 27 *f)* + +What is the essential element in logic, when all psychological additions have been stripped away? Only the fact of the continual removal of contradictories. It is a mere pleonasm in our intuitively based schema if one denies that contradiction *can* exist, as if there were yet another necessity behind the ground of the necessary. The fact is that a contradiction *does not exist,* that each judgement which oversteps the limits of this notion, is at once superseded by an opposed, better founded judgement. But this factual supersession is for logic the ultimate ground of all rules. Psychologically regarded, it can itself again be called 'necessary', in that it is seen as a special case of a more general law of nature. With this, however, logic has nothing to do, since it originates at the same + +point as its law of contradiction. + +*(op. cit.* p. 49) + +These doctrines of F. A. Lange have, in particular, had a plain influence on K. Kroman *(Unsere Naturerkenntnis,* trans. by Fischer-Benzon, Copenhagen, 1883) and G. Heymans *(Die Gesetze und Elemente des wissenschaftlichen Denkens,* Leipzig, 1890, 1894). To the latter we owe a systematic attempt to base epistemology on psychology in the most thoroughgoing manner. As an almost pure thought-experiment it must be warmly welcomed: we shall have occasion to go into it more fully. Similar notions have been expressed by O. Liebmann *(Gedanken und Tatsachen,* vol. 1(1882), pp. 25-7), to our surprise in the course of a discussion which quite correctly attributes to logical necessity an 'absolute validity for every rational, thinking being, whether or + +not the rest of his constitution agrees with ours or not'. + +It is plain from the above what our objections to these doctrines are. We do not deny the psychological facts mentioned in Lange's penetrating exposition, but we find nothing to justify talk of a *law of nature.* If we compare the various formulations of the supposed law with the facts, they reveal themselves as very careless expressions of the latter. If Lange had tried to describe and delimit these familiar experiences in an exact conceptual manner, he must have seen that they could not qualify as particular instances of an exact law, in the sense in which logical principles are such laws. What we have before us as a 'natural law of contradiction' is, in fact, a rough, empirical generalization, which suffers from a quite un specifiable degree of indefiniteness. It relates, moreover, merely to *normal* individual minds, for how abnormal minds behave is something on which the everyday experience + +here adduced has nothing to tell us. We miss, in short, the strictly scientific attitude, which is quite indispensable if pre-scientific judgements of experience are to be used for scientific purposes. We protest vigorously against the mixing *up* of a vague empirical generalization with an absolutely exact, purely conceptual law, which has its place in logic alone. We think it absurd to identify the one with the other, or to deduce the one from the other, or to weld both into the supposedly two-sided law of contradiction. Only sheer ignoring of the plain content of the logical law could permit us to ignore the further fact that this content is not at all relevant, directly or indirectly, to the actual elimination of contradiction in thought. This actual elimination plainly only concerns the judgement experienced by one and the same individual in one and the same time and act: it does not concern affirmation if divided among different individuals and in different times and acts. For the factual element here relevant such distinctions are essential, but they do not affect the logical law at all. For this says nothing concerning the conflict among contradictory judgements, among real, dated acts of this or that character; it only speaks of the law-based incompatibility of the timeless ideal unities we call contradictory propositions. The truth that the members of such a pair of propositions are not both true, contains no shadow of an empirical assertion about any consciousness and its acts of judgement. I think that one has only to make this quite clear to oneself, and take it seriously, to + +see the wrongness of the whole notion that we are now criticizing. + +**§29 Continuation. Sigwart's doctrine** + +Eminent thinkers before Lange have inclined to this disputed attribution of a double character to the basic laws of logic. Even Bergmann *(Reine Logik,* end of §2), otherwise little disposed to make concessions to psychologism, does so in one chance remark, but Sigwart above all is guilty. His wide influence over modern logic justifies a narrower discussion of the relevant + +passages. + +On the view of this important logician + +the principle of contradiction is a normative law in no other sense than it is a natural law, a law which simply establishes the meaning of negation. As a natural law, it merely says that it is impossible consciously to affirm that *A is B* and that *A is not B* at a given moment, but as a normative law it is applied to the whole range of standing concepts to which the unity of consciousness extends. Seen in this regard, it underlies the Principle of Contradiction ordinarily so called, which is not, however, to be coordinated with the Law of Identity (in the sense of the formula *A is A)* since it presupposes the fulfilment of this law, i.e. the + +absolute constancy of our concepts. + +Parallel things are said in the statements regarding the Law of Identity + +(interpreted as a principle of agreement): + +The difference between the principle of agreement treated as a natural and a normative law, does not lie in its own nature, but in the presupposition of its application. In the former case it is applied to what is present to consciousness: in the latter case to the ideal state of a persistent, unchanging presence of all ordered, presentative content to a single consciousness, a state which is empirically incapable of complete fulfilment. + +(Sigwart, *Logik,* 12, p. 383, §45,2) + +To this we object: How can a proposition which (as law of contradiction) 'establishes the meaning of negation', have the character of a law of nature? Sigwart of course does not mean that the law is a nominal definition which lays down the sense of the word 'negation', but only that it is rooted in the sense of 'negation', that it sets forth what pertains to the concept's meaning: Sigwart in other words only wants to say that to give up the law is to give up the meaning of 'negation'. This, however, can never make up the thoughtcontent of a law of nature, and, in particular, not of that law which Sigwart formulates in the following words: 'It is impossible consciously to affirm that *A* is *B* and that *A* is not *B* at a given moment.' Propositions whose roots lie in concepts (not mere applications of such conceptually rooted propositions to facts) can say nothing as to what we can or cannot consciously do at a given moment. If, as Sigwart elsewhere teaches, they are timeless, there can be nothing in their essential content which concerns the temporal, and which therefore concerns the factual. To drag facts into propositions of this sort is always to destroy their genuine sense. All this makes it clear that the natural law which concerns matters in time, and the normative law, the true principle of contradiction, that concerns timeless matters, differ completely in kind, and that we cannot accordingly be dealing with a single law which, *with unchanged sense merely functions differently or has a different sphere of application.* If the disputed view were correct, there should further be a general formula concerning both the law concerning facts and the law concerning ideal objects. A man who believes in a single law here, must have a single, definite conception of it. We see, however, that it is quite vain to ask for this unitary conception. To this objection I shall add another. The normative law of contradiction is thought to presuppose absolute constancy among our concepts. The law would then only hold on condition that we always used expressions with the same meaning, and where this condition was not fulfilled, it would not hold. This cannot be what the famous logician seriously believes. The *empirical* application of the law certainly presupposes that the concepts or propositions which function as the meanings of our expressions really are the same, since the law ideally extends to all possible pairs of propositions of opposed quality but *identical* subject-matter. But this of course is no condition of the + +law's *validity,* as if this were merely hypothetical, but conditions the possible *application* of the law to previously given instances. Just as it is a precondition for applying a numerical law, that we have, in a given case, numbers actually before us, and numbers of such a character as the law expressly refers to, so it is a precondition for applying the logical law of contradiction that propositions are before us; that they are propositions of identical subject- + +matter is also expressly stipulated. + +It does not seem to me helpful, furthermore, to relate the law to the Consciousness in General sketched by Sigwart. In such a concept all concepts (more exactly all expressions) would be used with absolutely identical meanings: there would be no flux of meanings, no ambiguities or *quaterniones terminorum.* The laws of logic have, however, no intrinsic, essential relation to this ideal, which we rather construct to fit them. The constant reference to an ideal consciousness makes us feel disagreeably that the logical laws perhaps only strictly hold for fictitious ideal cases, and not for such as we encounter in experience. The sense in which the laws of pure logic 'presuppose' identity of concepts has just been discussed. If our conceptions are in flux, if the same expression recurs with an altered content, we no longer have the same concept in the sense of logic, but a second one, and a new one for each further alteration. But each single concept is in itself a supraempirical unity, and falls under the logical rules which apply to its form. As the flux of empirical colour-contents and the imperfect identification of qualities do not affect colour-differentiations as *species* of qualities, as one species has ideal identity over against its manifold possible cases (which are not themselves colours, but instances of one colour), so meanings or concepts have identity in relation to the conceptions of which they are the 'contents'. Our capacity to ideate universals in singulars, to have a 'seeing' grasp of a concept in an empirical presentation, and to be assured of the identity of our conceptual intentions in repeated presentation, is presupposed by the possibility of knowledge. Just as, in the act of ideation, we intuitively lay hold of *one concept* - as the single species, whose unity over against actual instances, or instances thought of as actual, is given with *insight* - so we can apprehend the inward evidence of the logical laws as relating to concepts formed in this or that manner. Among concepts, in the sense of ideal unities, are also to be found the 'propositions' of which the principle of contradiction speaks, and so also the meanings of the algebraic signs used in the formal expression of logical principles. Wherever acts of conceptual presentation are carried out, we encounter concepts: our presentations have their 'contents', their ideal meanings, which we can lay hold of abstractively, in ideational abstraction, and this means that we can *apply* logical laws everywhere. The *validity* of these laws is, however, absolutely unrestricted, nor does it depend on our power, nor on anyone's power, to achieve acts of conceptual presentation, nor to sustain or repeat such acts in the conscious- + +**Syllogistic inferences** + +**psychologistically considered.** + +**Syllogistic and chemical formulae** + +**§30 Attempts at interpreting syllogistic principles** + +**psychologically** + +The discussions of our last chapter have mainly been on the ground of the law of contradiction, since in its case, as in the case of all fundamental logical principles, psychologistic interpretations are very tempting. The thought-motives that push our thinking in this direction have, in fact, a strong air of obviousness. Empiricistic doctrines are less often specially applied to the *laws of the syllogism:* their reducibility to the basic logical principles makes it seem needless to take further trouble with them. **If** the logical axioms are psychological laws, and the syllogistic rules follow in a purely deductive manner from these axioms, these syllogistic rules must also count as psychological. It might be thought that each fallacious inference would furnish a decisive counter-example, and that the deduction here in question would provide us with an argument against any psychological interpretation of the logical axioms. It might further be thought that the care needed in laying down, whether in thought or word, the supposed psychological content of the axioms, would convince the empiricists that such interpretations can contribute nothing whatever to proving the syllogistic formulae. Wherever such a proof succeeds, its premisses and conclusions alike have the status of laws, which differ *toto caelo* from what are called laws in psychology. But even the clearest refutations break upon the complacent conviction of the psychologistic doctrine. G. Heymans in his recent elaborate development of the doctrine, is so little dismayed by the existence of fallacious arguments, that he even regards his psychological view as confirmed by the possibility of pointing out such fallacies. For this pointing out does not consist in bettering our thought-habits, which do not as yet conform to the law of contradiction, but in drawing attention to an unnoticed contradiction in our wrong syllogism. One might well ask whether contradictions that pass unnoticed are not genuine contradictions, and whether our logical law merely affirms the impossibility of unifying contradictions that are noticed, while allowing unnoticed contradictions to be jointly true. Again, one need only + +reflect on the difference between psychological and logical incompatibility, to be quite clear that we are once more lost in the thick fog of the aforemen- + +tioned ambiguities. + +It would not profit us greatly to say that talk of 'unnoticed' contradictions in fallacious arguments is improper: that the contradiction first emerges as a novelty in the course of the thought-train that refutes it, that this emergence has as a further (psychological) consequence that we feel ourselves bound to reject this argument as invalid. One thought-movement has one consequence, another another: no psychological law connects a refutation with a fallacy. The fallacy makes an appearance on countless occasions without the refutation, and retains our conviction. What right has one thought-shift, which only follows the fallacy in certain psychological circumstances, to attribute absolute contradiction to the latter, and not merely to say that it is an invalidity in the circumstances, but that it is an objective, absolute invalidity? The same naturally holds in regard to the correct syllogistic forms in relation to their justifying demonstration through the logical axioms. How can the demonstrative thought-train that only arises in certain mental circumstances, rise to the claim that the syllogistic form it justifies is *absolutely* valid? The psychologistic doctrine has no acceptable answer to such questions. Here as elsewhere it lacks the capacity to make sense of the claim made by logical truths to objective validity, and therewith also their functioning as absolute norms of correct and false judgement. How often has it been observed and objected that the identification of logical with psychological law would also destroy every difference between correct and incorrect thinking, since the incorrect modes of judgement are no less governed by psychological laws than the correct ones? Or should we perhaps follow an arbitrary convention, and treat the outcome of certain laws as correct, of others as incorrect? How does the empiricist counter such objections? 'The thought that is directed to truth no doubt strives to achieve thought-combinations that are free from contradiction, but the *value* of these non-contradictory thought-combinations again plainly resides in the circumstance that the non-contradictory alone can be asserted, that the law of contradiction is therefore a natural law of thinking.'l Thought is here credited with an extraordinary *nisus* towards the non-contradictory, when there are, and can be, no other than non-contradictory combinations, if, indeed, there really is a law of nature to such an effect. Or is the argument any better if one says: 'We have no reason to condemn the combination of two mutually contradictory judgements as incorrect, beyond the fact that we instinctively and immediately experience it as impossible to assert two such judgements together? If one seeks to show, independently of this fact, that only the non-contradictory *may* be asserted, one finds repeatedly that the proof always presupposes what it has to prove' *(op. cit.* p. 69). One at once sees the operation of the ambiguities analysed above: our insight into the logical law that contradictory propositions are not both true, is identified + +with the instinctive, supposedly immediate 'sensation' of psychological inability to perform contradictory acts of judgement at the same time. Self-evidence and blind conviction, exact and empirical generality, logical incompatibility of states of affairs and psychological incompatibility of acts of belief, impossibility of joint truth and impossibility of joint belief, all run together. + +**§31 Syllogistic and chemical formulae** + +Heymans has tried to lend plausibility to the doctrine that syllogistic formulae express 'empirical laws of thinking' by likening them to chemical formulae. + +Just as the chemical formula 2H2 + O2 = 2H20 only expresses the general fact that, in suitable circumstances, two volumes of Hydrogen combine with one volume of Oxygen to form two volumes of water, so the logical + +formula + +*MaX* + *MaY= YiX* + *XiY* merely expresses the fact that, in suitable circumstances, two universal affirmative judgements with a common subject, produce two new particular judgements in consciousness, in which the predicate-concepts of the original judgement appear both as predicate- and as subjectconcepts. Why in this case two new judgements are produced, but not in the case of the combination *Mex* + *Me Y,* we are at present ignorant. Repeated experiment will, however, assure us of the irrefragable necessity which governs these relationships, a necessity which compels us to affirm + +the conclusion when we have conceded the premisses. + +(Heymans, *op. cit.* p. 62) + +The institution of these experiments of course demands 'an exclusion of disturbing influences', and this consists in 'representing the premiss-judgements to oneself as clearly as possible, letting the mechanism of thought operate, and then waiting for the generation or non-generation of a new judgement'. If a new judgement really arises, one must look closely to see whether there are not any intermediate stages in consciousness beside the beginning- and end-point, and must take note of these latter as exactly and completely as + +possible *(op. cit.* p. 57). + +What astonishes us in this conception is the assertion that, in the case of combinations excluded by logicians, no new judgements are generated. If we + +consider every fallacy of, e.g. the form + +*XeM* + *MeY= XeY* we shall have to say that generally, in suitable circumstances, two judgements of the forms *XeM* and *Me Y* generate a new judgement in consciousness. The analogy with the chemical formulae fits just as correctly or as badly as + +in the other cases. Naturally one is not permitted to reply that the 'circumstances' are unlike in the two cases. They are psychologically of equal interest, and the corresponding empirical propositions of equal value. Why then do we draw such a fundamental distinction between the two classes of formulae? If the question were put to us, we should naturally reply: Because we *see* in the case of the one that what they *express* are truths, while, in the case of the other, they are falsehoods. The empiricist, however, cannot give this answer. On the interpretations he accepts, the empirical propositions corresponding to fallacious inferences are valid in the same way as are those + +which correspond to other inferences. + +The empiricist appeals to the experience of 'irrefragable necessity', which, 'if the premisses are conceded, *compels* us also to hold the conclusion to be true'. But all syllogisms, whether logically justified or not, come about with psychological necessity, and the felt compulsion (when it is felt) is always the same. One who incurs a fallacy, and sustains it against critical objections, feels 'irrefragable necessity', the compulsion of not being able to think otherwise, in exactly the same way as the man who draws a correct conclusion and continues to recognize its correctness. Like all judgement, the drawing of conclusions is no arbitrary matter. This felt irrefragability so little proves real irrefragability that it may yield to the force of new reasons, even in the case of correctly drawn conclusions recognized as such. It should therefore not be confused with the genuine logical necessity that pertains to every syllogistic inference, which means, and can mean, nothing beyond the insightfully knowable (though not actually known by each judging person) validity of the syllogism, with its governance by ideal law. The law-governed character of this validity certainly first makes itself known in the insight with which we apprehend the syllogistic principle. In comparison with this, the insight accompanying a conclusion drawn here and now, seems to be an insight into the *necessary validity* ofthe particular case, i.e. a validity grounded in the law. The empiricist thinks that 'we are as yet ignorant' why the combinations of premisses condemned by Logic 'yield no conclusion'. Does he expect to discover more as knowledge widens? One would imagine that here at least we know everything that can be known, for here we *see* that each possible form of conclusion, i.e. each conclusion falling in the framework of syllogistic combinations, will combine with the combinations of premisses in question to yield a false syllogistic law. One would think that, in such a case, even an infinitely perfect intelligence could have nothing more to know. To such and like objections, one of another sort may be added; it is no less powerful, but seems less important for our purposes. It cannot be doubted that the analogy with chemical formulae does not reach far, not far enough, I consider, for us to treat very seriously the psychological laws that have been confused with the logical laws. In the chemical case, we know the circumstances in which the syntheses expressed in the formulae take place, they can be very precisely stated: this is why we count chemical equations as + +among the most valuable inductions of natural science. In the psychological case, on the other hand, our knowledge of the circumstances amounts to so little, that we have in the end nothing more to say than that people quite often think in conformity with logical laws. Circumstances which cannot be specified exactly, such as a certain 'concentration of attention', a certain 'mental freshness', a certain 'preparedness' etc., are favourable conditions for the emergence of a logical act of inference. The circumstance or conditions (in the strict sense), from which the inferential act of judgement follows with causal necessity, are entirely hidden from us. The situation being what it is, it is quite understandable that no psychologist has so far thought of introducing, one by one, into psychology, generalizations which can be connected with syllogistic formulae, and which involve the vague circumstances just mentioned. Nor has any psychologist tried to dignify such gen- + +eralizations with the title of 'laws of thought'. + +After all this, we may count as a 'hopeless' undertaking, in the sense of Kant, Heymans' interesting attempt - full of stimulating points that have not been mentioned here - at a 'theory of knowledge that could also be called a chemistry of judgements', and that is 'nothing more than a psychology of thinking'. It will at least not make us swerve from our rejection of psychologistic interpretations. Syllogistic formulae do not have the empirical content men attribute to them: their true sense is plainest when we state them in the equivalent form of *ideal incompatibilities,* e.g. It is universally the case that two propositions having the forms 'All *M's* are *X'* and 'No *P* is *M'* are not true unless a proposition having the form 'Some *X* are not *P'* is also true. And so in every case. Nothing is here said about a consciousness or the acts and circumstances of its judgement etc. If one keeps the true content of the syllogistic formulae in mind, one will vanquish the illusion that makes the experimental production of the insightful judgement which recognizes the syllogistic principle, into an experimental proof of that prin- + +ciple, or into something that can lead to such a proof. + +**Psychologism as a sceptical** + +**relativism** + +**§32 The ideal conditions for the possibility of a theory as such. The strict concept of scepticism** + +The worst objection that can be made to a theory, and particularly to a theory of logic, is that it goes against *the self-evident conditions for the possibility of a theory in general.* To set up a theory whose content is explicitly or implicitly at variance with the propositions on which the sense and the claim to validity of all theory rests, is not merely wrong, but basic- + +ally mistaken. + +There are two respects in which one can here talk of the self-evident 'conditions of the possibility' of any theory whatever. One can talk of these in a *subjective* respect. Here one's concern is with the *a priori* conditions upon which the possibility of immediate and mediate *knowledge!* depends, as also the possibility of rationally *justifying* any theory. The theory which validates knowledge is itself a piece of knowledge: its possibility depends on certain conditions, rooted, in purely conceptual fashion, in knowledge and its relation to the knowing subject. It is, e.g. part of the notion of knowledge, in the strict sense, that it is a judgement that does not merely claim to state truth, but is also certain of this claim's justification, and actually possesses the justification in question. If the judging person were never in a position to have direct personal experience and apprehension of his judgement's self-justifying character, if all his judgements lacked that inner evidence which distinguishes them from blind prejudices, and yields him luminous certainties, it would be impossible to provide a rational account and a foundation for knowledge, or to discourse on theory and science. A theory therefore violates the subjective conditions of its *own* possibility as a theory, when, following our example, it in no way prefers an inwardly evident judgement to a blind one. It thereby destroys the very thing that + +distinguishes it from an arbitrary, unwarranted assertion. + +It is plain that, by the subjective conditions of possibility, we do not here mean real conditions rooted in the individual judging subject, or in the varied species of judging beings (e.g. of human beings), but ideal conditions + +whose roots lie in the form of subjectivity as such, and in its relation to knowledge. We shall distinguish them by speaking of *noetic* conditions. **In** an *objective* respect, talk of the conditions for the possibility of any theory do not concern the theory as a subjective unity of items of knowledge, but theory as an objective unity of truths or propositions, bound together by relations of ground and consequent. The conditions here are all the *laws* whose foundation lies purely in the notion of theory, or more specifically, in the notions of truth, of proposition, of object, of property, of relation etc., the notions, i.e. which enter *essentially into the concept of theoretical unity.* To deny these laws amounts to an assertion that all such terms - theory, truth, object, property etc. -lack a *coherent sense.* A theory is selfdestroying, in this logico-objective respect, if its content offends against the laws without which theory as such can have no rational, no coherent sense. The logical offences of such a theory can lie in its *presuppositions,* in its forms of *theoretic connection,* or in the *thesis that it sets forth.* The violation of logical conditions is at its grossest when the *sense* of the theoretic thesis involves a rejection of those laws on which the rational possibility of any thesis, and the proof of any thesis, depend. The same holds of noetic conditions and of theories which violate them. We may distinguish (without attempting a classification) between false, nonsensical, logically and noetically absurd, and finally *sceptical theories.* The last cover all theories whose theses either plainly say, or analytically imply, that the logical or noetic conditions + +for the possibility of any theory are false. + +The term 'scepticism' is thus connected with a clear concept and is clearly divided into logical and noetic scepticism. The concept of such scepticism applies to the ancient forms of scepticism with theses such as: There is no truth, no knowledge, no justification of knowledge etc. Our previous treatments have shown2 that empiricism, whether moderate or extreme, is an instance of our pregnant concept of scepticism. That it is of the essence of a sceptical theory to be *nonsensical,* is at once plain from its definition. + +**§33 Scepticism in the metaphysical sense** + +The term 'scepticism' is commonly used with some vagueness. Ignoring its popular sense, we find that philosophical theories are called 'sceptical' if they try to limit human knowledge considerably and on principle, and especially if they remove from the sphere of possible knowledge wide fields of real being, or such especially precious sciences as metaphysics, natural science, + +or ethics as a rational discipline. + +Among such inauthentic forms of scepticism there is one which is readily confused with the purely epistemic scepticism here defined, which would limit knowledge to mental existence, and would deny the existence or knowability of 'things in themselves'. Such theories are plainly *metaphysical,* they have no connection with scepticism proper, their thesis is free from + +logical and noetic *absurdity,* their claim to validity is a mere question of arguments and proofs. Confusions and genuinely sceptical modifications then only arise from the paralogistic influence of tempting ambiguities or of sceptical convictions elsewhere fostered. If, e.g., a metaphysical sceptic states his view in the form 'There is no *objective* knowledge' (i.e. no knowledge of things in themselves), or 'All knowledge is *subjective'* (i.e. all factual knowledge is merely the knowledge of facts of consciousness), there is a great temptation to yield to the ambiguity of the subject-object terminology, and to transform the original sense which suits our metaphysical standpoint into a noetic-sceptical sense. The proposition 'All knowledge is subjective' becomes the totally new assertion 'All knowledge as a conscious phenomenon is subject to the laws of human consciousness: the so-called forms and laws of knowledge are merely functional forms of consciousness, or laws governing such functional forms, i.e. psychological laws'. When metaphysical scepticism thus wrongly favours epistemological scepticism, the latter, contrariwise, if taken to be self-evident, seems to provide powerful arguments + +for the former. People reason, e.g.: + +Logical laws, as laws for our functions of knowing, lack 'real meaning'; we can at least never know if they agree with things in themselves. To assume a 'preformation-system' is wholly gratuitous. If the comparison of an item of knowledge with its object (needed to establish an *adaequatio rei et intellectus)* is excluded by the notion of the thing-in-itself, this applies also to the comparison of the subjective laws of our conscious functions with the objective being of things and their laws. If there are things in themselves, we can know nothing whatever about them. + +Metaphysical questions do not concern us here. We have mentioned them only to have before us at an early stage, an instance of the confusion between + +metaphysical and logico-noetic scepticism. + +**§34 The concept of relativism and its specific forms** + +In order to criticize psychologism we have yet to discuss the concept of *subjectivism* or *relativism* which also is part of the above-mentioned metaphysical theory. One of its original forms is caught in the Protagorean formula: 'Man is the measure of all things', provided this last is interpreted as saying 'The individual man is the measure of all truth.' For each man that is true which seems to *him* true, one thing to one man and the opposite to another, if that is how he sees it. We can therefore also opt for the formula 'All truth (and knowledge) is relative - relative to the contingently judging subject'. If, however, instead of such a subject, we make some contingent *species* of judging beings the pivot of our relations, we achieve a new form of relativism. Man as *such* is then the measure of all human truth. Every + +judgement whose roots are to be found in what is *specific* to man, in the constitutive laws of man as species - is a true judgement, for us human beings. To the extent that such judgements belong to the form of common human subjectivity, the term 'subjectivism' is in place here too (in talk of the subject as the ultimate source of knowledge etc.). It is best to employ the term 'relativism', and to distinguish *individual* from *specific* relativism. The restriction of the latter to the human species, stamps it as *anthropologism.* We turn to criticism. Our interests demand that it should be very careful. + +**§35 Critique of individual relativism** + +Individual relativism is such a bare-faced and (one might almost say) 'cheeky' scepticism, that it has certainly not been seriously held in modern times. It is a doctrine no sooner set up than cast down, though only for one who recognizes the objectivity of all that pertains to logic. One cannot persuade the subjectivist any more than one can the open sceptic, a man simply lacking the ability to see that laws such as the law of contradiction have their roots in the mere meaning of truth, that from these it follows that talk of a subjective truth, that is one thing for one man and the opposite for another, must count as the purest nonsense. He will not bow to the ordinary objection that in setting up his theory he is making a claim to be convincing to others, a claim presupposing that very objectivity of truth which his thesis denies. He will naturally reply: My theory expresses my standpoint, what is true for me, and need be true for no one else. Even the subjective fact of his thinking, he will treat as true for himself, and not as true in itself. 3 That we should, however, be able to convince the subjectivist personally, and make him admit his error, is not important: what is important is to refute him in an objectively valid manner. Refutation presupposes the leverage of certain self-evident, universally valid convictions. Such are those trivial insights on which every scepticism must come to grief, insights which show up sceptical doctrines as in the strictest, most genuine sense nonsensical. The content of such assertions rejects what is part of the sense or content of every assertion and what accordingly cannot be significantly separated from any assertion. + +**§36 Critique of specific relativism and, in particular,** + +**of anthropologism** + +In the case of subjectivism, it is doubtful whether anyone seriously holds it. Modern and recent philosophy leans, however, so strongly towards specific relativism, and, in particular, towards anthropologism, that it is quite rare to encounter a thinker free from the taint of such erroneous doctrines. But such doctrines are, however, sceptical in the sense defined above, and so suffer from the grossest absurdities conceivable in a theory: we find in them, too, slightly masked, an evident contradiction between the sense of their + +thesis, and that which cannot be separated from the sense of any thesis *qua* + +thesis. It is not hard to show this in detail: + +1. Specific relativism makes the assertion: Anything is true for a given species of judging beings that, by their constitution and laws of thought, must count as true. This doctrine is absurd. For it is part of its sense that the same proposition or content of judgement can be true for a subject of the species *homo,* but may be false for another subject of a differently constituted species. The same content of judgement cannot, however, be both true and false: this follows from the mere sense of 'true' and 'false'. If the relativist gives these words their appropriate meaning, his thesis is in conflict with its own sense. It is plainly a vain evasion to plead that the words of the adduced principle of contradiction were incomplete, but that, when we unfolded the sense of the words 'true' and 'false', it was the humanly true and false that were in question. For the ordinary subjectivist could likewise plead that talk about the true and the false was inexact, and that truth (or falsehood) for the individual were what was really meant. And one would of course answer him by saying: An evidently valid law cannot have a plainly absurd meaning, and talk of what is true *for* this one or that one is absurd. It is absurd to regard it as an open possibility that the same judged content - with dangerous ambiguity we say 'the same judgement' - should be alike true and false, as one or other judges it. There will be a corresponding answer to specific relativism: 'Truth for this or that species', e.g. for the human species, is, as here meant, an absurd mode of speech. It can no doubt be used in a good sense, but it then means something wholly different, i.e. the circle of truths to which man as such has access. What is true is absolutely, intrinsically true: truth is one and the same, whether men or non-men, angels or gods apprehend and judge it. Logical laws speak of truth in this ideal unity, set over against the real multiplicity of races, individuals and experiences, and it is of this ideal unity that we all speak when we are not confused by relativism. 2. We saw that the principles of contradiction and excluded middle tell us what pertains to the mere sense of the words 'true' and 'false'. In this regard it is possible to restate our objection in the words: If the relativist says that there could be beings not bound by these principles - this assertion is easily seen as equivalent to the relativistic formula stated above - he *either* means that there could be propositions or truths, in the judgements of such beings, which do not conform to these principles, *or* he thinks that the course of judgement of such beings is not *psychologically* regulated by these principles. If he means the latter, his doctrine is not at all peculiar, since we ourselves are such beings. (One need only recall our objections to the psychologistic interpretation of logical principles.) But if he means the former, we may simply reply: Either such beings understand the words 'true' and 'false' in our sense, in which case it is irrational to speak of logical principles not holding, since they pertain to the mere sense of these words as understood by us. We should never dream of *calling* anything true or false, that was at + +variance with them. Alternatively, such beings use the words 'true' and 'false' in some different sense, and the whole dispute is then one of words. If, e.g., they call those things 'trees' which we call 'propositions', then the statements in which the logical laws are expressed of course do not hold, but they will also have lost the sense in which we asserted them. It therefore comes out that the sense of the word 'truth' has been totally altered by relativism, which yet pretends to talk of truth in the sense laid down by the logical laws, which is the only sense we all employ when we talk of truth. In a single sense there is only a single truth, in an equivocal sense there are + +naturally as many 'truths' as there are equivocal uses. + +3. The constitution of a species is a fact: from a fact it is only possible to derive other facts. To base facts relativistically on the constitution of the species therefore means to give it a factual character. This is absurd. Every fact is individually and therefore temporally determinate. In the case of truth, talk of temporal determination only makes sense in regard to a fact posited by a truth (provided, that is, that it is a truth about facts): it makes no sense in regard to the truth itself. It is absurd to think of truths as being causes or effects, as we have already indicated. If someone wished to argue from the fact that a true judgement, like any judgement, must spring from the constitution of the judging subject in virtue of appropriate natural laws, we should warn him not to confuse the 'judgement', *qua* content of judgement, i.e. as an ideal unity, with the individual, real act of judgement. It is the former that we mean when we speak of the judgement 2 x 2 = 4, which is the same whoever passes it. One should likewise not confuse the true judgement, as the correct judgement in accordance with truth, with the *truth* of this judgement or with the true content of judgement. My act of judging that 2 x 2 = 4 is no doubt causally determined, but this is not true of the + +truth 2 x 2 = 4. + +4. If, as anthropologism says, all truth has its source in our common human constitution, then, if there were no such constitution, there would be no truth. The thesis of this hypothetical assertion is absurd, since the proposition 'There is no truth' amounts in sense to the proposition 'There is a truth that there is no truth'. The absurdity of the thesis entails the absurdity of the hypothesis, but, since the hypothesis represents the negation of a valid proposition, having factual content, it admits of falsehood but not of absurdity. No one has in fact ever thought of rejecting as *absurd* those geological and physical theories which give the human race a beginning and an end in time. The stigma of absurdity therefore taints the whole hypothetical statement, since it connects an antecedent having a coherent ('logically possible') sense with an absurd ('logically impossible') consequent. The same stigma then taints anthropologism, and extends naturally, *mutatis mutandis,* to the wider form of relativism. 5. On a relativistic view the constitution of a species might yield the 'truth', valid for the species, that no such constitution existed. Must we then say that there is in reality no such constitution, or that it exists, but only for us? But + +what if all men, and all species of judging beings, were destroyed, with the exception of the species in question? We are obviously talking nonsense. The notion that the non-existence of a certain constitution should be based on this very constitution, is a flat contradiction: that the truth-conditioning, and therefore existent constitution should condition the truth (among other truths) of its own non-existence. The absurdity is not greatly lessened if we substitute existence for non-existence, and apply our arguments, not to an imaginary species, which from a relativistic standpoint is possible, but to our human species. Our contradiction then vanishes, but not the absurdity associated with it. The relativity of truth means that, what we call truth, depends on the constitution of the species *homo* and the laws which govern this species. Such a dependence will and can only be thought of as causal. The truth that such a constitution and such laws subsist must then have its real explanation in the fact of this subsistence: the principles of our explanation must be identical with such laws - again mere nonsense. Our constitution would be *causa sui* in respect of laws, which would cause themselves in virtue of themselves etc. 6. The relativity of truth entails the relativity of cosmic existence. For the world is merely the unified objective totality corresponding to, and inseparable from, the ideal system of all factual truth. One cannot subjectivize truth, and allow its object (which only exists as long as truth subsists) to count as absolutely existent, or as existent 'in itself'. There would therefore be no world 'in itself', but only a world for us, or for any other chance species of being. This may suit some, but it becomes dubious once we point out that the ego and its conscious contents also pertain to the world. That I am, and that I am experiencing this or that, might be false if my specific constitution were such as to force me to deny these propositions. And there would be absolutely no world, not merely no world for this or that one, if no actual species of judging beings in the world was so constituted as to have to recognize a world (and itself in that world). **If** we confine ourselves to the only species actually known to us, animal species, then a change in their constitution would mean a change in the world, and that although animal species are thought to be evolutionary products of the world. We are playing a pretty game: man evolves from the world and the world from + +man; God creates man and man God. + +The essential core of this objection lies in the self-evident conflict between relativism and the inner evidence of immediately intuited existence, i.e. with the evidence of 'inner observation' in the legitimate, indispensable sense. The inner evidence of judgements resting on intuition is rightly contested when such judgements intentionally transcend the content of the actual data of consciousness. They have true inward evidence when their intention rests on this content itself, and finds fulfilment in it, just as it is. This inner evidence is not attainted by the vagueness of all such judgements: one need only think of the ineliminable vagueness of the determination of time, and + +**§37 General observation. The concept of relativism** + +**in an extended sense** + +Our two forms of relativism are special cases of relativism in the widest sense of the word, as a doctrine which somehow derives the pure principles of logic from facts. Facts are 'contingent': they might very well not have been the case, they might have been different. If the facts then differ, logical principles also will differ; they will also be contingent, with a being relative to the facts on which they are founded. I do not wish to counter this by merely bringing in the apodeictic inner evidence of logical laws, points argued for in former chapters: I wish to bring in another point which is more important in this context (cf. §32 of the present chapter). Anyone can see from my statements up to this point that for me the pure truths of logic are all the ideal laws which have their whole foundation in the 'sense', the 'essence' or the 'content', of the concepts of Truth, Proposition, Object, Property, Relation, Combination, Law, Fact etc. More generally stated, they have their whole foundation in the sense of the concepts which make up the heritage of *all* science, which represent the categories of constituents out of which science as such is essentially constituted. Laws of this sort should not be violated by any theoretical assertion, proof or theory, not because such a thing would render the latter false - so would conflict with any truth - but because it would render them inherently absurd. An assertion, e.g., whose content quarrels with the principles whose roots lie in the *sense* of truth as such, is self-cancelling. For to assert, is to maintain the truth of this or that content. A proof whose content quarrels with the principles rooted in the *sense* of the relation of ground and consequent, is selfcancelling. For to prove, is to state that there is such and such a relation of ground and consequent etc. That an assertion is 'self-cancelling', is 'logically absurd', means that its particular content (sense, meaning) contradicts the general demands of its own, pertinent meaning-categories, contradicts what has its general root in the general meaning of those categories. It is now clear that, in this pregnant sense, any theory is logically absurd which deduces logical principles from any matters of fact. To do so is at variance with the general sense of the concepts of 'logical principle' and 'fact', or, to speak more precisely and more generally, of the concepts of 'truth based on the mere content of concepts' and 'truth concerning individual existence'. It is easy to see that the objections against the above discussed relativistic theory + +are, in the main, objections to relativism in the most general sense. + +**§38 Psychologism in all its forms is a relativism** + +In our attacks on relativism, we have of course had psychologism in mind. Psychologism in all its subvarieties and individual elaborations is in fact the same as relativism, though not always recognized and expressly allowed to + +be such. It makes no difference whether, as a formal idealism, based on a 'transcendental psychology', it seeks to save the objectivity of knowledge, or whether, leaning on empirical psychology, it accepts relativism as its + +ineluctable fate. + +Every doctrine is *ipso faeto* relativistic, a case of specific relativism, if, with the empiricists, it treats the pure laws of logic as empirical, psychological laws. It is likewise relativistic, if, with the apriorists, it deduces these laws, in more or less mythic fashion, from certain 'original forms' or 'modes of functioning' of the (human) understanding, from consciousness as such, conceived as generic (human) reason, from the psycho-physical constitution of man, from the *intel/eetus ipse* which, as an innate (generically human) disposition, precedes all actual thought and experience. All the objections we have made to specific relativism also affect such doctrines. One must of course take the somewhat shifting key-words of apriorism, e.g. 'understanding', 'reason', 'consciousness', in the natural sense which gives them an essential connection with the human species. It is the curse of the theories under consideration that they at one time give these words a real, at another time an ideal sense, and so weave an inextricable tangle of true and false statements. Aprioristic theories, to the extent that they yield to relativistic motives, must be counted as relativistic. Such relativism is no doubt restricted, i.e., to the realm of mathematics and natural science, when, as in the case of some Kantian thinkers, certain logical principles are set aside as principles of 'analytic' judgements, but sceptical absurdities are not thereby avoided. For, in their narrower field, they still deduce truth from generic human nature, the ideal from the real, or, more precisely, the necessity of + +laws from the contingency of facts. + +We are, however, more interested in the extreme, consistent psychologism which permits no such restrictions. To such a psychologism the main English empiricists, as well as the more recent German logicians, belong, i.e. thinkers such as Mill, Bain, Wundt, Sigwart, Erdmann and Lipps. To criticize all such works is neither possible nor desirable. In view, however, of the reformatory aims of these Prolegomena, I do not wish to pass over the main works of modern German logic, and especially not the important work of Sigwart, which, more than any other, has pushed logic in the last decades + +into psychological channels. + +**§39 Anthropologism in Sigwart's Logic** + +Isolated statements of a psychologistic tone and character are to be found, as passing misunderstandings, in thinkers whose logical works have a consciously antipsychologistic tendency. This is not so in the case of Sigwart. Psychologism is in his case not an unessential, eliminable addition, but the systematically dominant, basic conception of his work. Right at the beginning of this work, he expressly denies 'that the norms of logic (not merely + +technical, methodological rules, but the principles of pure logic, the law of contradiction, of sufficient ground etc.) can be otherwise known than by studying the natural powers and types of functioning that these norms are to regulate' *(Logik,* 12, p. 22). His whole mode of treating the discipline accords with this conception. Logic, according to Sigwart, is divided into an analytic, a law-giving and a technical part. If we ignore this last, as not concerning us here, the analytic part has as its task 'to investigate the nature of the function for which rules must be found'. On this the law-giving part is built, which has to set up the 'conditions and laws of its normal functioning' *(op. cit.* §4, p. 16). The 'demand that our thought should be necessarily and universally valid', if 'kept to the known functions of the judgement in all its factors and conditions', yields 'definite norms which judgement must satisfy'. These demands are concentrated in two points: '(I) that the elements of the judgement should be completely definite, conceptually fixed, and (2) that the act of judging should arise necessarily out of its presuppositions. This part therefore embraces the doctrine of concepts and syllogisms as the whole set of normative laws for the formation of perfect judgements' *(op. cit.* p. 20 *f).* In other words, this part contains all the principles and laws of pure logic (to the extent that these are envisaged by the traditional or the Sigwartian logic), and to Sigwart these principles and laws really have + +a psychological foundation. + +His detailed statements agree with this programme. Nowhere does he remove the laws and theorems of pure logic, and the objective elements out of which they are constituted, from the flux of psychological and practical research into knowledge. Sigwart always talks of *our* thought and its *junctions,* where he is trying to characterize logical necessity, with its ideal legality, as opposed to psychological contingencies. Pure laws like that of contradiction or sufficient ground, are constantly called 'laws of functioning' or 'fundamental forms of the movement of our thought' *(op. cit.* p. 184 and the whole context of pp. 184-5). We read, for instance: 'Though negation is rooted in a movement of our thought which goes beyond reality, and applies contents to one another that cannot be combined, yet there can be no doubt that Aristotle's principle only purports to touch *the nature oj our thought' (op. cit.* p. 253). 'The absolute validity of the law of contradiction, and of the consequent laws which deny a *contradictio in adjecto',* we read in another passage, rests 'on our immediate consciousness that we always do and always will do the same thing when we deny' *(op. cit.* p. 386). The same holds, on Sigwart's view, of the law of identity (as 'principle of agreement'), and of all purely conceptual propositions and propositions of pure 10gic.4 + +We read statements like the following: + +If we reject the possibility of knowing something as it is in itself, if being is no more than one of the ideas produced by ourselves, it still remains the case that objectivity is attributed by us to such ideas as we produce + +with a consciousness of necessity, and that, whenever we treat anything as existent, we assert thereby that all other thinking beings, even purely hypothetical ones, endowed with *the same nature as ourselves,* must + +produce it with the same necessity. + +*(op. cit.* p. 7 *f)* + +The same anthropological tendency pervades all the statements relative to basic logical concepts, and in the first place to the concept of truth. It is, says Sigwart, 'a fiction ... that a judgement could be true if we abstract from the fact that some intelligence thinks such a judgement'. A philosopher who speaks in this manner has accepted a psycho logistic reinterpretation of truth. On Sigwart's view, it would be a fiction to speak of truths that *hold* in themselves unknown to anyone, e.g. such truths as transcend men's capacity for knowledge. An atheist, at least, who rejects superhuman intelligences, could not speak in this fashion, nor could such as we, before we have proofs that there are such intelligences. The judgement expressed in the formula of gravitation was not true before the time of Newton, which makes it, strictly speaking, a self-contradictory and wholly false utterance, since an unrestricted validity for all times is plainly part of what it means to assert. To go further into Sigwart's many statements which concern the notion of *truth* would involve us in an inadmissibly long treatment. But it would at least show that we were right in taking the passage we quoted literally. Sigwart resolves truth into conscious experiences: though he often talks of objective truth, he renounces its true objectivity, which depends on its supraempirical ideality. Experiences are real particulars, temporally determinate, which come into being and pass away. Truth, however, is 'eternal', or, better put, it is an Idea, and so beyond time. It makes no sense to give truth a date in time, nor a duration which extends throughout time. Naturally one says of truth that on occasion it 'comes to mind', and is accordingly 'apprehended' or 'experienced' by us. But such 'apprehension', 'experiencing' and 'coming to consciousness', are spoken of in quite a different sense in relation to ideal being, from what they have in relation to empirical, individualized being. We do not 'apprehend' truth as we apprehend some empirical content which comes up, and again vanishes, in the stream of mental experiences: truth is not a phenomenon among phenomena, but is an experience in that totally different sense in which a universal, an Idea, is an experience. We are conscious of truth, as we are in general conscious of a + +Species, e.g. of 'the' Colour Red. + +A red object stands before us, but this red object is not the Species Red. Nor does the concrete object contain the Species as a 'psychological' or 'metaphysical' part. The part, the non-independent moment of red, is, like the concrete whole object, something individual, something here and now, something which arises and vanishes with the concrete whole object, and which is *like,* not identical, in different red objects. Redness, however, is an + +ideal unity, in regard to which it is absurd to speak of coming into being or passing away. The part (moment) red is not Redness, but an instance of Redness. And, as universal objects differ from singular ones, so, too, do our acts of apprehending them. We do something wholly different if, looking at an intuited concretum, we refer to its sensed redness, the individual feature it has here and now, and if, on the other hand, we refer to the Species Redness, as when we say that Redness is a Colour. And just as, while regarding some concrete case, we refer, not to it, but to its universal, its Idea, so, while regarding several acts of such Ideation, we rise to the inwardly evident recognition of the identity of these ideal unities which are meant in our single acts. These unities have identity in the authentic, strictest sense: they are *identical* Species, or are Species of the *same* Genus, etc. Truth now is likewise an Idea: like any other Idea it is given in an act of Ideation based upon an intuition - this last naturally is the act of insight and we are evidently clear as to truth's unity and identity over against the dispersed multitude of concrete, compared cases of inwardly evident judgement. And just as, in other cases, the being or 'holding' of something general amounts to an *ideal* possibility - i.e. a possibility in regard to the being of empirical cases falling under the general Idea - so too in this case: the statements 'It is the truth that .. .' and 'There could have been thinking beings having insight into judgements to the effect that .. .', are equivalent. If there are no intelligent beings, if the natural order excludes them, or if they are, in a *real* sense, impossible - or if there are no beings capable of knowing certain classes of truths - then such *ideal* possibilities remain without fulfilling actuality. The apprehension, knowledge, bringing to consciousness of truth (or of certain classes of truths), is nowhere ever realized. Each truth, however, remains in itself what it is, it retains its ideal being: it does not hang somewhere in the void, but is a case of validity in the timeless realm of Ideas. It belongs to the realm of the absolutely valid, into which we fit all cases of validity into which we have *insight* or at least well-founded surmises, and in which we further locate the vaguely presented range of things indirectly and indefinitely thought valid, i.e. the cases of validity not + +as yet known to us, and perhaps never to be known. + +In this situation, Sigwart does not seem to me to press forward to a clear position. He would like to save the objectivity of truth, and not let it sink under the tide of subjective phenomenalism. But, if we enquire just how Sigwart's psychological epistemology hopes to penetrate to the objectivity + +of truth, we come upon statements like the following: + +The certainty of keeping to a judgement, of the irrevocability of a synthesis, that I shall always say the same thing5 - this certainty can only be present when I see that it does not rest on *momentary, variable, psychological motives,* but on something that *stays unalterably the same wherever I think,* and is immune from all change. This, on the one hand, + +is my *self-consciousness itself,* the certainty that I am and that I think, that I am I, the being who now thinks and who has thought, who thinks of this and that. On the one hand, it is what I judge about, *what I think of, in its invariant content: recognized as identical by myself:* which is quite + +independent of the individual states of the thinker. + +*(op. cit.* §39.2, p. 310) + +A psychologism consistent in its relativism will naturally here reply: Not merely individual variation, but pervasive constancies, such as the whole invariant content and the abiding functional laws that govern it, are psychological facts. If there are such traits and laws essentially common to all men, then they make up the specific nature of man. All truth in its universal validity is therefore relative to the human species, or, more generally, to some species or other of thinking beings. If species differ, so do truths and + +laws of thought. + +We for our part would say: Universal likeness of content, and constant functional laws of nature which regulate the production of such content, do not constitute a genuine universal validity, which rather rests upon ideality. If all creatures of a genus are constitutionally compelled to judge alike, they are in empirical agreement, but, in the ideal sense demanded by a supraempirical logic, there might as well have been disagreement as agreement. To define truth in terms of a community of nature is to abandon its notion. If truth were essentially related to thinking intelligences, their mental functions and modes of change, it would arise and perish with them, with the species at least, if not with the individual. With the genuine objectivity of truth, the objectivity of being, even the objectivity of subjective being or the being of the subject, would be gone. What if, e.g., no thinking being were capable of seriously postulating its own being? Then such thinking beings would be and also not be. Truth and being are 'categories' in the same sense, and plainly correlative: truth cannot be relativized, while the objectivity of being is maintained. The relativization of truth presupposes the objective being of the point to which things are relative: this is the contradiction in + +relativism. + +Sigwart's doctrine of universality is in harmony with the rest of his psychologism: we must treat it here, since the ideality of truth presupposes the ideality of the universal, the conceptual. On occasion he says in jest that 'the universal as such is only in our heads' *(op. cit.* p. 103 Note): more seriously he remarks that it is 'something purely inward ... depending on nothing but the inner power of our thought' *(op. cit.* §45.9, p. 388). One may undoubtedly say this of our conceptual presentation, as a subjective act having this or that psychological content. But the 'what' of such presentation, the concept, can in no sense be regarded as a real part of this psychological content, as something here and now, which comes and goes with the + +Sigwart is consistent in practising the same relativization he uses on the notion of truth on the very closely connected concepts of *ground* and *necessity.* 'A logical ground', he says, 'that is unknown to us, is, in strictness a contradiction, for a ground only becomes a logical ground when we know it' *(op. cit.* §32.2, p. 248). The statement that mathematical theorems have their ground in mathematical axioms therefore relates, 'in strictness', to a fact of human psychology. Could we still hold this fact to be a fact whether or not anyone knew, knows or will know it? The usual manner of speaking, which gives objectivity to relations of ground and consequent, and talks of + +their *discovery,* must accordingly be mistaken. + +Despite Sigwart's earnest attempts to distinguish essentially different notions of ground, and the acuteness he shows therein - an acuteness only to be expected in so eminent a thinker - he is still hindered by the psychologistic tendency of his thought from making the most essential distinction of all, one which presupposes a sharp sundering of ideal from real. When he opposes the 'logical ground' or 'ground of truth' to the 'psychological ground of certainty', he finds the former merely in a certain universal alikeness, alikeness of what is presented, 'since only this, not an individual's mood etc., can be common to all'. We need not reiterate the objections raised above. The fundamental distinction between a *purely logical ground of truth* and a *normatively logical ground of judgement* is not to be found in Sigwart. On the one hand, a truth (not a true judgement, but the ideally valid unity), has a ground, which is tantamount to saying that there is a theoretical proof which deduces the truth from this objective, theoretical ground. The principle of sufficient ground is to be taken in this sense, and in this alone. And on *this* acceptation of ground, it is not at all the case that every judgement has a ground, let alone that it 'implicitly asserts' such a ground. Every principle of inference, every genuine axiom, is in this sense groundless, as in the opposite direction likewise every judgement of fact. Only the probability of a fact can be grounded, not the fact itself, or the judgement of fact. The expression 'ground of judgement', on the other hand - if we ignore the psychological 'grounds' or causes of judging and their motivating contents6 - means no more than our *logical right* to judge. In this sense, every judgement certainly 'claims' this right (though there are objections to saying that the right is 'implicitly asserted'). This means that we may demand of each judgement that it should declare to be true what is true. As craftsmen of knowledge, i.e. logicians in the ordinary sense, we must demand many things of our judgements with an eye to the further growth of knowledge. If these are unfulfilled, we reproach a judgement with logical imperfection, with 'groundlessness': the latter expression certainly involves a stretching of the + +word's ordinary meaning. + +There are similar objections to Sigwart's statements about necessity. We read: 'If we are to talk intelligibly, all logical necessity ultimately presupposes the *existence* of a thinking subject whose nature it is to think in this + +manner' *(op. cit.* §33.7, p. 262). Or we may follow up his statements regarding the difference between assertoric and apodeictic judgements, which Sigwart thinks unessential, 'since in every judgement uttered in full consciousness, the necessity of uttering it is also asserted' *(op. cit.* §31.1, p. 230 *ff).* Sigwart has not given reciprocal distinctness to two totally different concepts of necessity. The subjective necessity, the compulsive conviction, which colours every judgement (or rather, appears in each such judgement when, remaining under its sway, we try to assert its contrary) is not distinguished from entirely different concepts of necessity, from apodeictic necessity, in particular, the peculiar consciousness in which we apprehend *law,* or *conformity to law,* with insight. The latter (really twofold) concept of necessity is really quite lacking in Sigwart. He quite ignores the fundamental equivocation which permits us to apply the term 'necessary', not only to our apodeictic *consciousness* of necessity, but also to its *objective correlate,* i.e. the law, or the conformity to the law, of which this consciousness represents the insight. It is only in the latter sense that the expressions 'It is necessary that .. .' and 'It is a law that ... ' gain their objective equivalence, and likewise the expressions'S is necessarily *P'* and 'S's being *P* is grounded on a law'. It is naturally the second, *purely objective, ideal* notion, which underlies all apodeictic judgements in the objective sense of pure logic: it alone dominates and constitutes all theoretical unity, it determines the meaning of a hypothetical combination as an objectively ideal form of propositional truth, it connects the conclusion as a 'necessary' (ideally law-governed) con- + +sequence with the premisses. + +How little Sigwart does justice to these differences, how deeply he is enmeshed in his psychologism, is shown by his treatments of Leibniz's fundamental distinction between *verites de raison et celles de fait.* The 'necessity' of both sorts of truth, Sigwart thinks, is 'ultimately hypothetical', for 'from the fact that the contrary of a factual truth is not impossible *a priori,* it does not follow that it is not necessary for me to assert it, once the fact has occurred, or that the opposite assertion would be possible for one who knows the fact' *(op. cit.* §31.6, p. 239). And again: 'On the other hand, our possession of universal concepts on which propositions of identity rest, is ultimately a factual matter, which has to be there before the principle of identity can be applied to it, and so can generate a necessary judgement'. From which he thinks he can conclude that Leibniz's distinction 'in respect + +of necessity, breaks down' *(op. cit.* p. 240). + +What is here maintained at the outset is quite correct. Every judgement, while I make it, represents a necessary assertion for me, as its denial, while I remain sure of my judgement, represents an impossibility for me. But does Leibniz intend this psychological necessity when he denies necessity, rationality to factual truths? It is likewise certain that one can know no law without possessing the universal concepts out of which it is built. This possession, certainly, like the whole knowledge of a law, is a factual matter. But + +did Leibniz call the knowing of a law 'necessary', and not rather the truth of the law that we know? The necessity of the *verite de raison* surely accords quite well with the contingency of the act of judgement, to the extent that this amounts to insight and knowledge. Only through a confusion of two essentially different concepts of knowledge, a subjective, psycho logistic concept and Leibniz's objective, idealistic one, can Sigwart wind up his argument by holding that Leibniz's distinction 'in respect of the character of necessity breaks down'. There is undeniably a subjective, experiential distinction which corresponds to the fundamental objective-ideal distinction between law and fact. If we never had experienced the consciousness of rationality, of apodeicticity in its characteristic distinction from the consciousness of facticity, we should not have possessed the concept of law, nor been able to distinguish fact from law. We should not have been able to distinguish generic (Ideal, law-determined) generality from universal (factual, contingent) generality, nor necessary (i.e. law-determined, generic) implication from factual (i.e. contingently universal) implication. This follows from the fact that concepts not given as combinations of known concepts (nor as combinations of known forms of combination) could only have arisen in us from an intuition of individual instances. Leibniz's *verites de raison* are merely the laws, i.e. the ideal truths in the pure and strict sense, which are solely rooted in our concepts, which are given and known to us in pure, apodeictically evident generalizations. Leibniz's *verites de fait* are individual truths; they form a sphere of propositions which, even if expressed in universal form, e.g. 'All southerners are hot-blooded', are, above all, assertions of existence. + +**§40 Anthropologism in the Logic of B. Erdmann** + +Sigwart provides us with no explicit discussion of the relativistic consequences implicit in his whole treatment of the fundamental concepts and problems of logic. The same holds of Wundt. Wundt's *Logic* gives even freer rein to psychological motives than Sigwart's: it contains long epistemological chapters, but hardly touches on ultimate doubts of principle. The same is true of Lipps, in whose *Logic* psychologism is so originally and consistently sustained, so free from compromise and so thoroughly carried out in all branches of the discipline, as has not been the case since the time + +of Beneke. + +Erdmann is in a quite different case. At considerable length, and with instructive consistency, he decidedly comes down on the side of relativism, and points to possible changes in the laws of thought as a counter to the presumption 'which thinks that it can overleap the limits of our thought and find a standpoint for us beyond ourselves' (B. Erdmann, *Logik,* 11, §60, Nr. 370, p. 378 *f).* It will be useful to consider his teaching further. + +Erdmann begins by refuting the opposed standpoint. 'By a great major- + +it has been maintained, since Aristotle, that the necessity of these (logical) principles is unconditional, their validity therefore eternal ... The decisive reason for this has been sought in the impossibility of thinking judgements that contradict them. But this only proves that these principles mirror the essence of our presentation and thinking. For if they reveal this, it will not be possible to carry out their contradictories, since these seek to abolish the condition to which all our presentation + +and thinking, and so all our judgement, is bound. + +*(op. cit.* Nr. 369, p. 375) + +Some words on the sense of this argument, which seems to run: From the impossibility of successfully denying these principles, it follows that they mirror the essence of our presentation and thought, for, if they do so, this impossibility will necessarily follow. This cannot be the argument. For I cannot conclude from the fact that *A* follows from *B,* that *B* follows from *A.* The thought plainly is only that the impossibility of denying logical principles is explained by supposing that these principles 'mirror the essence of our presentation and thought'. By this last we mean that they are laws stating what generally pertains to human presentation and thought as such, 'that they state conditions to which all our presentation and thinking are bound'. Because they do this, judgements which contradict and deny them + +cannot, on Erdmann's view, be entertained. + +I can, however, neither approve this inference, nor the assertions which enter into it. It seems quite possible to me that, just on account of those laws to which all a creature's (e.g. a man's) thinking is subject, individual judgements may be framed denying the validity of these laws. The denial of these laws *contradicts* their *assertion,* but the denial as a *real act* is quite compatible with the objective validity of the laws, or with the real operation of the conditions on which the laws pronounce generally. If contradiction is an ideal relation among the contents of judgements, we are here dealing with a real relation between an act of judgement and its governing conditions. If it were the case that the laws of the association of ideas basically governed human presentation and judgement, as the association-psychology actually taught, should we then, we may ask, have to reject as absurd and impossible that a *judgement* denying these laws should itself arise through their working? (Cf. §22 above.) But even if the argument were sound, it must fail of its purpose. For the logical absolutist *(sit venia verba)* could rightly object: The *laws of thought* of which Erdmann speaks, are either not those laws of which I and everyone else speaks, in which case my thesis is untouched, or he attributes a character to them which is quite at variance with their sense. And again he would object: The *impossibility of thinking* the negation of these laws, which those laws themselves are thought to entail, is either what I and everyone mean by such an impossibility, in which case it *supports* my conception, or it is some- + +As regards the *former* alternative, the principles of logic only express certain truths whose roots are to be found in the mere sense (content) of such concepts as Truth, Falsehood, Judgement (Proposition) etc. But Erdmann calls them 'laws of thought', laws which express the essence of *our human thinking.* He thinks they state the conditions by which all *human* presentation and thinking are bound, that they would change, as he thereupon explicitly says, with a change in human nature. They accordingly have, on Erdmann's view, a real content. This, however, contradicts their character as purely conceptual propositions. No proposition whose roots lie in mere concepts, which merely states what those concepts contain, and what is given with them, makes an assertion about the real. One need only consider the genuine sense of the laws of logic to see that they do not do this. Even where they speak of judgements, they do not refer to what psychologicallaws seek to indicate by this word, i.e. judgements as real experiences, but they mean judgements in the sense of statement-meanings *in specie,* meanings which retain their identity whether serving to found actual acts of assertion or not, and without regard as to who asserts them. If logical laws are treated as laws of the real *(Realgesetze)* which, like natural laws, govern our real presentation and judgement, their whole sense is + +altered, as has been discussed at length above. + +One sees the danger of calling the principles of logic 'laws of thought'. They are only laws of thought, as we shall show more precisely in the next chapter, in the sense of being laws that have a part to play in the governance of our thinking, a mode of expression that shows that we are dealing with a practical function, a mode of use, and not with something that enters into their content. That they express the 'essence of thought' could be given a good sense in view of their normative function, provided the condition were fulfilled that in them lay the necessary and sufficient criteria for assessing the correctness of each judgement. Thus the matter was conceived by traditional rationalism, which never became clear that logical principles are no more than trivial generalities, with which our assertions may not clash on pain of being *absurd,* and that the harmony of thought with these norms guarantees no more than its formal consistency. On this ground it would be quite unfitting to go on speaking in this ideal sense of the 'essence of thinking', and to define it in terms of these laws 7 which, as we know, only keep us free from formal absurdity. It is a residue of rationalist prejudice that, even in our time, men speak of formal truth instead of formal consistency, a most + +deplorable, because misleading, play on the word 'truth'. + +Let us pass, however, to our second point. The *impossibility* of denying the laws of thought is conceived by Erdmann as the impossibility of *performing* such a denial. But we logical absolutists think these two concepts so little identical, that we deny the non-performability altogether, while maintaining the impossibility. It is not the act of denial that is impossible - this would mean, since it pertains to something real, that it is a real-impossibility + +- but it is the negative proposition which forms its content that is impossible, and this content, being ideal, is ideally impossible, which means that it is absurd, and therefore self-evidently false. This ideal impossibility of the negative proposition does not clash with the real possibility of the negative act of judgement. The last remaining equivocation should thus be eliminated, and we should say, with complete clarity, that the proposition is + +absurd, but that the act of judging it is not causally ruled out. + +In the actual thought of *normal* persons the actual denial of a law of thought does not usually occur, but it can scarcely be said that it cannot thus occur, since great philosophers like Epicurus and Hegel have denied the law of contradiction. Perhaps genius and madness are in this respect allied, perhaps there are also lunatic rejecters of the laws of thought: these will certainly also have to count as men. One should also reflect that it is in the same sense impossible to think the negation of the *consequences* of primitive logical principles as the negation of these principles themselves. It is well-known, however, that we can be mistaken regarding complicated syllogistic or arithmetical theorems, and this too is an unassailable argument. These are, however, disputed questions that do not touch anything essential. Logical impossibility, as absurdity of an ideal content of judgement, and psychological impossibility, as the non-performability of the corresponding act of judgement, are heterogeneous notions, even if the latter were to go with the former in all human cases, and the acceptance of absurdities were ruled out by natural laws. (ef. the discussions of §22 in chapter IV.) + +The logical absolutist makes use of the genuine logical impossibility of contradicting the laws of logic as an argument for the 'eternity' of these laws. What does such talk of eternity mean? Only that every judgement is bound by the pure laws of logic without regard to time and circumstances, or to individuals and species. This being bound is not meant psychologically in the sense of a thought-compulsion, but in the ideal sense of a norm: whoever judges differently, judges quite wrongly, no matter what species of mental creatures he may belong to. A relation to mental creatures plainly puts no restriction upon universality: norms for judgements bind judging beings, not stones. This is part of their sense, and so it would be ridiculous to treat stones and similar entities as in this respect exceptions. The logical absolutist's proof is now very simple. He will simply say: The following thought chain is one into which *I* have insight. Such and such principles are valid, and their validity depends merely on unfolding the content of their concepts. Any proposition, i.e. any possible content of judgement in the ideal sense, is therefore absurd, if it either immediately or mediately clashes with such principles. Such a mediate clash merely means that a purely deductive chain runs from the hypothetical truth of such contents of judgement to the consequent untruth of the principles in question. If then such contents of judgement are absurd, and as such false, any *actual judgement* which has them as its contents will be incorrect, since a judgement is called + +'correct' when what it judges, i.e. its content, is true, and incorrect when this + +content is false. + +I stress the reference to every judgement, to make plain that the sense of this strict universality rules out any restriction *eo ipso,* and so also the restriction to human or other kinds of judging persons. I can compel nobody to see what I see. But I myself cannot doubt; I once more see, here where I have insight, i.e. am embracing truth itself, that all doubt would be mistaken. I therefore find myself at a point which I have either to recognize as the Archimedean point from which the world of doubt and unreason may be levered on its hinges, or which I may sacrifice at the peril of sacrificing all reason and knowledge. I see that this is the case, and that in the latter case - if it were then still reasonable to speak of reason or unreason - I should have to pack in all rational striving for truth, all assertion and all demonstration. On all these points I find myself in conflict with our distinguished thinker + +who (following on the above citations) proceeds as follows: + +The necessity thus established of the formal logical laws could only be an unconditional one ... if our knowledge of it were such as to guarantee that the essence of the thought we find in ourselves and expressed in them, were unchangeable, or were the only possible essence of thinking, that these conditions of *our* thinking were the conditions of any possible thinking. But we only know about our own thinking. We are not in a position to construct the picture of a thought different from our own, nor therefore that of a genus of thought for all these different sorts of thinking ... Words that *appear* to describe such a genus have no sense that we can work out which would satisfy the claims raised by such an appearance. For every attempt to work out what they describe is bound to the conditions of our presentation and thinking, moves within their + +limits. + +If we lend to tempting expressions such as that of the 'essence of our thinking' a currency in purely logical contexts, if, following our analyses, we interpret them as the sum total of ideal laws which determine the formal consistency of our thinking, we should naturally also claim to give a strict proof of what Erdmann thinks unproveable: that the essence of thought is unchangeable, that it is unique in its possibility etc. It is clear, however, that Erdmann, in denying all this, does not stick to the only justifiable sense of 'essence of thinking', it is clear - as the quotation below will show more blatantly - that he thinks the laws of thought express the real essence of our thinking, that they are accordingly real laws, through which we have an immediate insight into the cognitive side of our common human constitution. This is unfortunately not the case. How could propositions which breathe no word regarding reality, which merely elucidate what is inseparably asserted in certain verbal or statement-meanings of great generality, + +guarantee important real knowledge regarding (as we read a little further + +on) the 'essence of mental events, and, in short, of our soul'? + +If, on the other hand, such laws or others *did* give us insight into the real essence of thinking, we should come to quite other conclusions than our esteemed thinker. 'We only know about our thinking.' More precisely, as scientific psychologists we not only know about our own individual thinking, but a little about human thought in general, and a little less about animal thinking. A type of thinking which differs from ours in this real sense, and species of thinking beings that exemplify it, are at least things that we can conceive: they admit of a significant description, just as this is possible in the case of imaginary natural species. Bocklin has painted most magnificent centaurs and water-sprites with the most concrete naturalness we believe in them, at least aesthetically. Who can say if the laws of nature allow of such? If, however, we enjoyed final insight into the law-governed ways in which organic elements could be combined to constitute the organism's living unity, if we knew what laws keep the stream of becoming in its typically formed channels, we could form scientifically exact concepts of many objectively possible species, and add these to those that *are* actual, and such possibilities could be as squarely discussed as are imaginary types of gravitation in the writings of theoretical physicists. The *logical possibility* of such fictions is at least unassailable, whether in the field of natural science or that of psychology. Only when we make a I-lETal3acns E1S OAAO yevos, and mix up the realm of psychological laws of thought with those of pure logic, and, further, misinterpret the latter psychologistically, will there be a shadow of justification for asserting our incapacity to imagine other modes of thinking, and for denying to the words that seem to describe these any achievable sense. Quite possibly we can form 'no real idea' of such modes of thinking, quite possibly this is unachievable for us, but such unachievability in no case amounts to impossibility in the sense of what is senseless or absurd. Possibly the following discussion will assist understanding. Theorems belonging to the theory of Abelian transcendents have no 'achievable sense' for babies in arms, or for 'babies in mathematics', as mathematicians jestingly call us laymen. As adults stand to children, as mathematicians stand to us laymen, so a higher species of thinking beings, e.g. of angels, could stand to men. Such words and concepts have no achievable sense for us, since certain peculiarities of our mental constitution stand in the way. A normal man takes about five years to understand the theory of Abelian functions or even to grasp its concepts. It might be the case that a millennium would be needed for a humanly constituted being to grasp angelic functions, though he can hardly hope to live as long as a century. But such an absolute un attainability, rooted in the natural limits of a specific constitution, would not be the one that absurdities and senseless statements offer. We are in one case concerned with propositions absolutely beyond our comprehension, though possibly consistent, and even valid in themselves. In the other case + +we understand propositions very well, but they are absurd, and we therefore 'cannot believe them', i.e. we see that, as absurd, they ought to be rejected. Let us now look at the extreme consequences which Erdmann deduces from his premisses. Basing ourselves on the 'empty postulate of an intuitive thought', we must, on his view, 'admit the *possible* existence of a thought differing in essence from our own', from which he draws the conclusion that + +logical laws only hold within the limits of our thinking, without our being able to guarantee that this thinking might not alter in character. For it is possible that such a transformation should occur, whether affecting all or only some of these laws, since they are not all analytically derivable from one of them. It is irrelevant that this possibility is unsupported by the deliverances of our self-consciousness regarding our thinking. Though nothing presages its actualization, it remains a possibility. We can only take our thought as it now is, and are not in a position to fetter its future character to its present one. We are, in particular, incapable of so grasping the essence of our mental states, in brief of our soul, that we can deduce therefrom the unalterability of + +thought as it is given to us. 8 + +According to Erdmann, + +we cannot help admitting that all the propositions whose contradictories we cannot envisage in thought, are only necessary if we presuppose the character of our thought, as definitely given in our experience: they are not absolutely necessary, or necessary in all possible conditions. On this view our logical principles retain their necessity for our thinking, but this necessity *is not seen as absolute, but as hypothetical* [in our sense, as relative]. We cannot help assenting to them - such is the nature of our presentation and thinking. They are universally valid, provided our thinking remains the same. They are necessary, since to think means for us to presuppose them, as long, that is, as they express the essence of + +our thinking. + +(cf. *op. cit.* Nr. 370, p. 378) + +I need not say, after my previous statement, how little I think these consequences are valid. It is certainly possible that there is a mental life essentially different from our own. Certainly we can only take our thinking for what it is, and it would certainly be stupid to try to deduce and permanence from 'the essence of our mental states, in brief of our soul'. But from this the totally different possibility does not follow, that changes in our specific constitution could affect all or some logical principles, and that such principles have a merely hypothetical necessity. All this is absurd, absurd in the pregnant sense which has always been employed here, a sense strictly scientific + +and free from emotive tincture. It is the curse of our ambiguous logical terminology that such doctrines can still come up and can deceive serious thinkers. If the primitive conceptual distinctions of elementary logic had been completed, and terminology clarified on their basis, and we no longer dragged around with the wretched equivocations that attach to all logical terms -law of thought, form of thought, real and formal truth, presentation, judgement, proposition, concept, character, property, ground, necessity etc. - it would not be possible for absurdities as gross as relativism to be theoretically represented in logic and epistemology, nor could they have the plausibility + +by which even eminent thinkers are blinded. + +Talk of the possibility of variable 'laws of thought', as *psychological* laws of presentation and judgement differing in many respects for varying species of mental being, and even from time to time for one and the same species all this has a good sense. For psychological 'laws' are for us 'empirical laws', approximate generalities of coexistence and succession, relating to matters of fact which may in one case be thus, in another case otherwise. We even gladly allow the possibility of varying *normative* laws of presentation and judgement. Normative laws can certainly be adapted to the specific constitution of judging beings, and so vary with them. This obviously affects the rules of practical logic as a doctrine of method, as well as the methodological prescriptions of the separate sciences. Mathematical angels may no doubt use other methods of calculation than ours - does this mean that they may have different axioms and theorems? This question carries us further. Talk of variable laws of thought only becomes absurd when we are referring to the laws of *pure logic* (to which may be added the pure laws of the theory of numbers, of ordinals, of sets etc.). The vague phrase 'normative laws of thought' by which these are likewise designated, favours the general temptation to dump them all in together with our former psychologically founded rules of thinking. They, however, are purely theoretical truths, ideal in character, rooted in their own semantic content and not straying beyond it. They can accordingly not be affected by any actual or imagined change in the + +world of 'matter of fact'. + +We must here keep in mind a threefold opposition: not merely the opposition between *practical rule* and *theoretical law,* or that between *ideal law* and *real law,* but also the opposition between an *exact law* and an *empirical law* (i.e. a statement of for-the-most-part or average universality, governed by the principle 'No law without its exception'). If our insight extended to the *exact* laws of mental process, these too would be eternal and unchangeable, as are the laws of theoretical natural science; they would therefore hold even if there were no mental processes at all. If all gravitating masses were eliminated, the law of gravitation would not thereby be suspended: it would merely lack the possibility of factual application. For it tells us nothing regarding the existence of gravitating masses, only regarding what pertains to gravitating masses as such. (No doubt, as acknowledged above, an + +idealizing fiction plays its part in the setting up of exact laws of nature: here we ignore this, confining ourselves to the mere intention of such laws.) As soon as the exact character of logical principles is conceded, and they are seen in their exactness, the possibility of their being changed by changes in the collocations of what actually is, and of consequent transformations of zoological and mental species, is ruled out, and the 'eternal' validity of such + +principles guaranteed. + +A defender of psychologism could here oppose our position by saying that the truth of logical principles, like all truth, has its seat in knowledge, and that knowledge as a mental experience is of course subject to psychological laws. But, without exhaustive discussion of the sense in which truth has its seat in knowledge, I yet point out that no change in psychological facts can turn knowledge into error, or error into knowledge. The arising and the perishing of phenomenal cases of knowledge, no doubt depends on psychological conditions, as does the arising and perishing of other mental phenomena, e.g. sensory ones. But, as no mental happenings can cause the Red I intuit not to be a Colour, but a Tone, or the lower of two tones to be the higher, or, more generally, as what rests on the general nature of an experience is elevated above all possible change, since all change affects what is individual, and makes no sense in regard to concepts, so the same holds of 'contents' of acts of knowledge. It pertains to the notion of knowledge that its content has the character of truth, a character which does not pertain to the evanescent phenomena of knowledge, but to their selfsame content, to the ideal, universal element we have in mind when we say, e.g., I know that *a* + *b* = *b* + *a,* and countless other persons know it too. Of course errors can develop out of cases of knowledge, e.g. through fallacious inferences, but this does not turn knowledge as such into error, for one is merely causally tied up with the other. It may likewise be the case that a species of beings capable of judgement may develop no knowledge, that what they suppose true may always be false, and what they suppose false true. This would leave truth and falsehood intrinsically unaffected: they are essentially properties of the contents of such judgements, not of judgements as acts. They pertain to such contents even if no one recognizes their presence. Colours, Tones, Triangles etc., always have the essential properties of Colours, Tones, Triangles etc., whether anyone in the world knows such a fact or not. The possibility, therefore, that Erdmann has sought to establish, that other beings might have quite different logical principles, cannot be accepted. An absurd possibility is an impossibility. One need only try to think out what his doctrine implies: that there might be peculiar beings, logical supermen, as it were, for whom *our logical principles do not hold,* but rather quite different principles, so that every truth for us is a falsehood for them. For them it is the case that the mental phenomena they are experiencing are not experienced by them. That we and they exist may be true for us, but is false for them etc. We everyday logicians would say: Such beings are mad, + +they talk of truth, yet destroy its laws, they say they have their own laws of thought, but they deny those on which the possibility of any such laws depends. They make assertions, yet countenance the denial of what they assert. Yes and No, truth and error, existence and non-existence, lose all their distinctness in their thought. Only they fail to notice their absurdities, which we notice, and see to be absurd in the most luminous fashion. Someone who tolerates such possibilities is divided only by a hairsbreadth from the extremest scepticism: the subjectivity of truth is applied to the species instead of to the individual person. He is a specific relativist in the sense defined above, and is exposed to the objections we developed, which we shall not here repeat. For the rest I see no reason why we should stop at the boundaries of imaginary racial differences. Why not recognize real racial differences, differences between sanity and insanity, and all individual differences, as having an equal + +right? + +Perhaps a relativist will object to our appeal to inner evidence, to the evidence with which we see the absurdity of the possibility here suggested, by repeating what we quoted above, 'that it is irrelevant that this possibility is unsupported by our self-observation', since it is obvious that our thought cannot be at variance with its own forms. Ignoring such psychologistic interpretation of our thought-forms, which was refuted above, we shall merely point out that such an expedient means absolute scepticism. If we have lost faith in the inwardly evident, how can we rationally make and sustain assertions? Perhaps, inasmuch as other people may be constituted as we are, and may incline to similar judgements in virtue of identical laws of thinking? But how can we know this, if we can know nothing whatever? Without insight, + +there can be no knowledge. + +It is really odd that men are prepared to put their trust in statements so dubious as those regarding what is common to human beings, but not in those mere trivialities, which though offering us only the slenderest instruction, grant us the clearest insight into what little they say. In this we can at least find nothing which relates to thinking beings and their specific peculiarities. The relativist cannot secure a temporarily improved position by saying that he is being treated as an extreme relativist: he is only a relativist as regards logical principles, while leaving other truths unassailed. This will not enable him to escape the general objections to specific relativism. For, if one relativizes the basic truths of logic, one relativizes all truth whatever. It is enough to consider the content of the law of contradiction and to draw + +some immediate consequences. + +Erdmann keeps far from such half-measures: he has founded his Logic on the *relativistic concept of truth* which his doctrine demands. His definition runs: The truth of a judgement consists in the fact that the logical immanence is subjectively, more specifically put, objectively, certain, and that the predicative expression of this immanence represents a necessity for thought' *(op. cit.* Nr. 278, p. 275). For an object is for Erdmann what is presented to + +us, and this in its turn is expressly identified with our presentation. In the same way, his 'objective or universal certainty' is only apparently objective, since it is 'based on the general agreement of judging subjects' *(op. cit.* p. 274). The expression 'objective truth' is to be found in Erdmann's writing, but he identifies it with 'universal validity', i.e. validity for all. This is divided for him into certainty for all, and, if I understand him rightly, also into a necessity of thought for all. This is just what is meant by the above definition. It might seem a problem how, on this definition, we should ever rise to the justified assertion of even a single case of objective truth, and how we can escape the infinite regress that his definition demands, and of which the distinguished thinker is fully conscious. He does not, unfortunately, tell us enough on this point. The judgements in which we assert that others will agree with us are of course not, as he says, this agreement itself, but how does this help us? And how are we helped by our subjective certainty regarding such agreement? Our assertion would only be *justified* if we knew of the agreement, and this means if we perceived its truth. One might also ask how one ever came to be subjectively certain of the agreement of *everyone,* and, ignoring this difficulty, whether it is at all proper to demand such universal certainty, and whether truth may not rather be the appurtenance of a select + +few than possessed by everyone. + +**The psychologistic prejudices** + +So far our attack has been mainly upon the consequences of psychologism. We now turn against its arguments: we shall try to show that what it regards + +as obvious truths are in fact delusive prejudices. + +**§41 First prejudice** + +A first prejudice runs: Prescriptions which regulate what is mental must obviously have a mental basis. It is accordingly self-evident that the normative principles of knowledge must be grounded in the psychology of knowledge. One's delusion vanishes as soon as one abandons general argumentation + +and turns to the 'things themselves'. + +We must first put an end to a distorted notion which both parties share, by pointing out that logical laws, taken in and for themselves, are not normative propositions at all in the sense of prescriptions, i.e. propositions which tell us, as part of their *content,* how one *should* judge. One must always distinguish between laws that *serve as norms* for our knowledge-activities, and laws which include normativity in their thought-content, and *assert* its + +universal obligatoriness. + +Let us take as an example the well-known syllogistic principle we expressed in the words: A mark of a mark is also a mark of the thing itself. This statement would be commendably brief if its expression were not also an obvious falsehood. lTo express it concretely, we shall have to adjust ourselves to a few more words. 'It is true of every pair of characters *A, B,* that if every object which has the character *A* also has the character *B,* and if any definite object S has the character *A,* then it also has the character *B.'* That this proposition contains the faintest thought of normativity must be strongly denied. We can employ our proposition for normative purposes, but it is not therefore a norm. Anyone who judges that every *A* is also *B,* and that a certain S is *A,* ought also to judge that this S is *B.* Everyone sees, however, that this proposition is not the original proposition of logic, but one that has been derived from it by bringing in the thought of + +The same obviously holds of all syllogistic laws, as of all laws of pure logic as such. 2 But not of such laws alone. A capacity for normative use is shared by the truths of other theoretical disciplines, and above all by those of pure mathematics, which are usually kept separate from 10gic.3 The well- + +known principle + +*(a* + *b) (a* - *b)* = *a2* - *b2* tells us, e.g. that the product of the sum and the difference of any two numbers equals the difference of their squares. Here there is no reference to our judging and the manner in which it *should* be conducted; what we have before us is a theoretical law, not a practical rule. If, however, we consider the corresponding practical proposition: 'To arrive at the product of the sum and difference of two numbers, one should find the difference of their squares', we have conversely uttered a practical rule and not a theoretical law. Here, too, the transformation of law into rule involves a bringing in of the notion of normativity; the rule is the obvious, apodeictic consequence + +of the law, but it none the less differs from it in thought-content. + +We can even go further. It is clear that *any* theoretical truth belonging to *any* field of theory, can be used in a like manner as the foundation for a universal norm of correct judgement. The laws of logic are not at all peculiar in this respect. In their proper nature, they are not normative but theoretical truths, and as such we can employ them, as we can the truths of all other + +disciplines, as norms for our judgement. + +We cannot, however, treat the general persuasion that the laws of logic are norms of thinking as quite baseless, nor the obviousness with which it impresses us as a mere delusion. These laws must have some intrinsic *prerogative* in the regulation of our thought. But does this mean that the idea of regulation, or of an 'ought', must therefore form part of the content of such laws? Can it not *follow* from that content with self-evident necessity? In other words: May not the laws of logic and pure mathematics have a distinctive meaning-content which gives them a *natural right* to regulate our + +thought? + +This simple treatment shows us how both sides have made their mistakes. The anti-psychologists went wrong by making the regulation of knowledge the 'essence', as it were, of the laws of logic. The purely theoretical character of formal logic, and its identity of character with formal mathematics, were thereby insufficiently recognized. It was correctly seen that the set of laws treated in traditional syllogistic theory were remote from psychology. Their natural right to regulate knowledge was recognized, for which reason they must be made the kernel of all practical logic. The difference between the proper content of these laws, and their function, their practical application, was, however, ignored. Men failed to see that so-called basic laws of logic were not in themselves norms, though they could be used normatively. Concern with this normative use had led men to speak of such + +laws as laws of thought, and so it appeared that these laws, too, had a psychological content, and that their only difference from what are ordinarily called psychological laws lay in this normative function, not possessed by + +other psychological laws. + +The psychologistic thinkers, on the other hand, went wrong in putting forward a presumed axiom whose invalidity we may expose in a few words: It is entirely obvious that each general truth, whether psychological or not, serves to found a rule for correct judgement, but this not only assures us of the meaningful possibility, but even of the actual existence of rules of judge- + +ment which do not have their basis in psychology. + +Not all rules which set standards for correct judgement are on that account *logical* rules. It is, however, evident that, of the genuinely logical rules which form the nucleus of a technology of scientific thinking, only one set permits and demands a psychological establishment: the technical precepts specifically adapted to human nature concerning the acquisition and criticism of scientific knowledge. The remaining, much more important group consists of normative transformations of laws, which belong solely to the objective or ideal content of the science. Psychological logicians, even such as are of the stature of a Mill or a Sigwart, treat science from its subjective side (as a methodology of the specifically human acquisition of knowledge), rather than from its objective side (as the Idea of the theoretical unity of truth), and therefore lay one-sided stress on the methodological tasks of logic. In doing so they ignore the *fundamental difference between the norms of pure logic and the technical rules of a specifically human art of thought.* These are totally different in character in their content, origin and function. The laws of logic, seen in their original intent, concern only what is ideal, while these methodological propositions concern only what is real. If the former spring from immediately evident axioms, the latter spring from empirical facts, belonging mainly to psychology. If the formulation of the former promotes our purely theoretical interests, and gives only subsidiary practical help, the latter, on the other hand, have an immediate practical aim, and they only give indirect help to our theoretical interests, in so far as they aim at the + +methodical progress of scientific knowledge. + +**§42 Elucidations** + +Every theoretical statement, we saw above, permits of a normative transformation. But the rules for correct judgement which thus arise, are not, in general, such as logic, considered as a technology, requires: few of them are, as it were, predestined to normativity. If such a logical technology is to be of real help in our scientific endeavours, it must not presuppose that full knowledge of the complete sciences which we hope to achieve by its means. We shall not be helped by the mechanical restatement of all given theoretical knowledge as norms: what we need are general norms, extending beyond all + +particular sciences to the critical evaluation of theoretical knowledge and its + +methods in general, as well as practical rules for its promotion. + +This is exactly what logic as a technology aims at, and if it aims at this as a scientific discipline, it must itself presuppose certain items of theoretical knowledge. It is clear from the start that it must attach exceptional worth to all knowledge resting only on the notions of Truth, Proposition, Subject, Predicate, Object, Property, Ground and Consequent, Relation and Relatum etc. For all science in its objective, theoretical aspects, i.e. in respect of *what* it tells us, consists of truths, truth pertains to propositions, all propositions have subjects and predicates, and refer by way of these to things or properties, propositions are connected as grounds and consequents etc. Those truths, it is now clear, which have their roots in such *essential constituents of all science considered as an objective theoretical unity,* truths which, accordingly, cannot be thought away without thinking away all that gives science as such its objective purchase and sense, such truths obviously provide the fundamental standards by which we can decide whether anything claiming to be a science, or to belong to one, whether as premiss, conclusion, syllogism, induction, proof or theory, really lives up to its intentions, or does not rather stand in an *a priori* conflict with the ideal conditions of the possibility of theory and science as such. Men should admit that truths which have their roots in the concepts which constitute the objectively conceived Idea of Science, cannot also belong to the field of any particular science. They should see that such truths, being ideal, cannot have their home-ground in the sciences of matter of fact, and therefore not in psychology. If these facts were realized, our case would be won, and it would be impossible to dispute the existence of a peculiar science of pure logic, absolutely independent of all other scientific disciplines, which delimits the concepts constitutive of the Idea of System or of theoretical unity, and which goes on to investigate the theoretical connections whose roots lie solely in these concepts. This science would have the unique peculiarity of itself, *qua* form, underlying the content of its laws; the elements and theoretical connections of which it, as a systematic unity of truths, consists, are governed by the very laws which form part + +of its theoretical content. + +That the science which deals with all sciences in respect of their form, should *eo ipso* deal with itself, may sound paradoxical, but involves no inner conflict. The simplest example will make this clear. The law of contradiction governs all truth, and since it is itself a truth, governs itself. To realize what such self-government means one need only apply the law of contradiction to itself: the resultant proposition is an obvious truism, having none of the marks of the remarkable or the questionable. This is invariably the case + +where pure logic is used to regulate itself. + +This pure logic is therefore the first and most essential foundation of methodological logic. The latter, however, has other quite different foundations contributed by psychology. Every science, as we stated above, permits + +of a double treatment: it is, on the one hand, an aggregate of human devices for acquiring, systematically delimiting and expounding this or that territory of truth. These devices are called methods, e.g. calculation by abacus or slide-rule, by written signs on a slate, by this or that computer, by logarithmic, sine- or tangent-tables, astronomical methods involving cross-wires or telescopes, physiological methods involving microscopy, staining etc. All these methods, and also all forms of exposition, are adapted to the human constitution as it at present normally is, and are in fact in part expressive of contingent, national features. Even physiological organization has a not unimportant part to play. Would our most refined optical instruments be of much use to a being whose sense of sight was attached to an end-organ + +differing considerably from our own? + +But all science permits of quite another treatment; it can be considered in regard to *what* it teaches, in regard to its theoretical content. What each statement states is - in the ideal case - a truth. No truth is, however, isolated in science: it occurs in combination with other truths in theoretical connections bound by relations of ground and consequent. This objective content of science, to the extent that it really lives up to its intent, is quite independent of the scientist's subjectivity, of the peculiarities of human nature in + +general. It is objective truth. + +Pure logic aims at this ideal side of science, in respect of its form. It does not aim at the peculiar material of the various special sciences, or the peculiarity of their truths and forms of combination: it aims at what relates to truths and theoretical combinations of truths as such. For this reason *every* science must, on its objective, theoretical side, conform to the laws of logic, + +which are of an entirely ideal character. + +In this way these ideal laws acquire a methodological significance, which they also have since mediate justification is provided by proofs whose norms are merely normative transformations of the ideal laws whose sole grounds lie in logical categories. The characteristic peculiarities of proofs mentioned in the first chapter of this work (§7) all have their origin and complete explanation in the fact that inner evidence in demonstration - whether in the syllogism, in connected, apodeictic proof, or in the unity of the most comprehensive, rational theory, or also in the unity of an argument in probabilities - is simply our consciousness of an ideal law. Purely logical reflection, whose first historic awakening occurred in the genius of Aristotle, abstracts the underlying law itself, and then brings the multiplicity of laws discoverable in this manner, and at first seen in isolation, under primitive basic laws, and so creates a scientific system which, in a purely deductive order, permits the derivation of all possible laws of pure logic, all possible forms of syllogisms, proofs etc. The forms of logic transform themselves into norms or rules telling us how we should conduct proofs, and - in relation to possible illegal formations - into rules telling us how we should + +Norms accordingly fall into two classes. One class of norms regulates all proof and all apodeictic connection *a priori;* it is purely ideal, and only relates to our human knowledge by way of a self-evident application. The other class is empirical, and relates essentially to the specifically human side of the science. It consists of what might be called mere auxiliary devices or substitutes for proofs (above §9). It has its roots in our general human constitution, in the main, in our mental constitution, since this is more important for logical technology, but also in part in our physical constitution. 4 + +**§43 A look back at the opposed arguments of idealism. Their defects and their justified sense** + +In the dispute over a psychological or objective foundation for logic, I, accordingly, occupy an intermediate position. The antipsychologists looked by preference on the ideal laws, called by us 'purely logical', while the psychologistic part fixed their gaze on the methodological rules that we have classed as 'anthropological'. This difference of orientation barred mutual understanding. The psycho logistic party were little inclined to do justice to the worthwhile core of their opponents' arguments, but this is understandable when we reflect how psychological motives and confusions played their part in these arguments, despite all pretensions to avoid them. The actual content of works which claim to expound 'formal' or 'pure' logic, must have confirmed the psychologistic party in their negative attitude, and must have made them feel that the projected discipline really only dealt with a piece of shamefaced, and therefore arbitrarily restricted psychology of cognition, or with a set of rules for cognition founded upon this. The antipsychologistic party were not at least in a position to put stress in their argument on the fact that psychology deals with laws of nature, whereas logic deals with normative laws (cf. above §19, and the citation from Drobisch in §13). The *opposite of a law of nature,* as an empirically based rule regarding what in fact is and occurs, *is not a normative law* or a prescription, but an *ideal law,* in the sense of one based purely on concepts, Ideas, purely conceived essences, and so not empirical. To the extent that formal logicians, in their talk of normative laws, were concerned with this purely conceptual, *a priori* character, their arguments hit on a point that was undoubtedly correct. But they overlooked the theoretical character of the laws of pure logic, they failed to recognize the difference between theoretical laws destined by their content to the regulation of cognition, and normative laws which are *intrin-* + +*sically* and *essentially* prescriptive. + +It is not even correct to say that the opposition between truth and falsehood is irrelevant to psychology, for truth is certainly apprehended in knowledge, and the ideal thereby becomes a determination of a real experience. But the propositions, on the other hand, which treat of this determination in its conceptual purity are not laws of real psychical happenings: the + +psychologistic party were wrong in this regard. Ignoring the essence of the ideal in general, they also ignored the ideality of truth. This important point + +will require further and fuller discussion. + +The final argument of the antipsychologistic party likewise combines truth with error. Since no logic, whether formal or methodological, can provide criteria by which every truth can be recognized as a truth, there is no circle in seeking a psychological basis for logic. It is, however, one thing to ask for such a psychological basis for logic (understanding 'logic' in the usual sense of a technology), and quite a different thing to seek such a basis for the theoretically closed group of logical propositions, that we styled 'purely logical'. It is in this respect quite repugnant (though only in a few circular cases) to deduce propositions rooted in the essential constituents of all theory, and so in the conceptual form of the systematic content of science as such, from the contingent content of some special science, and a factual science at that. Let one but conceive the principle of contradiction clearly, and then seek its foundation in some special science, let one conceive of a truth which rests on the sense of truth as such, and then base it on truths about numbers, stretches etc., or even about physical or mental matters of fact. The repugnance of such proceedings was at least clear to the exponents of formal logic, except that their confusion of purely logical with normative laws or criteria, obscured their good ideas and rendered them inoperative. The repugnancy consists basically in the fact that propositions relating to mere form (i.e. to the conceptual elements of scientific theory as such) were to be deduced from propositions having a wholly heterogeneous content. 5 In the case of primitive principles like the law of contradiction, the *modus ponens* etc., this repugnancy would plainly amount to a circle in so far as the deduction of these principles would involve steps that presupposed them not in the form of premisses, but in the form of deductive principles upon whose validity the sense and validity of the deduction depends. One could, in this respect, speak of a *reflective circle,* as against the usual, direct *circulus* + +*in demonstrando,* where premisses and conclusions overlap. + +Of all sciences only pure logic escapes such objections, since its premisses are homogeneous in respect of their objects with the conclusions they establish. Pure logic further escapes circularity in that, in a given deduction, it never proves principles which the deduction itself presupposes, and that it never proves principles that *every* deduction presupposes, but that it simply lays them down as axioms at the summit of all its deductions. Pure logic, therefore, has the extraordinarily difficult task of analytically ascending to such axioms as are indispensable starting-points for deduction, and are also irreducible to one another without a direct or a reflective circle, and then constructing and arranging a deduction for the theorems of logic - of which the rules of the syllogism form a small part - so that at each step, not only the *premisses,* but also the *principles* of our deductive transitions, are either + +**§44 Second prejudice** + +To confirm his first prejudice that rules for cognition must rest on the psychology of cognition, the psychologistic party appeals to the actual content oflogic (cf. the arguments of §15 above, p. 52, par. 2). What is logic about? Everywhere it concerns itself with presentations and judgements, with syllogisms and proofs, with truth and probability, with necessity and possibility, with ground and consequent, and with other closely related or connected concepts. But what can be thought of under such headings but mental phenomena and formations? This is obvious in the case of presentations and judgements. Syllogisms, however, are proofs of judgements by means of judgements, and proof is plainly a mental activity. Talk of truth, probability, necessity, possibility etc., likewise concerns judgements: what they refer to can only be manifested or experienced in judgements. Is it not, therefore, strange that one should wish to exclude from psychology propositions and theories which relate to psychological phenomena? In this regard the distinction between purely logical and methodological propositions is pointless, the objection affects both equally. Every attempt, therefore, to extrude even a part of logic from psychology, on ground of its pretended 'purity', must + +count as radically mistaken. + +**§45 Refutation. Pure mathematics would likewise be** + +**made a branch of psychology** + +Obvious as all this may seem, it *must* be mistaken. This is shown by the absurd consequences which, as we know, psychologism cannot escape. There is, however, another reason for misgiving: the natural affinity between purely logical and mathematical doctrine, which has often led to an assertion of + +their theoretical unity. + +We have already mentioned by the way that even Lotze taught that mathematics must be regarded as 'an independently developed branch of general logic'. 'Only a practically motivated division of teaching' can, he thinks, blind us to the fact that mathematics 'has its whole home-ground in the general field oflogic' *(Logik,* ed. 2, §18, p. 34 and §112, p. 138). To which Riehl adds that 'one could well say that logic coincides with the general part of purely formal mathematics (taken in the sense of H. Hankel), (A. Riehl, *Der philosophische Kritizismus und seine Bedeutung fur die positive Wissenschaft,* vol. II, Part **I,** p. 226). However this may be, an argument that is correct for logic must be approved in the case of arithmetic as well. Arithmetic sets up laws for numbers, for their relations and combinations: numbers, however, are the products of colligation and counting, which are mental activities. Relations arise from relating activities, combinations from acts of combination. Adding and multiplying, subtracting and dividing these are merely mental processes. That they require sensuous supports makes + +no difference, since this is true of any and every act of thinking. Sums, products, differences and quotients, and whatever may be determined in arithmetical propositions, are merely mental processes, and must as such obey mental laws. It may be highly desirable that modern psychology with its earnest pursuit of exactness should be widened to include mathematical theories, but it would hardly be much elevated by the inclusion of mathematics itself as one of its parts. For the heterogeneity of the two sciences cannot be denied. The mathematician, on the other hand, would merely smile if psychological studies were pressed upon him as supposedly providing a better and deeper grounding for his theoretical pronouncements. He would rightly say that mathematics and psychology belong to such different worlds, that the very thought of interchange among them was absurd: here, + +if anywhere, talk of a IJETO[3a6 + +**§46 The research domain of pure logic is, like** + +**that of mathematics, an ideal domain** + +These objections may have taken our argument far afield, but, when we attend to their content, they help us to state the basic errors of our opponents' position. *The comparison of pure logic with pure mathematics,* its mature sister discipline, which no longer needs fight for its right to independent existence, provides us with a reliable *Leitmotiv.* We shall first glance at mathematics. No one regards the theories of pure mathematics, e.g. the pure theory of numbers, as 'parts or branches of psychology', though we should have no numbers without counting, no sums without addition, no products without multiplication etc. The patterns of all arithmetical operations refer back to certain mental acts of arithmetical operation, and only in reflection upon these can we 'show' what a total, sum, product etc., is. In spite of the 'psychological origin' of arithmetical concepts, everyone sees it to be a fallacious IJETO[3a5 In this manner, the idea of an economy of thought, which to me seems welljustified and fruitful, has been given some definiteness and clarity: we have given an outline of the problem that it must solve, and the main paths that it must enter upon. Its *relation to logic,* in the practical sense of a technology of knowledge, is immediately understandable. It plainly yields an important foundation for such a technology, it gives essential aids towards constituting the Idea of technical methods of human knowledge, towards useful specifications of such methods, and to the deduction of rules for their assessment and discovery. + +**§SS The meaninglessness of an economy of thought for pure logic and epistemology, and its relation to** + +**psychology** + +To the extent that these thoughts coincide with those of R. Avenarius and E. Mach, we have no differences: I gladly agree with them. I am genuinely convinced, in particular, that we owe a vast amount of logical illumination to the historical-methodological labours of E. Mach, and that this is the case where one cannot altogether (or altogether cannot) agree with his conclusions. E. Mach, unfortunately, does not seem to me to have tackled the most fruitful problems of the economy of thought, the problems I tried to formulate above in a somewhat brief but quite sufficient fashion. His failure to do this is, in any case, partly due to the epistemological misinterpretations that he thought of as necessary foundations for his investigations. Mach's writings have, however, had an immense influence in respect of these very misinterpretations. This is the side of his thought that he shares + +with A venarius, in respect of which I must here oppose him. + +Mach's doctrine of an economy of thought, like Avenarius's doctrine of least action, relates, as we saw, to certain biological facts: ultimately we are dealing with a branch of the theory of evolution. This fact makes plain why such researches throw light on practical epistemology, on the methodology of scientific research, but not at all on pure epistemology, and especially not on the ideal laws of pure logic. *Per contra,* the writings of the school of Mach and A venarius, seem to aim at an epistemology rooted in an economy of thought. Against such a conception, or such a use of the economy of thought, we must train the whole arsenal of objections which we above opposed to psychologism and relativism. Attempts to found epistemology on an economy of thought ultimately reduce to attempts to found it on psychology: we need not here repeat, nor specially apply, our arguments. Cornelius increases the plain incongruities of his case by endeavouring to derive elementary psychological laws from a teleological principle of mental anthropology, which itself presupposes and is derived from these facts. He also tries, through the instrumentality of psychology, to provide an epistemological foundation for philosophy. This so-called principle, I must further remark, is not at all an ultimate, explanatory, rational principle, but a mere assemblage, a mass of facts regarding adaptation, facts ideally in need of an ultimate reduction to elementary facts and laws, whether we are able to + +provide such or not. + +To underpin psychology with teleological principles as its 'basic laws', principles devised to explain our varied mental functions, does not promise much for the progress of the science. No doubt it is instructive to point out the teleological significance of our mental functions, and of our more important mental structures, to show in detail, therefore, how and why the actually formed combinations of our mental elements have the utilitarian + +relation to survival that we expect *a priori.* But to treat the descriptively given facts as 'necessary consequences' of such principles, so as to seem to be giving a real explanation of these facts, and that particularly in contexts whose main aim is to lay bare the last foundations of psychology, all this + +can only breed confusion. + +A psychological or epistemological law concerned with an *endeavour* to achieve as much as *possible* in this or that respect, is a chimera. In the pure sphere of fact, there is no maximum possibility, in the sphere of law no endeavour. What happens in each case, as psychological matter of fact, is + +quite definite: there is so much of it and no more. + +The factual element in the principle of economy reduces to the fact that there are such things as presentations, judgements and other thought-experiences, which are further connected with feelings that, in the form of pleasure, promote certain directions of thought-formation, in the form of pain, discourage them. One can then assert, with rough generality, the existence of a progressive formation of presentations and judgements which lead first to the formation of single experiences *(Erfahrungen)* out of originally senseless elements, and then to the combination of such experiences into a *single, more or less orderly, unity of experience.* Psychological laws determine the emergence, out of our first roughly agreeing mental collocations, of the presentation of the *single* world common to everyone, and of an empirically blind belief in its existence. One should, however, note that this world is not the same for everyone, but only so 'on the whole'; it is the same only to an extent which affords a sufficient practical guarantee for our common presentations and actions. It is not the same for the ordinary man and the scientific research-worker: for the former it is a system merely approximate in its regularity, and shot through with countless accidents, whereas for the + +latter it is a nature ruled throughout by absolutely strict law. + +It is plainly an undertaking of great scientific import to show up the psychological ways and means through which the idea of a world as an object of experience, an idea sufficient for the needs of practical life and for survival, should have been developed and established, and, following this, to show up the psychological ways and means through which an objectively adequate Idea of a unified experience should have grown up in the minds of scientific research-workers, the Idea of a unified experience governed by strict laws, and embracing an ever enriched scientific content. This whole investigation is, however, irrelevant to epistemology. It can only have a highly indirect use for the latter, in assisting us to criticize epistemological prejudices, in whose case psychological motives really count. The question is not how experience, whether naive or scientific, arises, but what must be its content if it is to have objective validity: we must ask on what ideal elements and laws such objective validity of knowledge of the real is founded - more generally, on what any knowledge is founded - and how the performance involved in knowledge should be properly understood. We are, in other + +words, *not* interested in the origins and changes of our world-presentation, but in the objective right which the world-presentation of science claims as against any other world-presentation, which leads it to call *its* world the objectively true one. Psychology looks for perspicuous explanations of the formation of world-presentations. World-science (the sum total of the different sciences of the real) wishes to know perspicuously what obtains in reality, what makes up the true, the actual world. Epistemology, however, wishes to grasp perspicuously, from an objectively ideal standpoint, in what the possibility of perspicuous knowledge of the real consists, the possibility + +of science and of knowledge in general. + +**§56 Continuation. The OaTEpov lTp6TEpOV involved in any foundation of pure logic on an economy of** + +**thought** + +We seem, in the case of the principle of economy, to be dealing with an epistemological or a psychological principle: this appearance mainly stems from confusion between the factually given and the logically ideal, the former being tacitly substituted for the latter. We *perspicuously* see it to be the supreme goal, the ideally justified drift of all explanation which transcends mere description, that it should arrange facts which are in themselves 'blind' (facts at first found in a conceptually delimited field) under laws which are as general as possible, and that it should in this sense bring them together with the maximum possible rationality. This 'maximization' of the work of 'bringing together' is here quite clear: it is the ideal of a pervasive', allembracing rationality. If all matters of fact obey laws, there must be some minimum set of laws, of the highest generality and maximum deductive independence, from which all other laws can, by mere deduction, be derived. These 'basic laws' are, accordingly, laws of supreme coverage and efficacy, whose knowledge yields the absolute maximum of insight in some field, which permits the explanation of all that is in any way explicable in that field - idealizing the matter, we here assume that there are no limits to our power to deduce and subsume. In this manner the axioms of geometry are basic laws explaining and covering all the facts of space: through them every general spatial truth (i.e. every geometrical truth) achieves a self-evident + +reduction to its final explanatory grounds. + +This goal or principle of maximum rationality we recognize with insight to be the supreme goal of the rational sciences. It is self-evident that it would be better for us to know laws more general than those which, at a given time, we already possess, for such laws would lead us back to grounds deeper and more embracing. Plainly, however, our principle is no mere biological principle, or principle of thought-economy: it is a purely *ideal* principle, an eminently *normative* one. It accordingly permits no resolution or reinterpretation into facts of our mental life, or the life of human society. To identify + +the drift towards maximum possible rationality with a drift towards biological adaptation, or to derive it from the latter, to saddle it in addition with the function of a basic mental force - all this is a mass of confusions only paralleled by the psychologistic misreadings of the laws of logic, and their conception as laws of nature. To say that our mental life is in fact swayed by this principle is to run counter to obvious truth. Our actual thinking does not in fact conform to its ideals - as if ideals were some sort of natural forces. The *ideal* drift of logical thinking is as such towards rationality. The thought-economist *(sit venia verba)* turns it into a dominant *real* drift of human thought, bases it on the vague principle of power-saving, and ultimately on adaptation, and imagines that he has cleared up the norm that we *should* think rationally, has explained the objective sense and worth of rational science in general. Certainly one is justified in talking of an economy in thinking, of an economy of thought in the 'embrace' of facts by general propositions, of subordinate generalizations by higher ones, and the like. One is, however, only justified in that one compares one's actual thought with a perspicuously recognized ideal norm, which is accordingly npoTEpoV Tfj 2 + +**§60 Links with Leibniz** + +Leibniz was mentioned above as one of the great philosophers to whom our present conception of logic looks back. Our relation to him is relatively of the closest. Herbart's logical opinions, likewise, are only closer to ours than Kant's, to the extent that Herbart, as against Kant, revived Leibnizian ideas. But Herbart proved himself incapable even of an approximate exhaustion of all the valuable material to be found in Leibniz. He lags far behind the conceptions of the mighty thinker, for whom mathematics and logic form a single science. These conceptions stir a particular sympathy in us, and deserve a + +few words. + +The driving motive which set modern philosophy going, the Idea of the completion and transformation of the sciences, inspired Leibniz too to work + +unremittingly on a reformed logic. More penetrating than his predecessors, he did not heap scorn on scholastic logic as empty, formal rubbish, but saw in it a valuable step towards the true logic, which could truly help thought despite its incompleteness. (See, e.g. Leibniz's elaborate defence of traditionallogic, although it is 'hardly a shadow' of logic as 'he would wish it', in his letter to Wagner, *Opera Philosophica,* Erdmann, 418 *ff)* The development of this logic into a *discipline of mathematical form and strictness, into a universal mathematic in the highest and most comprehensive sense* is the goal + +towards which his efforts are continually devoted. + +I here follow the indications in *Nouveaux Essais,* Book IV, chapter XVII, cf. e.g. §4, *Opera philosophica,* Erdmann, 395a, where the doctrine of syllogistic forms, extended into a quite general doctrine of *argumens en forme,* is called 'une espece de mathematique universelle, dont l'importance n'est pas assez + +connue'. '11 faut savoir', he says there, + +que par les *argumens en forme* je n'entends pas seulement cette maniere scolastique d'argumenter, dont on se sert dans les colleges, mais tout raisonnement qui conclut par la force de la forme, et ou l'on n'a besoin de suppleer aucun article; de sorte qu'un *sorites,* un autre tissu de syllogisme, qui evite la repetition, meme un compte bien dresse, un calcul d'algebre, une analyse des infinitesimales me seront a peu pres des argumens en forme, puis que leur forme de raisonner a ete predemontree, + +en sorte qu'ou est sur de ne s'y point tromper. + +The sphere of the *mathematique universelle* here conceived would also be very much wider than that of the logical calculus to whose construction Leibniz devoted great pains, without quite reaching its boundaries. Leibniz ought rightly to have included in this universal mathematics the whole *mathesis universalis* in the usual quantitative sense (which constitutes the *narrowest* of Leibniz's concepts of *mathesis universalis),* especially since he had repeatedly called pure mathematical arguments *argumenta in forma* even in other contexts. The *Ars combinatoria, seu Speciosa generalis, seu doctrina de formis abstracta* (cf. the mathematical writings in Pertz's edition, vol. VII, pp. 24, 49 *ff,* 54, 159, 205 *ff)* should also likewise have been included in universal mathematics: it forms the fundamental part of *mathesis universalis* in a wider sense (though not in the above widest sense), while *mathesis universalis* is distinguished from logic as a subordinate territory. Leibniz defines his *Ars combinatoria* (pertz, VII, p. 61), which is of particular interest to us, as 'doctrina de formulis seu ordinis, similitudinis, relationis, etc. expressionibus in universum'. It is here opposed as 'scientia generalis de qualitate' to the 'scientia generalis de quantitate', which is universal mathematics in the ordinary sense. Compare with this the valuable passage in Gerhardt's edition of Leibniz's philosophical writings, vol. VII, + +Ars combinatoria speciatim mihi illa est scientia (quae etiam generaliter characteristic a sive speciosa dici posset) in qua tractatur de rerum formis sive formulis in universum, hoc est *de qualitate* in genere, sive de simili et dissimili, prout aliae atque aliae formulae ex ipsis *a, b,* c etc. (sive quantitates sive aliud quoddam repraesentent) inter se combinatis oriuntur, et distinguitur ab algebra quae agit de formulis ad quantitatem applicatis, sive de aequali et inaequali. Igitur Algebra subordinatur Combinatoriae, eiusque regulis continue utitur, quae tamen longe generaliores sunt, nec in Algebra tantum sed in arte deciphratoria, in variis ludorum generibus, in ipse geometria lineariter ad veterum morem tractata, denique in omnibus ubi similitudinis ratio habetur locum habent. + +The intuitions of Leibniz, which speed forth so far beyond their time, seem sharply defined and highly admirable to a modern acquainted with 'formal' mathematics and mathematical logic. This applies also, I must expressly note, to Leibniz's fragments on *scientia generalis* or the *calculus ratiocinator,* in which Trendelenburg's elegant but superficial criticism could pick out so + +little that was of use *(Historische Beitrage zur Philosophie,* vol. III). + +Leibniz likewise points, in repeated, express pronouncements, to the need to widen logic so as to include a mathematical theory of probabilities. He demands of mathematicians an analysis of the problems which lie hidden in games of chance, and expects great resultant advances in empirical thinking, and the logical criticism of it. 3 Leibniz, in short, had intuitions of genius: he foresaw the most splendid gains which logic has had to register since the time of Aristotle, the theory of probabilities and mathematical analyses of (syllogistic and non-syllogistic) arguments. The latter first matured in the second half of the nineteenth century. Through his *Combinatoria* he is also the intellectual father of the pure theory of manifolds, a discipline close to + +pure logic and in fact intimately one with it (cf. below §§69-70). + +In all this Leibniz bases himself on the same Idea of pure logic as we here support. Nothing is further from him than to think that the essential foundations of a fruitful art of knowledge could be found in psychology. They are for him altogether *a priori.* They constitute a discipline mathematical in form, which as such, just like, e.g. pure arithmetic, immediately includes a + +vocation for the practical regulation of knowledge. 4 + +**§61 Need for special investigations to provide an epistemological justification and partial realization of** + +**the Idea of pure logic** + +The authority of Leibniz must, however, count even less for us than that of Kant or Herbart, since he could not give to his great intentions the weight of completed achievements. He belongs to a past age, beyond which modern science feels that it has travelled a long way. Authorities do not in fact carry + +much weight as opposed to the broad advance of a science supposedly rich and secure in its results. Their influence must be less, in so far as they lack a sufficiently clarified, positively elaborated concept of the discipline in question. Clearly, if we do not want to stick half way, and to run the risk that our critical reflections may be barren, we must take up the task of *constructing the Idea of pure logic on a sufficiently broad basis.* Only in a series of meaty individual treatments, which will provide a more precise idea of the content and character of the essential logical researches, and which will work out the notion of logic more definitely, can one remove the prejudice which sees logic as an insignificant field of more or less trivial statements. As against this, we shall see that our discipline extends far and wide, not merely in respect of its content of systematic theories, but above all in regard to the difficult and important investigations needed for its philosophical founda- + +tion and assessment. + +But even the putative triviality of the field of purely logical truths, would in itself be no argument for its treatment as a mere aid towards a logical technology. The interests of pure theory require us to treat what constitutes a unified whole of theory in a theoretically closed manner, and not as a mere aid towards external ends. Our investigations so far have, we hope, made plain that a correct grasp of the essence of pure logic, and of its unique position in relation to all other sciences, is one of the most important questions in the whole of epistemology. If this is plain, it is likewise of vital interest to this fundamental philosophical science, that pure logic should be fully expounded in purity and independence. Epistemology must, of course, not be taken to be a discipline following upon or coinciding with metaphysics, but one which precedes metaphysics, as it precedes psychology and all + +other disciplines. + +**Appendix** + +**References to** *F. A. Lange and* **B.** *Bolzano* + +Wide as is the gulf which divides my logic from F. A. Lange's, I am in agreement with him, and regard him as having done the discipline a service, in that, in a period when pure logic was mainly despised, he definitely stood out for the view that 'science may expect important advances from attempts at a separate treatment of the purely formal elements of logic' *(Logische Studien,* p. 1). Our agreement extends further: in the most general features it also applies to the Idea of the discipline, which Lange could not indeed bring to essential clarity. He has good grounds for regarding the hiving off of pure logic as the hiving off of the doctrines which he calls 'the apodeictic element in logic', i.e. 'the doctrines which, like mathematical theorems, can be developed in an absolutely cogent manner'. His next remarks are well + +The mere fact of the *presence of cogent truths* is so important, that every trace of such truths must be carefully followed up. To omit such an investigation on account of the small value of formal logic, or its inadequacy as a theory of human thought, would have to be rejected from this point of view as a confusion of theoretical with practical aims. Such an objection would be as if a chemist refused to analyse a compound because in its compounded state it was very valuable, whereas its single + +constituents were unlikely to have any value. + +*(op. cit.* p. 7 f) + +He is just as right in another passage: 'F ormallogic as an apodeictic science, has a value totally independent of its validity: every system of truths which + +hold *a priori,* deserves the highest respect' *(op. cit.* p. 127). + +While Lange warmly supported the Idea of a purely formal logic, he had no notion that this Idea had already been realized to a relatively high degree. I am of course not referring to the many expositions of formal logic, which flourished especially in the schools of Kant and Herbart, and which did so little to live up to their own claims. I am referring to Bernhard Bolzano's *Wissenschaftslehre,* published in 1837, a work which, in its treatment of the logical 'theory of elements', far surpasses everything that world-literature has to offer in the way of a systematic sketch of logic. Bolzano did not, of course, expressly discuss or support any independent demarcation of pure logic in our sense, but he provided one *de facto* in the first two volumes of his work, in his discussions of what underlay a *Wissenschaftslehre* or theory of science in the sense of his conception; he did so with such purity and scientific strictness, and with such a rich store of original, scientifically confirmed and ever fruitful thoughts, that we must count him as one of the greatest logicians of all time. He must be placed historically in fairly close proximity to Leibniz, with whom he shares important thoughts and fundamental conceptions, and to whom he is also philosophically akin in other respects. Even he, however, did not quite exhaust the rich inspiration of Leibniz's logical intuitions, especially not in regard to mathematical syllogistics and to *mathesis universalis.* Too few of Leibniz's posthumous writings were, however, known at the time, and there was no 'formal' mathematics or theory of + +manifolds to provide a key to their understanding. + +In each line of his wonderful book, Bolzano shows himself to be an acute mathematician, who lets the same spirit of scientific strictness rule in logic which he himself first introduced into the theoretical treatment of the basic concepts and propositions of mathematical analysis, which thereby acquired a new foundation. For this the history of mathematics has *not* forgotten to grant him a famous place. Of the ambiguous profundity of that systematic philosophy, which rather aimed at thinking out world-conceptions and a worldwisdom, and which hindered the progress of scientific philosophy so badly by its unholy blend of discordant intentions, Bolzano - the contemporary of + +Hegel - shows no trace. His thought-patterns are of mathematical straightforwardness and plainness, but also of mathematical clearness and strictness. Only when one has gone more deeply into the sense and aim of these patterns throughout the whole discipline, does one find what great mental work and achievement lie hidden behind plain statements and formularized expositions. To philosophers bred in the prejudices, in the thought- and speech-habits of the idealistic schools - not all of us have completely outgrown such influences - such a scientific approach readily seems shallow and void of ideas, as well as ponderous and pedantic. Logic as a science must, however, be built upon Bolzano's work, and must learn from him its need for mathematical acuteness in distinctions, for mathematical exactness in theories. It will then reach a new standpoint for judging the mathematicizing theories of logic, which mathematicians, quite unperturbed by philosophic scorn, are so successfully constructing. These theories altogether conform to the spirit of Bolzano's logic, though Bolzano had not an inkling of them. It will at least be impossible for a future historian of logic to be so wrong as the otherwise thorough Ueberweg, who treats a work of the rank of the *Wissenschaftslehre* on a level with - Knigge's *Logicfor Females (Logikfur Frauenzimmer).5* Much as Bolzano's achievement is 'cast in one piece', it cannot be regarded (as such a deeply honest thinker would be the first to admit) as in any way final. To mention only one point, one particularly feels his defects in epistemological directions. There are either no investigations, or else only quite insufficient ones, which give genuine philosophical intelligibility to logical thought-achievements, and so provide a philosophical estimate of logic as a discipline. Such questions can be evaded by a thinker who, like a mathematician, is building theories upon theories, without having to bother himself about questions of underlying principle. They cannot be evaded by someone who undertakes to make clear, to those who either fail to see or to admit a discipline's validity, or who mix up essential tasks with quite heterogeneous ones, what the inherent justification of such a discipline really is, and what the nature of its tasks and objects may be. Our comparison of these present *Logical Investigations* with Bolzano's work is meant to make clear, not that our *Investigations* are in any sense mere commentaries upon, or critically improved expositions of, Bolzano's thought-patterns, but that + +they have been crucially stimulated by Bolzano (as also by Lotze). + +**The idea of Pure Logic** + +Wishing to gain a provisional image, sketched with a few characteristic touches, of the goal aimed at by the individual discussions which follow these Prolegomena, we shall now try to bring conceptual clarity to that Idea of Pure Logic, for which our critical discussions up to this point have more + +or less prepared us. + +**§62 The unity of science. The interconnection of** + +**things and the interconnection of truths** + +Science is, in the first place a unified item in anthropology: It IS a unity of acts of thinking, of thought-dispositions, as well as of certain external arrangements pertinent thereto. What makes this unified whole anthropological, and what especially makes it psychological, are not here our concern. We are rather interested in what makes science science, which is certainly not its psychology, nor any real context into which acts of thought are fitted, but a certain objective or ideal interconnection which gives these acts a unitary objective relevance, and, in such unitary relevance, an ideal validity. More definiteness and clearness are, however, needed at this point. Two meanings can be attached to this objective interconnection which ideally pervades scientific thought, and which gives 'unity' to such thought, and so to science as such: it can be understood as an *interconnection of the things* to which our thought-experiences (actual or possible) are intentionally directed, or, on the other hand, as an *interconnection of truths,* in which this unity of things comes to count objectively as being what it is. These two things are given together *a priori,* and are mutually inseparable. Nothing can be without being thus or thus determined, and that it is, and that it is thus and thus determined, is the self-subsistent truth which is the necessary correlate of the self-subsistent being. What holds of single truths, or single states of affairs, plainly also holds of interconnections of truths or of states of affairs. This self-evident inseparability is not, however, identity. In these truths or interconnections of truths the actual existence of things and of interconnections of things finds expression. But the interconnections of truths differ from the + +interconnections of things, which are 'truly' in the former; this at once appears in the fact that truths which hold of truths do not coincide with + +truths that hold of the things posited in such truths. + +To forestall misunderstandings, I must expressly emphasize the fact that I use the words 'objectivity', 'object', 'thing' etc., always in the widest sense, in accordance, therefore, with my preferred sense of the term 'knowledge'. An object of knowledge may as readily be what is real as what is ideal, a thing or an event or a species of a mathematical relation, a case of being or of what ought to be. This applies automatically to expressions like 'unified + +objectivity', 'interconnection of things' etc. + +Both sorts of unity are given to us, and can only by abstraction be thought apart, in judgement or, more precisely, in *knowledge* - the unity of objectivity, on the one hand, and of truth, on the other. The expression 'knowledge' is wide enough to cover both simple acts of knowing, as well as logically unified interconnections of knowledge, however complicated: either of these, considered as a whole, is a cognitive act. If now we perform an act of cognition, or, as I prefer to express it, live in one, we are 'concerned with the object' that it, in its cognitive fashion, means and postulates. If this act is one of knowing in the strictest sense, i.e. if our judgement is inwardly evident, then its object is *given* in primal fashion *(originiir).* The state of affairs comes before us, not merely putatively, but as actually before our eyes, and in it the object itself, *as* the object that it is, i.e. just as it is intended in this act of knowing and not otherwise, as bearer of such and such properties, as the term of such relations etc. It is not merely putatively, but actually thus, and *as* actually thus it is given to our knowledge, which means that it is not merely thought (judged) but known to be such. Otherwise put, its being thus is a truth actually realized, individualized in the experience of the inwardly evident judgement. If we reflect on this individualization, we perform an ideational abstraction, and the truth itself, instead of our former object, becomes our apprehended object. We hereby apprehend the truth as the ideal correlate of the transient subjective act of knowledge, as standing opposed in its unity to the unlimited multitude of possible acts of knowing, + +and of knowing individuals. + +To the interconnections of knowledge there ideally correspond interconnections of truths. Suitably understood, these are not merely complexes *of* truths, but complex truths, which therefore themselves in their totality fall under the concept of truth. There also the *sciences* belong, the word understood objectively in the sense of unified truth. In the general correlation which subsists between truth and objectivity, there is a unitary objectivity which corresponds to the unity of truth in one and the same science: this is the unity of the *scientific field.* In relation to this, all the singular truths of the same science *belong together in their subject-matter,* an expression which, as we shall see later, seems to be here used in a wider sense than + +**§63 Continuation. The unity of theory** + +We may now ask what constitutes the *unity of a science,* and therewith the unity of its field. For not every putting of truths together in a single association of truths, which might remain an entirely external one, constitutes a science. To a science, as we said in our first chapter,! a certain unified interconnection of demonstration pertains. This too, however, is not enough: it points to demonstration, to proof as something essentially pertaining to the Idea of Science, but fails to say what sort of unity of proof constitutes a + +SCIence. + +To reach clearness, we begin by making certain general pronouncements. Scientific knowledge is, as such, *grounded knowledge.* To know the ground of anything means to see the necessity of its being so and so. Necessity as an objective predicate of a truth (which is then called a necessary truth) is tantamount to the law-governed validity of the state of affairs in question. To see *a state of affairs as a matter of law* is to see *its truth as necessarily obtaining,* and to have knowledge of the *ground of the state of affairs* or of its truth: all these are equivalent expressions. 2 A natural equivocation, of course, leads us to call every general truth that itself utters a law, a necessary truth. Corresponding to our first defined sense, it would have been better to call it the explanatory ground of a law, from which a class of + +necessary truths follows. + +Truths divide into *individual* and *general* truths. The former contain (whether explicitly or implicitly) assertions regarding the actual existence of individual singulars, whereas the latter are completely free from this, and only permit us to infer (purely from concepts) the *possible* existence of what is individual. Individual truths are as such *contingent.* If in their case one speaks of a grounded explanation, one is concerned with a proof of their necessity under certain presupposed *circumstances.* If the interconnection of one fact with others is one of law, then its existence, resting on the laws which govern interconnections of the sort in question, and on the assumption of + +the pertinent circumstances, is determined as a *necessary existence.* + +If we are not dealing with the proof of a factual, but of a *general* truth (which again has the character of a law in respect of its possible application to facts falling under it) we are referred to certain general laws, which, by way of specialization (not individualization) and deductive consequence yield the proposition to be proved. The proof of general laws necessarily leads to certain laws which in their essence, i.e. intrinsically, and not merely subjectively or anthropologically, are not further proveable. These are called *basic laws.* The systematic unity of the ideally closed sum total of laws resting on *one* basic legality *(Gesetzlichkeit)* as their final ground, an arising out of it through systematic deduction, is the *unity of a systematically complete theory.* This basic legality may here either consist of one basic law or a + +We possess theories in this strict sense in universal arithmetic, in geometry, in analytical mechanics, in mathematical astronomy etc. Our concept of theory is usually a relative one, i.e. a theory is relative to a multiplicity of single items that it governs, for which it provides the explanatory grounds. Universal arithmetic gives us an explanatory theory for numerical and concrete number-propositions, analytical mechanics for mechanical facts, mathematical astronomy for the facts of gravitation etc. The possibility of taking on the function of explanation is an obvious consequence of the essence of a theory in our absolute sense. In a looser sense, we mean by a theory a deductive system in which the last grounds are not basic laws in the strict sense of the word, but, as genuine grounds, take us closer to these. In the gradations of a closed theory, a theory in this relaxed sense forms a step. We also note the following difference: every explanatory interconnection is deductive, but not every deductive interconnection is explanatory. All grounds are premisses, but not all premisses are grounds. Every deduction is indeed necessary, i.e. it obeys laws: but that its conclusions follow *according* to laws (the laws of inference) does not mean that they follow *from* laws which in a pregnant sense serve to 'ground' them. One tends, indeed, to call every premiss, and especially a universal one, a 'ground' for the consequences + +which flow from it, a noteworthy equivocation. + +**§64 The essential and extra-essential principles that give science unity. Abstract, concrete and** + +**normative sciences** + +We are now in a position to answer the question raised above: What makes truths belong together in a *single science,* what constitutes their unity of + +'subject-matter'? + +The principle of unity may be of two sorts, essential and extra-essential. The truths of a science are *essentially* one if their connection rests on what above all makes a science a science: a science is, as we know, grounded knowledge, i.e. explanation or proof (in the pointed sense). *Essential unity among the truths of a single science is unity of explanation.* But all explanation points to a theory, and has its goal in the knowledge of the basic laws, the principles of explanation. *Unity* of explanation means, therefore, *theoretical* unity, which means, on what was said above, homogeneous unity of + +legal base, and, lastly, *homogeneous unity of explanatory principles.* + +The sciences whose field is determined by the standpoint of theory, of unity of principle, which embrace in ideal closure all possible facts and general items whose principles of explanation have a single legal base, are called, not very suitably, *abstract sciences.* The best name for them would really be *theoretical* sciences. This expression is, however, used in opposition to practical and normative sciences, and we too have used it above in this sense. Following a suggestion of J. von Kries,3 one could say, almost as + +characteristically, that these sciences are *nomological,* in so far as their unifying principle, as well as their essential aim of research, is a law. The name 'explanatory science' which we have used from time to time, will also do, provided it is used to stress the unity reached by explanation, rather than + +explanation itself. + +There are, in the second place, *external* standpoints which range truths into *one* science: the nearest to hand is the *unity of the thing* in a more literal sense. One connects all the truths whose content relates *to one and the same individual object, or to one and the same empirical genus.* This is the case in regard to the *concrete,* or, to use von Kries's term, the *ontological sciences,* such as geography, history, astronomy, natural history, anatomy etc. The truths of geography are united by their relation to the earth, the truths of meteorology concern, even more restrictedly, the weather-phenomena of the earth etc. These sciences are also often called 'descriptive', and this name is allowable, since the unity of description is fixed by the empirical unity of the object or the class, and it is this descriptive unity which, in the sciences here involved, determines the science's unity. But the word should of course not be so understood as if descriptive sciences aimed at mere description, which + +would contradict our guiding concept of science. + +Since it is possible that explanation which is directed towards empirical unities, leads to widely divergent, or quite heterogeneous theories and theoretical sciences, we rightly call the unity of the concrete science an + +'extra-essential' one. + +It is at any rate clear that the abstract or nomological sciences are the genuine, basic sciences, from whose theoretical stock the concrete sciences must derive all that theoretical element by which they are made sciences. Quite understandably, it is enough if the concrete sciences attach the objects they describe to the lower rungs of law in the nomological sciences, and at best indicate the main direction of ascending explanation. For the reduction to principles, and the general build-up of explanatory theories, is the proper field of the nomological sciences; it already exists in such sciences, where fully developed, in the most universal form and as a finished achievement. We are of course not pronouncing on the relative worth of the two sorts of sciences; our interest in theory is not our only interest, nor the sole determinant of value. Aesthetic, ethical, and, in a wider sense, practical interests can attach to what is individual, and impart the highest value to its detailed description and explanation When, however, our purely theoretical interest sets the tone, the single individual and the empirical connection do not count intrinsically, or they count only as a methodological point of passage in the construction of a general theory. The theoretical natural scientist, or the natural scientist in the context of purely theoretic, mathematicizing discussion, sees the earth and stars quite differently from the geographer and the astronomer. They are to him *per se* indifferent and count merely as + +We must finally make mention of *yet another extra-essential principle* of scientific unity: the principle which grows out of a unitary evaluative interest, which is therefore objectively determined by a unitary basic value (or by a unitary basic norm) as has been fully discussed in chapter II, §14. This constitutes 'mutual belongingness' as regards subject-matter among the truths in the normative sciences, or the unity of the field in question. Talk of 'mutual belongingness as regards subject-matter' is most naturally taken to mean a belongingness grounded in things, in subject-matters themselves. Here only a unity in terms of theoretical law or of the concrete thing will be relevant, and our conception will place normative unity over against unity + +of subject-matter in a single opposition. + +As appears from our previous discussion, normative sciences depend on theoretical sciences - above all on sciences theoretical in the narrowest sense of being nomological- so that we can again say that they derive the theoretical element, which alone renders them scientific, from those theoretical sciences. + +**§65 The question as to the ideal conditions of the possibility of science or of theory in general.** *A.* **The question as it relates to actual knowledge** + +We now raise an important question as to the 'conditions of the possibility of science in general'. Since the essential aim of scientific knowledge can only be achieved through theory, in the strict sense of the nomological sciences, we replace our question by a question as to the *conditions of the possibility of theory in general.* A theory as such consists of truths, and its form of connection is a deductive one. To answer our question is therefore also to answer the more general question as to the conditions of the possibility of *truth in general,* and again of *deductive unity* in general. The historical echoes in the form of our question are of course intentional. We are plainly concerned with a quite necessary generalization of the question as to the 'conditions of the possibility of experience' *(Erfahrung).* The unity of an experience is for Kant the unity of objective legality: it falls, therefore, under + +the concept of theoretical unity. + +The sense of our question needs, however, to be more precisely fixed. It might very well be at first understood in the *subjective* sense, in which case it would be better expressed as a question as to the conditions of the possibility of *theoretical knowledge* in general, or, more generally, of inference in general or knowledge in general, and in the case of any *possible* human being. Such conditions are in part *real,* in part *ideal.* We shall ignore the former, the psychological conditions. Naturally the possibility of knowledge in a psychological regard embraces all the causal conditions on which our thinking depends. *Ideal* conditions for the possibility of knowledge may, as said before,4 be of two sorts. They are either *noetic* conditions which have their grounds, *a priori,* in the Idea of Knowledge as such, without any regard + +to the empirical peculiarity of human knowledge as psychologically conditioned, or they are purely *logical* conditions, i.e. they are grounded purely in the 'content' of our knowledge. It is evident *a priori,* as regards the former, that thinking subjects must be in general able to perform, e.g., all the sorts of acts in which theoretical knowledge is made real. We must, in particular, as thinking beings, be able to see propositions as truths, and to see truths as consequences of other truths, and again to see laws as such, to see laws as explanatory grounds, and to see them as ultimate principles etc. But it is also, on the other hand, inwardly evident that truths are what they are, and that, in particular, laws, grounds, principles are what they are, whether we have insight into them or not. Since they do not hold in so far as we have insight into them, but we can only have insight into them in so far as they hold, they must be regarded as objective or ideal conditions of the possibility of our knowledge of them. *A priori* laws, accordingly, relating to truth as such, to deduction as such and to theory as such (i.e. to the universal essence of these ideal unities) must be characterized as laws which express the conditions for knowledge in general, or for deductive and theoretical knowledge in general, conditions which have their 'pure' foundation is the 'content' of knowledge. Plainly we are here concerned with *a priori* conditions of knowledge, which can be discussed and investigated apart from all relation to the thinking subject and to the Idea of Subjectivity in science. The laws in question have a meaning-content which is quite free from such relation, they do not talk, even in ideal fashion, of knowing, judging, inferring, representing, proving etc., but of truth, concept, proposition, syllogism, ground and consequent etc., as we fully said above (§47). Obviously these laws may undergo self-evident transformations through which they acquire an express relation to knowledge and the knowing subject, and now themselves pronounce on real possibilities of knowledge. Here as elsewhere, *a priori* assertions regarding ideal possibilities arise through the transferred application of ideal relationships (expressed in purely general propositions) to empirical instances + +(cf. the arithmetical example in §23 above). + +The ideal conditions of knowledge which we have called 'noetic' as opposed to those which are logically objective, are, basically, no more than such modifications of the insights, the laws which pertain to the pure content of knowledge, as render them fruitful for the criticism of knowledge, and, by further modifications, for practical, logical normativity. For the *normative* modifications of the laws of pure logic, which we spoke of above, + +also come in here. + +**§66 8. The question as it relates to the content** + +**of knowledge** + +Our treatment has shown that questions as to the ideal conditions of the possibility of *knowledge* in general, and of theoretical knowledge in + +particular, ultimately lead us back to certain *laws,* whose roots are to be found purely in the content of knowledge, or of the categorial concepts that it falls under, and which are so abstract that they contain no reference to knowledge as an act of a knowing subject. These laws (or the categorial concepts which enter into them) are what are to be understood as constituting the conditions of the possibility of *theory* in general, in the objectively ideal sense. For it is possible to raise questions as to the conditions of possibility, not only in regard to theoretical knowledge, as we have so far done, but also in regard to its *content,* i.e. we can raise them directly in regard to theory itself. We then understand by 'theory', let us again stress, a certain *ideal content* of possible knowledge, just as in the case of 'truth', 'law' etc. There is a single truth, which corresponds to the multitude of individual acts of knowledge having the same content, which is just their ideally identical content. In like manner, the ideally identical content of a theory corresponds to the multitude of individual knowledge-combinations, in each of which - whether occurring now or then, in these subject or in those - the *same* theory comes to be known. It is accordingly not *made up of acts* but of purely *ideal* elements, of truths, and that in purely ideal forms, + +those of *ground and consequent.* + +If we now directly relate our question as to conditions of possibility, to theory in the objective sense and to theory in general, such a possibility can only have the sense which applies to other objects of pure conception. From such objects, we are led back to concepts, and 'possibility' means no more than the 'obtaining' *(Geltung)* or rather essentiality *(Wesenhaftigkeit)* of the concepts in question. This is what is often called the 'reality' as opposed to the 'imaginariness' of concepts, which latter could better be called 'essencelessness'. In such a sense, one speaks of real definitions which guarantee the possibility, the 'obtaining', the reality of the defined concept, and again of the opposition between real and imaginary numbers, geometrical figures etc. Talk of possibility in regard to concepts becomes equivocal through a transfer. What is in an authentic sense possible is the existence of objects falling under the relevant concepts, a possibility guaranteed *a priori* through knowledge of conceptual essence, which flashes upon us, e.g., as the result of such an object's being intuitively presented. The essentiality of the concept is then likewise spoken of as a possibility in a transferred sense. In this connection questions as to the *possibility* of a theory as such, and as to the conditions on which such possibility depends, gain an easily grasped sense. The possibility or essentiality of a theory in general is assured by our perspicuous knowledge of some definite theory. The wider question will however be: What are the universal, law-governed conditions of this possibility of theory in general? *What therefore constitutes the ideal essence of theory as such?* What are the primitive 'possibilities' out of which the possibility of theory is constituted, or, what is the same, what are the *primitive essential concepts* out of which the concept of theory, itself an essential + +concept, is constituted? And further: What are the pure laws which, rooted in these concepts, impart unity to all theory as such, laws which pertain to the form of theory as such, and which determine, in *a priori* fashion, the + +possible (essential) modifications or species of theory? + +If these ideal concepts or laws delimit the possibility of theory in general, if, in other words, they express what essentially pertains to the Idea of Theory, it immediately follows that each putative theory only is a theory to the extent to which it accords with these concepts or laws. The logical justification of a concept, i.e. of its ideal possibility, is achieved by going back to its intuitive or deducible essence. Logical justification of a given theory as such, i.e. justification in virtue of its pure form, demands that we go back to the essence of its form, and so to the *concepts and laws which are ideal constituents of theory in general* (the 'conditions of its possibility'), which regulate, in *a priori,* deductive fashion, all specialization of the Idea of Theory in its possible kinds. Things are here as they are in the wider field of deduction, e.g. in the case of simple syllogisms. Though they may be intrinsically illuminated by insight, they none the less receive their final, deepest justification by recourse to the formal, syllogistic law which imparts insight into the *a priori* ground of syllogistic interconnection. The same holds in the case of any deduction, however complicated, and especially in the case of a theory. In perspicuous, theoretical thought we gain insight into the grounds of some state of affairs explained: but the deeper-going insight into the essence of the theoretical linkage which itself constitutes the theoretical content of such thought, and the *a priori* laws on which such thought-achievement depends, are first reached when we track down the form, the law, and the interweavings of theory, at the quite different level of knowledge to which they belong. To point to pro founder insights and justifications, serves to bring out the supreme value of the theoretical investigations which help to solve our suggested problem. We are dealing with *systematic theories which have their roots in the essence of theory,* with an *a priori. theoretical, nomological science which deals with the ideal essence of science as such,* and which accordingly has parts relating to systematic theories whose empirical, anthropological aspect it excludes. In a profound sense, we are dealing with the theory of theory, with the science of the sciences. Its achievement in enriching our knowledge must, of course, be kept separate from its problems themselves, + +and from the proper content of their solution. + +**§67 The tasks of pure logic. First: the fixing of the pure categories of meaning, the pure categories of** + +**objects and their law-governed combinations** + +Having provisionally fixed the Idea of the *a priori* discipline whose deeper understanding will be the goal of our efforts, we may now summarize the tasks that we shall assign to it. Three sets of tasks must be distinguished. + +We *must,jirst* of all, lay down the more important concepts, in particular all the *primitive* concepts which 'make possible' the interconnected web of knowledge as seen objectively, and particularly the web of theory. We must also clarify these concepts scientifically. We are, in other words, concerned with the concepts which constitute the Idea of unified theory, or with the concepts which are connected with these through ideal laws. Into such a constitution second-order concepts, i.e. concepts of concepts and of other ideal unities, naturally enter. A given theory is a certain deductive combination of given propositions which are themselves certain sorts of combinations of given concepts. The Idea of the pertinent 'form' of the theory arises if we substitute variables for these given elements, whereby concepts of concepts and of other Ideas, replace straightforward concepts. Here belong the con- + +cepts: Concept, Proposition, Truth etc. + +The concepts of the *elementary connective forms* naturally playa constitutive role here, those connective forms, in particular, which are quite generally constitutive of the deductive unity of propositions, e.g. the conjunctive, disjunctive, hypothetical linkage of propositions to form new propositions. Such a role is also played by the forms of connection of inferior elements of meaning into one simple proposition, which in their turn lead to the varied subject-forms, predicate-forms, forms of conjunctive and disjunctive connection, plural forms etc. Fixed laws govern the gradual complications through which an unending multiplicity of ever new forms emerges out of our primitive set. These *laws of complication* make possible a sweeping oversight of the concepts derivable from the primitive concepts and forms; these naturally belong, together with this sweeping oversight itself, in the field of + +research dealt with here. (Cf. Investigation IV in vol. n.) + +In close connection with the concepts so far mentioned, i.e. the categories of meaning, and married to them by ideal laws, are other correlative concepts such as Object, State of Affairs, Unity, Plurality, Number, Relation, Connection etc. These are the pure, the formal *objective categories.* These too must be taken into account. In both cases we are dealing with nothing but concepts, whose notion makes clear that they are independent of the particularity of any material of knowledge, and under which all the concepts, propositions and states of affairs that specially appear in thought, must be ordered. They arise therefore solely in relation to our varying thought-functions: their concrete basis is solely to be found in possible acts of thought, as such, or in the correlates which can be grasped in these. (See + +§62 above and Investigation VI, §44 in vol. n.) + +All these concepts must now be pinned down, their 'origin' must in each case be investigated. Not that psychological questions as to the origin of the conceptual presentations or presentational dispositions here in question, have the slightest interest for our discipline. This is not what we are enquiring into: we are concerned with a *phenomenological origin* or - if we prefer to rule out unsuitable talk of origins, only bred in confusion - we are concerned + +with *insight into the essence* of the concepts involved, looking methodologically to the fixation of unambiguous, sharply distinct verbal meanings. We can achieve such an end only by *intuitive representation* of the essence in adequate Ideation, or, in the case of complicated concepts, through knowledge of the essentiality of the elementary concepts present in them, and of + +the concepts of their forms of combination. + +All these are seemingly trivial, preparatory tasks. To a large extent they are necessarily clothed in the form of discussions of terminology, and readily seem to the layman to be barren, pettifogging word-exercises. But as long as concepts are not distinguished and made clear to ideational intuition, by going back to their essence, further effort is hopeless. In no field of knowledge is equivocation more fatal, in none have confused concepts so hindered the progress of knowledge, or so impeded the insight into its true aims, as in the field of pure logic. The critical analyses of these Prolegomena have + +everywhere shown this. + +It is impossible to overestimate the importance of this first group of problems; it is doubtful whether they do not in fact involve the greatest difficulties + +in the whole discipline. + +**§68 Secondly: the laws and theories which have their** + +**grounds in these categories** + +Our *second* group of problems lies in the search for the *laws* grounded in the two above classes of categorial concepts, which do not merely concern possible forms of complication and transformation of the theoretical items they involve (see Investigation IV), but rather the *objective validity* of the formal structures which thus arise: on the one hand, the truth or falsity of *meanings* as such, purely on the basis of their categorial formal structure, on the other hand (in relation to their *objective* correlates), the being and not being of objects as such, of states of affairs as such, again on the basis of their pure, categorial form. These laws, which concern meanings and objects as such, with the widest universality conceivable, the universality of logical categories, are in themselves theories. (See Investigation **I,** §29.) We have, on the *one* side, the side of meaning, theories of inference, e.g. syllogistics, which is however only one such theory. On the other side, the side of the correlates, we have the pure theory of pluralities, which has its roots in the concepts of a plurality, the pure theory of numbers, which has its roots in the concept of a number - each an independently rounded-off theory. All the laws here belonging lead to a limited number of primitive or basic laws, which have their immediate roots in our categorial concepts. They must, in virtue of their homogeneity, serve to base an all-comprehensive theory, which will contain the separate theories just mentioned, as relatively closed elements in itself. We are here concerned with the territory of those laws, which in formal universality span all possible meanings and objects, under which every particular + +theory or science is ranged, which it must obey if it is to be valid. Not that every such theory presupposes every such law as the ground of its possibility and validity. The ideal completeness of the categorial theories and laws in question, rather yields the all-comprehensive fund from which each particular valid theory derives the ideal grounds of essential being appropriate to its form. These are the laws to which it conforms, and through which, as a theory validated by its form, it can be ultimately justified. In so far as theory is an all-embracing unity built out of single, interwoven truths, it is plain that the laws governing the concept of truth, as well as the laws governing the possibility of single combinations of this or that form, will be included in the delimited territory. In spite of, or rather on account of, the fact that theory is the narrower notion, the task of exploring the conditions of its possibility, comprehends more content than the corresponding task in the case of truth in general, and in the case of the primitive forms of propositional + +combinations (cf. above, §65). + +**§69 Thirdly: the theory of the possible forms of** + +**theories or the pure theory of manifolds** + +When all these investigations have been concluded, we shall have done justice to the Idea of a science of the conditions of the possibility of theory in general. We see at once, however, that this science points beyond itself to a completing science, which deals *a priori* with the *essential sorts (forms) of theories and the relevant laws of relation.* The Idea therefore arises, all of this being taken together, of a more comprehensive science of theory in general. In its fundamental part, the essential concepts and laws which pertain constitutively to the Idea of Theory will be investigated. It will then go over to differentiating this Idea, and investigating *possible theories* in *a priori* fash- + +ion, rather than the possibility of theory in general. + +The tasks mentioned have been carried out to a sufficient extent, and it is possible to construct, out of purely categorial concepts, many definite concepts of possible theories or pure 'forms' of theories, whose essential status has been deduced from laws. These distinct forms are not mutually unrelated. There will be a definite, ordered procedure which will enable us to construct the possible forms of theories, to survey their legal connections, and to pass from one to another by varying their basic determining factors etc. There will be universal propositions, if not for the forms of theory generally, then at least for forms of theory belonging to defined classes, which will govern the legal connection, the transformation and the mutual + +interchange of these forms. + +The propositions that must here be affirmed will plainly be of a different content and character from the basic propositions and theorems of theories of the second group, from, e.g., syllogistic or arithmetical laws. It is, however, clear from the start that the deduction of such propositions (for there + +can be no true basic laws in this case) must have their entire basis in the + +previously, mentioned theories. + +This is a last, highest goal for a theoretical science of theory in general. It is also not indifferent from the point of view of the practical side of knowledge. To fit a theory into its formal class may rather be of the greatest methodological importance. For, with the extension of the deductive, theoretical sphere, the liveliness and freedom of theoretical research also increases: there is increased richness and fruitfulness of method. The solution of problems raised within a theoretical discipline, or one of its theories, can at times derive the most effective methodical help from recourse to the categorial type or (what is the same) to the form of the theory, and perhaps also by going over to a more comprehensive form or class of forms and to + +its laws. + +**§70 Elucidation of the Idea of a pure theory** + +**of manifolds** + +These indications will perhaps seem somewhat obscure. That we are not here dealing with vague fantasies, but with conceptions definite in their content, is shown by 'formal mathematics' in a most entirely general sense, or by the 'theory of manifolds', the fine flower of modern mathematics. The theory is in fact none other than the partial realization, correlatively transformed, of the ideal just sketched: this is not to say, of course, that mathematicians themselves, guided and likewise limited by interests which concern the field of number and magnitude, have correctly discerned the ideal essence of the new discipline, or have risen to the height of abstraction of an all-comprehensive theory. The *objective correlate* of the concept of a possible theory, definite only in respect of form, is *the concept of a possible field of knowledge over which a theory of this form will preside.* Such a field is, however, known in mathematical circles as a *manifold.* It is accordingly a field which is uniquely and solely determined by falling under a theory of such a form, whose objects are such as to permit of *certain* associations which fall under *certain* basic laws of this or that *determinate* form (here the only determining feature). The objects remain quite indefinite as regards their matter, to indicate which the mathematician prefers to speak of them as 'thought-objects'. They are not determined directly as individual or specific singulars, nor indirectly by way of their material species or genera, but solely by the *form* of the connections attributed to them. These connections are therefore as little determined in content as are their objects, only their form is determined, and determined through the forms of the elementary laws which are assumed to hold of them. These laws then, as they determine a *field* and its *form,* likewise determine the theory to be constructed, or, more correctly, *the theory's form.* **In** the theory of manifolds, e.g. '+' is not the sign for numerical addition, but for any connection for which laws of + +the form *a* + *b* = *b* + *a* etc., hold. The manifold is determined by the fact that its thought-objects permit of these 'operations' (and of others whose com- + +patibility with these can be shown *a priori).* + +The *most general Idea of a Theory of Manifolds* is to be a science which definitely works out the form of the essential types of possible theories or fields of theory, and investigates their legal relations with one another. All actual theories are then specializations or singularizations of corresponding forms of theory, just as all theoretically worked-over fields of knowledge are *individual* manifolds. If the formal theory in question is actually worked out in the theory of manifolds, then all deductive theoretical work in construct- + +ing all actual theories of the same form has been done. + +This is a point of view of the highest methodological importance, without which there can be no talk of understanding the method of mathematics. Not less important than such a going back to pure form, is the closely related ranging of each such form in more comprehensive forms or classes of forms. That we here have a central item in the wonderful, methodological art of mathematics, becomes plain if we look, not merely at the theories of manifolds which arose from generalizations of geometric theory and its forms, but at the first, simplest case of this sort, the extension of the field of real numbers (i.e. of the corresponding form of theory, the 'formal theory of real numbers') into the formal, two-dimensional field of ordinary complex numbers. In this concept we indeed have the key to the only possible solution of the problem that has not as yet been cleared up: how, e.g., in the field of numbers impossible (essenceless) concepts can be methodically treated like real ones. This is not, however, the place to discuss this more closely. When I spoke above of theories of manifolds which arose out of generalizations of geometric theory, I was of course referring to the theory of n-dimensional manifolds, whether Euclidean or non-Euclidean, to Grassmann's theory of extensions, and, among others, to the related theories of a W. Rowan Hamilton, which can be readily purged of anything geometric. Lie's theory of transformation-groups and G. Cantor's investigations into num- + +bers and manifolds also belong here. + +The manner in which variation of curvature makes the various sorts of space-like manifolds pass into one another, gives the philosopher who has familiarized himself with the elements of the Riemannian-Helmholtzian theory a certain picture of the manner of the mutual legal connection among pure forms of theory of determinately distinct types. It would be easy to show that a knowledge of the true intention of such theories, as pure categorial forms of theory, would banish all metaphysical fog and all mysticism from the mathematical investigations in question. If we use the term 'space' of the familiar type of order of the world of phenomena, talk of 'spaces' for which, e.g. the axiom of parallels does not hold, is naturally senseless. It is just as senseless to speak of differing geometries, when 'geometry' names the science of the space of the world of phenomena. But if we + +mean by 'space' the categorial form of world-space, and, correlatively, by 'geometry' the categorial theoretic form of geometry in the ordinary sense, then space falls under a genus, which we can bound by laws, of pure, categorially determinate manifolds, in regard to which it is natural to speak of 'space' in a yet more extended sense. Just so, geometric theory falls under a corresponding genus of theoretically interrelated theory-forms determined in purely categorial fashion, which in a correspondingly extended sense can be called 'geometries' of these 'spatial' manifolds. At any rate, the theory of n-dimensional spaces forms a theoretically closed piece of the theory of theory in the sense above defined. The theory of a Euclidean manifold of three dimensions is an ultimate ideal singular in this legally interconnected series of *a priori,* purely categorial theoretic forms (formal deductive systems). This manifold itself is related to 'our' space, i.e. space in the ordinary sense, as its pure categorial form, the ideal genus of which the latter represents so to sayan individual singular rather than a specific difference. Another fine example is the theory of complex number-systems, within which the theory of 'ordinary' complex numbers is a single item, a last specific difference. In relation to such theories, the arithmetics of number, of ordinal number, of magnitude, of quantite dirigee etc., are more or less like mere individual singulars. To each a formal generic Idea corresponds, a theory of absolute integers, of real numbers, of ordinary complex numbers etc., in + +whose case 'number' is to be taken in a generalized, formal sense. + +**§71 Division of labour. The achievement of the mathematicians and that of the philosophers** + +These therefore are the problems that we range in the field of pure or formal logic in the above defined sense: we thereby give this field its widest possible extension compatible with the Idea sketched by us of a science of theory in general. A considerable part of the theories which belong here has been developed as 'pure analysis' or, better, as *formal* mathematics, and is worked on by mathematicians together with other disciplines not in the full sense pure (i.e. formal), such as geometry (as the science of 'our' space), analytical mechanics etc. The nature of the case really demands a thoroughgoing *division of labour* here. The construction of theories, the strict, methodical solution of all formal problems, will always remain the home domain of the mathematician. Peculiar methods and set-ups of research are here presupposed, and are essentially the same in all pure theories. Even the elaboration of syllogistic theory, long enthroned in the very home territories of philosophy and thought to be completed long ago, has recently been taken over by mathematicians, in whose hands it has received undreamt of developments. Theories of new types of inference, ignored or misunderstood by the traditional logic, have at the same time been discovered and worked out with true mathematical elegance. No one can debar mathematicians from staking + +claims to all that can be treated in terms of mathematical form and method. Only if one is ignorant of the modern science of mathematics, particularly of formal mathematics, and measures it by the standards of Euclid or Adam Riese, can one remain stuck in the common prejudice that the essence of mathematics lies in number and quantity. It is not the mathematician, but the philosopher, who oversteps his legitimate sphere when he attacks 'mathematicizing' theories of logic, and refuses to hand over his temporary foster-children to their natural parents. The scorn with which philosophical logicians like to speak of mathematical theories of inference, does not alter the fact that the mathematical form of treatment is in their case (as in the case of all strictly developed theories in the proper sense of this word) the only scientific one, the only one that offers us systematic closure and completeness, and a survey of all possible questions together with the possible + +forms of their answers. + +If the development of all true theories falls in the mathematician's field, what is left over for philosophers? Here we must note that the mathematician is not really the pure theoretician, but only the ingenious technician, the constructor, as it were, who, looking merely to formal interconnections, builds up his theory like a technical work of art. As the practical mechanic constructs machines without needing to have ultimate insight into the essence of nature and its laws, so the mathematician constructs theories of numbers, quantities, syllogisms, manifolds, without ultimate insight into the essence of theory in general, and that of the concepts and laws which are its conditions. The like holds of all 'special sciences': what is rrp6TEpoV Tfj 2 + +**§2 Elucidation of the aims of such investigations** + +All theoretical research, though by no means solely conducted in acts of verbal expression or complete statement, none the less terminates in such statement. Only in this form can truth, and in particular the truth of theory, become an abiding possession of science, a documented, ever available treasure for knowledge and advancing research. Whatever the connection of thought with speech may be, whether or not the appearance of our final judgements in the form of verbal pronouncements has a necessary grounding + +in essence, it is at least plain that judgements stemming from higher intellectual regions, and in particular from the regions of science, could barely arise + +without verbal expression. + +The objects which pure logic seeks to examine are, in the first instance, therefore given to it in grammatical clothing. Or, more precisely, they come before us embedded in concrete mental states which further function either as the *meaning-intention* or *meaning-fulfilment* of certain verbal expressions - in the latter case intuitively illustrating, or intuitively providing evidence for, our meaning - and forming a *phenomenological unity* with such expressions. In these complex phenomenological unities the logician must pick out the components that interest him, the characters of the acts, first of all, in which logical presentation, judgement and knowledge are consummated: he must pursue the descriptive analysis of such act-types to the extent that this helps the progress of his properly logical tasks. We cannot straightway leap, from the fact that theory 'realizes' itself in certain mental states, and has instances in them, to the seemingly obvious truth that such mental states must count as the primary object of our logical researches. The pure logician is not primarily or properly interested in the psychological judgement, the concrete mental phenomenon, but in the logical judgement, the identical asserted meaning, which is one over against manifold, descriptively quite different, judgement-experiences.3 There is naturally, in the singular experiences which correspond to this ideal unity, a certain pervasive common feature, but since the concern of the pure logician is not with the concrete instance, but with its corresponding Idea, its abstractly apprehended universal, he has, it would seem, no reason to leave the field of abstraction, nor to make concrete experiences the theme of his probing interest, instead of Ideas. Even if phenomenological analysis of concrete thought-experiences does not fall within the true home-ground of pure logic, it none the less is indispensable to the advance of purely logical research. For all that is logical must be given in fully concrete fashion, if, as an object of research, it is to be made our own, and if we are to be able to bring to self-evidence the *a priori* laws which have their roots in it. What is logical is first given us in imperfect shape: the concept as a more or less wavering meaning, the law, built out of concepts, as a more or less wavering assertion. We do not therefore lack logical insights, but grasp the pure law with self-evidence, and see how it has its base in the pure forms of thought. Such self-evidence depends, however, on the verbal meanings which come alive in the actual passing of the judgement regarding the law. Unnoticed equivocation may permit the subsequent substitution of other concepts beneath our words, and an appeal on behalf of an altered propositional meaning may quite readily, but wrongly, be made on the self-evidence previously experienced. It is also possible, conversely, that a misinterpretation based on equivocation may distort the sense of the propositions of pure logic (perhaps turning them into empirical, psychological propositions), and may tempt us to abandon previously + +experienced self-evidence and the unique significance of all that belongs to + +pure logic. + +It is not therefore enough that the Ideas of logic, and the pure laws set up with them, should be given in such a manner. Our great task is now *to bring the Ideas of logic, the logical concepts and laws, to epistemological clarity and* + +*definiteness.* + +Here *phenomenological analysis* must begin. Logical concepts, as valid thought-unities, must have their origin in intuition: they must arise out of an ideational intuition founded on certain experiences, and must admit of indefinite reconfirmation, and of recognition of their self-identity, on the reperformance of such abstraction. Otherwise put: we can absolutely not rest content with 'mere words', i.e. with a merely symbolic understanding of words', such as we first have when we reflect on the sense of the laws for 'concepts', 'judgements', 'truths' etc. (together with their manifold specifications) which are set up in pure logic. Meanings inspired only by remote, confused, inauthentic intuitions - if by any intuitions at all- are not enough: we must go back to the 'things themselves'. We desire to render self-evident in fully-fledged intuitions that what is here given in actually performed abstractions is what the word-meanings in our expression of the law really and truly stand for. In the practice of cognition we strive to arouse dispositions in ourselves which will keep our meanings unshakably the same, which will measure them sufficiently often against the mark set by reproducible intuitions or by an intuitive carrying out of our abstraction. Intuitive illustration of the shifting meanings which attach to the same term in differing propositional contexts likewise convinces us of the fact of equivocation: it becomes evident to us that what a word means in this or that case has its fulfilment in essentially different intuitive 'moments' or patterns, or in essentially different general notions. By distinguishing among concepts confounded by us, and by suitably modifying our terminology, we then likewise achieve + +a desired 'clearness and distinctness' for our logical propositions. + +The phenomenology of the logical experiences aims at giving us a sufficiently wide descriptive (though not empirically-psychological) understanding of these mental states and their indwelling sense, as will enable us to give fixed meanings to all the fundamental concepts of logic. Such meanings will be clarified both by going back to the analytically explored connections between meaning-intentions and meaning-fulfilments, and also by making their possible function in cognition intelligible and certain. They will be such meanings, in short, as the interest of pure logic itself requires, as well as the interest, above all, of epistemological insight into the essence of this discipline. Fundamental logical and noetic concepts have, up to this time, been quite imperfectly clarified: countless equivocations beset them, some so pernicious, so hard to track down, and to keep consistently separate, that they yield the main ground for the very backward state of pure logic and theory + +We must of course admit that many conceptual differentiations and circumscriptions of the sphere of pure logic can become evident to the natural attitude without phenomenological analysis. The relevant logical acts are carried out and adequately fitted to their fulfilling intuitions, though there is no reflection on the phenomenological situation itself. What is most completely evident can, however, be confused with something else, what it apprehends can be misconstrued, its assured directives can be rejected. Clarifying researches are especially needed to explain our by no means chance inclination to slip unwittingly from an objective to a psychological attitude, and to mix up two bodies of data distinguishable in principle however much they may be essentially related, and to be deceived by psychological misconstructions and misinterpretations of the objects of logic. Such clarifications can, by their nature, only be achieved within a phenomenological theory of the essences of our thought- and knowledge-experiences, with continuous regard to the things essentially meant by, and so belonging to the latter (in the precise manners in which those things are *as such* 'shown forth', 'represented' etc.). Psychologism can only be radically overcome by a pure phenomenology, a science infinitely removed from psychology as the empirical science of the mental attributes and states of animal realities. In our sphere, too, the sphere of pure logic, such a phenomenology alone offers us all the necessary conditions for a finally satisfactory establishment of the totality of basic distinctions and insights. It alone frees us from the strong temptation, at first inevitable, since rooted in grounds of essence, to turn the logically objective + +into the psychological. + +The above mentioned motives for phenomenological analysis have an obvious and essential connection with those which spring from *basic questions of epistemology.* For if these questions are taken in the *widest* generality, i.e. in the 'formal' generality which abstracts from all matter of knowledge - they form part of a range of questions involved in the full clarification of the Idea of pure logic. We have, on the one hand, the fact that all thought and knowledge have as their aim *objects* or *states of affairs,* which they putatively 'hit' in the sense that the 'being-in-itself' of these objects and states is supposedly shown forth, and made an identifiable item, in a multitude of actual or possible meanings, or acts of thought. We have, further, the fact that all thought is ensouled by a thought-form which is subject to ideal laws, laws circumscribing the objectivity or ideality of knowledge in general. These facts, I maintain, eternally provoke questions like: How are we to understand the fact that the intrinsic being of objectivity becomes 'presented', 'apprehended' in knowledge, and so ends up by becoming subjective? What does it mean to say that the object has 'being-in-itself', and is 'given' in knowledge? How can the ideality of the universal *qua* concept or law enter the flux of real mental states and become an epistemic possession of the thinking person? What does the *adaequatio rei et intellectus* mean in various cases of knowledge, according as what we apprehend and know, is + +individual or universal, a fact or a law etc.? These and similar questions can, it is plain, not be separated from the above-mentioned questions regarding the clarification of pure logic, since the task of clarifying such logical Ideas as Concept and Object, Truth and Proposition, Fact and Law etc., inevitably leads on to these same questions. We should in any case have to tackle them so that the essence of the clarification aimed at in phenomenological + +analyses should not itself be left obscure. + +**§3 The difficulties of pure phenomenological analysis** The difficulties of clearing up the basic concepts of logic are a natural consequence of the extraordinary difficulties of strict phenomenological analysis. These are in the main the same whether our immanent analysis aims at the *pure* essence of experiences (all empirical facticity and individuation being excluded) or treats experiences from an empirical, psychological standpoint. Psychologists usually discuss such difficulties when they consider introspection as a source of our detailed psychological knowledge, not properly however, but in order to draw a false antithesis between introspection and 'outer' perception. The source of all such difficulties lies in the unnatural direction of intuition and thought which phenomenological analysis requires. Instead of becoming lost in the performance of acts built intricately on one another, and instead of (as it were) naively positing the existence of the objects intended in their sense and then going on to characterize them, or of assuming such objects hypothetically, of drawing conclusions from all this etc., we must rather practise 'reflection', i.e. make these acts themselves, and their immanent meaning-content, our objects. When objects are intuited, thought of, theoretically pondered on, and thereby given to us as actualities in certain ontic modalities, we must direct our theoretical interest away from such objects, not posit them as realities as they appear or hold in the intentions of our acts. These acts, contrariwise, though hitherto not objective, must now be made objects of apprehension and of theoretical assertion. We must deal with them in new acts of intuition and thinking, we must analyse and describe them in their essence, we must make them objects of empirical or ideational thought. Here we have a direction of thought running counter to deeply ingrained habits which have been steadily strengthened since the dawn of mental development. Hence the well-nigh ineradicable tendency to slip out of a phenomenological thought-stance into one that is straightforwardly objective, or to substitute for mental acts, or for the 'appearances' or 'meanings' immanent in them, characters which, in a naive performance of such acts, were attributed to their objects. Hence, too, the tendency to treat whole classes of genuinely subsistent objects, e.g. Ideas - since these may be evidently given to us in ideating intuitions - as phenomenological constituents of presentations + +A much discussed difficulty - one which seems to threaten in principle all possible immanent description of mental acts or indeed all phenomenological treatment of essences - lies in the fact that when we pass over from naively performed acts to an attitude of reflection, or when we perform acts proper to such reflection, our former acts necessarily undergo change. How can we rightly assess the nature and extent of such change? How indeed can we know anything whatever about it, whether as a fact or as a + +necessity of essence? + +In addition to this difficulty of reaching firm results, capable of being self-evidently reidentified on many occasions, we have the further difficulty of *stating such results,* of *communicating them to others.* Completely selfevident truths of essence, established by the most exact analysis, must be expounded by way of expressions whose rich variety does not compensate for the fact that they only fit familiar natural objects, while the experiences in which such objects become constituted for consciousness, can be directly referred to only by way of a few highly ambiguous words such as 'sensation', 'perception', 'presentation' etc. One has, further, to employ expressions which stand for what is intentional in such acts, for the object to which they are directed, since it is, in fact, impossible to describe referential acts without using expressions which recur to the things to which such acts refer. One then readily forgets that such subsidiarily described objectivity, which is necessarily introduced into almost all phenomenological description, has undergone a change of sense, in virtue of which it now belongs to the sphere + +of phenomenology. + +If we ignore such difficulties, others emerge concerned with the persuasive communication of our resultant insights to others. These insights can be tested and confirmed only by persons well-trained in the ability to engage in pure description in the unnatural attitude of reflection, trained in short to allow phenomenological relations to work upon them *in full purity.* Such purity means that we must keep out the falsifying intrusion of all assertions based on the naIve acceptance and assessment of objects, whose existence has been posited in the acts now receiving phenomenological treatment. It likewise prohibits any other going beyond whatever is essential and proper to such acts, any application to them of naturalistic interpretations and assertions. It forbids us, i.e., to set them up as psychological realities (even in an indefinitely general or exemplary fashion), as the states of 'mindendowed beings' of any sort whatsoever. The capacity for such researches is not readily come by, nor can it be achieved or replaced by, e.g., the most + +elaborate of trainings in experimental psychology. + +Serious as are the difficulties standing in the way of a pure phenomenology in general, and of the phenomenology of the logical experiences in particular, they are by no means such as to make the whole attempt to overcome them appear hopeless. Resolute cooperation among a generation of research-workers, conscious of their goal and dedicated to the main issue, + +would, I think, suffice to decide the most important questions in the field, those concerned with its basic constitution. Here we have a field of *attainable* discoveries, fundamentally involved in the possibility of a *scientific* philosophy. Such discoveries have indeed nothing dazzling about them: they lack any obviously useful relation to practice or to the fulfilment of higher emotional needs. They also lack any imposing apparatus of experimental methodology, through which experimental psychology has gained so much + +credit and has built up such a rich force of cooperative workers. + +**§4 It is essential to keep in mind the grammatical** + +**side of our logical experiences** + +Analytic phenomenology, needed by the logician in his preparatory laying of foundations, is concerned, among other things, with 'presentations' and with them primarily; it is, more precisely, concerned with those presentations to which *expression* has been given. In the complex objects of its study, its primary interest attaches to the experiences lying behind 'mere expressions', experiences which perform roles either of meaning-intention or of meaning-fulfilment. It cannot, however, quite ignore the sensuous-linguistic side of its complex objects (the element of 'mere expression' in them) nor the way in which this element is associated with the meaning that 'ensouls' it. Everyone knows how readily and how unnoticeably an analysis of meaning can be led astray by grammatical analysis. Since the direct analysis of meaning is, however, difficult, we may welcome each aid, however imperfect, that indirectly anticipates its results, but grammatical analysis is even more important in virtue of the errors its use promotes when it replaces a *true analysis of meaning,* than for any positive aid. Rough reflection on our thoughts and their verbal expression, conducted by us without special schooling, and often needed for the practical ends of thinking, suffice to indicate a certain parallelism between thinking and speaking. We all know that words mean something, and that, generally speaking, different words express different meanings. If we could regard such a correspondence as perfect, and as given *a priori,* and as one particularly in which the essential categories of meaning had perfect mirror-images in the categories of grammar, a phenomenology of linguistic forms would include a phenomenology of the meaningexperiences (experiences of thinking, judging etc.) and meaning-analysis + +would, so to speak, coincide with grammatical analysis. + +Deep reflection is not, however, needed to show that a parallelism satisfying such far-reaching demands has as little foundation in grounds of essence as it obtains in fact. *Grammatically relevant distinctions of meaning* are at times *essential,* at times *contingent,* according as the practical aims of speech dictate peculiar forms for essential or contingent differences of meaning. (The latter are merely such as have a frequent occurrence in human + +It is well-known, however, that differentiation of expressions does not merely depend on differences of meaning. I need point only to 'shades' of meaning, or to aesthetic tendencies which fight against any bare uniformity of expression, or against discord in speech-sound or rhythm, and so demand + +an abundant store of available synonyms. + +The rough concomitances among verbal and thought-differences, and particularly among *forms* of words and thoughts, makes us naturally tend to seek logical distinctions behind expressed grammatical distinctions. It is, therefore, *an important matter for logic that the relation between expression and meaning should be made analytically clear.* We should perceive clearly that, in order to decide whether a distinction should, in a given case, count as logical or merely grammatical, we must go back from *vague* acts of meaning to the correspondingly clear, articulate ones, acts saturated with the + +fulness of exemplary intuition in which their meaning is fulfilled. + +It is not enough to have the common knowledge, easily garnered from suitable examples, that grammatical differences need not coincide with logical ones. The common knowledge that such distinctions do not always go hand in hand - that languages, in other words, express material differences of meaning, widely used in communication, in forms as pervasive as the fundamental logical differences having their *a priori* roots in the general essence of meanings - such common knowledge may open the way to a dangerous radicalism. The field of logical forms may be unduly restricted. A wide range of logically significant forms may be cast forth as merely grammatical: only a few may be kept, such as suffice to leave some content to traditional syllogizing. Brentano's attempted reform of formal logic, valuable as it no doubt still is, plainly suffered from this exaggeration. Only a complete clearing-up of the essential phenomenological relations between expression and meaning, or between meaning-intention and meaning-fulfilment, can give us a firm middle stance, and can enable us to give the requisite clearness to the relations between grammatical and meaning-analysis. + +**§5 Statement of the main aims of the following** + +**analytical investigations** + +We accordingly pass to a series of analytic investigations which will clear up the constitutive Ideas of a pure or formal logic, investigations which relate in the first place to the pure theory of logical forms. Starting with the empirical connection between meaning-experiences and expressions, we must try to find out what our variously ambiguous talk about 'expressing' or 'meaning' really amounts to. We must try to see what essential phenomenological or logical distinctions apply *a priori* to expressions, and how we may in essence describe, and may place in pure categories, the experiences - to deal first with the phenomenological side of expressions - that have an *a priori* fitness for the meaning-function. We must find out how the 'presenting' + +and 'judging' achieved in such experiences stand to their corresponding 'intuition', how they are 'illustrated', or perhaps 'confirmed' or 'fulfilled', in the latter, or rendered 'evident' by it etc. It is not hard to see that investigations of such matters must precede all clarifications of the basic concepts and categories of logic. Among our introductory investigations we shall have to raise fundamental questions as to the acts, or, alternatively, the ideal meanings, which in logic pass under the name of 'presentations' *(Vorstellungen).* It is important to clarify and prise apart the many concepts that the word 'presentation' has covered, concepts in which the psychological, the epistemological and the logical are utterly confused. Similar analyses deal with the concept of *judgement* in the sense in which logic is concerned with it. So-called 'judgement-theory' neglects this task: it is in the main, in respect of its essential problems, a theory of presentation. We are naturally not interested in a psychological theory, but in a phenomenology of presentationand judgement-experiences as delimited by our epistemological interests. As we probe the essence of the expressive experiences, we must also dig more deeply into their *intentional subject-matter,* their objective intention's ideal sense, i.e. into the unity of its meaning and the unity of its object. We must, above all, dwell upon the enigmatic double sense or manner, the twosided context, in which the same experience has a 'content', and the manner in which in addition to its real *(reell)* and proper content, an ideal, inten- + +tional content must and can dwell in it. + +Here also belong questions relating to the 'object-directedness' or 'objectlessness' of logical acts, to the sense of the distinction between intentional and true objects, to the clarification of the Idea of truth in relation to the Idea of judgemental self-evidence, to the clarification of the remaining, closely connected logical and noetic categories. These investigations in part cover the same ground as those dealing with the constitution of logical forms, to the extent, of course, that we settle questions as to the acceptance or rejection of putative logical forms, or doubts as to their logical or merely grammatical distinctness from forms already recognized, in the course of our clarification + +of form-giving, categorial concepts. + +We have thus vaguely indicated the range of problems to which the ensuing investigations will be oriented. These investigations make no claim to be exhaustive. Their aim is not to provide a logical system, but to do the initial spadework for a philosophical logic which will derive clearness from basic phenomenological sources. The paths taken by such an analytic investigation will also naturally differ from those suitable to a final, systematic, logically + +ordered statement of established truth. + +**§6 Additional Notes** + +*Note 1* Our investigations will often inevitably take us beyond the narrow phenomenological sphere whose study is really required for giving direct + +evidence to the Ideas of logic. This sphere is itself not given to us initially, but becomes delimited in the course of our investigation. We are, in particular, forced beyond this sphere of research when we prise apart the many confused concepts obscurely confounded in our understanding of logical + +terms, and when we find which of them are truly logical. + +*Note* 2 The phenomenological founding of logic involves the difficulty that we must, in our exposition, make use of all the concepts we are trying to clarify. This coincides with a certain wholly irremovable defect which affects the systematic course of our basic phenomenological and epistemological investigations. If a type of thought requires prior clarification, we should not make uncritical use of its terms or concepts in that clarification itself. But one should not expect that one should only be required to analyse such concepts critically, when the actual interconnection of one's logical materials has led up to them. Or, put differently, systematic clarification, whether in pure logic or any other discipline, would in itself seem to require a stepwise following out of the ordering of things, of the systematic interconnection in the science to be clarified. Our investigation can, however, only proceed securely, if it repeatedly breaks with such systematic sequence, if it removes conceptual obscurities which threaten the course of investigation *before* the natural sequence of subject-matters can lead up to such concepts. We search, as it were, in zig-zag fashion, a metaphor all the more apt since the close interdependence of our various epistemological concepts leads us back again and again to our original analyses, where the new confirms the old, and the + +old the new. + +*Note* 3 If *our* sense of phenomenology has been grasped, and if it has not been given the current interpretation of an ordinary 'descriptive psychology', a part of natural science, then an objection, otherwise justifiable, will fall to the ground, an objection to the effect that all theory of knowledge, conceived as a systematic phenomenological clarification of knowledge, is built upon psychology. On this interpretation pure logic, treated by us as an epistemologically clarified, *philosophical* discipline, must in the end likewise rest upon psychology, if only upon its preliminary descriptive researches into intentional experiences. Why then so much heated resistance + +to psychologism? + +We naturally reply that if psychology is given its old meaning, phenomenology is not descriptive psychology: its peculiar 'pure' description, its contemplation of pure essences on a basis of exemplary individual intuitions of experiences (often freely *imagined* ones), and its descriptive fixation of the contemplated essences into pure concepts, is no empirical, scientific description. It rather excludes the natural performance of all empirical (naturalistic) apperceptions and positings. Statements of descriptive psychology regarding 'perceptions', 'judgements', 'feelings', 'volitions' etc., use such names + +to refer to the real states of animal organisms in a real natural order, just as descriptive statements concerning physical states deal with happenings in a nature not imagined but real. All general statements have here a character of empirical generality: they hold for *this* nature. Phenomenology, however, does not discuss states of animal organisms (not even as belonging to a possible nature as such), but perceptions, judgements, feelings *as such,* and what pertains to them *a priori* with unlimited generality, as *pure* instances of *pure* species, of what may be seen through a purely intuitive apprehension of essence, whether generic or specific. Pure arithmetic likewise speaks of numbers, and pure geometry of spatial shapes, employing pure intuitions in their ideational universality. Not psychology, therefore, but phenomenology, underlies all clarifications in pure logic (and in all forms of rational criticism). Phenomenology has, however, a very different function as the necessary basis for every psychology that could with justification and in strictness be called scientific, just as pure mathematics, e.g. pure geometry and dynamics, is the necessary foundation for all exact natural science (any theory of empirical things in nature with their empirical forms, movements etc.). Our essential insights into perceptions, volitions and other forms of experience will naturally hold also of the corresponding empirical states of animal + +organisms, as geometrical insights hold of spatial figures in nature. + +*Translator's Additional Note* 4 The above Note 3 is a typical account of what Husserl had come to mean by 'phenomenology' by the time that the Second Edition of the *Logical Investigations* was published in 1913. It replaces the following Note, which indicates what he meant by the term when + +the First Edition was published in 1901: + +Phenomenology is descriptive psychology. Epistemological criticism is therefore in essence psychology, or at least only capable of being built on a psychological basis. Pure logic therefore also rests on psychology what then is the point of the whole battle against psychologism? + +The necessity of *this* sort of psychological foundation of pure logic, i.e. a strictly descriptive one, cannot lead us into error regarding the mutual independence of the two sciences, logic and psychology. For pure description is merely a preparatory step towards theory, not theory itself. One and the same sphere of pure description can accordingly serve to prepare for very different theoretical sciences. It is *not the full science of psychology that serves as a foundation for pure logic,* but certain classes of descriptions which are the step preparatory to the theoretical researches of psychology. These in so far as they describe the empirical objects whose genetic connections the science wishes to pursue, also form the substrate for those fundamental abstractions in which logic seizes the essence of its ideal objects and connections with inward evidence. Since it is epistemologically of unique importance that we + +should separate the purely descriptive examination of the knowledgeexperience, disembarrassed of all theoretical psychological interests, from the truly psychological researches directed to empirical explanation and origins, it will be good if we rather speak of 'phenomenology' than of descriptive psychology. It also recommends itself for the further reason that the expression 'descriptive psychology', as it occurs in the talk of many scientists, means the sphere of scientific psychological investigation, which is marked off by a methodological preference for inner experience and by an abstraction from all psychophysical explanation. + +**§7 'Freedom from presuppositions' as a principle in** + +**epistemological investigations** + +An epistemological investigation that can seriously claim to be scientific must, it has often been emphasized, satisfy the *principle of freedom from presuppositions.* This principle, we think, only seeks to express the strict exclusion of all statements not permitting of a comprehensive *phenomenological* realization. Every epistemological investigation that we carry out must have its pure foundation in phenomenology. The 'theory' that it aspires to, is no more than a thinking over, a coming to an evident understanding of, thinking and knowing as such, in their pure generic essence, of the specifications and forms that they essentially have, of the immanent structures that their objective relations involve, of the meaning of 'validity', 'justification', 'mediate' and 'immediate evidence', and their opposites, as applied to such structures, of the parallel specifications of such Ideas in relation to varying regions of possible objects of knowledge, of the clarified sense and role of the formal and material 'laws of thought' seen in their *a priori* structural connections with the knowing consciousness etc. If such a 'thinking over' of the meaning of knowledge is itself to yield, not mere opinion, but the evident knowledge it strictly demands, it must be a pure intuition of essences, exemplarily performed on an actual *given* basis of experiences of thinking and knowing. That acts of thought at times refer to transcendent, even to non-existent and impossible objects, is not to the case. For such direction to objects, such presentation and meaning of what is not really *(reel!)* part of the phenomenological make-up of our experiences, is a descriptive feature of the experiences in question, whose sense it should be possible to fix and clarify by considering the experiences themselves. In no + +other way would it be possible. + +We must keep apart from the pure theory of knowledge questions concerning the justifiability of accepting 'mental' and 'physical' realities which transcend consciousness, questions whether the statements of scientists regarding them are to be given a serious or unserious sense, questions whether it is justifiable or sensible to oppose a second, even more emphatically 'transcendent' world, to the phenomenal nature with which science is correlated, + +and other similar questions. The question as to the existence and nature of 'the external world' is a metaphysical question. The theory of knowledge, in generally clearing up the ideal essence and valid sense of cognitive thought, will of course deal with general questions regarding the possibility and manner of a knowledge or rational surmise about 'real' objective things, things in principle transcending the experiences which know them, and regarding the norms which the true sense of such a knowledge requires: it will not enter upon the empirically oriented question as to whether we as men really can arrive at such knowledge from the data we actually have, nor will it attempt to realize such knowledge. On our view, theory of knowledge, properly described, is no theory. It is not science in the pointed sense of an explanatorily unified theoretical whole. *Theoretical explanation* means an ever increased rendering intelligible of singular facts through general laws, and an ever increased rendering intelligible of general laws through some fundamental law. In the realm of facts, our task is to know that what happens under given groups of circumstances, happens *necessarily,* i.e. according to *natural laws.* In the realm of the *a priori* our task is to understand the *necessity* of specific, lower-level relationships in terms of comprehensive general necessities, and ultimately in terms of those most primitive, universal relational *laws* that we call axioms. The theory of knowledge has nothing to explain in this theoretical sense, it neither constructs deductive theories nor falls under any. This is clear enough if we consider the most general, the so-to-say formal theory of knowledge that came before us in our *Prolegomena* as the philosophical completion of pure mathematics conceived in absolute width as including all *a priori,* categorial knowledge in the form of systematic theories. This theory of theories goes together with, and is illuminated by, a formal theory of knowledge which precedes all empirical theory, which precedes, therefore, all empirical knowledge of the real, all physical science on the one hand, and all psychology on the other, and of course all metaphysics. Its aim is not to *explain* knowledge in the psychological or psychophysical sense as *a/actual* occurrence in objective nature, but to *shed light* on the *Idea* of knowledge in its constitutive elements and laws. It does not try to follow up the real connections of coexistence and succession with which actual acts of knowledge are interwoven, but to understand the *ideal* sense of the *specific* connections in which the objectivity of knowledge may be documented. It endeavours to raise to clearness the pure forms and laws of knowledge by tracing knowledge back to an adequate fulfilment in intuition. This 'clearing up' takes place in the framework of a phenomenology of knowledge, a phenomenology oriented, as we saw, to the essential structures of pure experiences and to the structures of sense *(Sinnbestande)* that belong to these. From the beginning, as at all later stages, its scientific statements involve not the slightest reference to real existence: no metaphysical, scientific and, above all, no psychological assertions can therefore occur among + +A purely phenomenological 'theory' of knowledge naturally has an application to all naturally developed, and (in a good sense) 'naIve' sciences, which it transforms into 'philosophical' sciences. It transforms them, in other words, into sciences which provide us with clarified, assured knowledge in every sense in which it is possible to desire the latter. As regards the sciences of 'reality', such epistemological clarification can as much be regarded as a + +'scientific' as a 'metaphysical' evaluation. + +The investigations which follow aspire solely to such freedom from metaphysical, scientific and psychological presuppositions. No harm will of course be done by occasional side-references which remain without effect on the content and character of one's analyses, nor by the many expository devices addressed to one's public, whose existence (like one's own) is not therefore presupposed by the content of one's investigations. Nor does one exceed one's prescribed limits if one starts, e.g., from existent languages and discusses the merely communicative meaning of their many forms of expression, and so on. It is easily seen that the sense and the epistemological worth of the following analyses does not depend on the fact that there really are languages, and that men really make use of them in their mutual dealings, or that there really are such things as men and a nature, and that they do + +not merely exist in imagined, possible fashion. + +The real premisses of our putative results must lie in propositions satisfying the requirement that what they assert permits of an *adequate phenomenological justification,* a fulfilment through *evidence* in the strictest sense. Such propositions must not, further, ever be adduced in some other sense + +than that in which they have been intuitively established. + +**Expression and meaning** + +**Essential distinctions** + +§ **I An ambiguity in the term 'sign'** + +The terms 'expression' and 'sign' are often treated as synonyms, but it will not be amiss to point out that they do not always coincide in application in common usage. Every sign is a sign for something, but not every sign has 'meaning', a 'sense' that the sign 'expresses'. In many cases it is not even true that a sign 'stands for' that of which we may say it is a sign. And even where this can be said, one has to observe that 'standing for' will not count as the 'meaning' which characterizes the expression. For signs in the sense of indications (notes, marks etc.) *do not express* anything, unless they happen to fulfil a significant as well as an indicative function. If, as one unwillingly does, one limits oneself to expressions employed in living discourse, the notion of an indication seems to apply more widely than that of an expression, but this does not mean that its content is the genus of which an expression is the species. To mean is *not a particular way of being a sign in the sense of indicating something.* It has a narrower application only because meaning - in communicative speech - is always bound up with such an indicative relation, and this in its turn leads to a wider concept, since meaning is also capable of occurring without such a connection. *Expressions* function meaningfully even in *isolated mental life, where they no longer serve to indicate anything.* The two notions of sign do not therefore really stand in the relation of more extensive genus to nar- + +rower speCIes. + +The whole matter requires more thorough discussion. + +**§2 The essence of indication** + +Of the two concepts connected with the word 'sign', we shall first deal with that of an *indication.* The relation that here obtains we shall call the *indicative relation.* In this sense a brand is the sign of a slave, a flag the sign of a nation. Here all marks belong, as characteristic qualities suited to help us in + +But the concept of an indication extends more widely than that of a mark. We say the Martian canals are signs of the existence of intelligent beings on Mars, that fossil vertebrae are signs of the existence of prediluvian animals etc. Signs to aid memory, such as the much-used knot in a handkerchief, memorials etc., also have their place here. If suitable things, events or their properties are deliberately produced to serve as such indications, one calls them 'signs' whether they exercise this function or not. Only in the case of indications deliberately and artificially brought about, does one speak of standing for, and that both in respect of the action which produces the marking (the branding or chalking etc.), and in the sense of the indication itself, i.e. taken in its relation to the object it stands for or that it is to signify. These distinctions and others like them do not deprive the concept of indication of its essential unity. A thing is only properly an indication if and where it in fact serves to indicate something to some thinking being. If we wish to seize the pervasively common element here present we must refer back to such cases of 'live' functioning. In these we discover as a common circumstance the fact that certain objects or states of affairs *of whose reality someone has actual knowledge* indicate to him *the reality of certain other objects or states of affairs,* in the sense that *his belief in the reality of the one* is *experienced* (though not at all evidently) *as motivating a belief or surmise in the reality of the other.* This relation of 'motivation' represents a *descriptive unity* among our acts of judgement in which indicating and indicated states of affairs become constituted for the thinker. This descriptive unity is not to be conceived as a mere form-quality founded upon our acts of judgement, for it is in their unity that the essence of indication lies. More lucidly put: the 'motivational' unity of our acts of judgement has itself the character of a unity of judgement; before it as a whole an objective correlate, a unitary state of affairs, parades itself, is meant in such a judgement, appears to be in and for that judgement. Plainly such a state of affairs amounts to just this: that certain things *mayor must* exist, *since* other things have been given. This 'since', taken as expressing an objective connection, is the objective correlate of 'motivation' taken as a descriptively peculiar way of combining + +acts of judgement into a single act of judgement. + +**§3 Two senses of 'demonstration' (,indication'** + +**and 'proof')** + +We have sketched the phenomenological situation so generally that what we have said applies as much to the 'demonstration' of genuine inference and proof, as to the 'demonstration' of indication. These two notions should, however, be kept apart. Their distinctness has already been suggested by our stress on the *lack of insight* in indications. In cases where the existence of one state of affairs is evidently inferred from that of another, we do not in fact speak of the latter as an indication or sign of the former, and, + +conversely, we only speak of demonstration in the strict logical sense in the case of an inference which is or could be informed by insight. Much, no doubt, that is propounded as demonstrative or, in the simplest case, as syllogistically cogent, is devoid of insight and may even be false. But to propound it is at least to make the claim that a relation of consequence could be seen to hold. This is bound up with the fact that there is an objective syllogism or proof, or an objective relationship between ground and consequent, which corresponds to our subjective acts of inferring and proving. These ideal unities are not the experiences of judging in question, but their ideal 'contents', the propositions they involve. The premisses prove the conclusion no matter who may affirm the premisses and the conclusion, or the unity that both form. An ideal rule is here revealed which extends its sway beyond the judgements here and now united by 'motivation'; in supraempirical generality it comprehends as such all judgements having a like content, all judgements, even, having a like form. Such regularity makes itself subjectively known to us when we conduct proofs with insight, while the precise rule is made known to us through ideative reflection on the contents of the judgements experienced together in the actual context of 'motivation', in the actual inference and proof. These contents are the pro- + +positions involved. + +**In** the case of an indication there is no question of all this. Here insight and (to put the matter objectively) knowledge regarding the ideal connections among the contents of the judgements concerned, is quite excluded. When one says that the state of affairs *A* indicates the state of affairs *B,* that the existence of the one points to that of the other, one may confidently be expecting to find *B* true, but one's mode of speech implies no objectively necessary connections between *A* and *B,* nothing into which one could have insight. The contents of one's judgements are not here related as premisses are to a conclusion. At times no doubt we do speak of 'indications' even in cases where there is an objective relation of entailment (a mediate one, in fact). A mathematician may make use (so he says) of the fact that an algebraic equation is of uneven order as a sign that it has at least one real root. To be more exact, we are here only concerned with the possibility that someone who fails to carry out and see the cogency of the relevant thought-chain, may make use of a statement about an equation's uneven order as an immediate, blind motive for asserting the equation to have some necessarily connected property which he needs for his mathematical purposes. **In** such situations, where certain states of affairs readily serve to indicate others which are, in themselves, their consequences, they do not function in thought as logical grounds of the latter, but work through connections which previous actual demonstration, or blind learning on authority, has established among our convictions, whether as actual mental states or as dispositions for such. Nothing is of course altered in all this by the possible presence of an accompanying merely habitual knowledge of an objectively present rational connection. + +If an indication (or the connection of 'motivation' in which such a soidis ant objective relation makes its appearance) is without essential relation to a necessary connection, the question arises whether it may not claim to be essentially related to a connection of probability. Where one thing indicates another, where belief in the one's existence furnishes one with an empirical motive or ground ~ not necessary but contingent ~ for belief in the existence of the other, must the motivating belief not furnish a *ground of probability* for the belief it motivates? This is not the place for a close discussion of this pressing question. We need only observe that the question may correctly be answered in the affirmative in so far as such empirical 'motivations' all fall under an ideal jurisdiction in virtue of which they may be spoken of as 'justified' or 'unjustified', or, objectively expressed, in which they may be spoken of as real, i.e. valid, motivations which lead to a probability or perhaps to an empirical certainty, or *per contra,* as merely apparent, i.e. invalid, motivations, which do not lead to such a probability. One may, e.g., cite the controversy as to whether volcanic phenomena do or do not indicate that the earth's interior is molten, and so on. One thing is sure, that to talk of an indication is not to presuppose a definite relation to considerations of probability. Usually such talk relates not to mere surmises but to assured judgements. The ideal jurisdiction to which we have here accorded authority must first demand, therefore, that we should scale down our confident judge- + +ments to modest surmises. + +I shall here observe, further, that we cannot avoid talking about 'motivation' in a general sense which covers strict demonstration as much as empirical indication. Here in fact we have a quite undeniable phenomenological affinity, obvious enough to register itself in ordinary discourse. We commonly speak of reasoning and inference, not merely in the sense of logic, but in a sense connected with empirical indications. This affinity plainly extends more widely: it covers the field of emotional, and, in particular, of volitional phenomena, to which talk of 'motives' was at first alone confined. Here too 'because' has a part to play, covering as wide a linguistic territory as does the most general sense of 'motivation'. I cannot therefore approve of Meinong's censure of Brentano's terminology, which I have here adopted. l But I entirely agree with him that in perceiving something as 'motivated' we + +are not at all perceiving it as caused. + +**§4 Digression on the origin of indication in association** The mental facts in which the notion of indication has its 'origin', i.e. in which it can be abstractively apprehended, belong to the wider group of facts which fall under the historical rubric of the 'association of ideas'. Under this rubric we do not merely have those facts which concern the 'accompaniment' and 'reactivation' of ideas stated in the laws of association, but the further facts in which association operates creatively, and produces + +peculiar descriptive characters and forms of unity.2 Association does not merely restore contents to consciousness, and then leave it to them to combine with the contents there present, as the essence or generic nature of either may necessarily prescribe. It cannot indeed disturb such unified patterns as depend solely on our mental contents, e.g. the unity of visual contents in the visual field. But it can create additional phenomenological characters and unities which do not have their necessary, law-determined ground in the experienced contents themselves, nor in the generic forms of their abstract aspects. 3 If *A* summons *B* into consciousness, we are not merely simultaneously or successively conscious of both *A* and *B,* but we usually *feel* their connection forcing itself upon us, a connection in which the one points to the other and seems to belong to it. To turn mere coexistence into mutual pertinence, or, more precisely, to build cases of the former into intentional unities of things which seem mutually pertinent, is the constant result of associative functioning. All unity of experience, all empirical unity, whether of a thing, an event or of the order and relation of things, becomes a phenomenal unity through the felt mutual belongingness of the sides and parts that can be made to stand out as units in the apparent object before us. That one thing points to another, in definite arrangement and connection, is itself apparent to us. The single item itself, in these various forward and backward references, is no mere experienced content, but an apparent object (or part, property etc., of the same) that appears only in so far as experience *(Erfahrung)* endows contents with a new phenomenological *character,* so that they no longer count separately, but help to present an object different from themselves. In this field of facts the fact of indication also has its place, in virtue whereof an object or state of affairs not merely recalls another, and so points to it, but also provides evidence for the latter, fosters the presumption that it likewise exists, and makes us immediately + +feel this in the manner described above. + +**§5 Expressions as meaningful signs. Setting aside of a sense of 'expression' not relevant for our purpose** + +From indicative signs we distinguish *meaningful* signs, i.e. *expressions.* We thereby employ the term 'expression' restrictively: we exclude much that ordinary speech would call an 'expression' from its range of application. There are other cases in which we have thus to do violence to usage, where concepts for which only ambiguous terms exist call for a fixed terminology. We shall lay down, for provisional intelligibility, that each instance or part of *speech,* as also each sign that is essentially of the same sort, shall count as an expression, whether or not such speech is actually uttered, or addressed with communicative intent to any persons or not. Such a definition excludes facial expression and the various gestures which involuntarily accompany speech without communicative intent, or those in which a man's mental + +states achieve understandable 'expression' for his environment, without the added help of speech. Such 'utterances' are not expressions in the sense in which a case of speech is an expression, they are not phenomenally one with the experiences made manifest in them in the consciousness of the man who manifests them, as is the case with speech. **In** such manifestations one man communicates nothing to another: their utterance involves no intent to put certain 'thoughts' on record expressively, whether for the man himself, in his solitary state, or for others. Such 'expressions', in short, have properly speaking, *no meaning.* It is not to the point that another person may interpret our involuntary manifestations, e.g. our 'expressive movements', and that he may thereby become deeply acquainted with our inner thoughts and emotions. They 'mean' something to him in so far as he interprets them, but even for him they are without meaning in the special sense in which verbal + +signs have meaning: they only mean in the sense of indicating. + +**In** the treatment which follows these distinctions must be raised to com- + +plete conceptual clarity. + +**§6 Questions as to the phenomenological and** + +**intentional distinctions which pertain to expressions** + +**as such** + +It is usual to distinguish two things in regard to every expression: + +1. The expression physically regarded (the sensible sign, the articulate + +sound-complex, the written sign on paper etc.); + +2. A certain sequence of mental states, associatively linked with the expression, which make it be the expression of something. These mental states are generally called the 'sense' or the 'meaning' of the expression, this being taken to be in accord with what these words ordinarily mean. But we shall see this notion to be mistaken, and that a mere distinction between physical signs and sense-giving experiences is by no means enough, and not at all + +enough for logical purposes. + +The points here made have long been observed in the special case of names. We distinguish, in the case of each name, between what it 'shows forth' (i.e. mental states) and what it means. And again between what it means (the sense or 'content' of its naming presentation) and what it names (the object of that presentation). We shall need similar distinctions in the case of all expression, and shall have to explore their nature precisely. Such distinctions have led to our distinction between the notions of 'expression' and 'indication', which is not in conflict with the fact that an expression in living speech also functions as an indication, a point soon to come up for discussion. To these distinctions other important ones will be added which will concern the relations between meaning and the intuition which illustrates meaning and on occasion renders it evident. Only by paying heed to these relations, can the concept of meaning be clearly delimited, and can the + +fundamental opposition between the symbolic and the epistemological func- + +tion of meanings be worked out. + +**§7 Expressions as they function in communication** + +Expressions were originally framed to fulfil a communicative function: let us, accordingly, first study expressions in this function, so that we may be able to work out their essential logical distinctions. The articulate soundcomplex, the written sign etc., first becomes a spoken word or communicative bit of speech, when a speaker produces it with the intention of 'expressing himself about something' through its means; he must endow it with a sense in certain acts of mind, a sense he desires to share with his auditors. Such sharing becomes a possibility if the auditor also understands the speaker's intention. He does this inasmuch as he takes the speaker to be a person, who is not merely uttering sounds but *speaking to him,* who is accompanying those sounds with certain sense-giving acts, which the sounds reveal to the hearer, or whose sense they seek to communicate to him. What first makes mental commerce possible, and turns connected speech into discourse, lies in the correlation among the corresponding physical and mental experiences of communicating persons which is effected by the physical side of speech. Speaking and hearing, intimation of mental states through speaking and + +reception thereof in hearing, are mutually correlated. + +If one surveys these interconnections, one sees at once that all expressions in *communicative* speech function as *indications.* They serve the hearer as signs of the 'thoughts' of the speaker, i.e. of his sense-giving inner experiences, as well as of the other inner experiences which are part of his communicative intention. This function of verbal expressions we shall call their *intimating function.* The content of such intimation consists in the inner experiences intimated. The sense of the predicate 'intimated' can be understood more narrowly or more widely. The *narrower* sense we may restrict to *acts which impart sense,* while the *wider* sense will cover *all* acts that a hearer may introject into a speaker on the basis of what he says (possibly because he tells us of such acts). If, e.g., we state a wish, our judgement concerning that wish is what we intimate in the narrower sense of the word, whereas the wish itself is intimated in the wider sense. The same holds of an ordinary statement of perception, which the hearer forthwith takes to belong to some actual perception. The act of perception is there intimated in the wider sense, the judgement built upon it in the narrower sense. We at once see that ordinary speech permits us to call an experience which is intimated an experi- + +ence which is *expressed.* + +To understand an intimation is not to have conceptual knowledge of it, not to judge in the sense of asserting anything about it: it consists simply in the fact that the hearer *intuitively* takes the speaker to be a person who is expressing this or that, or as we certainly can say, *perceives* him as such. + +When I listen to someone, I perceive him as a speaker, I hear him recounting, demonstrating, doubting, wishing etc. The hearer perceives the intimation in the same sense in which he perceives the intimating person - even though the mental phenomena which make him a person cannot fall, for what they are, in the intuitive grasp of another. Common speech credits us with percepts even of other people's inner experiences; we 'see' their anger, their pain etc. Such talk is quite correct, as long as, e.g., we allow outward bodily things likewise to count as perceived, and as long as, in general, the notion of perception is not restricted to the adequate, the strictly intuitive percept. If the essential mark of perception lies in the intuitive persuasion that a thing or event is itself before us for our grasping - such a persuasion is possible, and in the main mass of cases actual, without verbalized, conceptual apprehension - then the receipt of such an intimation is the mere perceiving of it. The essential distinction just touched on is of course present here. The hearer perceives the speaker as manifesting certain inner experiences, and to that extent he also perceives these experiences themselves: he does not, however, himself experience them, he has not an 'inner' but an 'outer' percept of them. Here we have the big difference between the real grasp of what is in adequate intuition, and the putative grasp of what is on a basis of inadequate, though intuitive, presentation. In the former case we have to do with an experienced, in the latter case with a presumed being, to which no truth corresponds at all. Mutual understanding demands a certain correlation among the mental acts mutually unfolded in intimation and in the receipt of such intimation, but not at all their exact resemblance. + +**§8 Expressions in solitary life** + +So far we have considered expressions as used in communication, which last depends essentially on the fact that they operate indicatively. But expressions also playa great part in uncommunicated, interior mental life. This change in function plainly has nothing to do with whatever makes an expression an expression. Expressions continue to have meanings as they had before, and the same meanings as in dialogue. A word only cases to be a word when our interest stops at its sensory contour, when it becomes a mere sound-pattern. But when we live in the understanding of a word, it expresses something and the same thing, whether we address it to anyone or not. It seems clear, therefore, that an expression's meaning, and whatever else pertains to it essentially, cannot coincide with its feats of intimation. Or shall we say that, even in solitary mental life, one still uses expressions to intimate something, though not to a second person? Shall one say that in soliloquy one speaks to oneself, and employs words as signs, i.e. as indications, of one's own inner experiences? I cannot think such a view acceptable. Words function as signs here as they do everywhere else: everywhere they can be said to point to something. But if we reflect on the relation of + +expression to meaning, and to this end break up our complex, intimately unified experience of the sense-filled expression, into the two factors of word and sense, the word comes before us as intrinsically indifferent, whereas the sense seems the thing aimed at by the verbal sign and meant by its means: the expression seems to direct interest away from itself towards its sense, and to point to the latter. But this pointing is not an indication in the sense previously discussed. The existence of the sign neither 'motivates' the existence of the meaning, nor, properly expressed, our belief in the meaning's existence. What we are to use as an indication, must be perceived by us as existent. This holds also of expressions used in communication, but not for expressions used in soliloquy, where we are in general content with imagined rather than with actual words. In imagination a spoken or printed word floats before us, though in reality it has no existence. We should not, however, confuse imaginative presentations, and the image-contents they rest on, with their imagined objects. The imagined verbal sound, or the imagined printed word, does not exist, only its imaginative presentation does so. The difference is the difference between imagined centaurs and the imagination of such beings. The word's non-existence neither disturbs nor interests us, since it leaves the word's expressive function unaffected. Where it *does* make a difference is where intimation is linked with meaning. Here thought must not be merely expressed as meaning, but must be communicated and intimated. + +We can only do the latter where we actually speak and hear. + +One of course speaks, in a certain sense, even in soliloquy, and it is certainly possible to think of oneself as speaking, and even as speaking to oneself, as, e.g., when someone says to himself: 'You have gone wrong, you can't go on like that.' But in the genuine sense of communication, there is no speech in such cases, nor does one tell oneself anything: one merely conceives of oneself as speaking and communicating. In a monologue words can perform no function of indicating the existence of mental acts, since such indication would there be quite purposeless. For the acts in question + +are themselves experienced by us at that very moment. + +**§9 Phenomenological distinctions between the physical appearance of the expression, and the** + +**sense-giving and sense-fulfilling act** + +If we now turn from experiences specially concerned with intimation, and consider expressions in respect of distinctions that pertain to them equally whether they occur in dialogue or soliloquy, two things seem to be left over: the expressions themselves, and what they express as their meaning or sense. Several relations are, however, intertwined at this point, and talk about 'meaning', or about 'what is expressed', is correspondingly ambiguous. If we seek a foothold in pure description, the concrete phenomenon of the senseinformed expression breaks up, on the one hand, into the *physical phenomenon* + +fonning the physical side of the expression, and, on the other hand, into the *acts* which give it *meaning* and possibly also *intuitive fulness,* in which its relation to an expressed object is constituted. In virtue of such acts, the expression is more than a merely sounded word. It *means* something, and in so far as it means something, it relates to what is objective. This objective somewhat can either be actually present through accompanying intuitions, or may at least appear in representation, e.g. in a mental image, and where this happens the relation to an object is realized. Alternatively this need not occur: the expression functions significantly, it remains more than mere sound of words, but it lacks any basic intuition that will give it its object. The relation of expression to object is now unrealized as being confined to a mere meaning-intention. A *name,* e.g., names its object whatever the circumstances, in so far as it *means* that object. But if the object is not intuitively before one, and so not before one as a named or meant object, mere meaning is all there is to it. If the originally *empty* meaning-intention is now fulfilled, the relation to an object is realized, the naming becomes an actual, + +conscious relation between name and object named. + +Let us take our stand on this fundamental distinction between meaningintentions void of intuition and those which are intuitively fulfilled: if we leave aside the sensuous acts in which the expression, *qua* mere sound of words, makes its appearance, we shall have to distinguish between two acts or sets of acts. We shall, on the one hand, have acts essential to the expression if it is to be an expression at all, i.e. a verbal sound infused with sense. These acts we shall call the *meaning-conferring acts* or the *meaningintentions.* But we shall, on the other hand, have acts, not essential to the expression as such, which stand to it in the logically basic relation of *fulfilling* (confirming, illustrating) it more or less adequately, and so actualizing its relation to its object. These acts, which become fused with the meaningconferring acts in the unity of knowledge or fulfilment, we call the *meaningfulfilling* acts. The briefer expression 'meaning-fulfilment' can only be used in cases where there is no risk of the ready confusion with the *whole* experience in which a meaning-intention finds fulfilment in its correlated intuition. In the realized relation of the expression to its objective correlate,4 the senseinfonned expression becomes one with the act of meaning-fulfilment. The sounded word is first made one with the meaning-intention, and this in its turn is made one (as intentions in general are made one with their fulfilments) with its corresponding meaning-fulfilment. The word 'expression' is nonnally understood - wherever, that is, we do not speak of a 'mere' expression - as the *sense-animated* expression. One should not, therefore, properly say (as one often does) that an expression *expresses its meaning* (its intention). One might more properly adopt the alternative way of speaking according to which the *fulfilling act* appears as *the act expressed by the complete expression:* we may e.g., say, that a statement 'gives expression' to an act of perceiving or imagining. We need not here point out that both meaning- + +conferring and meaning-fulfilling acts have a part to play in intimation in the case of communicative discourse. The former in fact constitute the inmost core of intimation. To make them known to the hearer is the prime aim of our communicative intention, for only in so far as the hearer attri- + +butes them to the speaker will he understand the latter. + +§ I **0 The phenomenological unity of these acts** + +The above distinguished acts involving the expression's appearance, on the one hand, and the meaning-intention and possible meaning-fulfilment, on the other, do not constitute a mere aggregate of simultaneously given items in consciousness. They rather form an intimately fused unity of peculiar character. Everyone's personal experience bears witness to the differing weight of the two constituents, which reflects the asymmetry of the relation between an expression and the object which (through its meaning) it expresses or names. Both are 'lived through', the presentation of the word and the sense-giving act: but, while we experience the former, we do not live *in* such a presentation at all, but solely in enacting its sense, its meaning. And in so far as we do this, and yield ourselves to enacting the meaning-intention and its further fulfilment, our whole interest centres upon the object intended in our intention, and named by its means. (These two ways of speaking have in fact the same meaning.) The function of a word (or rather of an intuitive word-presentation) is to awaken a sense-conferring act in ourselves, to point to what is intended, or perhaps given intuitive fulfilment in this act, and to + +guide our interest exclusively in this direction. + +Such pointing is not to be described as the mere objective fact of a regular diversion of interest from one thing to another. The fact that two presented objects *A* and *B* are so linked by some secret psychological coordination that the presentation of *A* regularly arouses the presentation of *B,* and that interest is thereby shifted from *A* to *B* - such a fact does not make *A* the expression of the presentation of *B.* To be an expression is rather a descrip- + +tive aspect of the *experienced unity* of sign and thing signified. + +What is involved in the descriptive difference between the physical signphenomenon and the meaning-intention which makes it into an expression, becomes most clear when we turn our attention to the sign *qua* sign, e.g. to the printed word as such. If we do this, we have an external percept (or external intuitive idea) just like any other, whose object loses its verbal character. If this object again functions as a word, its presentation is wholly altered in character. The word *(qua* external singular) remains intuitively present, maintains its appearance, but we no longer intend it, it no longer properly is the object of our 'mental activity'. Our interest, our intention, our thought - mere synonyms if taken in sufficiently wide senses - point exclusively to the thing meant in the sense-giving act. This means, phenomenologically speaking, that the intuitive presentation, in which the + +physical appearance of the world is constituted, undergoes an essential phenomenal modification when its object begins to count as an *expression.* While what constitutes the object's appearing remains unchanged, the intentional character of the experience alters. There is constituted (without need of a fulfilling or illustrative intuition) an act of meaning which finds support in the verbal presentation's intuitive content, but which differs in essence from the intuitive intention directed upon the word itself. With this act, the new acts or act-complexes that we call 'fulfilling' acts or act-complexes are often peculiarly blended, acts whose object coincides with the object meant + +in the meaning, or named through this meaning. + +In our next chapter we shall have to conduct additional researches into the question as to whether the 'meaning-intention', which on our view characteristically marks off an expression from empty 'sound of words' consists in the mere association of mental imagery of the intended object with the sounded words, or at least necessarily involves such an act of fancy, or whether, on the other hand, mental imagery lies outside of the essence of an expression, and rather performs a fulfilling role, even if only of a partial, indirect or provisional character. In order not to blur the main outlines of our thought, we shall not here enter more deeply into phenomenological questions. In this whole investigation, we need only do as much phenom- + +enology as is required to establish essential, primary distinctions. + +The provisional description so far given will have shown how complex is the correct description of a phenomenological situation. Such complexity appears inevitable once we clearly see that all objects and relations among objects only are what they are for us, through acts of thought essentially different from them, in which they become present to us, in which they stand before us as unitary items that we *mean.* Where not the phenomenological, but the naIvely objective interest dominates, where we live in intentional acts without reflecting upon them, all talk of course becomes plain sailing and clear and devoid of circumlocution. One then, in our case, simply speaks of 'expression' and of 'what is expressed', of name and thing named, of the steering of attention from one to the other etc. But where the phenomenological interest dominates, we endure the hardship of having to describe phenomenological relationships which we may have experienced on countless occasions, but of which we were not normally conscious as objects, and we have also to do our describing with expressions framed to deal with + +objects whose appearance lies in the sphere of our normal interests. + +§ I **I The ideal distinctions between (I) expression and** + +**meaning as ideal unities** + +We have so far considered 'the well-understood expression' as a concrete experience. Instead of considering its two types of factor, the expression's appearance and the sense-conferring or sense-fulfilling experience, we wish + +to consider what is, in a certain fashion, given 'in' these: the expression itself, its sense and its objective correlate. We turn therefore from the real relation of acts to the ideal relation of their objects or contents. A subjective treatment yields to one that is objective. The ideality of the relationship between expression and meaning is at once plain in regard to both its sides, inasmuch as, when we ask for the meaning of an expression, e.g. 'quadratic remainder', we are naturally not referring to the sound-pattern uttered here and now *(hic et nunc),* the vanishing noise that can never recur identically: we mean the expression *in specie.* 'Quadratic remainder' is the same expression by whomsoever uttered. The same holds of talk about the expression's meaning, which naturally does not refer to some meaning- + +conferring experience. + +Every example shows that an essential distinction must here be drawn. If I sincerely say ~ we shall always presume sincerity ~ 'The three perpendiculars of a triangle intersect in a point', this is of course based on the fact that I judge so. If someone hears me and understands my assertion, he likewise knows this fact; he 'apperceives' me as someone who judges thus. But is the judging here *intimated* the meaning of my assertion, is it what my assertion asserts, and in that sense expresses? Plainly not. It would hardly occur to anyone, if asked as to the sense or meaning of my assertion, to revert to my judgement as an inner experience. Everyone would rather reply by saying: What this assertion asserts is *the same* whoever may assert it, and on whatever occasion or in whatever circumstances he may assert it, and what it asserts is precisely this, *that the three perpendiculars of a triangle intersect in a point,* no more and no less. One therefore repeats what is in essence 'the same' assertion, and one repeats it because it is the one, uniquely adequate way of expressing the same thing, i.e. its meaning. In this selfsame meaning, of whose identity we are conscious whenever we repeat the statement, nothing at all about judging or about one who judges is discoverable. We thought we were sure that a state of affairs held or obtained objectively, and what we were sure of we expressed by way of a declarative sentence. The state of affairs is what it is whether we assert that it obtains or not. It is intrinsically an item, a unity, which is capable of so obtaining or holding. But such an obtaining is what appeared before us, and we set it forth as it appeared before us: we said 'So the matter is'. Naturally we could not have done this, we could not have made the assertion, if the matter had not so appeared before us, if, in other words, we had not so judged. This forms part of an assertion as a psychological fact, it is involved in its intimation. But only in such intimation; for while what is intimated consists in inner experiences, what we assert in the judgement involves nothing subjective. My act of judging is a transient experience: it arises and passes away. But what my assertion asserts, the content *that the three perpendiculars of a triangle intersect in a point,* neither arises nor passes away. It is an identity in + +It is the same in the case of all assertions, even if what they assert is false and absurd. Even in such cases we distinguish their ideal content from the transient acts or affirming and asserting it: it is the meaning of the assertion, a unity in plurality. We continue to recognize its identity of intention in evident acts of reflection: we do not arbitrarily attribute it to our assertions, + +but discover it in them. + +If 'possibility' or 'truth' is lacking, an assertion's intention can only be carried out symbolically: it cannot derive any 'fulness' from intuition or from the categorial functions performed on the latter, in which 'fulness' its value for knowledge consists. It then lacks, as one says, a 'true', a 'genuine' meaning. Later we shall look more closely into this distinction between intending and fulfilling meaning. To characterize the various acts in which the relevant ideal unities are constituted, and to throw light on the essence of their actual 'coincidence' in knowledge, will call for difficult, comprehensive studies. It is plain, however, that each assertion, whether representing an exercise of knowledge or not ~ whether or not, i.e., it fulfils or can fulfil its intention in corresponding intuitions, and the formative acts involved in these ~ involves an intention, in which intention, as its unified specific char- + +acter, its meaning is constituted. + +It is this ideal unity men have in mind when they say that 'the' judgement is the meaning of 'the' declarative sentence. Only the fundamental ambiguity of the word 'judgement' at once tends to confuse the evidently grasped ideal unity with the real act of judging, to confuse what the assertion intimates + +with what it asserts. + +What we have here said of complete assertions readily applies also to actual or possible parts of assertions. If I judge *If the sum of the angles in a triangle does not equal two right angles, the axiom of parallels does not hold,* the hypothetical antecedent is no assertion, for I do not say that such an inequation holds. None the less it says something, and what it says is once more quite different from what it intimates. What it says is not my mental act of hypothetical presumption, though I must of course have performed this in order to speak sincerely as I do. But it is rather the case that, when this subjective act is intimated, something objective and ideal is brought to expression: the hypothesis whose conceptual content can appear as the same intentional unity in many possible thought-experiences, and which evidently stands before us in its unity and identity in the objectively-ideal treatment + +characteristic of all thinking. + +The same holds of the other parts of our statements, even of such as do + +not have the form of propositions. + +**§ 12 Continuation: the expressed objectivity** + +Talk of *what an expression expresses* has, in the discussion so far, several essentially different meanings. It relates, *on the one hand,* to intimation in + +general, and especially in that connection to sense-giving acts, at times also to sense-fulfilling acts (if these are present at all). In an assertion, e.g., we express our judgement (we intimate it), but we also express percepts and other sense-fulfilling acts which illustrate our assertion's meaning. *On the other hand,* such talk relates to the 'contents' of such acts, and primarily to + +the meanings, which are often enough said to be 'expressed'. + +It is doubtful whether the examples analysed, in our last section, would suffice even to lend provisional intelligibility to the notion of meaning, if one could not forthwith introduce a new sense of 'expression' for purposes of comparison. The terms 'meaning', 'content', 'state of affairs' and all similar terms harbour such powerful equivocations that our intention, even if expressed most carefully, still can promote misunderstanding. The third sense of 'being expressed', which we must now discuss, concerns the *objec-* + +*tive correlate* meant by a meaning and expressed by its means. + +Each expression not merely says something, but says it *of* something: it not only has a meaning, but refers to certain *objects.* This relation sometimes holds in the plural for one and the same expression. But the object never coincides with the meaning. Both, of course, only pertain to an expression in virtue of the mental acts which give it sense. And, if we distinguish between 'content' and object in respect of such 'presentations', one's distinction means the same as the distinction between what is meant or said, on the one hand, and what is spoken of, by means of the expression, on the other. The necessity of distinguishing between meaning (content) and object becomes clear when a comparison of examples shows us that several expressions may have the same meaning but different objects, and again that they may have different meanings but the same object. There is of course also the possibility of their differing in both respects and agreeing in both. The last occurs in the cases of synonymous expressions, e.g. the corresponding expressions in different languages which mean and name the same thing + +(,London', 'Londres'; 'zwei', 'deux', 'duo' etc.). + +Names offer the plainest examples of the separation of meaning from the relation to objects, this relation being in their case usually spoken of as 'naming'. Two names can differ in meaning but can name the same object, e.g. 'the victor at Jena' - 'the vanquished at Waterloo'; 'the equilateral triangle' - 'the equiangular triangle'. The meaning expressed in our pairs of names is plainly different, though the same object is meant in each case. The same applies to names whose indefiniteness gives them an 'extension'. The expressions 'an equilateral triangle' and 'an equiangular triangle' have the + +same objective reference, the same range of possible application. + +It can happen, conversely, that two expressions have the same meaning but a different objective reference. The expression 'a horse' has the same meaning in whatever context it occurs. But if on one occasion we say 'Bucephalus is a horse', and on another 'That cart-horse is a horse', there has been a plain change in our sense-giving presentation in passing from the one state- + +ment to the other. The expression 'a horse' employs the same meaning to present Bucephalus on one occasion and the cart-horse on the other. It is thus with all general names, i.e. names with an 'extension'. 'One' is a name whose meaning never differs, but one should not, for that reason, identify the various 'ones' which occur in a sum: they all mean the same, but they + +differ in objective reference. + +The case of proper names is different, whether they name individual or general objects. A word like 'Socrates' can only name different things by meaning different things, i.e. by becoming *equivocal.* Wherever the word has *one* meaning, it also names *one* object. The same holds of expressions like 'the number two', 'redness' etc. We therefore distinguish equivocal names that have *many meanings* from general or class-names that have *many values.* The same holds of other types of expression, though in their case talk of objective reference involves certain difficulties in virtue of its manifoldness. If we consider, e.g., statements of the form'S is *P'* we generally regard the subject of the statement as the object about which the statement is made. Another view is, however, possible, which treats the *whole* state of affairs which corresponds to the statement as an analogue of the object a name names, and distinguishes this from the object's meaning. If this is done one can quote as examples pairs of sentences such as *'a* is bigger than *b'* - *'b* is smaller than *a',* which plainly say different things. They are not merely grammatically but also 'cogitatively' different, i.e. different in meaningcontent. But they express the same state of affairs: the same 'matter' is predicatively apprehended and asserted in two different ways. Whether we define talk of the 'object' of a statement in one sense or the other - each has its own claims - statements are in either case possible which differ in mean- + +ing while referring to the same object. + +**§ 13 Connection between meaning and** + +**objective reference** + +Our examples entitle us to regard the distinction between an expression's meaning and its power to direct itself as a name to this or that objective correlate - and of course the distinction between meaning and object itself as well-established. It is clear for the rest that the sides to be distinguished in each expression are closely connected: an expression only refers to an objective correlate *because* it means something, it can be rightly said to signify or name the object *through* its meaning. An act of meaning is the determinate manner in which we refer to our object of the moment, though this mode of significant reference and the meaning itself can change while the objective + +reference remains fixed. + +A more profound phenomenological clarification of this relation can be reached only by research into the way expressions and their meaningintentions function in knowledge. This would show that talk about *two* + +*distinguishable sides* to each expression, should not be taken seriously, that the essence of an expression lies solely in its meaning. But the same intuition (as we shall show later) can offer fulfilment of different expressions: it can be categorially apprehended in varying ways and synthetically linked with other intuitions. Expressions and their meaning-intentions do not take their measure, in contexts of thought and knowledge, from mere intuition - I mean phenomena of external or internal sensibility - but from the varying intellectual forms through which intuited objects first become intelligibly determined, mutually related objects. And so expressions, even when they function outside of knowledge, must, as symbolic intentions, point to categorially *formed* unities. Different meanings may therefore pertain to the same intuitions regarded in differing categorial fashion, and may therefore also pertain to the same object. But where a whole range of objects corresponds to a single meaning, this meaning's own essence must be *indeterminate:* it + +must permit a sphere of possible fulfilment. + +These indications may suffice for the moment. They must guard in advance against the error of seriously thinking that sense-giving acts have two distinct sides, one which gives them their meaning, while the other gives them + +their determinate direction to objects. 5 + +**§ 14 Content as object, content as fulfilling sense and** + +**content as sense or meaning simpliciter** + +Relational talk of 'intimation', 'meaning' and 'object' belongs *essentially* to every expression. Every expression intimates something, means something and names or otherwise designates something. In each case, talk of 'expression' is equivocal. As said above, relation to an actually given objective correlate, which fulfils the meaning-intention, is *not* essential to an expression. If this last important case is also taken into consideration, we note that there are two things that can be said to be expressed in the realized relation to the object. We have, on the one hand, the *object itself,* and the object as meant in this or that manner. On the other hand, and more properly, we have the object's ideal correlate in the acts of meaning-fulfilment which constitute it, *the fulfilling sense.* Wherever the meaning-intention is fulfilled in a corresponding intuition, i.e. wherever the expression actually serves to name a given object, there the object is constituted as one 'given' in certain acts, and, to the extent that our expression really measures up to the intuitive data, as given *in the same manner* in which the expression *means* it. In this unity of coincidence between meaning and meaning-fulfilment, the essence of the meaning-fulfilment corresponds with, and is correlative, to the essence of meaning: the essence of the meaning-fulfilment is the *fulfilling* sense of the expression, or, as one may also call it, the sense expressed by the expression. One says, e.g., that a statement of perception expresses a perception, but also that it expresses the *content* of a perception. We distinguish, in + +a perceptual statement, as in every statement, between *content* and *object;* by the 'content' we understand the self-identical meaning that the hearer can grasp even if he is not a percipient. We must draw the same distinction in the case of fulfilling acts, in the case, therefore, of perceptions and their categorial formations. Through these acts the objective correlate of our act of meaning stands before us intuitively as the very object we mean. We must, I say, distinguish again, in such fulfilling acts, between their *content,* the meaning-element, as it were, in the categorially formed percept, and the *object* perceived. In the unity of fulfilment, the fulfilling content coincides with the intending content, so that, in our experience of this unity of coincidence, the object, at once intended and 'given', stands before us, not as two objects, but as *one* alone. The ideal conception of the act which *confers meaning* yields us the Idea of the *intending meaning,* just as the ideal conception of the correlative essence of the act which *fulfils* meaning, yields the *fulfilling meaning,* likewise *qua* Idea. This is the *identical content* which, in perception, pertains to the totality of possible acts of perception which intended the same object perceptually, and intend it actually as the same object. This content is therefore the ideal correlate of this *single* object, + +which may, for the rest, be completely imaginary. + +The manifold ambiguities in talk about what an expression expresses, or about an *expressed content,* may therefore be so ordered that one distinguishes between a content in a *subjective,* and a content in an *objective* sense. + +In the latter respect we must distinguish between: + +The content as intending sense, or as sense, *meaning simpliciter,* + +the content as fulfilling sense, and + +the content as object. + +**§ 15 The equivocations in talk of meaning and meaninglessness connected with these distinctions** + +The application of the terms 'meaning' and 'sense', not merely to the content of the meaning-intention inseparable from the expression, but also to the content of the meaning-fulfilment, engenders a most unwelcome ambiguity. It is clear from previous indications, where we dealt with the fact of fulfilment, that the acts on either side, in which intending and fulfilling sense are constituted, need not be the same. What tempts us to transfer the same terms from intention to fulfilment, is the peculiar way in which the unity of fulfilment is a unity of identification or coincidence: the equivocation which one hoped a modifying adjective might render innocuous, can scarcely be avoided. We shall continue, of course, to understand by 'meaning' *simpliciter* the meaning which, as the identical element in our intention, is essential to + +'Meaning' is further used by us as synonymous with 'sense'. It is agreeable to have parallel, interchangeable terms in the case of this concept, particularly since the sense of the term 'meaning' is itself to be investigated. A further consideration is our ingrained tendency to use the two words as synonymous, a circumstance which makes it seem rather a dubious step if their meanings are differentiated, and if (as G. Frege has proposed)6 we use one for meaning in our sense, and the other for the objects expressed. To this we may add that both terms are exposed to the same equivocations, which we distinguished above in connection with the term 'expression', and to many more besides, and that this is so both in scientific and in ordinary speech. Logical clarity is much impaired by the manner in which the sense or meaning of an expression is, often in the same thought-sequence, now looked upon as the acts intimated by it, now as its ideal sense, now as the objective correlate that it expresses. Since fixed terminological landmarks are lacking, the concepts themselves run confusedly into one another. + +Fundamental confusions arise from these facts. General and equivocal names are, e.g., repeatedly lumped together, since both can be predicatively referred to a plurality of objects. Lacking fixed concepts, men did not know how to distinguish the *multiple senses* of the equivocal names from the *multiple values* of the general ones. Here we also meet with the frequent unclearness as to the true essence of the difference between collective and general names. For, where collective meanings are fulfilled, we intuit a plurality of items: fulfilment is articulated into a plurality of individual intuitions, and so, if intention and fulfilment are not kept apart, it may well + +seem that the collective expression in question has many meanings. + +It is more important for us to set forth precisely the most detrimental equivocations in talk which concerns *meaning* and *sense,* on the one hand, or *meaningless* or *senseless* expressions, on the other. Ifwe separate the blurred + +concepts, the following list emerges: + +1. It is part of the notion of an expression to have a meaning: this precisely differentiates an expression from the other signs mentioned above. A meaningless expression is, therefore, properly speaking, no expression at all: it is at best something that claims or seems to be an expression, though, more closely considered, it is not one at all. Here belong articulate, word-like sound-patterns such as 'Abracadabra', and also combinations of genuine expressions to which no unified meaning corresponds, though their outer + +form seems to pretend to such a meaning, e.g. 'Green is or'. + +2. In meaning, a relation to an object is constituted. To use an expression significantly, and to refer expressively to an object (to form a presentation of it), are one and the same. It makes no difference whether the object exists or is fictitious or even impossible. But if one gives a very rigorous interpretation to the proposition that an expression, in so far as it has meaning, relates to an object, i.e. in a sense which involves the existence of the object, then an expression has *meaning* when an object corresponding to it exists, and + +it is *meaningless* when no such object exists. Meanings are often spoken of as signifying the *objects* meant, a usage that can scarcely be maintained consistently, as it springs from a confusion with the genuine concept of + +meanmg. + +3. If the meaning is identified with the objective correlate of an expression, a name like 'golden mountain' is meaningless. Here men generally distinguish objectlessness from meaninglessness. As opposed to this, men tend to use the word 'senseless' of expressions infected with contradiction and obvious incompatibilities, e.g. 'round square', or to deny them meaning by some equivalent phrase. Sigware, e.g., says that a self-contradictory formula such as 'square circle' expresses no concept we can think, but that it uses words to set up an insoluble task. The existential proposition 'There is no square circle', on his view denies the possibility of connecting a concept with these words, and by a concept he expressly wants us to understand (if we get him right) the 'general meaning of a word', which is just what we mean by it. Erdmann8 has similar opinions in regard to the instance 'A square circle is frivolous'. We should, in consistency, have to apply the word 'senseless', not merely to expressions immediately absurd, but to those whose absurdity is mediate, i.e. the countless expressions shown by mathematicians, in lengthy indirect demonstrations, to be objectless *a priori.* We should likewise have to deny that concepts like *regular decahedron* etc., are concepts at all. + +Marty raises the following objection to the thinkers just mentioned. 'If the words are senseless, how could we understand the question as to whether such things exist, so as to answer it negatively? Even to reject such an existence, we must, it is plain, somehow form a presentation of such contradictory material'9 ... 'If such absurdities are called senseless, this can only mean that they have no rational sense'. 10 These objections are clinching, in so far as these thinkers' statements suggest that they are confusing the true meaninglessness mentioned above under I, with another quite different meaninglessness, i.e. *the* a priori *impossibility of a fulfilling sense.* An expression has meaning in this sense if a possible fulfilment, i.e. the possibility of a unified intuitive illustration, corresponds to its intention. This possibility is plainly meant ideally. It concerns no contingent acts of expression or fulfilment, but their ideal contents: meaning as an ideal unity, here to be called 'intending meaning', on the one hand, and fulfilling meaning, standing to it in a certain relation of precise adequacy, on the other. We apprehend this ideal relation by ideative abstraction based on an act of unified fulfilment. In the contrary case we apprehend the real impossibility of meaning-fulfilment through an experience of the incompatibility of the partial meanings in the + +intended unity of fulfilment. + +The phenomenological clarification of these relationships calls for long, + +difficult analyses, as will appear in a later investigation. + +4. If we ask what an expression means, we naturally recur to cases where it actually contributes to knowledge, or, what is the same, where its meaning- + +intention is intuitively fulfilled. In this manner the 'notional presentation', i.e. the meaning-intention, gains clarity, it shows itself up as 'correct', as 'really' capable of execution. The draft it makes on intuition is as it were cashed. Since in the unity of fulfilment the act of intention coincides with the fulfilling act, and fuses with it in the most intimate fashion - if indeed there is any difference left over here at all - it readily seems as if the expression first got its meaning here, as if it drew meaning from the act of fulfilment. The tendency therefore arises to treat the *fulfilling intuitions* categorially formative acts are here in general passed over - as meanings. But fulfilment is often imperfect - we shall have to devote closer study to all such possibilities - and expressions often go with remotely relevant, only partially illustrative intuitions, if with any at all. Since the phenomenological differences of these cases have not been closely considered, men have come to locate the significance of expressions, even of such as could make no claim to adequate fulfilment, in accompaniments of intuitive imagery. This + +naturally led to a total denial of meaning to absurd expressions. + +The new concept of meaning therefore originates in a confusion of meaning with fulfilling intuition. On this conception, an expression has meaning if and only if its intention - we should say its 'meaning-intention' - is in fact fulfilled, even if only in a partial, distant and improper manner. The understanding of the expression must be given life through certain 'ideas of + +meaning' (it is commonly said), i.e. by certain *illustrative* images. + +The final refutation of highly attractive, opposed notions is an important task which requires lengthy discussions. These we shall postpone to the next chapter, and here go on enumerating different concepts of meaning. + +**§ 16 Continuation: meaning and connotation** + +Another equivocation in our talk about meaninglessness was introduced by John Stuart Mill, and again rests on anew, fifth concept of meaning. He locates the essence of the meaning of names in their connotation, and therefore treats non-connotative names as meaningless. (Sometimes he says, more carefully but less clearly, that they are meaningless in the 'proper' or 'strict' sense.) It is well-known that by 'connotative names' Mill understands such as designate a subject and imply an attribute, by 'non-connotative names' such as designate a subject without (as it is here more clearly put) indicating an attribute as attaching to it.l! Proper names are non-connotative and so too are names of attributes (e.g. 'whiteness'). Mill compares proper names to the distinctive chalk-marks which the robber, in the well-known tale from the *Arabian Nights,* made on the house. 12 And he goes on to say: 'When we impose a proper name, we perform an operation in some degree analogous to what the robber intended in chalking the house. We put a mark, not indeed upon the object itself, but upon the idea of the object. A proper name is but an unmeaning mark which we connect in our minds with the + +idea of the object, in order that whenever the mark meets our eyes or occurs to our thoughts, we may think of that individual object ... When we predicate of anything its proper name; when we say, pointing to a man, this is Brown or Smith, or pointing to a city, this is York, we do not, merely by so doing, convey to the reader any information about them, except that those are their names ... It is otherwise when objects are spoken of by connotative names. When we say, "The town is built of marble", we give the hearer what may be entirely new information, and this merely by the signification of the many-worded connotative name "built of marble". Such names ... are not mere marks, but more, that is to say significant marks; and the connotation + +is what constitutes their significance.,\3 + +If we set our own analyses alongside of these utterances of Mill's, we cannot help seeing that he confuses distinctions that should in principle be kept apart. Above all, he blurs the distinction between indicating and expressing. The chalk-mark of the robber is a mere indication, while a proper + +name is an expression. + +Like every expression a proper name functions as an indication, i.e. in its intimating role. Here there is a real analogy with the robber's chalk-mark. If the robber sees the chalk-mark he knows: This is the house I must rob. If I hear a proper name uttered, the corresponding presentation is aroused in me, and I know: This is the presentation the speaker is framing in his mind, and that he likewise wishes to arouse in mine. A name, however, has an additional expressiveness to which the intimating function is merely auxiliary. A man's presentation is not of primary importance: we are not concerned to direct interest to it but to the *object* it presents, to what it *refers to* and therefore *names,* and to set this before us as such. In a statement it makes its first appearance as the object about which something is asserted, in a wish-sentence as the object about which something is wished etc. Only in order to perform this task will a proper name, like any other name, become an element in complex, unified expressions, in statements, wish-sentences and the like. But in its relation to its *object* the proper name is not an index. This is at once clear when we reflect on the fact that it is of the essence of an index to point to a fact, an existence, whereas the object named need not be taken to exist at all. When Mill extending his analogy, holds a proper name to be associated with the idea of the person it names in essentially the same manner as the chalk-mark is associated with the house, but *at once* adds that the point of the association is that we may *think* of the individual object whenever the sign meets our eye or enters our thought, his + +addition cracks the analogy wide asunder. + +Mill correctly stresses the difference between names that are a means towards 'knowing' an object and names which are not, but neither this distinction, nor the equivalent distinction between connotative and non-connotative names, has anything to do with the distinction between the meaningful and the meaningless. The first-mentioned pair of differences are in fact not merely + +logically equivalent but identical. The difference is simply one of attributive and non-attributive names: to mediate the 'knowledge' of a thing and to mediate its attributes mean exactly the same. It is, no doubt, important, whether a name means a thing directly or only by way of the attributes that pertain to it. But this is a difference within the unitary genus Expression, just as the very important, parallel difference between nominal meanings (or logical 'presentations') which are attributive and those which are not + +attributive, is a difference within the unitary genus Meaning. + +Mill *after a fashion* 'feels' the difference in question by being at times obliged to speak of a meaning of proper names in a sense contrasting with the 'strict' and 'proper' sense ascribed to the meaning of connotative names. He would have done better had he introduced a wholly new sense of meaning (though not, we may say, one to be recommended). The way, at least, in which the distinguished logician brings in his valuable distinction between connotative and non-connotative names has done much to confuse the quite + +different distinctions we have here been discussing. + +One must note, further, that Mill's distinction between what a name *denotes* and what it *connotes* must not be confused with the merely cognate distinction between what a name *names* and what it *means.* This confusion is + +greatly aided by Mill's exposition. + +How important all these distinctions are, and how little it helps to treat them with superficial contempt as being 'merely grammatical', will be shown in further investigations. These will make plain, we hope, that if one blurs the straightforward distinctions we have proposed, we cannot hope for a trustworthy elaboration of the concepts of Presentation and Judgement, in + +the sense relevant to logic. + +**Towards a characterization of the** + +**acts which confer meaning** + +**§ 17 Illustrative mental pictures as putative meanings** We have oriented our concept of meaning, or meaning-intention, towards the phenomenological character essential to an expression as such, which distinguishes it descriptively in consciousness from a merely sounded word. Such a character is, on our view, possible, and quite often actual, though the expression does not help us to know anything, does not stand in the loosest, remotest relation to sensualizing intuitions. It is now time to take up our stance towards a widely held, perhaps almost dominant conception, which, as against our own, sees the whole role of the expression, with all its living meaning, in the arousal of certain images which regularly accompany it. To understand an expression means, on this view, to meet with pertinent mental pictures. Where these are absent, an expression is void of sense. These mental pictures are themselves often said to be the meanings of words, and those who say so, claim to be getting at what ordinary speech means by + +the 'meaning of an expression'. + +It shows the retarded state of descriptive psychology that such speciously obvious doctrines should be entertained, and entertained despite longstanding objections urged against them by unprejudiced thinkers. Verbal expressions are no doubt often accompanied by images, which may stand in an intimate or a distant relation to their meanings, but to treat such accompaniments as necessary conditions for understanding runs counter to the plainest facts. Thereby we know that the meaningfulness of an expression let alone its very meaning - cannot consist in the existence of such images, and cannot be disturbed by their absence. A comparison of a few casually observed imaginative accompaniments will soon show how vastly they vary while the meanings of words stay constant, and how they often are only very distantly related to the latter, whereas true illustrations, which genuinely carry out or confirm the meaning-intention of our expression, can often only be evoked with difficulty or not at all. Let a man read a work in an abstract field of knowledge, and understand the author's assertions perfectly, and let him then try to see what *more* there is to such reading than the + +words he understands. The circumstances of observation are most favourable to the view we reject, since an interest in finding images tends psychologically to evoke images, while the tendency to read back the findings of reflection into the original situation, makes us include all new images which stream in during the observation in the psychological content of our expression. Despite these favouring circumstances, the view we oppose, which sees the essence of the meaningful in accompanying imagery, must at least cease to look for introspective confirmation in the sort of case in question. Take, e.g., well-understood algebraical signs, or complete formulae, or verbal propositions such as 'Every algebraical equation of uneven grade has at least one real root', and carry out the needful observations. To report my own findings in the last case: I see an open book which I recognize as Serret's *Algebra,* I see the sensory pattern of an algebraical equation in Teubnerian type, while accompanying the word 'root', I see the familiar *--J.* I have however read the sentence very many times and have understood it perfectly, without experiencing the slightest trace of accompanying images that have anything to do with its presented object. The same happens when expressions like 'culture', 'religion', 'science', 'art', 'differential calculus' etc., are intuitively illustrated. We may further point out that what we have said applies not only to expressions which stand for highly abstract objects, mediated by complex relations, but to names of individual objects, well-known persons, cities, landscapes. A readiness for intuitive representation may be present, but it + +remains unfulfilled at the moment in question. + +**§ 18 Continuation of the above. Arguments and** + +**counter-arguments** + +Should someone object that there are highly evanescent images even in such cases, that a mental picture emerges only to disappear forthwith, we reply that the full understanding of words, their complete living sense, persists after such an image has vanished, and cannot therefore consist in its presence. If the objecter shifts to saying that the mental image has become unobservable, perhaps always was so, but that, whether observable or not, it still exists, and makes continued understanding possible, we need not be in doubt as to our answer. We reply that whether or not such an assumption is necessary or plausible on grounds of genetic psychology, this is not anything that need be gone into here. It is quite irrelevant to our essentially descriptive question. Let us grant that there often are unobservable images. Despite this, however, an expression can quite often be understood, and quite observably so. But surely it is absurd to suppose that an abstract, sensemaking aspect of an image should be observable, while the whole complete, concrete image-experience remains unobservable? How does the matter stand, further, in cases where our meaning is absurd? Unobservability can here not depend on the contingent limits of mental capacity, since such an image + +cannot exist at all: if it could, it would provide us with a self-evident guarantee of the possibility, the semantic consistency, of the thought in question. It can, or course, be pointed out that we do, after a fashion, illustrate even absurdities, such as a straight line enclosing a space, or triangles the sum of whose angles is greater or less than two right angles. In metageometric treatises there are even drawings of such forms. No one would, however, dream of taking intuitions of this sort as truly illustrating the concepts in question, or of letting them pass as owning such verbal meanings. Only in cases where the image of a thing meant is really adequate to it, are we tempted to seek the sense of our expression in such an image. But if we rule out absurd expressions - which none the less have their sense - are images normally adequate? Even Descartes cited his 'chiliagon' to shed light on his distinction between *imaginatio* and *intel/eetio.* Our imaginative idea of a chiliagon is no more adequate than are our images of space-enclosing straight lines or intersecting parallels: in both cases we have rough, merely partial illustrations of a thing thought of, not complete exemplifications. We speak of a closed straight line, and draw a closed curve, thereby only illustrating the curvature. In the same fashion we think of a chiliagon, while we imagine + +any polygon with 'many' sides. + +We need not look for recondite geometrical illustrations to prove the inadequacy of illustration even in the case of consistent meanings. It is a well-known fact that no geometrical concept whatsoever can be adequately illustrated. We imagine or draw a stroke, and speak or think of a straight line, and so in the case of all figures. The image everywhere provides only a foothold for *intelleetio.* It offers no genuine instance of our intended pattern, only an instance of the sort of sensuous form which is the natural startingpoint for geometrical 'idealization'. In these intellectual thought-processes of geometry, the idea of a geometrical figure is constituted, which is then expressed in the fixed meaning of the definitory expression. Actually to perform this intellectual process may be presupposed by our first formation of primitive geometrical expressions and by our application of them in knowledge, but not for their revived understanding and their continued significant use. Elusive sensuous pictures function, however, in a phenomenologically graspable and describable manner, as mere aids to understanding, and not + +as themselves meanings or carriers of meaning. + +Our conception will perhaps be censured for its extreme nominalism, for identifying word and thought. To many it will seem quite absurd that a symbol, a word, a sentence, a formula should be understood, while in our view nothing intuitive is present beyond the mindless sensible body of thought, the sensible stroke on paper etc. But we are far from identifying words and thoughts, as our statements in the previous chapter show. We do not at all think that, where symbols are understood without the aid of accompanying images, the mere symbol alone is present: we think rather that an understanding, a peculiar act-experience relating to the expression, is present, that + +it shines through the expression, that it lends it meaning and thereby a relation to objects. What distinguishes the mere word, as a sense-complex, from the meaningful word, is something we know full well from our own experience. We can indeed ignore meaning and pay attention only to a word's sensuous character. It may also be the case that some sensible feature first arouses interest on its own account, and that its verbal or other symbolic character is only then noted. The sensuous habit of an object does not change when it assumes the status of a symbol for us, nor, conversely, does it do so when we ignore the meaning of what normally functions as a symbol. No new, independent content is here added to the old: we do not merely have a sum or association of contents of equal status before us. One and the same content has rather altered its psychic habit: we are differently minded in respect of it, it no longer seems a mere sensuous mark on paper, the physical phenomenon counts as an *understood* sign. Living thus understandingly, we perform no act of presentation or judgement directed upon the sign as a sensible object, but another act, quite different in kind, which relates to the thing designated. It is in this sense-giving act-character - which differs entirely according as our interest plays on the sensible sign or the object presented through it, with or without representative imagery - that meaning consists. + +**§ 19 Understanding without intuition** + +In the light of our conception it becomes wholly understandable that an expression should be able to function significantly without illustrative intuition. Those who locate the meaning-aspect of symbols in intuition, must find purely symbolic thinking insolubly enigmatic. Speech without intuition must likewise be senseless to them. But truly senseless speech would be no speech at all: it would be like the rattle of machinery. This we of course meet with in the case of verses or prayers learnt by rote and repeated unthinkingly, but not in the cases which here require explanation. Popular comparisons with the squawking of parrots or the cackling of geese, the well-known adage 'Where ideas fail us, words come up at the right moment' and so on, are not, soberly considered, to be taken literally. Expressions such as 'talk without judgement' or 'senseless talk' may and should certainly not be otherwise interpreted than such expressions as 'a heartless', 'brainless', 'empty-headed man' etc. 'Talk without judgement' plainly does not mean talk unbacked by judgements, but talk backed by judgements not based on independent, intelligent consideration. Even 'senselessness', understood as absurdity or nonsense, is significantly constituted: the sense of an absurd expression is such as to refer to what cannot be objectively put together. The opposite view can now only take refuge in the strained hypothesis of unconscious, unnoticed intuitions. How little this helps becomes plain if we consider what basic intuition achieves in cases where it is noticeably present. In the vast majority of cases it is by no means adequate to our + +meaning-intention, a fact, which, on our conception, presents no problem. If the meaningful is not to be found in intuition, speech without intuition need not be speech deprived of thought. If intuition lapses, an act like that which otherwise hangs about intuition, and perhaps mediates the knowledge of its object, continues to cling to the sense-given expression. The act in + +which meaning is effective is therefore present in either case. + +**§20 Thought without intuition and the 'surrogative** + +**function' of signs** + +It should be quite clear that over most of the range both of ordinary, relaxed thought and the strict thought of science, illustrative imagery plays a small part or no part at all, and that we may, in the fullest sense, judge, reason, reflect upon and refute positions, without recourse to more than symbolic presentations. This situation is quite inadequately described if one talks of the 'surrogative function of signs', as if the signs themselves did duty for something, and as if our interest in symbolic thinking were directed to the signs themselves. Signs are in fact not objects of our thought at all, even surrogatively; we rather live entirely in the consciousness of meaning, of understanding, which does not lapse when accompanying imagery does so. One must bear in mind that symbolic thinking is only thinking in virtue of a new, intentional act-character: this distinguishes the meaningful sign from the mere sign, i.e. the sounded word set up as a physical object in our mere presentations of sense. This act-character is a *descriptive* trait in the sign-experience which, stripped of intuition, yet understands the sign. + +It will perhaps be objected to our present interpretation of symbolic thinking that it conflicts with quite certain facts involved in the analysis of *arithmetical symbolic thought,* facts that I myself have stressed elsewhere (in my *Philosophy of Arithmetic).* In arithmetical thought mere signs genuinely do duty for concepts. 'The reduction of the theory of things to the theory of signs' (to quote Lambert) is what all calculation achieves. Arithmetical signs are 'so selected and perfected, that the theory, combination, transformation etc. of signs can do what would otherwise have to be done by concepts.'! Looked at more closely, however, it is not signs, in the mere sense of *physical* objects, whose theory, combination etc., would be of the slightest use. Such things would belong to the sphere of physical science and practice, and not to that of arithmetic. The true meaning of the signs in question emerges if we glance at the much favoured comparison of mathematical operations to rule-governed games, e.g. chess. Chessmen are not part of the chess-game as bits of ivory and wood having such and such shapes and colours. Their phenomenal and physical constitution is quite indifferent, and can be varied at will. They become chessmen, counters in the chess-game, through the game's rules which give them their fixed *games-meaning.* And so arithmetical signs have, besides their original meaning, their so-to-say + +games-meaning, a meaning oriented towards the game of calculation and its well-known rules. If one treats arithmetical signs as mere counters in the rule-sense, to solve the tasks of the reckoning game leads to numerical signs or formulae whose interpretation in their original, truly arithmetical senses also represents the solution of corresponding arithmetical problems. + +We do not therefore operate with *meaningless signs* in fields of symbolicarithmetical thought and calculation. For mere signs, in the sense of *physical* signs bereft of all meaning, do duty for the same signs alive with arithmetical meaning: it is rather that signs taken in a certain *operational or gamessense* do duty for the same signs in full *arithmetical meaningfulness.* A system of natural, and, as it were, unconscious equivocations bears endless fruit, and the much greater mental work which our original array of concepts demanded is eased by 'symbolic' operations employing a parallel array of + +games-concepts. + +Naturally such a procedure must be logically justified and its boundaries reliably fixed: here we were only concerned to remove confusions readily caused by misunderstanding of the nature of such 'merely symbolical' mathematical thought. If one grasps the sense, set out above, in which the 'mere signs' of arithmetic do duty for arithmetical concepts (or for signs in their full arithmetical meaning) it is clear that talk of the surrogative function of arithmetical signs is irrelevant to our present question, the question whether an expression of thought is or is not possible without an accompaniment of illustrative, instantiating or demonstrative intuitions. Non-intuitive symbolic thought in the sense just mentioned, and symbolical thought in the sense of thought which employs surrogative operational concepts, are two quite + +different things. + +**§21 A difficulty regarding our necessary recourse to corresponding intuitions in order to clarify meanings** + +**or to know truths resting on them** + +One might here ask: If the sense of expressions functioning purely symbolically lies in an act-character which distinguishes the understanding grasp of a verbal sign from the grasp of a sign stripped of meaning, why is it that we have recourse to intuition when we want to establish differences of meaning, + +to expose ambiguities, or to limit shifts in our meaning-intention? + +Again one might ask: Why, if our conception of meaning is right, do we employ corresponding intuitions in order to know purely conceptual truths, i.e. truths known through an analysis of meanings? One can say in general, that in order to be quite clear as to the sense of an expression (or as to the content of a concept) one must construct a corresponding intuition: in this + +intuition one sees what the expression 'really means'. + +But an expression functioning symbolically also means something, and means the same thing as an expression intuitively clarified. Meaning cannot + +first have been acquired through intuition: otherwise we should have to say that much the greater part of our experience in speaking and reading is merely an external perceiving or imagining of optic and auditory complexes. We need not again stress that this plainly conflicts with the phenomenological data, that we *mean* this or that with our spoken or written signs, and that this meaning is a *descriptive character* of intelligent speech and hearing, even when these are purely symbolic. Our first question is answered by observing that purely symbolic meaning-intentions often do not clearly keep themselves apart, and do not permit of the easy, sure distinctions and identifications which are needed for practically useful judgements, even if these are not self-evident. To recognize differences of meaning such as that between 'moth' and 'elephant', requires no special procedures. But where meanings shade unbrokenly into one another, and unnoticed shifts blur boundaries needed for firm judgement, intuitive illustration naturally promotes lucidity. Where an expression's meaning-intention is fulfilled by divergent, conceptually disparate intuitions, the sharp difference in the direction of fulfilment + +shows up the cleavage of meaning-intentions. + +Answering our second question, we recall that all self-evidence of judgement (all realized knowledge in the strong sense of the word) presupposes meanings that are intuitively fulfilled. Where there is talk of a knowledge 'springing from the analysis of the mere meanings of words', more is meant than these words suggest. The knowledge meant is one whose self-evidence calls only for pure representation of the 'conceptual essences', in which the general word-meanings find their perfect fulfilments: all question as to the existence of objects corresponding to such concepts, or falling under such conceptual essences, is ruled out. But these 'conceptual essences' are not the verbal meanings themselves, so that the phrases 'based purely on the concepts (essences)', and 'springing from a mere analysis of word-meanings', are only by equivocation equivalent. Conceptual essences are rather the fulfilling sense which is 'given' when the word-meanings (i.e. the meaningintentions of the words) terminate in corresponding, directly intuitive presentations, and in certain cogitative elaborations and formations of the same. Such analysis is not therefore concerned with empty thought-intentions, but with the objects and forms by which they are fulfilled. What it therefore offers us are not mere statements concerning elements or relations of meanings, but evident necessities concerning the *objects* thought of in these + +meanings, and thought of as thus and thus determined. + +These discussions point to a field of phenomenological analyses which we have already repeatedly seen to be unavoidable, analyses which bring self-evidence into the *a priori* relations between meaning and knowing, or between meaning and clarifying intuition. They will therefore also have to bring complete clarity into our concept of meaning, both by distinguishing meaning from *fulfilling* sense, and by investigating the sense of such + +**§22 Varying marks of understanding and the** + +**'quality of familiarity'** + +Our conception presupposes a certain separation, even if not quite a sharp one, among the act-characters which confer meaning even in cases which lack intuitive illustration. One cannot indeed think that the 'symbolic presentations' which govern the grasp or the significant application of signs, are descriptively equivalent, that they consist in one *undifferentiated* character, the same for all expressions, as if only the sound of the words, the chance sensuous carriers of meaning, made all the difference. Examples of equivocal expressions readily show that we can effect and can recognize sudden changes of meaning, without in the least needing accompanying illustrations. The descriptive difference, here evidently apparent, cannot be the sensuous sign, which remains the same: it must concern the act-character, which is specifically altered. One can likewise point to cases where meaning remains identical while a word changes, in the case, e.g., of mere differences of idiom. Sensuously different signs here count as equivalent (we perhaps even speak of the 'same' word, only occurring in different languages), they at once greet us as the same, even before reproductive fancy can furnish images + +that illustrate their meaning. + +Such examples reveal the untenability of the view, plausible at first, that the note of understanding is no more ultimately than what Riehl2 called the 'character offamiliarity', and what HOffding,3 not so suitably, called the 'quality offamiliarity'.4Words not understood are just as capable of coming before us in the form of old acquaintances: well-memorized Greek verses stick in our memories longer than our understanding of their sense, they appear familiar but are no longer understood. The missing grasp often comes in a flash afterwards, possibly some time before mother-tongue translations or other aids come up in memory, and the note of understanding now adds its obvious novelty to the note of familiarity, not altering the content sensuously, yet giving it a new mental character. One may similarly recall the way in which the reading or recitation of familiar poetry, unthinking at first, suddenly becomes charged with understanding. There are countless other examples which make evident the peculiar character of understanding. + +**§23 Apperception as connected with expression and** + +**with intuitive presentations** + +The grasp of understanding,S in which the meaning of word becomes effective, is, in so far as *any* grasp is in a sense an understanding and an interpretation, akin to the divergently carried out 'objective interpretations' in which, by way of an experienced sense-complex, the intuitive presentation, whether percept, imagination, representation etc., of an object, e.g. an external thing, arises. The phenomenological structure of the two sorts of 'grasp' is, however, + +somewhat different. If we imagine a consciousness prior to all experience, it may very well have the same *sensations* as we have. But it will intuit no things, and no events pertaining to things, it will perceive no trees and no houses, no flight of birds nor any barking of dogs. One is at once tempted to express the situation by saying that its sensations *mean* nothing to such a consciousness, that they do not *count as signs* of the properties of an object, that their combination does not count as a sign of the object itself. They are merely lived through, without an objectifying *interpretation* derived from experience. Here, therefore, we talk of signs and meanings just as we do in + +the case of expressions and cognate signs. + +To simplify comparison by restricting ourselves to the case of perception, the above talk should not be misread as implying that consciousness first looks at its sensations, then turns them into perceptual objects, and then bases an interpretation upon them, which is what really happens when we are objectively conscious of physical objects, e.g. sounded words, which function as signs in the strict sense. Sensations plainly only become presented objects in psychological reflection: in naIve, intuitive presentations they may be *components* of our presentative experience, parts of its descriptive content, but are not at all its objects. The perceptual presentation arises in so far as an experienced complex of sensations gets informed by a certain act-character, one of conceiving or meaning. To the extent that this happens, the perceived *object* appears, while the sensational complex is as little perceived as is the act in which the perceived object is as such constituted. Phenomenological analysis teaches us, further, that sense-contents provide, as it were, the analogical building-stuff for the content of the object presented by their means. Hence talk of colours, extensions, intensities etc., as, on the one hand, sensed, and as, on the other hand, perceived or imagined. Examples readily show that what corresponds in the two cases is in no sense the same, but only generically allied. The *uniform* colouring of a sphere as + +*seen* by us (i.e. perceived, imagined etc.), was never *sensed* by us. + +Signs in the sense of expressions rest on a similar 'interpretation', but only in their first conception. In the simpler case where an expression is understood, but is not as yet given life by intuitive illustrations, this first conception makes the *mere sign* appear before us as a physical object, e.g. as a sounded word, given here and now. On this first conception, however, a second is built, which goes entirely beyond the experienced sense-material, which it no longer uses as analogical building-material, to the quite new object of its present meaning. The latter is meant in the act of meaning, but is not presented in sensation. Meaning, the characteristic function of the expressive sign, presupposes the sign whose function it is. Or to talk pure phenomenology: meaning is a variously tinctured act-character, presupposing an act of intuitive presentation as its necessary foundation. In the latter act, the expression becomes constituted as a physical object. It becomes an expression, in the full, proper sense, only through an act founded upon this former act. + +What is true in this simplest case of an expression understood and not as yet intuitively illustrated, must also hold in the more complex case where an expression is bound up with a *corresponding* intuition. One and the same expression, significantly used with or without illustrative intuition, cannot + +derive its meaningfulness from different sorts of act. + +It is certainly not easy to analyse the descriptive situation in certain finer gradations and ramifications that have been passed over here. It is extremely hard to achieve a right conception of the part played by illustrative presentations in confirming meaning-intentions or in conferring self-evidence on them, as well as their relation to the characteristic note of understanding or meaning, the experience which lends sense to an expression even in default of intuition. Here we have a broad field for phenomenological analysis, a field not to be by-passed by the logician who wants to bring clarity into the relations between meaning and object, between judgement and truth, between vague opinion and confirmatory evidence. The analysis in question + +will receive a thoroughgoing treatment later.6 + +**Fluctuation in meaning and the** + +**ideality of unities of meaning** + +**§24 Introduction** + +In our last chapter we dealt with the act of meaning. But among the conclusions of our first chapter was a distinction between the act of meaning, on the one hand, and meaning itself, on the other, the ideal unity as against the multiplicity of possible acts. This distinction, like the others which go along with it - the distinction between expressed content taken in a subjective, and the same taken in an objective sense, and, in the latter respect, the distinction between content as significatum and content as nominatum - are in countless cases undoubtedly clear. This holds of all expressions which occur in the context of an adequately expounded scientific theory. There are, however, cases where the situation is different, which require particular consideration if they are not to plunge all our hard-won distinctions back into confusion. Expressions whose meaning shifts, especially such as are occasional or vague, here raise serious problems. To solve these problems by distinguishing between shifting acts of meaning, on the one hand, and ideal + +units of meaning, on the other, is the theme of the present chapter. + +**§25 Relations of coincidence among the contents of** + +**intimation and naming** + +Expressions may relate to the contemporary mental state of the person using them as much as they relate to other objects. They accordingly divide into those that also *intimate what they name* (or what they generally stand for), and those in whose case *named and intimated contents fall asunder.* Instances of the former class are interrogative, optative and imperative sentences, of the latter, statements relating to external things, to one's own past experiences, to mathematical relationships etc. If someone utters the wish 'I should like a glass of water', this serves to indicate to the hearer the speaker's wish, which is also the object of the statement. What is intimated and what is named here coincide in part. I say 'in part', since the intimation obviously goes further. It extends to the judgement expressed in the words 'I + +should like etc.'. The like naturally holds of statements about the ideas, judgements, and surmises of the speaker which are of the forms 'I imagine that .. .', 'I am of the opinion that .. .', 'I judge that .. .', 'I conjecture that .. .'. A case even of total coincidence seems at first sight possible, in, e.g., the words 'the state of mind intimated by the words I am now uttering', though the interpretation of our example breaks down on closer examination. But intimation and the state of affairs asserted fall quite apart in statements such as '2 x 2 = 4'. This statement does not say what is said by 'I judge that 2 x 2 = 4'. They are not even equivalent statements, since the one + +can be true when the other is false. + +One must of course stress that if the notion of 'intimation' is given the *narrower* sense defined above, the objects named in the above examples are *not* among the experiences they intimate. A man saying something about his contemporary mental state, communicates its presence through a judgement. Only as intimating such a judgement (whose content is that he wishes, hopes etc., this or that) is the man apperceived by the hearer as one who wishes, hopes etc. The meaning of such a statement lies in this judgement, whereas the inner experiences in question are among the objects judged *about.* If we limit intimation in the narrower sense to experiences which carry an expression's meaning, the contents of intimation and naming re- + +main as distinct here as they are generally. + +**§26 Essentially occasional and objective expressions** The expressions which name the momentary content of intimation belong to a wider class of expressions whose meaning varies from case to case. This happens, however, in so peculiar a manner, that one hesitates to speak of 'equivocation' in this case. The same words 'I wish you luck' which express my wish, can serve countless other persons to express wishes having 'the same' content. Not only do the wishes themselves differ from case to case, but the meanings of the wish-utterances do so too. At one time a person *A* confronts a person *B,* at another time a person *M* confronts a person *N.* If *A* wishes *B* 'the same' that *M* wishes *N,* the sense of the wish-utterances, which includes the idea of the confronting persons, is plainly different. This ambiguity is, however, quite different from that of the word 'dog' which at one time means a type of animal, and at another a foot or a grate. lThe class of ambiguous expressions illustrated by this last example are what one usually has in mind when one speaks of 'equivocation'. Ambiguity in such cases does not tend to shake our faith in the ideality and objectivity of meanings. We are free, in fact, to limit our expression to a *single* meaning. The ideal unity of each of the differing meanings will not be affected by their attachment to a common designation. But how do things stand in the case of the other expressions? Can we there still stick to self-identical meaningunities, elsewhere made clear in their opposition to varying persons and + +their experiences, when here our meanings must vary *with* such persons and their experiences? Obviously we are here dealing with a case of unavoidable rather than chance ambiguity, one that cannot be removed from our lan- + +guage by an artificial device or convention. + +To promote clearness we shall define the following distinction between *essentially subjective and occasional* expressions, on the one hand, and *objective* expressions, on the other. For simplicity's sake we shall deal only with + +expressions in their normal use. + +We shall call an expression *objective* if it pins down (or can pin down) its meaning merely by its manifest, auditory pattern, and can be understood without necessarily directing one's attention to the person uttering it, or to the circumstances of the utterance. An objective expression may be in varying ways equivocal: it may stand in the stated relation to several meanings, so that it depends on the psychological context (on the chance drift of the hearer's thoughts, on the tenor of the talk already in progress and the tendencies it arouses etc.) which of these meanings it arouses and means. It may be that a glance at the speaker and his situation may help all this. But whether or not the word *can* be understood in one or other of such mean- + +ings does not depend on this glance as a *sine qua non.* + +On the other hand, we call an expression essentially subjective and occasional, or, more briefly, *essentially occasional,* if it belongs to a conceptually unified group of possible meanings, in whose case it is essential to orient actual meaning to the occasion, the speaker and the situation. Only by looking to the actual circumstances of utterance can one definite meaning out of all this mutually connected class be constituted for the hearer. Since we regularly understand such expressions in normal circumstances, the very idea of these circumstances, and of their regular relation to the expression, involves the presence of generally graspable, sufficiently reliable clues to + +guide the hearer to the meaning intended in the case in question. + +Among objective expressions we have, e.g., all expressions in theory, expressions out of which the principles and theorems, the proofs and theories of the 'abstract' sciences are made up. What, e.g., a mathematical expression means, is not in the least affected by the circumstances of our actual use of it. We read and understand it without thinking of a speaker at all. The case is different with expressions which serve the practical needs of ordinary life and with expressions which, in the sciences, prepare the way for theoretical results. I mean by the latter expressions with which the investigator accompanies his own thought, or acquaints others with his considerations and endeavours, with his methodical preparations and his provisional beliefs. Every expression, in fact, that includes a *personal pronoun* lacks an objective sense. The word 'I' names a different person from case to case, and does so by way of an ever altering meaning. What its meaning is at the moment, can be gleaned only from the living utterance and from the intuitive circumstances which surround it. If we read the word without knowing who wrote it, it is + +perhaps not meaningless, but is at least estranged from its normal sense. Certainly it strikes us differently from a wanton arabesque: we know it to be a word, and a word with which whoever is speaker designates himself. But the conceptual meaning thus evoked in not what the word 'I' means, otherwise we could simply substitute for it the phrase 'whatever speaker is designating himself'. Such a substitution would lead to expressions, not only unusual, but also divergent in sense, if, e.g., instead of saying 'I am pleased' I said 'Whatever speaker is now designating himself is pleased'. It is the universal *semantic function* of the word'!, to designate whoever is speaking, but the notion through which we express this function is not the notion + +immediately constitutive of its meaning. + +In solitary speech the meaning of 'I' is essentially realized in the immediate idea of one's own personality, which is also the meaning of the word in communicated speech. Each man has his own I-presentation (and with it his individual notion of I) and this is why the word's meaning differs from person to person. But since each person, in speaking of himself, says '1', the word has the character of a universally operative indication of this fact. Through such *indication* the hearer achieves understanding of the meaning, he takes the person who confronts him intuitively, not merely as the speaker, but also as the immediate object of this speaker's speech. The word'!, has not itself directly the power to arouse the specific I-presentation; this becomes fixed in the actual piece of talk. It does not work like the word 'lion' which can arouse the idea of a lion in and by itself. In its case, rather, an indicative function mediates, crying as it were, to the hearer + +'Your *vis-a-vis* intends himself'. + +We must, however, add something to what has been said. Properly speaking, we should not suppose that the immediate presentation of the speaker sums up the entire meaning of the word '1'. The word is certainly not to be regarded as an equivocal expression, with meanings to be identified with all possible proper names of persons. Undoubtedly the idea of self-reference, as well as an implied pointing to the individual idea of the speaker, also belong, *after a certain fashion,* to the word's meaning. We shall have to admit that two meanings are here built upon one another in peculiar fashion. The one, relating to the word's general function, is so connected with the word that its indicative function can be exercised once something is actually presented: this indicative function is, in its turn, exercised *for* the other, singular presentation, and, by subsumption, makes the latter's object known as what is here and now meant. The former meaning can be called the *indicating* + +meaning, the latter the meaning *indicated.* + +What is true of personal pronouns is of course also true of demonstratives. If someone says 'this', he does not directly arouse in the hearer the idea of what he means, but in the first place the idea or belief that he means something lying within his intuitive or thought-horizon, something he wishes to point out to the hearer. In the concrete circumstances of speech, this thought + +is an adequate guide to what is really meant. 'This' read in isolation likewise lacks its proper meaning, and is understood only to the extent that it arouses the notion of its demonstrative function (which we call its indicating meaning). In each case of normal use, its full, actual meaning can only grow out + +of the prominent presentation of the thing that it makes its object. + +We must grant, of course, that a demonstrative often works in a manner that can claim equivalence with an objective use. A 'this' in a mathematical context points to something determined in a conceptually fixed manner, that is understood as meant in this manner, without our needing to regard the actual utterance. A mathematical exposition, after expressly stating a proposition, may go on to say 'This follows from the fact that .. .'. Here the proposition in question could itself have been substituted for the word 'this' without greatly altering the sense; this follows from the exposition's objective sense. One must of course attend to the continuous exposition since, not the intended meaning, but only the thought of an indication, belongs to the demonstrative considered by itself. Mediation by indicating meanings merely promotes brevity and increases mastery over the main drift of one's thoughtintentions. The same plainly does not apply in the common case where the demonstrative 'this' and similar forms stand for the house confronting the speaker, for the bird flying up before him etc. Here individual intuition, varied from case to case, must do duty: it is not enough to look back to pre- + +viously uttered objective thoughts. + +In the sphere of essentially occasional expressions one has also the subjectbound determinations 'here', 'there', 'above', 'below', 'now', 'yesterday', 'tomorrow', 'later' etc. 'Here' (to think out a last example) designates the speaker's vaguely bounded spatial environment. To use the word is to refer to one's place on the basis of an intuitive, believing presentation of one's own person and location. This changes from case to case, and changes likewise from person to person, though each can say 'here'. It is again the general function of the word to name the spatial environment of the speaker, so that the genuine meaning of the word is first constituted in the variable presentation of this place. The meaning of 'here' is in part universal and conceptual, inasmuch as it always names a place as such, but to this universal element the direct place-presentation attaches, varying from case to case. In the given circumstances of speech, it acquires heightened intelligibility by + +subsumption under the conceptual indicating presentation of 'here'. + +An essentially indicating character naturally spreads to all expressions which include these and similar presentations as parts: this includes all the manifold speech-forms where the speaker gives normal expression to something concerning himself, or which is thought of in relation to himself. All expressions for percepts, beliefs, doubts, wishes, fears, commands belong here, as well as all combinations involving the *definite article,* in which the latter relates to something individual and merely pinned down by class- or property-concepts. When we Germans speak of *the* Kaiser we of course + +mean the present German Kaiser. When we ask for *the* lamp in the evening, + +each man means his own. + +*Note.* Expressions with essentially occasional meaning, as dealt with in this section, do not fit into Paul's useful division of expressions into those of usual and those of occasional meaning. His division is based on the fact 'that the meaning which a word has in each application need not coincide with what usage accords in it in and for itself' (H. Paul, *Prinzipien der Sprachgeschichte,* p. 68). Paul has, however, included our essentially occasional expressions in his treatment, for he says: 'There are some words in occasional use which are essentially framed to designate the concrete, but which none the less lack their own relation to a definite concretum till individual application gives them one. Here belong personal pronouns, possessive and demonstrative adjectives, demonstrative adverbs, also words like "now", "today", "yesterday".'2 It seems to me that occasional expressions in this sense fall outside of Paul's definitory antithesis. For it pertains to the *usual* sense of this class of expressions, that they owe their determinate meaning to the occasion, and are therefore occasional in a somewhat *different* sense. Expressions of usual meaning (in Paul's sense) can be divided into those usually univocal and those usually equivocal, and the latter into expressions usually varying among definite meanings assignable in advance (such as the casual equivoca 'cock', 'bear' etc.) and those in which this is not so, since their meaning is oriented in each case to the individual instance, + +though the manner of this orientation is a matter of usage. + +**§27 Other sorts of fluctuating expressions** + +The variation of essentially occasional expressions is heightened by the incompleteness with which they often express the speaker's meaning. The distinction between essentially occasional and objective expressions cuts across many other distinctions standing for new forms of ambiguity, the distinctions, e.g., between complete and incomplete (enthymematic) expressions, between expressions functioning normally and expressions functioning abnormally, between exact and vague expressions. The impersonalia of ordinary speech are good examples as to how apparently firm, objective expressions really vary subjectively in virtue of enthymematic abbreviation. No one would understand the sentence 'There are cakes' as he understands the mathematical sentence 'There are regular solids'. **In** the first case we do not mean that cakes exist absolutely and in general, but that there are cakes *here* and *now* - for coffee. 'It is raining', likewise, does not have the general meaning that rain is falling, but that it is doing so *now, outside.* What the expression lacks is not merely unspoken, it is not even expressly thought: it certainly belongs, however, to what our speech means. **If** additions are made, we plainly get expressions that must be called 'essentially occasional' in the + +There is an even greater difference between the properly expressed content of speech, i.e. the content picked out and pinned down by the uniform meaning-functions of the words involved, and its meaning on occasions when expressions are so shortened as not to express complete thoughts without the aids given to understanding by the fortuitous occasion, e.g. 'Onward!', 'You!', 'Man alive!', 'But my dear, my dear' etc. Through the common intuitive situation in which both speaker and hearer find themselves, these last can supplement or differentiate mutilated and subjectively indeterminate + +meanings: the defective expressions thus become understandable. + +Among the distinctions relating to ambiguity of expressions, we mentioned those between *exact* and *vague* expressions. Most expressions used in ordinary life, such as 'tree', 'shrub', 'animal', 'plant' etc., are vague, whereas all expressions integral to pure theories and laws are exact. Vague expressions have no single meaning-content, the same in all cases of their application: their meaning is oriented towards types, only partially conceived with clearness and definiteness, types which tend to vary from case to case, perhaps even in a single train of thought. The types, stemming from what are, or from what seem to be, genuinely unified fields, yield a number of concepts, more or less cognate or related, which emerge in turn according to the circumstances of our talk and its varied thought-promptings. These do not permit, for the most part, of definite identifications and distinctions such as might guard against unnoticed confusions among closely connected + +concepts. + +Similar to the haziness of such vague expressions, is the haziness of expressions standing for relatively simple genera and species of phenomenal properties, which shade continuously into one another, whether spatially, temporally, qualitatively or intensively. The typical characters which press in upon us in perception and experience, characters, e.g., of space- and timepattern, of colour- and tone-pattern etc., lead to significant expressions which, in virtue of the fluid transitions among such types (i.e. among their higher genera) must themselves be fluid. Within certain ranges and limits their application is unhesitant, i.e. in fields where the type appears clearly, where it can be evidently identified and evidently distinguished from remotely unlike characters, e.g. 'signal-red' and 'coal-black', *andante* and *presto.* But these fields have vague borders, and flow over into correlative spheres comprehended in the same genus, and so give rise to transitional regions where + +application varies and is wholly uncertain. 3 + +**§28 Variations in meanings as variations in the** + +**act of meaning** + +We have become acquainted with various classes of expressions changeable in meaning, which count as subjeCtive and occasional, since chance circumstances of speaking influence their change. To these expressions other + +expressions stand opposed, which are, in a correspondingly wide sense, objective and fixed, their meaning being normally free from all variation. If we take this freedom from all variation quite strictly, only exact expressions are ranged on this side, whereas vague expressions and expressions which, for differing reasons, vary with the occasion, stand ranged on the other side. We have now to consider whether these important facts of fluctuation of meaning are enough to shake our conception of meanings as ideal (i.e. rigorous) unities, or to restrict its generality significantly. Those ambiguous expressions we called *essentially* subjective, in particular, as also our distinction between vague and exact expressions, might make us doubtful on this point. Do meanings *themselves* divide into objective and subjective, into meanings fixed and meanings changeable on occasion? Must we, in other words, so interpret this difference, with seeming obviousness, that it becomes one between meanings that are ideal unities, on the one hand, fixed species untouched by the flux of our subjective picturing and thinking, and such, on the other hand, as live submerged in the flux of subjective mental experiences, and are transitory events, at one time there, and at the next + +moment not? + +We shall have to look on such a notion as invalid. The content meant by the subjective expression, with sense oriented to the occasion, is an ideal unit of meaning in precisely the same sense as the content of a fixed expression. This is shown by the fact that, ideally speaking, each subjective expression is replaceable by an objective expression which will preserve the identity of + +each momentary meaning-intention. + +We shall have to concede that such replacement is not only impracticable, for reasons of complexity, but that it cannot in the vast majority of cases, be + +carried out at all, will, in fact, never be so capable. + +Clearly, in fact, to say that each subjective expression could be replaced by an objective expression, is no more than to assert the *unbounded range of objective reason.* Everything that is, can be known 'in itself'. Its being is a being definite in content, and documented in such and such 'truths in themselves'. What is, has its intrinsically definite properties and relations, and if it has natural, thinglike reality, then it has also its quite definite extension and position in space and time, its quite definite ways of persisting and changing. But what is objectively quite definite, must permit objective determination, and what permits objective determination, must, ideally speaking, permit expression through wholly determinate word-meanings. To being-initself correspond truths-in-themselves, and, to these last, fixed, unambiguous assertions. Of course, to be able to say all this actually, would require, not merely the necessary number of well-distinguished *verbal signs,* but a corresponding number of *expressions* having precise meanings - in the strict sense of expressions. We must be able to build up all expressions covering all meanings entering into our theory, and to identify or distinguish such + +We are infinitely removed from this ideal. One need only think of the defective way in which we pin down time- and space-positions, our necessary recourse to relations to previously given individual existents, these last themselves inaccessible to an exact pinning down without making use of expressions having an essentially subjective sense. Strike out the essentially occasional expressions from one's language, try to describe any subjective experience in unambiguous, objectively fixed fashion: such an attempt is + +always plainly vain. + +Plainly therefore, considered as such, meanings do not differ essentially among themselves. Actual word-meanings are variable, often changing in a single spell of thought, by their nature mainly adjusted to the occasion. Rightly seen, however, such change in meanings is really *change in the act of meaning.* In other words, the subjective acts which confer meaning on expressions are variable, and that not merely as individuals, but, more particularly, in respect of the specific characters in which their meaning consists. But the meanings themselves do not alter: this is in fact an absurd manner of speech if we adhere to our view of meanings as ideal unities, whether in the case of equivocal, subjectively defective expressions, or in the case of univocal, objectively fixed ones. This is not merely a view demanded by our ordinary orientation to fixed expressions, and by our talk of meanings which stay the same, whenever anyone uses the same expression; it fits in with the + +whole guiding aim of our analyses. + +**§29 Pure logic and ideal meanings** + +Pure logic, wherever it deals with concepts, judgements, and syllogisms, is exclusively concerned with the *ideal* unities that we here call 'meanings'. If we take the trouble to detach the ideal essence of meanings from their psychological and grammatical connections, if we try, further, to clear up their *a priori* relations of adequacy, founded in this essence, to the objective correlates that they mean, we are already within the domain of pure logic. This is clear from the start if we *first* think of the position logic takes up to the many sciences, the position of nomological science, concerned with the ideal essence of science as such, or, what is the same, the position of nomological science, of scientific thought in general, taken purely in its theoretic content and connection. It is clear, *secondly,* when we note that the theoretic content of a science is no more than the meaning-content of its theoretical statements, disembarrassed of all contingent thinkers and occasions of judgement, and that such statements are given *unity* by the theory's pattern, which in its turn acquires objective validity through the ideally guaranteed adequacy of its unified meaning to the objective correlate meant by it (which is 'given' to us in self-evident knowledge). Undeniably what we call 'meaning' in this sense covers only ideal unities, expressed through manifold expressions, and thought of in manifold act-experiences, but none the + +less clearly separable from such chance expressions and from such chance + +experiences of thinking subjects. + +If all given theoretic unity is in essence a unity of meaning, and if logic is the science of theoretic unity in general, then logic evidently is the science of meanings as such, of their essential sorts and differences, as also of the ideal laws which rest purely on the latter. Among such essential differences we have those between meanings which have, and meanings which have no objects, between true and false meanings, and, among such laws, we have the pure 'laws of thought', which express the *a priori* connection between + +the categorial form of meanings and their objectivity or truth. + +This notion of logic as a science of meanings is of course at odds with the mode of speech and treatment of the traditional logic, which operates with psychological or psychologically slanted terms such as 'idea', 'judgement', 'affirmation', 'denial', 'presupposition', 'inference' etc., and which thinks it is really only establishing differences of psychology and tracking down psychological laws relating to these. After the critical investigations of our *Prolegomena* we can no more be taken in by all this. It only shows how far logic still is from a proper understanding of the objects which make up its own true field of research, and how much it has still to learn from the objective sciences, whose essence it none the less claims to make theoretic- + +ally intelligible. + +Where the sciences unfold systematic theories, when they no longer merely communicate the progress of personal research and proof, but set forth the objectively unified, ripe fruit of known truth, there is absolutely no talk of judgements, ideas and other mental acts. The objective researcher of course *defines* his expressions. He says: By *'vis viva',* by 'mass', by an 'integral', by a 'sine' etc., this or that is meant. But he only points thereby to the *objective meaning* of his expressions, he indicates what 'contents' he has in mind, which play their part as constitutive moments in the truths of his field. He is not interested in understanding, but in the concepts, which are for him ideal unities of meaning, and also in the truths, which themselves are made up out + +of such concepts. + +The investigator then propounds propositions, and naturally, in so doing, he asserts or judges. But he has no wish to speak of his own or of anyone else's judgements, but of the correlated *states of affairs,* and when his critical discussions concern propositions, he means by the latter the ideal meanings of statements. He does not say that judgements are true or false, but that propositions are so: his premisses are propositions, and so are his conclusions. Propositions are not constructed out of mental acts of presentation or belief: when not constructed out of other propositions, they ultimately point + +back to concepts. + +Propositions are themselves the elements of *inferences.* Here too there is a distinction between acts of inferring and their unified contents, syllogisms, i.e. the self-identical *meanings* of certain complex statements. The relation of + +necessary consequence in which the form of an inference consists, is not an empirical-psychological connection among judgements as experiences, but an ideal relation among possible statement-meanings, among propositions. It 'exists' or 'subsists', i.e. it is valid, and such validity is something without essential relation to an empirical thinker. If a natural scientist deduces a machine's working from the laws of the lever, gravitation etc., he no doubt experiences all sorts of subjective acts. What, however, he thinks of, and what he knits together in unity, are concepts and propositions together with their objective relations. An objective unity of meaning, i.e. one adequate to the objectivity which is self-evidently 'given', thereby corresponds to his subjective thought-connections: this is whatever it is, whether anyone realizes + +this in thought or not. + +This holds in general. Though the scientific investigator may have no reason to draw express distinctions between words and symbols, on the one hand, and meaningful thought-objects, on the other, he well knows that expressions are contingent, and that the thought, the ideally selfsame meaning, is what is essential. He knows, too, that he does not *make* the objective validity of thoughts and thought-connections, of concepts and truths, as if he were concerned with contingencies of his own or of the general human mind, but that he *sees* them, *discovers* them. He knows that their ideal being does not amount to a psychological 'being in the mind': the authentic objectivity of the true, and of the ideal in general, suspends *all* reality, including such as is subjective. If some scientists at times think differently on this point, they do so, not in their professional scientific settings, but on subsequent reflection. If, with Hume, we may hold that men's true beliefs are better documented by their deeds than by their words, then we may twit such thinkers with not understanding themselves. They pay no unprejudiced heed to what they think in their unreflective enquiries and demonstrations, but are led astray by the supposed authority of logic, with its psychologistic + +fallacies and subjectively distorted terminology. + +All theoretical science consists, in its objective content, of *one* homogeneous stuff: it is an ideal fabric of *meanings.* We can go even further and say that the whole, indefinitely complex web of meanings that we call the theoretical unity of science, falls under the very category that covers all its elements: it + +is itself a unity of meaning. + +If meaning, rather than the act of meaning, concept and proposition, rather than idea and judgement, are what is essential and germane in science, they are necessarily the general object of investigation in the science whose theme is the essence of science. Everything that is logical falls under the two correlated categories of *meaning* and *object.* If we speak in the plural of *logical categories,* we have only to do with the pure species distinguishable *a priori* within the genus of meaning, or with the correlated forms of *categorially considered objectivity.* In such categories the laws formulable in logic have their foundation. We have, on the one hand, such laws as + +abstract from the ideal relations between meaning-intention and meaningfulfilment, and so from any possible knowledge-use of meanings, and consider only how meanings can be compounded to form novel meanings (whether 'real' or 'imaginary').4 We have, on the other hand, *logical laws,* in the more emphatic sense, which consider meanings in respect of their having or not having objects, in respect of their truth or their falsity, their consistency or their absurdity, to the extent that such things are merely determined by the categorial form of such meanings. Corresponding with these latter laws, we have equivalent, correlated *laws for objects in general, objects determined in thought by mere categories.* All valid assertions regarding existence and truth, that are capable of being framed in abstraction from all material of knowledge on a mere foundation of meaning-forms, find their place among + +such laws. + +**The phenomenological and ideal** + +**content of the experiences of** + +**meaning** + +**§30 The content of the expressive experience taken** + +**in its psychological sense and in the sense of a** + +**unified meaning** + +The essence of meaning is seen by us, not in the meaning-conferring experience, but in its 'content', the single, self-identical intentionall unity set over against the dispersed multiplicity of actual and possible experiences of speakers and thinkers. The 'content' of a meaning-experience, in this ideal sense, is not at all what psychology means by a 'content', i.e. any real part or side of an experience. If we understand a name - whether standing for what is individual or general, physical or psychic, existent or non-existent, possible or impossible - or if we understand a statement - true in content or false, consistent or absurd, believed or figmentary - then what either expression 'says' - the meaning which forms its *logical* content and which, in contexts of pure logic, is called either an idea or concept, or a judgement or proposition - is nothing which could, in a real sense, count as part of our act of understanding. This experience naturally has its psychological components, is a content, consists of contents, in the ordinary sense of psychology. Here belong primarily all the sensuous elements of our experience, the appearances of words, in their purely visual, auditory or motor content, and, in the next place, the acts of objective reference which locate such words in space and time. The psychic stuff here involved is well-known to be vastly manifold, varying greatly from one individual to the next, and for the same individual from one moment to another, even in respect of 'one and the same' word. The verbal presentations which accompany and support my silent thinking sometimes involve picturings of words spoken by my own voice, sometimes of letters written by *me* in shorthand or longhand - all these are individual peculiarities, and belong merely to the psychological content of *my* presentational experience. Among contents in this psychological sense are also many differences in respect of act-character, not always easily seized descriptively, such as the subjective difference which constitutes reference or understanding. If I hear the name 'Bismarck' it makes not the slightest difference to my understanding of the word's unified + +meaning, whether I imagine the great man in a felt hat or coat, or in a cuirassier's uniform, or whatever pictorial representation I may adopt. It is not even of importance whether *any* imagery serves to illustrate my con- + +sciousness of meaning, or to enliven it less directly. + +Battling against a seductive notion, we laid it down that the essence of expression lies in a meaning-intention, and not in the more or less perfect, more or less close or remote, illustration that accompanies or fulfils that intention. If, however, such illustrations are present, they will be intimately fused with the meaning-intention. It is therefore understandable that our unified experience of the meaningfully functioning expression should, from case to case, reveal considerable psychological differences even on the meaning side, whereas its meaning remains strictly the same. We have also shown that there is *something* in the correlated acts which really corresponds to such selfsameness of meaning, that what we call a meaning-intention is not an undifferentiated character to which a connection with fulfilling intuitions first imparts an *external* differentiation. Meaning-intentions of intrinsically different character belong rather with differing meanings, or with expressions used with differing meanings, whereas all expressions understood with like sense are clothed with the same meaning-intention as an invariant mental character. Through this character, expressive experiences strongly differing in psychological make-up first become experiences endowed with the same meaning. Fluctuation of meaning here certainly involves restric- + +tions which make no essential difference. + +**§31 The act-character of meaning and the ideally** + +**unified meaning** + +We have opposed what is psychologically common to what is psychologically variable, but we have not thereby hit off the distinction we wanted to clarify: that between the psychological and logical content of our expressions and expressive acts. For the psychological content as much includes what is constant from case to case as what varies with the occasion. It is not, therefore, our doctrine that an act-character which stays the same in all cases, is itself our meaning. What, e.g., the statement 'rr is a transcendental number' says, what *we* understand when we read it, and mean when we say it, is no individual feature in our thought-experience, which is merely repeated on many occasions. Such a feature is always individually different from case to case, whereas the sense of the sentence should remain *identical.* If we or others repeat the same sentence with like intention, each of us has his own phenomena, his own words and his own nuances of understanding. Over against this unbounded multiplicity of individual experiences, is the selfsame element expressed in them all, 'selfsame' in the very strictest sense. Multiplication of persons and acts does not multiply propositional mean- + +That we here insist on the strict identity of what is meant, and oppose it to the constant mental character of meaning it, does not spring from our personal fondness for subtle distinctions, but from the firm theoretical belief that so alone can we do justice to a fact fundamental for the understanding of logic. We are not here dealing with a mere hypothesis, justifiable only by explanatory fruitfulness; we are appealing to an immediately graspable truth, following in this the self-evidence which is the final authority in all questions of knowledge. I see that in repeated acts of presentation and judgement I mean, or can mean, the same concept or proposition: I see that, wherever there is talk of the *proposition* or *truth* that TI *is a transcendental number,* there is nothing I have less in mind than an individual experience, or a feature of an individual experience of any person. I see that such reflective talk really has as its object what serves as a meaning in straightforward talk. I see lastly that what I mean by the sentence in question or (when I hear it) grasp as its meaning, is the same thing, whether I think and exist or not, and whether or not there are *any* thinking persons and acts. The same holds of all types of meanings, subject-meanings, predicate-meanings, relational and combinatory meanings etc. It holds, above all, in the case of the ideal properties which pertain primarily to meanings. Here belong, to mention a few only of the most important, the predicates *true* and *false, possible* and + +*impossible, general* and *singular, determinate* and *indeterminate* etc. + +The genuine identity that we here assert is none other than the *identity of the species.* As a species, and only as a species, can it embrace in unity (~V~j3O:AAEIV Els EV), and as an ideal unity, the dispersed multiplicity of individual singulars. The manifold singulars for the ideal unity Meaning are naturally the corresponding act-moments of meaning, the *meaning-intentions.* Meaning is related to varied acts of meaning - Logical Presentation to presentative acts, Logical Judgement to acts of judging, Logical Syllogism to acts of syllogism - just as Redness *in specie* is to the slips of paper which lie here, and which all 'have' the same redness. Each slip has, in addition to other constitutive aspects (extension, form etc.), its own individual redness, i.e. its instance of this colour-species, though this neither exists in the slip nor anywhere else in the whole world, and particularly not 'in our thought', in so far as this latter is part of the domain of real being, the sphere of + +temporality. + +Meanings constitute, we may say further, a class of concepts in the sense of 'universal objects'. They are not for that reason objects which, though existing nowhere in the world, have being in a TOTIOS OVpO:V10S or in a divine mind, for such metaphysical hypostatization would be absurd. If one has accustomed oneself to understand by 'being' only real being, and by 'objects' only real objects, then talk of universal objects and of their being, may well seem basically wrong; no offence will, however, be given to one who has first used such talk merely to assert the validity of certain judgements, such in fact as concern numbers, propositions, geometrical forms etc., and + +who now asks whether he is not evidently obliged, here as elsewhere, to affix the label 'genuinely existent object' to the correlate of his judgement's validity, to what it judges about. In sober truth, the seven regular solids, are, logically speaking, seven objects precisely as the seven sages are: the principle of the parallelogram of forces is as much a single object as the city of + +Paris. 2 + +**§32 The ideality of meanings is no ideality in the** + +**normative sense** + +The ideality of meanings is a particular case of the ideality of what is specific in general. It has not the sense of *normative ideality,* as if we were here dealing with an ideal of perfection, an ideal limiting value, over against particular cases which realized it more or less approximately. No doubt the 'logical concept', i.e. the term in the sense of *normative* logic, is an ideal in respect of its meaning. For the demand of the craft of knowledge runs: 'Use words with an absolutely selfsame meaning: exclude all meaning-variations. Distinguish meanings and keep them distinct in declarative thought, and + +employ sharply distinct sensible signs.' + +This prescription relates, however, as it only can relate, to the formation of meaningful terms, to care in the subjective sifting out and expression of one's thoughts. Meanings 'in themselves' are, as we have argued, specific unities, however much the act of meaning may vary: they themselves are not ideals. Ideality in the ordinary, normative sense does not exclude reality. An ideal is a concrete original that may exist, and that may confront one in reality, as when a young artist takes the work of a great master as the ideal that he relives and that he strives after in his own creations. Even where an ideal is not realizable, it is at least an individual in our presentative intention. The ideality of what is specific is, contrariwise, the complete opposite of reality or individuality; it represents no end of possible endeavour, its ideality lies in a 'unity in multiplicity'. Not the species itself, but the indi- + +vidual falling under it, can be a practical ideal. + +**§33 The concepts meaning and concept (in the sense** + +**of species) do not coincide** + +Meanings, we said, constitute a *class* of 'universal objects' or species. Each species, if we wish to speak of it, presupposes a meaning, in which it is presented, and this meaning is itself a species. But the meaning in which an object is thought, and its object, the species itself, are not one and the same. Just as in the sphere of individuals, we distinguish, e.g., between Bismarck himself and presentations of Bismarck, e.g. *Bismarck* - *the greatest of German statesmen* etc., so also, in the field of species, we distinguish between, + +e.g., the number 4 itself and the presentations, i.e. meanings, which have 4 as their object, as, e.g., *the number* 4 - *the second even number in the numberseries* etc. The universality *that* we think of, does not therefore resolve itself into the universality of the meanings *in which* we think of it. Meanings, although as such they are universal objects, fall, *in respect of the objects to which they refer, into individual and specific meanings,* or (to conform to a readily understandable linguistic preference) *into individual and general meanings.* Individual presentations, e.g., are therefore *generalia, qua* unities of + +meaning, though their objects are *individualia.* + +**§34 In the act of meaning we are not conscious of** + +**meaning as an object** + +In the actual experience of meaning an individual feature, a singular case of the species (we said) corresponds to the unitary meaning, just as to the specific difference Redness the aspect of red in the object corresponds. If we perform the act and live in it, as it were, we naturally refer to its object and not to its meaning. If, e.g., we make a statement, we judge about the thing it concerns, and not about the statement's meaning, about the judgement in the logical sense. This latter first becomes objective to us in a reflex act of thought, in which we not only look back on the statement just made, but carry out the abstraction (the Ideation) demanded. This logical reflection is not an act that takes place only under exceptional, artificial conditions: it is a normal component of *logical* thinking. What is characteristic of such thought is the context of theory, and the theoretical consideration of the latter, which is carried out in step-by-step reflections on the *contents* of the thought-acts just performed. A very common form of thoughtful pondering may serve as an instance: 'Is S *P?* That could very well be. But from this proposition it would follow that *M* is the case. This cannot be, and so what I first thought possible, *that* S *is P,* must be false etc.' The italicized words should be noted, as well as the idealizations they express. *This* proposition, that S *is P,* which is the pervasive theme of discussion, is plainly not the fleeting moment of meaning in the thought-act in which the notion first occurred to us. Logical reflection rather sets in at later stages, and an identical propositional meaning is continuously meant in it, idealized and identified in our unified thought-context, and thought of as one and the same. The same is the case wherever a unified theoretical demonstration is being wound up. We could utter no 'therefore' unless there was also a glance at the meaning-content of the premisses. In judging the premisses, we not merely live in our judgements, but reflect on their contents: only by glancing back at these does the conclusion appear 'motivated'. Thus and only thus can the logical form of the premisses - which of course is not stressed in that universal, conceptual way that finds expression in syllogistic formulae - + +**§35 Meanings 'in themselves' and meanings expressed** We have so far preferred to speak of meanings which, as the normal, relational sense of the word suggests, are meanings of expressions. There is, however, no intrinsic connection between the ideal unities which in fact operate as meanings, and the signs to which they are tied, i.e. through which they become real in human mental life. We cannot therefore say that all ideal unities of this sort are expressed meanings. Wherever a new concept is formed, we see how a meaning becomes realized that was previously unrealized. As numbers - in the ideal sense that arithmetic presupposes neither spring forth nor vanish with the act of enumeration, and as the endless number-series thus represents an objectively fixed set of general objects, sharply delimited by an ideal law, which no one can either add to or take away from, so it is with the ideal unities of pure logic, with its concepts, propositions, truths, or in other words, with its meanings. They are an ideally closed set of general objects, to which being thought or being expressed are alike contingent. There are therefore countless meanings which, in the common, relational sense, are merely possible ones, since they are never expressed, and since they can, owing to the limits of man's cognitive + +powers, never be expressed. + +The ideal unity of the + +species and modern + +theories of abstraction + +**Introduction** + +Following the discussions of the last Investigation, we grasp the ideal unity of a meaning in the light of the act-character of signification; this signification's peculiar 'tincture' distinguishes the meaning-consciousness of a given expression from that of one which differs in meaning. This does not of course mean that this act-character is the concrete reality upon whose basis the meaning as Species is constituted for us. The relevant concrete reality is rather the total experience of the understood expression, which is informed by this act-character as its animating 'tincture'. The relation between the meaning and the significant expression (or its 'meaning-tincture') is the same as the relation, e.g., between the Species Red and a red object of intuitive experience (or the 'moment' of red which appears in this object). When we mean Red *in specie,* a red object appears before us, and in this sense we look towards the red object to which we are nevertheless not referring. The moment of red is at the same time emphasized in this object, and to that extent we can again say that we are looking towards this moment of red. But we are not referring to this individually definite trait in the object, as we are referring to it when, e.g., we make the phenomenological observation that the moments ofred in the separate portions of the apparent object's surface are themselves separate. While the red object and its emphasized moment of red appear before us, we are rather 'meaning' the single identical Red, and are meaning it in a novel conscious *manner,* though which precisely the Species, and not the individual, becomes our object. The same would apply also to a meaning in its relation to an expression, and an expression's meaningful orientation, + +whether this expression relates to a corresponding intuition or not. + +Meaning as a Species therefore arises out of the above-mentioned background through *abstraction,* but not through abstraction in that improper sense by which empiricist psychology and epistemology are dominated, a sense which altogether fails to seize what is specific, and whose inability to do so is even counted as a virtue. The issue of abstraction has a twofold relevance to a philosophical laying down of the foundations of pure logic. It is relevant in the first place since among the categorial distinctions of meanings which pure logic must essentially consider, we find a distinction which + +corresponds to the opposition between individual and universal objects. But it also has, in the second place, a particular relevance, since meanings as such, i.e. meanings in the sense of specific unities, constitute the domain of pure logic, so that to misread the essence of the Species must in each case be to strike at the very essence of logic. It will accordingly not be unsuitable to tackle the problem of abstraction even at this early point in our introductory series of investigations, so as to assure the basic foundations of pure logic and epistemology by defending the intrinsic right of specific (or ideal) objects to be granted objective status alongside of individual (or real) objects. This is the point on which relativistic, empiricistic psychologism differs from idealism, which alone represents the possibility of a self-consistent theory of + +knowledge. + +To talk of 'idealism' is of course not to talk of a metaphysical doctrine, but of a theory of knowledge which recognizes the 'ideal' as a condition for the possibility of objective knowledge in general, and does not 'interpret it + +away' in psycho logistic fashion. + +**Universal objects and the** + +**consciousness of universality** + +§ **I We are conscious of universal objects in acts which differ essentially from those in which we are** + +**conscious of individual objects** + +Our own position has been indicated above in a few words; its justification should require few additional explanations. All that we maintain - the validity of the distinction between specific and individual objects, and the difference of the manner in which each type of objects is present to us, is brought clearly before our consciousness - has the guarantee of self-evidence. This self-evidence automatically emerges as soon as the relevant presentations are clarified. We need only refer to cases where individual or specific presentation are intuitively 'fulfilled', to be utterly clear as to the sorts of objects 'meant' by such presentations, and as to what counts as an essential homogeneity or disparity in their sense. Reflection on both classes of acts simply makes plain whether or not there are essential differences in the manner in + +which they are performed. + +**In** the latter regard comparison shows that the act in which we mean the Species, is in fact essentially different from the act in which we mean the individual, whether, in this later case, we refer to a whole concrete thing, or to an individual piece or property attaching to it. There are, of course, certain phenomenal communities in either case. **In** either case the same concrete thing makes its appearance, and to the extent that it does so, the same sense-contents are given and interpreted in an identical manner, i.e. the same course of actually given sense and image-contents serves as a basis for the same 'conception' or 'interpretation', in which the appearance of the *object* with the *properties* presented by those contents is constituted for us. But the same appearance sustains different acts in the two cases. **In** the first case it provides the presentative basis for an act of *individual* reference, i.e. for an act in which we apply ourselves to the apparent thing itself, and 'mean' this thing or this feature, this part of the thing. **In** the latter case it provides the presentative basis for an act of conception and reference directed to a Species: i.e. while the thing appears, or rather the feature in the thing, it is not + +this objective feature, this feature here and now, that we mean. We mean its *content,* its 'Idea'; we mean, not this aspect of red in the house, but Red as such. This act of meaning is plainly an act 'founded' on underlying apprehensions (see Investigation VI, §45); a new mode of apprehension has been built on the intuition of the individual house or of its red aspect, a mode of apprehension constitutive of the intuitive presence of the Idea of Red. And as the character of this mode of apprehension sets the Species before us as a universal object, so too there develop, in intimate connection with such an object, formations like 'red thing' (thing containing an instance of red), 'this case of red' (the red of this house) etc. The primitive relation between Species and Instance emerges: it becomes possible to look over and compare a range of instances, and perhaps to judge with self-evidence: 'In all these cases individual moments differ, but in each the same Species is realized: this Red is the same as that - specifically treated it is the same colour - and yet again this red differs from that one - i.e. individually treated, it is a different objective individual feature'. This distinction, like all fundamental logical distinctions, is categorial. It pertains to the pure form of possible + +objects of consciousness as such. (See also Investigation VI, ch. *6f)* + +**§2 The indispensability of talk about universal objects** The excesses of conceptual realism have led men to dispute, not merely the reality, but the objectivity of the Species. This is certainly quite wrong. The question as to whether it is possible or necessary to treat Species as objects can plainly only be answered by going back to the meaning (the significance, the sense) of the names standing for Species, and to the meaning of the assertions claiming to hold for Species. If these names and assertions can be interpreted as making the true objects of our intention individual, if the intention of the nominal and propositional thoughts which give them meaning can be thus understood, then we must yield to our opponents' doctrine. But if this is not so, if the semantic analysis of such experiences, shows that their direct, true intention is plainly not directed upon individual objects, and if in particular their universal relation to a range of individual objects is plainly shown up as merely an indirect pointing to logical connections whose content (sense) will first be unfolded in new thoughts, or which will require new expressions - then our opponents' doctrine is evidently false. Now in fact we cannot at all help distinguishing between *individual* singulars, like the 'things' of experience, and *specific* singulars, like the numbers and manifolds of mathematics, or like the presentations and judgements (the concepts and propositions) of pure logic. *Number* is a concept which, as has often been stressed, has 1, 2, 3 ... as its subordinate singulars. *A* number is, e.g., the number 2, not any group of two individual objects. If we mean these, even quite indefinitely, we should also say so; our thought will then at + +The difference between individual and specific singulars corresponds to the no less essential difference between individual and specific universals (or between individual and specific universality). These differences at once carry over into the field of judgement, and run through the whole of logic. Singular judgements divide into *individually singular* judgements such as *Socrates is a man,* and *specifically singular* judgements such as *Two is an even number,* or *A Round Square is a nonsensical concept.* Universal judgements divide into *individually* universal judgements such as *All men are mortal,* and *specifically universal* judgements such as *All analytic functions can be differentiated,* + +or *All propositions of pure logic are* a priori. + +These distinctions and others like them are quite irremovable. We are not merely dealing with abbreviated expressions: we cannot eliminate such dif- + +ferences through any elaboration or circumscription. + +Inspection of each instance will, for the rest, yield the conviction that a Species really becomes an object in knowledge, and that judgements of the same logical forms are possible in relation to it, as is the case with individual objects. We may choose an instance from the group that concerns us particularly. Logical ideas, unitary meanings as such, are, as we said, ideal objects, whether they present what is universal or what is individual, e.g. *the city of Berlin* as an identical sense which recurs in talk and reference, or the direct idea of the theorem of Pythagoras (whose explicit utterance need not + +be carried out), or this very idea *the theorem of Pythagoras.* + +We, from our point of view, would point out that each such meaning certainly counts as a unit in our thought and that on occasion we pass evident judgements upon it as a unit: it can be compared with other meanings and distinguished from them. It can be an identical subject for numerous predicates, an identical term in numerous relations. It can be summed together with other meanings and can be counted as a unit. As self-identical, it can in its turn serve as the object for many new meanings. All these things are the same in its case as in the case of other objects, e.g. horses, stones, mental acts etc., that are not meanings. A meaning can be treated as self-identical only because it is self-identical. This argument we find unassailable: it applies of course to all specific unities, even to such as are not meanings. + +**§3 Must the unity of the Species be regarded as a** + +**spurious unity? Identity and exact likeness** + +We wish to follow tradition in upholding a strict view of the identity of the Species, in contrast with prevailing doctrines which pin their faith on the wide diffusion of improper uses of 'identity'. Very often we speak of *the same* thing in the case of exactly like things. We speak, e.g., of 'the same cupboard', 'the same dress', 'the same hat' in the case of exactly similar products framed on the same pattern, products, i.e., exactly like one another in such respects as interest us in connection with such things. We speak in this sense of 'the + +same conviction', 'the same doubt', 'the same question', 'the same wish' etc. etc. Such impropriety of usage is thought likewise to be present in talk of the 'same Species' and, in particular, in talk of the 'same meaning'. We speak of 'the same meaning' ('the same concept', 'the same proposition') in relation to a pervasively like meaning-experience, we speak of 'the same red' (red in general) 'the same blue' etc., in respect to a pervasively like colouring. Against this argument I object, that an improper use of identity in the case of like things, refers us back, through its very impropriety, to a proper use of the same term, i.e. to an identity. We find in fact that wherever things are 'alike', an identity in the strict and true sense is also present. We cannot predicate exact likeness of two things, without stating the respect in which they are thus alike. Each exact likeness relates to a Species, under which the objects compared, are subsumed: this Species is not, and cannot be, merely 'alike' in the two cases, if the worst of infinite regresses is not to become inevitable. If we specify the respect of our comparison, we point by way of a more general class-term to the range of specific differences among which the one which appears in our compared members is to be found. If two things are 'alike' as regards form, then the Form-Species in question is the identical element, if they are 'alike' as regards colour, the Colour-Species is this element etc. etc. Not every Species has of course an unambiguous verbal expression, and so at times a suitable expression for a 'respect' is lacking, and to state it clearly might be difficult. We none the less keep it in view, and it governs our talk of 'alikeness'. It would of course appear as a total inversion of the true state of things, were one to try to define identity, even in the sensory realm, as being essentially a limiting case of 'alikeness'. Identity is wholly indefinable, whereas 'alikeness' is definable: 'alikeness' is the relation of objects falling under one and the same Species. If one is not allowed to speak of the identity of the Species, of the respect in which there + +is 'alikeness', talk of 'alikeness' loses its whole basis. + +**§4 Objections to the reduction of ideal unity to** + +**dispersed multiplicity** + +We now direct attention to another point. Should anyone wish to reduce talk about a single attribute to a subsistence of certain relations of exact likeness, we ask him to consider the difference which comes out in the following + +opposition. We make a comparison between: + +1. Our intention, when we grasp any group of intuitively like objects in unitary fashion, or when we recognize their exact likeness *at a single glance,* or when in single acts of *comparison* we recognize the likeness of one definite object to certain others and ultimately to all objects in the group,l and 2. Our intention when, possibly basing ourselves on the same intuitive foundations, we apprehend as an *ideal unity* the attribute which constitutes + +It is plain that, in our two cases, the target of our intention, the object meant and named as subject of our assertion, is quite different. However many like objects may float before us in intuition or comparison, they and their 'alikenesses' are certainly not what we mean in our second case. What we mean is the 'universal', the ideal unity, and not these units and pluralities. The two intentional situations are utterly different, not merely logically, but also psychologically. In the second case no intuition of likeness, not even a comparison, is at all needed. I recognize this paper as paper and as white, and thereby make clear to myself the general sense of the expressions 'paper' and 'white as such', but I need not carry out any intuitions of likeness nor any comparisons. One can say for the rest, no doubt, that these conceptual ideas would never have arisen had like objects never appeared together, nor been intuitively related by their likeness. This psychological fact is, however, totally irrelevant here, where the question weighed concerns what an attribute counts as in knowledge, and what it should count as in the full light of 'evidence'. It is clear, further and lastly, that when we try to make plain an intention to a Species by somehow presenting singulars as belonging to groups of exact similars, such presented singulars only comprise a few members of such groups, and can never exhaust their total range. One may then well ask what will give unity to this range, what will make it a possible object for awareness and knowledge, if the unity of the Species altogether lapses, and together with it the thought-form of 'allness', which gives the Species a bearing on the whole host of *A's* represented in our thought, which we refer to through the sense of the expression 'the totality of *A's'.* To point to the 'same' universally shared moment will of course not help us at all. It is numerically present as often as there are single objects represented within the range of the Species. How can anything unify if it must itself first be unified? + +We can also derive no assistance from the objective possibility of recognizing all members of the range to be *like* one another: it cannot give unity to this range for our thought and knowledge. For, as a possibility, it is nothing for our consciousness, unless we think of it and grasp it. But such a grasp would, on the one hand, presuppose the thought of the unity of the range, and this range would itself also confront us as an ideal unity. Each attempt to transform the being of what is ideal into the possible being of what is real, must obviously suffer shipwreck on the fact that possibilities themselves are ideal objects. Possibilities can as little be found in the real + +world, as can numbers in general, or triangles in general. + +The empiricistic attempt to dispense with Species as objects by having recourse to their extensions can therefore not be carried out. It cannot tell us what gives unity to such extensions. The following objection makes this particularly clear. The conception we are criticizing operates with 'circles of similars', but makes too much light of the difficulty that each object belongs to a plurality of 'circles of similars', and that we must be in a position to say what distinguishes these 'circles of similars' among themselves. It is plain + +that, in default of a previously given Specific Unity, we cannot avoid a regress *in infinitum.* An object *A* is similar to other objects, to one object in the respect *a,* to another in the respect *b* etc. But such 'respects' do not imply that a Species is there, which effects unity. What then unifies the circle of similars determined, e.g., by Redness, as against the circle determined by Triangularity? The empiricistic conception only says: These are differing similarities. If *A* and *B* are similar in respect of red, and *A* and C in respect of triangularity, these similarities must differ *in kind.* But here we again come up against kinds. Similarities are compared, and form genera and species, just as their absolute members do. We should then have to have + +recourse to similarities of such similarities, and so on *in infinitum.* + +**§5 Continuation. The controversy between John** + +**Stuart Mill and H. Spencer** + +It has doubtless been felt often enough that psychologistic approaches which splinter specific unities into the multiplicity of their subordinate objects involve some difficulties: men have, however, acquiesced too readily in 'solutions' of such difficulties. It is interesting to observe how J. Stuart MilV in opposition to his own psycho logistic doctrine, wants to keep to talk about the *identity* of attributes, and to justify it against Spencer, who is much more consistent in only wanting to permit talk of *exactly similar* attributes. 3 The sight of different people does not arouse identical sensations in us, but only exactly similar ones: Spencer therefore thinks that the humanity in each such person must be a different attribute. The same should, however, apply, Mill objects, to the humanity of the same man at this moment, and a half- + +hour later. 'No', he says, + +if every general conception instead of being 'the One in the Many', were considered to be as many different conceptions as there are things to which it is applicable, there would be no such thing as general language. A name would have no general meaning, if 'man' connoted one thing when predicated of John and another though closely resembling thing + +when predicated of William.4 + +The objection is valid, but it affects Mill's own doctrine no less. For a few lines further on he says: 'The meaning of any general name is some outward or inward phenomenon, consisting in the last resort of feelings; and these feelings, if their continuity is for an instant broken, are no longer the same feelings in the sense of individual identity.' Mill thinks he can easily escape + +the difficulty he has so sharply emphasized. 'What then,' he asks, + +is the common something which gives a meaning to the general name? Mr Spencer can only say: it is the similarity of the feelings, and I rejoin, + +the attribute is precisely the similarity. The *names of attributes* are in their ultimate analysis names *for the resemblances of our sensations* (or other feelings). Every general name, whether abstract or concrete, + +denotes or connotes one or more of these resemblances. 5 + +An extraordinary solution. Connotation therefore no longer consists in attributes in the ordinary sense of the word, but in these similarities. What has been achieved by this change-over? Each such similarity does not mean a momentary, individual *feeling* of similarity, but an identical one-in-many; it therefore presupposes what it should explain away. We have not even reduced the number of such inexplicabilities, since a distinct similarity corresponds to each distinct attribute. But to what extent can we even speak of a single similarity, since to each single *case* of comparison a particular similarity corresponds, so that an indefinite number of similarities pertains to each attribute? This leads to the question discussed above, as to what may underlie the unitary mutual belongingness of all these similarities, a question that need only be raised to show up the wrongness of the relativistic + +conception. + +Mill himself feels how dubious his explanation is, for he makes the fol- + +lowing statements: + +It will not, probably, be denied, that if a hundred sensations are undistinguishably alike, their resemblance ought to be spoken of as one resemblance, and not a hundred resemblances that merely *resemble* one another. The *things compared* are *many,* but the something common to all of them must be conceived as *one,* just as the name is conceived as one, though corresponding to numerically different sensations of sound + +each time it is pronounced. + +Remarkable self-deception: as if by laying down a mode of speech we could decide whether a unitary thought-object corresponds to a multitude of acts or not, and as if our talk did not derive its unitary sense from an ideal unity of intention. Certainly there are many compared 'things' and certainly we must conceive what is common to them as one: but this 'must' plainly rests on the fact that this common element is one. And if this is true of the similarities, it is true of the undisguised attributes themselves, which must in this respect be essentially kept apart from the 'feelings'. One must therefore cease to speak as if one were doing psychology where concepts are being + +investigated. + +'The question between Mr Spencer and me,' says Mill, + +is merely one of language, for neither of us believes an attribute to be a real thing, possessed of objective existence; we believe it to be a particular mode of naming our sensations, or our expectations of sensation, + +when looked at in their relation to an external object which excites them. The question raised by Mr Spencer does not, therefore, concern the properties of any really existent thing, but the comparative appropriateness, for philosophical purposes, of two different ways of *using a name.* + +We also, of course, do not believe in the *reality* of attributes, but we demand a somewhat keener analysis of what lies behind such 'ways of using a name', and of what establishes the 'appropriateness of names for philosophical purposes'. Mill fails to see that the unitary sense of a name, and of every expression, is a Specific Unity, and we merely push the problem back a stage when we reduce the Unity of the Species to the unity of a verbal meaning. + +**§6 Transition to the following chapters** + +We have, in our last treatment, been forced to react critically to conceptions opposed to ours. In this we encountered a line of thought common to all forms of empiricistic theories of abstraction, however much they may otherwise differ in content. It seems necessary, however, to grant greater play to such criticism, so as to draw more profit from our conception of the essence of universal objects and universal presentations, in analysing and testing the various main types of modern theories of abstraction. Critically to point out errors in other thinkers' views will provide an opportunity to round off and complete our own conception, and at the same time to test its reliability. The empiricistic 'theorl of abstraction', like most parts of modern epistemological theory, suffers from the mixture of two essentially different scientific interests, one concerned with the psychological *explanation of experiences,* the other with the 'logical' *classification* of their *thought-content* or *sense,* and the criticism of their possible achievement as acts of knowing. In the former regard we seek to establish empirical bonds tying the thoughtexperiences in question to other facts in the flux of real happenings, facts responsible for them causally, or on which they exert effects. In the latter regard we are intent upon the 'origin of the concepts' which pertain to our words: we seek to clarify their 'true meaning' or significance through plainly establishing their intention in the sense of their *fulfilments,* which are first realized when suitable intuitions are adduced. To study the essence of these phenomenological connections is to lay bare the indispensable foundation for an epistemological clarification of the 'possibility' of knowledge. It is also, in our case, to give essential clearness to the possibility of making valid assertions regarding universal objects (or regarding individual objects *as* objects of corresponding universal concepts) and, in connection therewith, to set forth in self-evident fashion the correct sense in which a universal counts as an 'entity', and an individual as a thing ranged under universal predicates. If a theory of abstraction is to have an epistemological function, if it is to clarify knowledge, it must set forth the immediate descriptive situation + +in which a Species comes to consciousness, it must through this clarify the sense of names of attributes, and thence go on to resolve perspicuously the many misinterpretations that the essence of the Species has suffered. It will go astray from the start if it loses itself in empirical-psychological analyses of the abstractive process and its cause and effects, and if, rapidly dismissing the descriptive content of the abstractive consciousness, it directs its main concern to unconscious dispositions and hypothetical associative linkages. What generally happens in such cases is that the essential immanent content of the consciousness of universality, which could have been classified prop- + +erly without more ado, goes disregarded and unmentioned. + +And, even if a theory of abstraction aims at the field of what is immanently discoverable in all true (and therefore intuitive) abstraction, and steers clear of the misguided confusion between essential (i.e. epistemologically clarifying) and empirical (i.e. psychologically explanatory) analysis, it will still go astray from the start if it falls into the other confusion (strongly suggested by ambiguous talk of 'general representation') between *phenomenological* and *objective* analysis. What our acts of meaning merely assign to their objects, will be assigned to these acts themselves as their real *(reelles)* constituent. Here the regulative field of consciousness and its immanent essence are again covertly abandoned, and all given over to confusion. The following analyses will show that our sketchy characterization fits the most influential modern theories of abstraction, and that these really go + +astray for reasons that we have just summarily stated. + +**The psychological hypostatization** + +**of the universal** + +**§7 The metaphysical and psychological** + +**hypostatization of the universal. Nominalism** + +Two misunderstandings have dominated the development of doctrines con- + +cerning universal objects: + +First: the metaphysical hypostatization of the universal, the assumption + +that the Species really exists *externally* to thought. + +Secondly: the *psychological hypostatization* of the universal, the assump- + +tion that Species really exists *in* thought. + +The older nominalism, whether of an extreme or a conceptualistic type, attacked the first misunderstanding, the misunderstanding which underlies Platonic realism (in the sense in which this is traditionally conceived). To combat the second misunderstanding, especially in the form of Locke's abstract ideas, has inspired the development of the modern theory of abstraction since Berkeley's time, and has given it its definite trend towards extreme nominalism (which is now usually called 'nominalism' *simpliciter,* and opposed to conceptualism). It was thought needful, to avoid the absurdities of Locke's abstract ideas, altogether to reject universal objects as peculiar thought-unities, and universal presentations as peculiar acts of thought. Ignoring the difference between universal intuitions on the one hand - among which not only such abstract ideas, but the general images of traditional logic belong - and universal meanings on the other, men rejected 'conceptual presentations', with their peculiar presentative intentions, if not in word, then at least in the sense of these words, and replaced them by individual + +presentations merely functioning in an extraordinary manner. + +Nominalism therefore adds itself, as a third misunderstanding, to our previous two: in various forms it seeks to transform what is universal in + +object and act of thought, into what is individual. + +These misunderstandings, in so far as they are still of actual interest, must be gone through in order. It lies in the nature of our subject-matter, as our discussions up to this point have made plain, that we cannot separate vexed issues regarding the essence of universal objects from issues regarding the essence of universal presentations. It is vain to seek to make out a + +persuasive case validating talk about universal objects, if one does not also remove doubts as to how such objects can be presented, and if one does not further refute theories apparently proving, by scientific psychological analysis, that only individual presentations exist, that only individual objects therefore can be, and ever have been brought to consciousness, and that talk about universal objects can only be understood as fictitious or as gravely improper. We may leave aside, as long disposed of, the misunderstandings of Platonic realism. But the thought-motives pressing towards a psychologizing realism are obviously still operative, as appears particularly in the manner in which Locke tends to be criticized. We must go deeper into such motives in this chapter. + +**§8 A deceptive line of thought** + +The following line of thought might be opposed to our conception, not so much out of serious conviction, as in order to give an apagogic proof of the + +untenability of talk about Species as universal objects: + +If Species are nothing real *(reales),* and if they are also nothing in thought, then they are nothing at all. How can we talk about something if it does not at least exist *in our thought?* The being of the ideal is therefore obviously a being in consciousness; the name 'content of consciousness' rightly applies to it. As opposed to this, real being *(reales Sein)* is no mere being in consciousness, or being-a-content: it is being-in-itself, transcendent being, being + +outside of consciousness. + +We do not wish to lose ourselves in the erring paths of such a metaphysics. For us what is 'in' consciousness counts as real *(real)* just as much as what is 'outside' of it. What is real *(real)* is the individual with all its constituents: it is something here and now. For us temporality is a sufficient mark of reality. Real being and temporal being may not be identical notions, but they coincide in extension. We do not, of course, suppose that psychical experiences are in a metaphysical sense 'things'. But even they belong to a thinglike unity, if the traditional metaphysical conviction is right in holding that all temporal existents must be things, or must help to constitute things. Should we wish, however, to keep all metaphysics out, we may simply define 'reality' in terms of temporality. For the only point of importance is to + +oppose it to the timeless 'being' of the ideal. + +It is further clear that the universal, as often as we speak of it, is a thing thought of by us: it is not therefore a thought-content in the sense of a real *(realen)l* constituent in our thought-experiences, and likewise not a thoughtcontent in the sense of an intension, but is rather an object that we think of. Is it not obvious that an object, even when real *(real)* and truly existent, cannot be conceived as a real part of the act which thinks it? And isn't even the fictitious and the absurd, whenever we speak of it, something we + +think of? + +It is naturally not our intention to put the *being of what is ideal* on a level with the *being-thought-of which characterizes the fictitious of the nonsensical. 2* + +The latter does not exist at all, and nothing can properly be predicated of it: if we none the less speak of it as having its own, 'merely intentional' mode of being, we see on reflection that this is an improper way of speaking. There are, in fact, merely certain necessary and valid connections among 'objectless ideas', whose analogy with truths governing ideas having objects, has prompted this talk of objects merely presented which do not genuinely exist. Ideal objects, on the other hand, exist genuinely. Evidently there is not merely a good sense in speaking of such objects (e.g. of the number 2, the quality of redness, of the principle of contradiction etc.) and in conceiving them as sustaining predicates: we also have insight into certain categorial truths that relate to such ideal objects. If these truths hold, everything presupposed as an object by their holding must have being. If I see the truth that 4 is an even number, that the predicate of my assertion actually pertains to the ideal object 4, then this object cannot be a mere fiction, a mere + +*far;on de parler,* a mere nothing in reality. + +This does not exclude the possibility that the sense of this being, and the sense also of this predication, does not coincide exactly with their sense in cases where a real *(reales)* predicate, a *property* is asserted or denied of a real subject. Otherwise put: we do not deny but in fact emphasize, that there is a fundamental categorial split in our unified conception of being (or what is the same, in our conception of an object as such); we take account of this split when we distinguish between ideal being and real being; between being as Species and being as what is individual. The conceptual unity of predication likewise splits into two essentially different sub-species according as we affirm or deny properties of individuals, or affirm or deny general determinations of Species. This difference does not, however, do away with a supreme unity in the concept of an object, nor with the correlated concept of a categorial propositional unity. In either case something (a predicate) pertains or does not pertain to an object (a subject), and the sense of this most universal pertinence, together with the laws governing it, also determines the most universal sense of being, or of an object, as such; exactly as the more special sense of generic predication, with its governing laws, determines (or presupposes) the sense of an ideal object. If everything which has being is rightly recognized as having being, and as having such and such a being, in virtue of the evidence with which, in thought, we apprehend it as being, then without doubt we may not reject the self-justifying claims of ideal being. No interpretative skill in the world can in fact eliminate ideal + +objects from our speech and our thought. + +**§9 Locke's doctrine of abstract ideas** + +The psychological hypostatization of the universal in Locke's philosophy had, as we saw, an extraordinary historical influence. It grew out of the + +In actual reality nothing like a universal exists; only individual things, arranged into genera and species by their exact or less exact resemblances, have real existence. If we remain within the sphere of what is immediately given and experienced, in the sphere of 'ideas' in Locke's sense, phenomenal things are complexes of 'simple ideas', in which the same simple ideas, the same phenomenal attributes, recur simply or in groups. Things now receive names, and not merely proper names, but for the most part common names; the fact that many things can be unambiguously named by one and the same universal name, shows that a universal sense or 'idea' must correspond to such a name. If we consider how the general name applies to the objects of the pertinent class, it becomes plain that it does so because one and the same attribute (or complex of attributes) is common to all these objects. The univocality of the universal name extends only as far as objects are named by way of this + +and no other attribute (or *idea* of an attribute). + +The universal thought carried out in such universal meanings therefore presupposes that we have the *power of abstraction,* i.e. the power to separate off partial ideas, ideas of such attributes, from the phenomenal things given to us as complexes of attributes, and to associate them with words of which they are the general meanings. The possibility and actuality of such separation is guaranteed by the fact that each universal name has its own meaning, conveys an attributive idea exclusively bound up with itself; as also by the fact that we can at will pick *out* any attributes and make them + +the specific meanings of new general names. + +The formation of 'abstract' or 'universal ideas', those 'creations' and 'arte- + +facts' of the word, is indeed not without difficulty: + +they do not so easily offer themselves as we are apt to imagine. For example: does it not require some pains and skill to form the general idea of a triangle (which is yet none of the most abstract, comprehensive and difficult) for it must be neither oblique, nor rectangle, neither equilateral, equicrural nor scalenon, but all and none of these at once. In effect, it is something imperfect, that cannot exist, an idea wherein some parts of several different and inconsistent ideas are put together. It is true, the mind in this imperfect state has need of such ideas, and makes all the haste to them it can, for the conveniency of communication and enlargement of knowledge ... But yet one has reason to suspect + +such ideas are marks of our imperfection.3 + +§ I **0 Criticism** + +In this line of thought several fundamental errors are intertwined. The basic defect of Locke's theory of knowledge, and of the English theory of knowledge in general, its unclear concept of 'idea', is very plainly revealed in its + +1. An 'idea' is defined as any object of interior perception: 'Whatever the mind perceives in itself, or is the immediate object of perception, thought or understanding, that I call idea.'4 By a ready extension - perception need not actually follow - every *possible* object of interior perception, and finally every content in the immanent-psychological sense, is ranged under the rubric + +of 'idea'. + +2. 'Idea' also has for Locke the narrower sense of *presentation,* in the sense which marks out a very restricted class of experiences, i.e. intentional experiences. Each idea is an idea of *something,* it presents something. + +3. Locke confuses presentation with what is as such presented, appearance with what appears, the act or act-phenomenon, as a really immanent element in the stream of consciousness, with the object intended. The appar- + +ent object therefore becomes an idea, its attributes partial ideas. + +4. The confusion mentioned in 3 is connected with the fact that Locke confounds the attributes pertaining to the object with the immanent contents constituting the sensuous kernel of the presentative act, the *sensations* on which the interpretative act puts an objective interpretation, or by way of which it putatively perceives, or otherwise envisages, the object's attributes. 5. Under the rubric of 'general idea', properties as specific attributes, and + +properties as objective aspects, are confused. + +6. It is of great significance, lastly, that Locke altogether fails to distinguish between an idea in the sense of an intuitive presentation (a phenomenon, a floating image), and an idea in the sense of a significant reference. This latter likewise can be interpreted either as meaning-intention or as a meaning- + +fulfilment, for these two also are never separated by Locke. + +These confusions (still rampant in contemporary epistemology) gave Locke's doctrine of abstract general ideas an air of obviousness which could impose on its author. Objects of intuitive presentation, animals, trees etc., conceived as they appear to us, and not as being the patterns of 'primary qualities' and 'powers' which real things are for Locke - these certainly are not the things which appear in our intuitive presentation - cannot be allowed by us to be complexes of 'ideas', and therefore themselves 'ideas'. They are not objects of possible 'interior perception', as if they constituted a complex phenomenological content in consciousness, in which they could be + +picked out as real data. + +We should not be led astray by the fact that we make an equivocal use of the same words to refer to the sensuously apparent determinations of things, and to the presentative aspects of our percepts, and that we at one time speak of 'colour', 'smoothness', 'shape' etc., in the sense of objective properties, and at another time in the sense of sensations. An opposition of principle divides the two. Sensations, animated by interpretations, present objective determinations in corresponding percepts of things, but they are not themselves these objective determinations. The apparent object, as it appears in the appearance, transcends this appearance as a phenomenon. We may be + +led by certain reasons to distinguish apparent determinations into merely apparent and genuine ones, perhaps as in the sense of the traditional distinction between secondary and primary qualities. The subjectivity of the secondary qualities can never amount to the nonsensical assertion that they are real constituents of phenomena. The apparent objects of external intuition are *meant* unities, not 'ideas' or complexes of ideas in the Lockean sense of these terms. Naming by means of universal names does not, moreover, consist in picking out particular universal ideas from such complexes of ideas, and attaching them to words as their 'meanings'. The naming which, in the true sense of the word, rests on intuition, may direct itself specially to an isolated attribute, but this self-direction is an act of meaning in a sense analogous to the sense in which the self-direction to the concrete object is itself such an act of meaning. This act of meaning means something *for itself,* which, in the meaning of the concrete object, is, we may say, meant *along with* some- + +thing else. But this does not mean that it achieves a separation. + +We may say generally: what an intention is directed to, is thereby made the intention's peculiar object. But to say that it is made the intention's peculiar object, and to say that it is made an object separated from all other objects, are two totally different assertions. Properties understood as attributive aspects, are plainly inseparable from their concrete basis. Contents of this sort cannot exist independently, but they can none the less be independently meant. The intention does not separate, but it refers, and what it refers to, it *eo ipso* shuts off to the extent that it means this and nothing else. This holds of every sort of meaning, and one must be clear that not every meaning is an intuitive beholding, and not every intuition an adequate beholding of its object, embracing that object perfectly and exhaustively in itself. All this does not suffice to decide our question. The single individual objective aspect is not the attribute *in specie.* If the former, the aspect, is meant, the meaning is individual in character, if the Species is meant, the meaning is specific in character. Naturally again the emphasis which the attributive aspect receives, does not mean a separation of the same. Our meaning, in the latter case, certainly in a fashion directs itself to the apparent aspect, but in an essentially new manner; the intuitive foundation being identical, the act-character makes all the difference. Similar differences are observable between the generic idea in the usual sense (e.g. *tree, horse* etc.), and direct presentations of things or concrete realities in general. Everywhere we must distinguish between simple intuitions, whether total or partial, which form our foundation, and the changing act-characters, which, as thoughts, are built on this foundation, without the least change in their + +sensuous, intuitive basis. + +For a closer analysis we should here have to start discussing many more distinctions of acts than we need in criticizing Locke. The intuitively-singular is on one occasion directly meant as *that thing there,* on another occasion as *sustaining a universal,* as subject of an attribute or as individual member of + +an empirical class, on yet another occasion the *universal itself* is meant, e.g. the Species of an attribute stressed in a partial intuition, or, yet again, such *a species is meant as a sub-species of an ideal genus* etc. One and the same sensuous intuition can on occasion serve as a basis for all these modes of + +conceiving. + +To these differences of genuine thought, in which manifold categorial forms are actually constituted, correspond the *symbolic intentions* of our expressions. As merely asserting and meaning, we can say and mean everything which we perhaps do not actualize at all in the genuine, intuitively fulfilled manner. Our 'thought' is then of a 'merely symbolic', 'non-authentic' sort. Locke cannot do justice to this phenomenological state of things. The sensuous-intuitive image, through which the significant intention fulfils itself, is taken by Locke, as said above (sixth confusion), for the meaning itself. Our last assertion confirms and explains our objection. For Locke's identification is inept, whether we understand by a 'meaning' the intending or the fulfilling variety. The former lies in an expression as such; its significant intention constitutes a universal presentation in the sense of a universal meaning, and as such it is possible without any actual intuitive foundation. If fulfilment now enters, our discussions show that the sensuous-intuitive image is not the fulfilment of meaning itself, but the mere foundation for this fulfilling act. To the universal thought, merely symbolically realized, i.e. the mere meaning of the universal word, the 'authentically' carried out thought corresponds, which in its turn rests on an act of sensuous intuition, + +without being identical with the latter. + +Now we completely see the deceptive confusions in Locke's train of thought. From the obvious truth that each universal name has its own peculiar universal meaning, he passes on to assert that *a general idea* corresponds to every general name, which idea is for him simply a *separate intuitive presentation* (a separate appearance) of an attribute. This follows necessarily from the fact that he confuses the word's meaning, whose fulfilment tests this appearance, with the appearance itself: the separated meaning (whether intending or fulfilled) of the attribute, becomes a separated intuition of this attribute. Since Locke fails to hold apart an attribute's appearance from the attribute which appears (Confusion 3), and as little holds apart an attributive aspect from an attribute *specifically* understood (Confusion 5), he indeed achieves a *psychological hypostatization of the universal* in his 'general + +idea', he makes of the universal a real datum in consciousness. 5 + +§ I **I Locke's universal triangle** + +These errors avenge themselves in the absurdities into which, in his example of the universal idea of a triangle, they plunge the great thinker. This idea is the idea of *a* triangle which is neither rectangular nor acute-angled etc. So it readily seems, if one first takes the universal idea of the triangle for the + +universal meaning of the name, and then replaces the latter in consciousness by the separated intuitive presentation, or by the intuited separate existence of the attributive complex in question. Thus we might have an interior image which is triangular and no more, the generic attributes torn adrift from their + +specific differences, and turned into a psychic reality. + +That this conception is not merely false but nonsensical, need scarcely be said. The inseparability of the universal, its incapacity for being made real, holds *a priori,* it is rooted in the essence of the Genus as such. One might perhaps say more impressively, with Locke's example in view, that geometry uses the definition of 'triangle' to prove *a priori* that every triangle is either acute-angled or obtuse-angled or right-angled, etc. It knows no distinction between triangles 'in reality' and triangles 'in idea', i.e., triangles floating as pictures before the mind. What is incompatible *a priori,* is absolutely so, and so also in a picture. The adequate picture of a triangle is itself a triangle. Locke therefore is deceived when he thinks to combine his express recognition of the plain non-existence of a real universal triangle, with its existence in our presentations. He forgets that mental existence is also real existence, and that, when being-presented is opposed to being-real one does not and ought not to point to the opposition between the mental and the extramental, but to the opposition between what is presented, in the sense of being merely *meant,* and what is *true,* in the sense of corresponding to such a meaning. To be meant does not, however, mean to have mental reality. Locke should, above all, have reminded himself that a triangle is something which has triangularity, but that triangularity is not itself something that has triangularity. The universal idea of triangle, as an idea of triangularity, is therefore the idea of what every triangle as such possesses, but it is not therefore itself the idea of *a* triangle. If one calls the general meaning a concept, the attribute itself the *concept's content,* and every subject having this attribute the *concept's object,* one can put the point in the form: It is absurd to treat a concept's content as the same concept's object, or to + +include a concept's content in its own conceptual extension.6 + +One sees further how Locke piles up his absurdities in not only thinking of the universal triangle as a triangle stripped of all specific differences, but also as a triangle which *unites all such differences together,* and so puts into the content of the concept of triangle the extension of the sub-species which divide it. This is, however, merely a passing lapse in Locke. It is plain at least that difficulties regarding universal meanings give no ground for serious complaints regarding the 'imperfections' of the human mind. *Note:* How little the errors of the Lockean doctrine of general ideas have been clarified up to date, is shown among other things by the recent treatment of the doctrine of universal objects, which, following Erdmann, are now accorded a place alongside of individual objects, though not indeed in *our* sense. Thus Twardowski thinks that, what is presented in the universal idea 'is an objece specifically peculiar to it' and that this is 'a group of + +*constituents* which several objects have in common'.8 The object of the universal idea is 'a part of the object of an idea subordinated to it, which stands in relation of exact likeness to definite parts of the objects of other individual ideas'. The general idea is 'to this extent spurious' that it is held + +by many to be incapable of an actual carrying-out. + +But that there nevertheless are such ideas, must be granted by the man who sees that we can say something about their objects. This we plainly can do. No one can represent a universal triangle *intuitively,* a triangle neither right-angled, nor obtuse-angled nor acute-angled, which is without colour or definite size, but it is as plain that we have an indirect idea of such triangles as that we have indirect ideas of a female stallion9 or of + +a steel cannon made of wood etc. + +We read further that 'Plato's ideas are no more than objects of universal ideas. Plato attributes existence to these objects. This we no longer do. The object of the universal idea is represented by us, but does not exist .. .'10 Here it is clear that Locke's absurdities are with us again. We certainly have an 'indirect presentation' of 'a universal triangle', for this merely refers to the meaning of that nonsensical expression. But one would not grant that the universal presentation of *the triangle* is this indirect presentation of *a universal* triangle, or that it is the presentation of a triangle concealed in all triangles, but without being acute-angled, obtuse-angled etc. Twardowski is consistent in rejecting the existence of universal objects - he is right in so regarding the absurd objects he has substituted for them. But what is the case in regard to such existential propositions as *There are concepts, There are propositions, There are algebraic numbers* etc. For Twardowski as for us, + +existence does not mean the same as real *(reale)* existence. + +It is also hard to understand how the universal object, which is supposed to be a 'constituent' of the subsumed concrete object, should lack intuitive givenness, and should not rather share in the intuitive quality of this concrete object. If a total content is intuited, all its single traits are intuited together with, and in it, and many are independently noted, 'set in relief', and so made objects of their own proper intuitions. May we no longer say that we see the tree's green colouring in the tree precisely as we see the green tree? The notion of *Green* can indeed not be seen, whether this be the notion in the sense of the meaning of 'green', or the notion in the sense of the attribute green, the Species *Green.* But it is also absurd to treat concept as a part + +of the individual object, the 'object of the concept'. + +**§ 12 The doctrine of generic images** + +The above discussions have made clear without further analysis that the other way of hypostatizing the universal, which has played its part in traditional + +logic under the rubric of 'generic images', is infected with the same absurdities as Locke's notion and has grown out of similar confusions. The vagueness and elusiveness of generic images in respect of specific differences makes no difference to their concreteness. Vagueness is a definite *feature* of certain contents, it consists in a certain mode of continuity in qualitative transition. And as to elusiveness, it makes no difference to the concreteness of each rapidly changing content. The essence of the matter does not reside in changing contents, but in the unity of an intention directed to constant attributes. + +**Abstraction and attention** + +**§ 13 Nominalistic theories which regard abstraction** + +**as an achievement of attention** + +We now pass on to analyse an influential theory of abstraction, first framed by J. S. Mill in his polemic against Hamilton, according to which abstraction is merely an achievement of attention. There are, it is held, neither general presentations nor general objects, but we may, while forming intuitive presentations of individual concrete things, devote exclusive attention or exclusive interest to various parts and sides of our object. The attribute which neither can actually exist 'in and for itself', i.e. *separately,* nor be represented as such, can be regarded *by itself,* can become the object of an exclusive interest which ignores all associated attributes. The double use of the word 'abstraction', positive in one content and negative in another, + +thereby becomes understandable. + +These main lines of thought are then supplemented by treatments of the associative linkage of general names with stressed traits of intuited objects, and of the influence which names exert on such traits, whether by arousing them reproductively, or by habitually concentrating attention on them. It is pointed out how they dominate and direct the drift of further association through the content of such stressed attributes, and so promote unity of theme in the course of our thinking. The detailed execution of these thoughts is best taken from the above-mentioned polemic of Mill, who for the rest borrows his notion of abstraction as a function of attention from his conceptualistic opponent Hamilton. We read: The formation of a concept, does not consist of separating the attributes which are said to compose it from all other attributes of the same object, and enabling us to conceive those attributes, disjoined from any others. We neither conceive them, nor think them, nor cognize them in any way, as a thing apart, but solely as forming, in combination with numerous other attributes, the idea of an individual object. But, though thinking them only as part of a larger agglomeration, we have the power of fixing our attention on them, to the neglect of the other attributes with which we think them combined. While + +the concentration of attention actually lasts, if it is sufficiently intense, we may be temporarily unconscious of any of the other attributes, and may really, for a brief interval, have nothing present to our mind but the attributes constituent of the concept. In general, however, the attention is not so completely exclusive as this: it leaves room in consciousness for other elements of the concrete idea: though of these the consciousness is faint, in proportion to the energy of the concentrative effort, and the moment the attention relaxes, if the same concrete idea continues to be contemplated, its other constituents come out into consciousness. General concepts, therefore, we have, properly speaking, none; we have only complex ideas of objects in the concrete: but we are able to attend exclusively to certain parts of the concrete idea: and by that exclusive attention, we enable those parts to determine exclusively the course of our thoughts as subsequently called up by association; and are in a condition to carryon a train of meditation or reasoning relating to those parts only, exactly as if we were able to + +conceive them separately from the rest. + +'What principally enables us to do this is the employment of signs, and particularly the most efficient and familiar kind of signs, viz., Names.'l We read further, in connection with a passage from Hamilton's Lectures: 2 + +The rationale of this is, that when we wish to be able to think of objects in respect of certain of their attributes - to recall no objects but such as are invested with those attributes, and to recall them with our attention directed to those attributes exclusively - we effect this by giving to that combination of attributes, or to the class of objects which possess them, a specific name. We create an artificial association between those attributes and a certain combination of articulate sounds, which guarantees to us that when we hear the sound, or see the written characters corresponding to it, there will be raised in the mind an idea of some object possessing those attributes, in which idea those attributes alone will be suggested vividly to the mind, our consciousness of the remainder of the concrete idea being faint. As the name has been directly associated only with those attributes, it is as likely, in itself, to recall them in anyone concrete combination as in any other. What combination it shall recall in the particular case, depends on recency of experience, accidents of memory, or the influence of other thoughts which have been passing, or are even then passing, through the mind: accordingly, the combination is far from being always the same, and seldom gets itself strongly associated with the name which suggests it; while the association of the name with the attributes that form its conventional signification is constantly becoming stronger. The association of that particular set of attributes with a given word, is what keeps them together in the mind by a stronger tie than that with which they are associated with the remainder of the concrete image. To express the meaning in + +Sir W. Hamilton's phraseology, this association gives them an unity in our consciousness. It is only when this has been accomplished, that we possess what Sir W. Hamilton terms a concept: and this is the whole of the mental phenomenon involved in the matter. We have a concrete representation, certain of the component elements of which are distinguished by a mark, designating them for special attention; and this attention, in cases of exceptional intensity, excludes all consciousness of the others. + +**§ 14 Objections to any and every form of nominalism.** + +**(0) The lack of a descriptive fixation of aims** + +We see from the above, and from similar expositions, how, despite great elaboration, no attempt has really been made to pin down what is descriptively given and what demands clarification, and to relate the two to one another. Let us once more run through our own undoubtedly clear, natural train of thought. What we are *given* are certain differences in the field of names: among others, the difference between such names as name what is individual, and such as name what is specific. If we confine ourselves, for the sake of simplicity to direct names ('proper names' in an extended sense of the word), names like 'Socrates' or 'Athens', on the one hand, stand opposed to names like 'Four' (the number-Four as a *single* member of the number-series), *'C'* (the note C as *one member* of the musical scale), 'Red' (as the name of *one* colour), on the other. To these names certain meanings correspond, and through these we refer to objects. What these named objects are can, one would imagine, not be in doubt. In the one case it is the person Socrates, the city of Athens, or any other *individual* object, in the other case the Number Four, the note C, the colour Red, or any other *ideal* object. What we mean by the significant use of words, what objects we name by them, and what these objects count as when we name them, this no one can dispute with us. It is accordingly *evident* that when I say 'Four' in the generic sense, as, e.g., in the statement 'Four is a prime number relatively to seven', I am meaning the Species *Four,* I have *it* as object before my logical regard, and am passing judgement on it, and not on anything individual. I am not judging about any individual group of four things, nor about any constitutive moment, piece or side of such a group, for each part, *qua* part of what is individual, is itself likewise individual. But to make an object of something, to make it a subject of predications or attributions, merely differs in name from having a presentation of it, and having a presentation in a sense which, while not the only one, is none the less the standard one for logic. We therefore assert with self-evidence: There are 'universal presentations', i.e. presentations of what is specific, just as there are presentations of + +what is individual. + +We spoke of self-evidence, but self-evidence in respect of objective differences of meanings implies that we go beyond the merely symbolic use of + +expressions and refer ourselves to corresponding intuitions for final correction. Basing ourselves on intuitive presentations, we carry out the fulfilments of meanings corresponding to our merely significant intentions, we realize their 'genuine' purport. If we do this in our present case, some individual group of four units certainly floats pictorially before us, and to that extent underlies our presentation and our judgement. But we do not pass judgement on this group of four, we do not mean *it* in the subject-idea of our above example. Not the pictured group, but the number Four, the Specific Unity is our subject, and it is of *this* that we say that it is prime relatively to Seven. Strictly speaking, this Specific Unity is likewise nothing in, or attached to, the apparent group, for, if it were, it would be something individual, a thing here and now. But our reference, though itself existing now, refers to nothing less than what is now, it refers to Four, the ideal, timeless unity. Reflecting on our experiences of individual and specific meaning - whether purely intuitive, purely symbolic, or at once a symbolic and a fulfilled significant intention - we must now carry out further phenomenological descriptions. Their task would be to lay bare the relations, fundamental to a clarification of knowledge, which hold between blind (or pure symbolic reference) and intuitive ( or authentic) reference, and in the case of the latter to show the varying manner in which individual images function in consciousness, according as we intend what is individual or what is specific. This would enable us, e.g., to answer questions as to how, and in what case, the universal is brought to subjective awareness in the individual act of thought, and perhaps achieves self-evident givenness, and how it can acquire a connection with the boundless sphere of individual cases ranged under it, of which we can of course form no adequate pictorial presentation. In Mill's exposition, as in all similar expositions, there is no question of simply recognizing evident data and consequently proceeding on the path we have just sketched. What should have been a fixed point in reflective clarification, is pushed aside unnoticed; the theory therefore misses its target, which it had lost sight of before, or rather never clearly seen. What it tells us may be informative in regard to this or that psychological precondition or component of our intuitively achieved consciousness of universality, or in regard to the psychological role of signs in directing unitary trains of thought etc. etc. This has, however, no immediate relevance to the objective use of universal meanings, and to the undoubted truth enshrined in talk about universal objects (subjects, singulars) and in predications which relate to these; that it has mediate relevance must first be established. Mill's conception, like all empiricistic conceptions, can indeed not appeal to such evident starting-points or goals, since its whole concern is to prove the nullity of what such self-evidence shows to have genuine subsistence, namely universal objects and the universal presentations in which such objects are constituted for consciousness. Expressions such as 'universal object', 'universal presentation' certainly arouse memories of old, burdensome errors. But, + +however much they may have been historically misinterpreted, they must still have a normal interpretation which justifies them. Empirical psychology cannot teach us this normal meaning: we can learn it only by going back to the self-evident sense of propositions which are built upon general presentations and which relate to general objects as subjects of their predications. + +**§ 15** *(b)* **The origin of modern nominalism as an exaggerated reaction to Locke's doctrine of general ideas. The essential character of this nominalism, and of the theory of abstraction in terms of attention** + +The theory of abstraction held by Mill and his empiricist followers, like the theories of abstraction held by Berkeley and Hume, gets stuck in its attack on the error of 'abstract ideas'. It gets stuck by allowing itself to be misled by the chance circumstance that Locke, in his interpretation of general ideas, hit on his absurd general triangle: it thinks that serious talk of such ideas necessarily demands Locke's absurd interpretation. The fact is overlooked that this error is especially due to the unclarified ambiguity of the word 'idea' (and of the German word *Vorstellung),* and that what is absurd for one concept of 'idea' is possible and justifiable for another. How could this fact be apparent to Locke's opponents, when their notion of an 'idea' remained in the same obscurity that had misled Locke? In consequence of this fact, men fell into that *modern nominalism,* whose essence no longer lies in the rejection of realism, but of what is, properly speaking, conceptualism. Not only did men reject the absurd general ideas of Locke, but also general concepts in the full, true sense of the word, in the sense, that is, that is evidently revealed by an analysis of the objective meaning-content of our thinking as constitutive of the Idea of what is a unity-for-thought *(Denkeinheit).* + +Such a view is fostered by wrongly interpreted psychological analyses. We tend naturally to turn our gaze among logical phenomena to whatever has primary intuitive palpability; we are then misled into taking the inner pictures which are found to accompany our names as the meanings of those names. If we become clear, however, that a meaning is merely what we mean, or what we understand by an expression, we cannot maintain such a conception. For if meaning consisted in the intuitive individual presentations which 'illustrate' the sense of general names, the objects of such presentation, precisely as they are intuitively presented, would be just what we meant by those names, and each name would be an equivocal proper name. To cope with such differences, intuitive individual presentations are said to sustain new psychological functions when they occur in association with general *names:* they determine other trains of ideas, they fit otherwise into the course of our thoughts, they influence this course in a different fashion. All this is quite irrelevant to the phenomenological facts. Here and now, at the very moment that we significantly utter a general name, we mean what + +is general, and our meaning differs from our meaning when we mean what is individual. This difference must be pinned down *in the descriptive content of the isolated experience,* in the individually and actually performed general assertion. What things are causally connected with such an experience, what psychological consequences may follow from it, all this does not concern us. Such things concern the psychology of abstraction, not its phenomenology. The nominalistic currents of our time have certainly threatened to change our notion of conceptualism so that the nominalism of John Stuart Mill, avowed by him so decisively, has lately been disputed. 3 We should not, however, see it as the essence of nominalism that, in its attempted clarification of the sense and theoretical achievement of universals, it loses itself in a blind associative play of names as mere verbal noises; its essence lies in the fact that its attempted clarifications overlook the *peculiar consciousness* exemplified in our living sense of the meaning of signs, in our actual understanding of them, in the grasped sense of our assertions, and also exemplified in correlative acts of fulfilment, which yield us the 'true' Idea of the universal, the wholly evident ideation in which the universal 'itself' is given to us. This consciousness means what it means to us, whether or not we know anything about psychology, or about mental antecedents and consequences, associative dispositions, etc. **If** the nominalist wishes to give an empirical explanation of this consciousness of the universal, as a fact of our human nature, if he wishes to connect it causally with such and such factors, such and such previous experiences, such and such unconscious dispositions, we should not object in principle. We should merely deny the interest, for pure logic and epistemology, of such empirical psychological facts. Instead of this, however, the nominalist says that to differentiate general ideas from individual ones, and to oppose the former to the latter, is really to talk senselessly. He denies that there is abstraction in the sense of a peculiar consciousness of the universal which lends evidence to general names and meanings: in reality only individual intuitions exist, some with an interplay of conscious and unconscious happenings, which never take us beyond the sphere of what is individual, nor constitute, i.e. bring to awareness and perhaps to self- + +presentation, any essentially new sort of objectivity. + +Each thought-experience, like every mental state, has, empirically treated, its descriptive content, as well as its causal antecedents and consequents; it makes itself felt in the rush of life, and exercises its productive functions. But in the field of *phenomenology* and, above all, in the sphere of *epistemology* the phenomenological clarification of ideal thought- and knowledge-unities - only essence and sense matter: what we mean when we make assertions, what object is set up for us by our act of meaning as such, in virtue of its sense, what partial meanings enter essentially into the make-up of our act of meaning, what essential forms and differences it exhibits, and so on. What is of interest to epistemology, must be shown up exclusively in the *content* of the *meaning-experiences and the fulfilment-experiences themselves,* and be + +shown up as essential. If we also find, in the range of what can be thus evidently shown up, the distinction between universal presentations and individual, intuitive presentations (which we undoubtedly do), then no talk of genetic functions and associations can be relevant to such a distinction, + +or contribute a jot to its clarification. + +It carries the matter no further and fails to remove our objections, if, like Mill, we look on *exclusive attention* to some single attribute (or dependent feature) of the intuited object, as being the act which, in our actual consciousness, in the supposed genetic situation, gives the name its 'generic' meaning. Though recent thinkers, who share Mill's ideas without sharing his extreme empiricist tendencies, may call themselves 'conceptualists', thinking that the interest which turns 'attributes' into objects will also guarantee the existence of general meanings - their doctrine is and remains essentially + +nominalistic. + +*Generality* remains for them a matter of the associative function of signs, it consists in the psychologically regulated association of 'the same sign' with 'the same' objective feature - or rather with the feature which always recurs in the same determinate form and is at times emphasized by attention. This *generality of a psychological function* is, however, quite removed from the *generality which belongs to the intentional content of the logical experiences themselves,* or which, described objectively and ideally, belongs to our *meanings and our meaning-fulfilments.* This last generality escapes + +nominalism entirely. + +**§ 16 (c) Generality of psychological function and generality as a meaning-form. Different senses of the relation of a universal to an extension** + +To bring complete clearness to this important distinction between generality of psychological function, and generality as pertaining to a significant content itself, we must pay heed to the differing logical functions of general names and meanings, and in connection therewith to the differing senses of talk of their generality, or of their relation to a range of particulars. + +Let us set the following three forms side by side: *an A, all A, A in general,* e.g. *a triangle, all triangles, the triangle,* the last taken as in the sentence 'The + +triangle is a species of figure'. 4 + +The expression 'an *A'* can function predicatively as the predicate of innumerable categorical assertions, and the aggregate of the true, or intrinsically possible assertions of this sort, determines all the possible subjects to which being an *A* either actually pertains, or could without contradiction pertain, in other words the actual or possible 'range' ('extension') of the 'concept' *A.* This universal concept *A,* or the universal predicate 'an *A',* applies to all the objects in this range - we take for the sake of simplicity the range to which it applies truly - i.e., the assertions in the aggregate in question are all true: + +there are, phenomenologically speaking, as possibilities, self-evident judgements with a corresponding content. This generality belongs, therefore, to the logical function of the predicate; it is not represented in the individual act, the single case where the meaning *an A* is enacted, or where we mean the corresponding adjectival predicate. It appears in these only as a form of indefiniteness; the word 'A' expresses a form, which evidently pertains to our meaning-intention or our meaning-fulfilment, and is connected with *what* either intends. This form is a wholly irreducible moment; its peculiarity can only be recognized, not explained away by any sort of psychologicalgenetic treatment. Ideally put: the word 'A' expresses a primitive logical form. The same plainly holds of the formation 'an *A',* which likewise rep- + +resents a primitive logical structure. + +The generality of which we are here speaking, belongs, we say, to the *logical* function of predicates, it consists in the *logical possibility* of propositions of a certain sort. We stress the logical character of this possibility, to show that we are concerned with a possibility that can be seen *a priori* to belong to meanings as Specific Unities, not to psychologically contingent acts. If we see that Red is a universal predicate, one associable with many possible subjects, our meaning no longer relates to something whose existence is in a real *(realen)* sense governed by those natural laws which govern the coming and going of experiences in time. We are not talking of experiences at all, but of the single self-identical predicate Red, and of the possibility of certain sentences, each single in the same sense, in which this same predicate + +occurs. + +If we now pass to the form 'all *A's',* generality pertains to the form of the act itself. We expressly mean *all A's,* to all such *A's* our presentation and predication relates in the universal judgement, though perhaps no single *A* is 'itself' 'directly' presented. This idea of a range, is however, no complex of the ideas of the members of this range; so little is this the case, that such individual presentations as perhaps float before us have nothing at all to do with the significant intention to *all A's.* Here also the word 'all' points to a peculiar semantic form: we leave aside the question whether it can be + +resolved into simpler forms or not. + +Ifwe deal finally with the form *the A (in specie),* generality again pertains to our significant content itself. Here, however, we encounter a wholly different sort of universality, the universality of the Species, which, while it may have the closest *logical* relations to universality of range, none the less evidently differs from the latter. The forms *the A* and *all A's* -likewise *any A, no matter which* are not the same in meaning: theirs is no mere grammatical difference, determined in the end by mere verbal noise. They are *logically* distinct forms, giving expression to essential differences of meaning. The consciousness of Specific Generality must count as an essentially new mode of 'presentation', as one, namely, that does not merely present individual singulars in a new manner, but makes us aware of a new sort of singulars, + +i.e. Singular Species. What sort of singulars these are, and how they stand *a priori* to individual singulars, or how they differ from these latter, must of course be gleaned from the logical truths which, grounded in pure forms, govern both sorts of singulars and their mutual *a priori* relations (i.e. their relations of essence or Idea). Here there is no obscurity or possible error as long as one keeps to the straight sense of these truths, or, what is the same, to the straight sense of the meaning-forms in question, whose self-evident interpretations are called truths of logic. Only an erroneous sideslip into psycho logistic and metaphysical trains of thought produces obscurity; it creates pseudo-problems and frames pseudo-theories to solve + +them. + +**§ 17** *(d)* **Application to the critique of nominalism** + +If we now look back on the nominalistic theory of abstraction, we see from the above that its main error lies in quite ignoring the irreducible peculiarities of the forms of consciousness (of the forms of our intentions and of their correlative fulfilments). Its defective descriptive analysis makes it blind to the fact that the forms of logic are no more than these forms of significant intention which have themselves been made objects of a consciousness which treats them as unities, and so turns them into Ideal Species. Generality is also to be found among these forms. Nominalism further confuses the various concepts of generality that we have separated above. It one-sidedly prefers the generality which belongs to concepts in their predicative function, as a possibility of associating the same concept predicatively with several subjects. Being blind to the logically ideal character of this possibility, with its roots in semantic form, it puts psychological associations in its place, associations necessarily alien to, even incommensurable with, the predicates and propositions in question. Since it claims to have completely cleared up the nature of general meanings through such psychological analyses, its confusions grossly distort the generality of universal and specific presentations; this generality we saw belonged to the semantic essence of the individual act as such, as an indwelling meaning-form. What belongs phenomenologically to the immanent essence of the individual act, is turned into a psychological play of events, that throw no light, whether as causes or effects, on the individual act in which the entire total consciousness of + +universality comes alive. + +**§ 18 The doctrine of attention as a generalizing power** One last critical observation will of course not affect certain recent followers of Mill (or, more remotely, of Berkeley), who recognize a distinct problem in the emergence of the Species as an undifferentiated unity opposed to its manifold cases, and who do not attempt to solve it by having recourse to the + +generality of associative functioning, or to the general application of the + +same name and concept to all objects in their range. + +Their idea runs as follows: + +*Abstraction as exclusive concern* eo ipso *produces generalization.* The abstracted attribute is *de facto* an element in the appearance of the individual complex of attributes that we call the phenomenal object. But the 'same' attribute, i.e. one fully agreeing with it in content, can occur in countless such complexes. What distinguishes the repetitions of this same attribute from case to case, is uniquely and solely their individualizing association. Abstraction, therefore, as exclusive concern, causes the distinction, the individualization, of what is abstracted to vanish. The reverse side of our concentrated concern is the ignoring of all individualizing aspects, which yields the attribute as what is everywhere one and the same, since it cannot present + +itself as different to the abstraction performed in each case. + +**In** this conception, it is said, we have all we need for the understanding of general thinking. Here it will be best to let the inspired Bishop of Cloyne speak, since it was he who first inspired the doctrine in question, though his own doctrine also gave influence to other thoughts than are here touched + +upon. It seems, he thinks, to be a difficulty + +how we can know any proposition to be true of all particular triangles, except we have first seen it demonstrated of the abstract idea of a triangle which equally agrees to all. For, because a property may be demonstrated to agree to some one particular triangle, it will not thence follow that it equally belongs to any other triangle, which in all respects is not the same with it. For example, having demonstrated that the three angles of an isosceles rectangular triangle are equal to two right ones, I cannot therefore conclude this affection agrees to all other triangles, which have neither a right angle nor two equal sides. It seems therefore that, to be certain this proposition is universally true, we must either make a particular demonstration for every particular triangle, which is impossible, or once for all demonstrate it of the abstract idea of a triangle, in which all the particulars do indifferently partake, and by + +which they are all equally represented. + +To which I answer, that though the idea I have in view whilst I make the demonstration, be, for instance, that of an isosceles rectangular triangle, whose sides are of a determinate length, I may nevertheless be certain it extends to all other rectilinear triangles, of what sort of bigness whatsoever. And that, because neither the right angle, nor the equality, nor the determinate length of the sides, are at all concerned in the demonstration. It is true, the diagram I have in view includes all these particulars, but then there is not the least mention made of them in the proof of the proposition. It is not said, the three angles are equal to two right ones, because one of them is a right angle, or because the + +sides comprehending it are of the same length. Which sufficiently shows that the right angle might have been oblique, and the sides unequal, and for all that the demonstration have held good. And for this reason it is, that I conclude that to be true of any obliquangular or scalenon which I had demonstrated of a particular right-angled, equicrural triangle; and not because I demonstrated the proposition of the abstract idea of a triangle. And here it must be acknowledged, that a man may consider a figure merely as triangular, without attending to the particular qualities of the angles, or relations of the sides. So far he may abstract: but this will never prove that he can frame an abstract general inconsistent idea of a triangle. In like manner we may consider Peter so far forth as man, or so far forth as animal, without framing the forementioned abstract idea, either of man or of animal, inasmuch as all that is perceived is not + +considered.5 + +**§ 19 Objections. (0) Exclusive attention to one attributive aspect does not remove its individuality** + +That we must reject this conception, so attractive at first sight, is clear when we envisage the aim that a theory of abstraction must subserve, i.e. the clarification of the difference between general and individual meanings, the setting forth of its intuitive essence. We must envisage those intuitive acts in which mere verbal intentions, symbolic meanings, are intuitively fulfilled, and so fulfilled that we can see what is 'really meant' by our expressions and our meanings. Abstraction must here be the act, in which the consciousness of universality, as fulfilment of the intention of general names, is achieved. We must bear this in mind. Let us now consider whether selective attention is capable of the performance just set forth, and particularly on the assumption so essential to the theory: that the content which abstractive attention selects is a *constitutive aspect* of the concrete object of intuition, a property + +really present in it. + +However attention may be characterized, it is a function which, in a descriptively peculiar fashion, *prefers* certain objects of consciousness, and which (apart from certain differences of degree) only differs from one case to another in virtue of the objects to which it gives this preference. The theory, therefore, which identifies abstraction with attention, can see no essential difference between the meaning of the individual which pertains to the intention of proper names, and the meaning of the universal which attaches to the names of attributes. The difference consists merely in the fact that, in the one case, our mind's eye, as it were, fixates the whole individual object, in the other case, only the attribute. We must ask, however, whether the attribute which, in the sense of the theory, forms a *constituent property of the object,* must not be as precisely and individually singular as the whole + +object. Suppose we concentrate attention on the green of the tree which stands before us. If this can be done, let us increase our concentration till we achieve the complete unawareness of associated aspects which Mill thought possible. Then, it is said, all graspable points from which individualizing distinction can be carried out have vanished. If another object with exactly the same colouring were suddenly substituted, we should see no difference; the green, which we are exclusively minding, would for us be one and the same. Suppose all this is so. *Would* this green, however, *really* be the same as the other? Can our forgetfulness or deliberate blindness towards all that is distinctive, alter the fact that what is objectively distinct is still as distinct as before, and that the objective aspect we are heeding in *this* aspect which + +exists here and now and no other? + +We surely cannot doubt that such a difference really exists. Comparison of two concrete, separated phenomena of the same quality, e.g. green, evidently shows that each has *its own* green. The two phenomena have not become fused, they have not the 'same' green in common as something individually identical. The green of the one is rather as much separated from the green of the other, as are the concrete wholes in which these 'greens' are. How else could there be qualitatively patterned unities in which the same quality occurs repeatedly, and what would it mean to speak of the spread of a colour over a whole surface? Each geometrical fragmentation of the surface evidently corresponds to a fragmentation of the unitary colouring, even though, when the colouring is exactly alike, we say, and say rightly, + +that 'the' colour is the 'same' everywhere. + +Our theory therefore does not throw light on the sense of talk about an identically single attribute, about the Species as a unity in multiplicity. Such talk, it is clear, means something different from the objective aspect, the instance of the Species which occurs in the sensuous phenomenon. Assertions significant and true for the instance are false and even nonsensical for the Species. The colouring has its place and its time, it is spread out and has its intensity, it arises and vanishes. Applied to the colour as Species these predicates yield complete nonsense. When a house burns down, all its parts burn down: its individual forms and qualities, its constituent parts and aspects, all are gone. Shall we say that the relevant geometrical, qualitative and other Species have been burnt? Is such talk not the height of absurdity? To sum up, if the attention-theory of abstraction is correct, if, as it supposes, attention to the whole object, and attention to its parts and aspects, are in essence one and the same act, only distinct in respect of the objects to which this act is directed, then there are no Species for our consciousness, for our knowledge, or for our statements. However we distinguish or shift matters around, consciousness always directs itself to what is individually singular, which is present to it as individually singular. One cannot, however, deny that we speak of Species in a distinct sense, that in countless cases + +we both mean and give a name, not to the individual, but to its Idea, that we can make assertions having what is ideally one as their subject, just as we can make assertions about what is individually singular. Our theory has therefore missed its target, its aim was to clarify our consciousness of the universal, and it has managed to lose sight of this consciousness in the course + +of its clarifications. + +**§20** *(b)* **Refutation of the argument from** + +**geometrical thought** + +How do matters stand in regard to the advantages claimed for the theory as making general thinking understandable? Is Berkeley not right in insisting that, when we prove a proposition relating to all triangles, we have, on any occasion, only one individual triangle in mind, the one in our drawing, and that we only make use of the features that characterize a triangle as a triangle, while ignoring all others? 'We only make use of these features' means that we attend to them only, make them objects of an exclusive attention. We can therefore get along without assuming general ideas. We can certainly get along without general ideas if by the latter we mean the general ideas of Locke's doctrine. But to avoid this shoal we need not lose ourselves in the false paths of nominalistic theory. We may in essentials approve of Berkeley's account while we reject the interpretation he puts upon it. He confuses the basis of abstraction with what is abstracted, the concrete instance, from which our consciousness of the universals draws intuitive fulness, with the object our thought intends. Berkeley speaks as if geometrical proofs were conducted for the triangle drawn in ink on the paper or in chalk on the blackboard, as if the chance singulars which float before us in general thought, were not mere aids to our thought's intention, but its actual objects. A geometrical procedure that took its lead from the *drawn* figure in Berkeley's sense, might yield astonishing results, but scarcely very happy ones. No geometrical proposition holds for the drawn figure as a physical object, since the latter is not really rectilinear, nor a geometrical figure at all. We can find no ideal geometrical properties in it, as colour is found in an intuited coloured object. Certainly the mathematician looks at the drawing, which appears to him just as other intuited objects do. In none of his acts of thought, however, does he *refer* to this drawing, nor to any individual feature in it. He refers, if he does not wander, to 'a rectilinear figure as such'. This thought forms the subject-member of his theoretical proof. What we therefore *attend to,* is neither the concrete object of intuition, nor an 'abstract partial content' (i.e. a non-independent aspect) in the latter; it is an Idea, in the sense of a Specific Unity, as abstractum in the logical sense. In logic and epistemology, therefore, abstraction must not be said to be a mere stress on a partial content, but a peculiar consciousness which, on + +**§21 The difference between attending to a** + +**non-independent moment of an intuited object and attending to the corresponding attribute** *in specie* + +It will not be profitless to explore the difficulties of our contested theory a little further. Our own conception will become clearer when its whole + +contrast with this theory has been worked out. + +Concentrated attention to an attributive moment is looked on as intuitively fulfilling (as yielding the 'true sense') of the general meaning attaching to the name of the corresponding attribute. To mean the Species intuitively, and to perform an act of concentrated attention, are looked on as one and the same. But how do things stand, we may ask, in cases where *we expressly refer to the individual moment?* What differentiates the two types of case? If we are struck by an individual trait of an object, by its peculiar colouring, e.g., or by its noble form etc., we pay special attention to this trait, and yet have no general presentation. The same question applies to complete concrete things. What is the difference between exclusive attention to the individually apparent statue, and the intuitive grasp of the corresponding Idea, + +that could be realized in countless real statues? + +Our opponents might reply: in individual treatment, individualizing moments enter our sphere of interest, in specific treatment, they are shut out. Our interest is confined to what is general, i.e. to a content which in itself provides no individual distinctions. Instead of pressing our previous objection - whether attention to individuating determinations creates individuality, while inattention destroys it - we ask rather whether, in individual treatment, we also necessarily *mean* the individuating moments, which it is held must be concurrently noticed? Does an individual proper name also implicitly name individuating determinations, those, e.g., of time and place? Here is my friend Hans and I call him 'Hans'. He is no doubt individually determined, he is always at a particular point in space and time. If these determinations were, however, concurrently meant, the name 'Hans' would change its meaning with every step that my friend takes, on every occasion that I address him by name. Such a thing can scarcely be maintained, nor would one care to take refuge in saying that a proper name is really general. For the peculiar generality in respect of the varied times, positions, situations of the same individual thing differs in form from the specific generality + +of the thing's attribute or of the generic Idea 'thing in general'. + +Often enough, at least, we are indifferent to the here and the now in attending to some part or characteristic trait of an object. We do not therefore consider it *in specie,* as we certainly do not mean to perform an 'abstraction' + +in the sense of a general presentation. + +Perhaps one might here have recourse to the assumption that individuating determinations are *marginally* noticed. This cannot give much help. A great deal is marginally noticed, but is not for that reason really meant. Where the + +consciousness of the universal is intuitively achieved, as a true and genuine abstraction, the individual object of the underlying intuition certainly has a subsidiary place in consciousness, but is not at all meant. Mill's talk about our unconsciousness of the determinations that we abstract from is a useless, strictly speaking an absurd fiction.6 In the numerous cases where, looking to some singular intuitive fact, we utter the corresponding generality, the singular element stays before our eyes, we do not suddenly become blind to what is individual in our case; this certainly does not happen when, e.g., we look at this jasmine in bloom, and inhaling its scent, say 'Jasmine has a + +heady scent'. + +If finally one grasps at a new evasion and admits that the individuating element is not specially picked out like the preferred point of our interest, not even marginally noticed, as are objects lying outside of our main interest, but that it is rather *subsidiarily* noticed *(mitbeachtet),* as being part of our main interest and peculiarly implied in its intention - then the whole ground of the theory is abandoned. For the theory claimed to make do with the mere emphasis of regard towards the concrete given object, or a peculiar feature given in it, and it now ends by postulating a variety of forms of + +consciousness that it should surely have dispensed with. + +**§22 Fundamental deficiencies in the phenomenological analysis of attention** + +This leads us at once to the weakest point of the theory; which is to be found in the question 'What is attention?' We are of course not reproaching the theory for failing to offer us a perfected phenomenology and psychology of attention, but for failing to clear up the nature of attention to an extent absolutely required by its aims. It should have ascertained what gives the word 'attention' its unitary sense, in order to see how far its range of application extends, or what the objects in each case are that we can (in a normal sense) claim to attend to. Above all, it should have inquired into the relation of attention to the meaning or reference which gives names and other expressions their significance. The sort of theory of abstraction just disputed, is possible only through the Lockean prejudice according to which the objects to which consciousness in its acts is immediately and properly directed, and the objects, particularly, of attention, must necessarily be mental contents, real occurrences in consciousness. It seems perfectly obvious that an act of consciousness can immediately act only on what is actually *(wirklich)* given in consciousness, i.e. on contents that it *really (reell)* includes among its elements. What is outside consciousness can only be the mediate object of a conscious act; and this occurs simply when the immediate content of the act, its primary object, serves as a representation, an image, a sign, of + +Once accustomed to this mode of approach, one readily tries to clear up the objective relations and forms inherent in the intention of acts, by looking predominantly to their present conscious contents as their supposedly immediate objects, and, misled by the seeming intelligibility of talk about representations and signs, entirely ignores the true, supposedly mediate objects of the acts. Unthinkingly one credits to *contents* everything which acts, in their straightforward reference, place in the *object;* its attributes, its colours, forms etc., are forthwith called 'contents' and actually interpreted + +as contents in the psychological sense, e.g. as sensations. + +How far this whole conception is at odds with the plain phenomenological situation, and how thoroughly it has debauched epistemology, we shall yet have many opportunities to observe. Here it may suffice to point out that when, e.g., we have a presentation or judgement about a horse, it is a horse, not our sensations of the moment, that is presented and judged about. Our sensations are only presented and judged about in psychological reflection, whose modes of conception should not be read into the immediate situation. That an appropriate train of sensations or images is *experienced,* and is in this sense conscious, does not and cannot mean that this is the *object* of an act of consciousness, in the sense that a perception, a presentation or a + +judgement is directed upon it. + +This mistaken conception has further had a detrimental effect on the theory of abstraction. Led astray by the seemingly obvious, one takes experienced contents to be the normal objects to which one pays attention. The concrete phenomenal thing is treated as a complex of contents, i.e. of attributes grown together in a single intuitive image. And it is then said of these attributes, taken as experienced mental contents, that their non-independence precludes their separation from the concretely complete image: they can only be noticed in the latter. How could such a theory of abstraction intelligibly account for the formation of abstract ideas of that class of attributive determinations which are indeed perceived, but which by their nature never are adequately perceived, which cannot be given in the form of a mental content? I need only mention three-dimensional spatial shapes, in particular closed surfaces of solids or complete solids, such as the sphere and the cube. And how does the matter stand with the myriads of conceptual presentations, perhaps realized with the help of sensuous intuition, but which no intuitive aspect, even from the sphere of inner sense, instantiates? Here one can certainly not talk of a mere heeding of what is given in (sensuous) + +intuition, nor of a heeding of experienced contents. + +Our own point of view inclines us first to draw a distinction in the sphere of sensuous abstraction - the sphere usually stressed for simplicity's sake between acts in which an attributive aspect is intuitively 'given', and acts built upon these, which are not mere acts of attention to such an aspect, but rather acts of a new kind, referring in general fashion to the corresponding Species. Whether intuition presents the attributive aspect adequately or in- + +adequately, is beside the point. We should then draw the further distinction between cases of sensuous abstraction, i.e. of an abstraction straightforwardly and perhaps adequately adjusted to sensuous intuition, and cases of non-sensuous or of at most partially sensuous abstraction, i.e. cases where the realized consciousness of the universal is at most only partially built on acts of sensuous intuition, and for the rest on non-sensuous acts, and accordingly related to thought-forms or categories whose nature does not permit of sensuous fulfilment. Suitables examples of the former, are unmixed concepts from outer or inner sense, such as colour, noise, pain, judgement, will, of the latter, concepts such as series, sense, disjunctive member, identity, being etc. etc. This difference will again seriously engage us in future investigations. + +**§23 Significant talk of attention embraces the whole sphere of thinking and not merely the** + +**sphere of intuition** + +The unitary sense to talk of 'attending' so little calls for 'contents' in the psychological sense (as the objects to which we attend), that it ranges beyond the sphere of intuition, and embraces the whole sphere of thinking. It makes no difference how thought is conducted, whether on an intuitive basis or in pure symbols. If we are theoretically concerned with *the culture of the Renaissance,* with *ancient philosophy,* with *the development of astronomical ideas,* with *elliptical functions,* with *curves of the nth order,* with *laws of algebraic operations* etc., we attend to all these matters. If our judgement is of the form *All A's are B's,* our attention is given to this universal state of affairs, we are concerned with allness, and not with this or that single matter. And so in general. Each thought, or at least each consistent thought, can no doubt become intuitive, to the extent that it is built in a certain fashion on 'corresponding' intuition. But the attention performed on such an intuition, whether of inner or outer sense, does not amount to attention to that intuition's phenomenological content, and just as little to attention to the object apparent in it. The *a certain,* or the *any,* the *all* and the *each,* the *and,* the *or,* the *not,* the *if* and the *then* etc., are not things we can point to in an object of basic sensuous intuition, that can be 'had' sensationally or externally represented or painted. Certain acts naturally correspond to all of them. The words have their meaning; in understanding them we realize certain forms pertaining to our objective intention. But these acts are not the *objects* that we mean: they are the activity of meaning or presenting, which only becomes objective to psychological reflection. The *object* we mean is variously the universal state of affairs *All A's are B's,* or the generic state of affairs *The A (in specie)* is *a B,* or the indefinitely singular state of affairs *Any A* is *a B* etc. We do not attend to the individual intuition, which perhaps accompanies our thought-presentations, and on which their evidence is founded: we do not attend to those act-characters + +which either give our intuition form, or which find their fulfilment in formed intuition. What we attend to are the *objects of our thinking,* the objects and states of affairs seen by thought in this or that manner, which are revealed to our insight when we perform such acts on such a foundation. And an abstraction in which we seize some point of conception or meaning, where we do not merely look to what is individual and intuitive (perceiving it attentively and what not), means no more than that we perform certain thought-acts with insight, acts sometimes of one form and sometimes of + +another. + +The range of the unitary notion of attention is therefore so wide that it doubtless embraces the whole field of intuitive and cogitative *reference (Meinens),* the field of presentation *(Vorstellens)* in a well-defined but sufficiently wide sense, which comprehends both intuition and thought. Ultimately it extends as far as the concept: Consciousness of something. To talk distinctively of attention, as of a certain selectivity in the sphere of consciousness, takes account therefore of a certain difference which is not dependent on the species of our mode of consciousness (on the manner of our consciousness). We have certain 'presentations' while not 'concentrating' + +on their objects, but upon the objects of other presentations. + +Attending is thus represented as a straightforward, not further describable *way* in which contents, otherwise lost in the undivided flow of consciousness, achieve separate consciousness, in which they are 'emphasized' or 'discovered' by us. If, in a similar sense, all differences in the manner of presentation are denied, attention is then seen as an illuminating and indicative function operating within *this* field. But all this involves an extreme narrowing of concepts whose wider meanings cannot be eliminated, and to which one must unavoidably have recourse. Dazed by the confusion between object and mental content, one forgets that the objects of which we are 'conscious', are not simply *in* consciousness as in a box, so that they can merely be found in it and snatched at in it; but that they are first *constituted* as being what they are for us, and as what they count as for us, in varying forms of objective intention. One forgets that, from the mere finding of a mental content, i.e. the pure immanent intuition of such a content, up to the external perception and imagination of objects neither found immanently in consciousness, nor capable of being so found, and from these on to the loftiest thought-formations with their manifold categorial forms and appropriately correlated semantic forms, an *essentially* single concept runs continuously: in all cases, whether we *intuit* in perceptual, fancying or remembering fashion, or whether we think in empirical and logico-mathematical forms, an intending, or reference *(Vermeinen)* is present, that *aims* at an object, a consciousness is present that is the consciousness *of* this object. The mere existence of a content in the psychic interplay is, however, not at all this being-meant or being-referred-to. This first arises when this content is 'noticed', such notice being a look directed towards it, a presentation of + +it. To define the presentation of a content as the mere fact of its being experienced, and in consequence to give the name 'presentations' to all experienced contents, is one of the worst conceptual distortions known to philosophy. It is without doubt responsible for an untold legion of epistemological and psychological errors. If we stick to the intentional concept of presentation, which alone sets a standard for epistemology and logic, we shall be unable to judge that all differences between presentations reduce to differences in their presented 'contents'. It is clear, on the contrary, and particularly in the field of pure logic, that *to each primitive logical form a peculiar 'manner of consciousness', a peculiar 'manner of presentation',* corresponds. In so far, of course, as *each new mode of intentional reference always in a manner also concerns objects,* i.e. constitutes novel forms with which the object is brought to consciousness, one can no doubt say that all difference in presentation lies in what is presented. One must carefully note, however, that there are *two sorts of differences in the object, in what is presented,* differences of *categorial form* and differences in the *'thing itself';* this 'thing' can be brought to consciousness *as* the same in a variety of forms. More will + +be said on these heads in later Investigations. + +**Abstraction and representation** + +**§24 The general idea as a device for economizing** + +**thought** + +There is an error originating from mediaeval nominalism which likes to represent general concepts and names as *mere devices* in an economy of thinking, devices which will spare us the individual consideration and naming of all individual things. The function of concepts, it is said, is to enable the thinking mind to transcend the limits set it by the unsurveyable multiplicity of individual singulars; their economizations of thinking enable the mind to reach its goal of knowledge indirectly, as it could never have reached it directly. General concepts make it possible for us to treat things in bundles as it were, to make assertions about whole classes of objects at a single 'go'; we can therefore talk about countless objects, instead of conceiving and + +judging each object 'on its own'. + +Locke brings this thought into modern philosophy when he says, e.g., in the last part of Book III, chapter III of his *Essay .* .. 'that men making abstract ideas, and settling them in their minds with names annexed to them, do thereby enable themselves to consider things, and discourse of them as it were in bundles, for the easier and readier improvement and communication of their knowledge; which would advance but slowly were their words and + +thoughts confined only to particulars'. 1 + +This exposition reveals itself as nonsensical if one reflects that, without general meanings, one can make no assertions at all, not even such as are singular, and that one cannot talk of thinking, judging or knowing, in a sense relevant to logic, on a mere foundation of the direct presentations of individuals. The most ideal adaptation of the human mind to the multiplicity of individual things, the genuine, effortless realization of adequate individual conceptions, would not render thought superfluous. For performances attain- + +able in this manner are not performances of thinking. + +Along intuitive pathways, e.g., no laws come to light. A knowledge of laws may very well promote the survival of thinking beings, it may usefully govern the formation of forward looking intuitive presentations, and may + +be much more useful in this respect than the natural pull of association. But the relation of the function of thought to the preservation of thinking beings, i.e. of human beings, has its place in psychological anthropology, not in the theory of knowledge. What is performed by a law as an ideal unity, its *logical* embrace of innumerable instances in a general propositional meaning, is something that no intuition can perform, not even the universal intuition of a God. For to intuit is plainly not to think. The perfection of thought lies doubtless in intuitive, i.e. in 'authentic' thinking, in that knowledge in which our thought-intention is 'satisfied' (as it were) by passing over into intuition. Even the brief discussions of the previous chapter permit us, however, to speak of a grave misinterpretation of this fact, when intuition - understood in the usual sense of acts of external or internal sense - is regarded as the proper intellectual function, and when the true role of conceptual thought is taken to be its use of indirect devices which economize intuition, and overcome the all too narrow limits of the latter. Certainly we are accustomed to using an all-seeing mind as a logical ideal, but only because we quietly add to its all-seeing capacities, capacities for knowing and thinking all. We imagine this mind as one not merely active in mere intuitions, i.e. in intuitions perhaps adequate but none the less unthinking, but as also casting these intuitions into categorial forms and combining them synthetically, and finding in such formed, combined intuitions the ultimate fulfilment of its thought-intentions, thereby realizing the ideal of all-inclusive knowledge. We shall, therefore have to say: Not mere intuition, but adequate, categorially formed intuitions, completely accommodated to thought, or conversely, thought which draws its evidence from intuition, constitute the goal of true knowledge. The 'economy of thought' only makes sense, and has its rich field within the sphere of thought and knowledge: it is + +in fact really an economy of knowledge. 2 + +**§25 Whether general representation can serve as an essential characteristic of our general presentations** The notion just sketched of general concepts as thought-saving devices is more fully elaborated in the theory of *representation.* There are, it is held, really only intuitive, individual presentations, and in these all thinking is carried on. Need or comfort, however, leads us to substitute certain ideas to do duty for the presentations that we ought properly to have. The ingenious device of a *general representation which relates to a whole class* has the same results as if the proper presentations were present, or results rather in concentrated performances which sum up all the individual results that could + +ever be reached through actual presentation. + +This doctrine, likewise, is naturally refuted by our previous objections. But the thought of representation plays a part, also, in doctrines of abstraction that attach little or no weight to the supposedly valuable thought-economies + +that such a representative function effects. It may be asked whether the thought of such a representation, freed from all doctrines of thoughteconomy, might not be of some use in characterizing the essence of general meanings. The word 'representation' has in any case a shifting multiplicity of senses, One could certainly say that the general name, or the individual intuition on which it reposes, serves to 'represent' the class. One must, however, see whether the various meanings of the word are not mutually confusing, and whether its use in a characterization does not promote confusion + +and definite error rather than clarity. + +Our discussions have shown that the mark which distinguishes general presentations ~ whether we understand by these general meaning-intentions or the corresponding fulfilments of meaning ~ from intuitive individual presentations, can be no mere difference of psychological function, no mere difference in the part played by certain individual presentations of inner or outer sense in the continuous stream of mental life. We need not, accordingly, pay any further attention to expositions of the theory of representation merely as such a psychological function, and say nothing about the fundamental phenomenological fact, the new modes of consciousness responsible for the whole character of our individual experiences of general expression and thinking. This cardinal point may be touched on here and there in passing: individual utterances show that the phenomenological facts are not wholly ignored. Such theorists would in most cases reply to our remonstrances that what we emphasize is, likewise, what they think. Naturally the representative function will reveal itself by way of some phenomenally peculiar character. A general presentation is thereby only an individual presentation, but one *tinged in a somewhat distinctive manner:* what is intuitively presented, when tinged in this fashion, counts as a *representative* of a whole class of mutually resembling individuals. Such a concession will not help much, if what is logically and epistemologically most important gets treated as a trivial addition to an individual intuition, making no important difference to the descriptive content of such an experience. The new type of act which animates word and illustrative image with thought, may not be wholly overlooked, but is not thought to require special descriptive interest directed upon itself: superficial talk of 'representation' is treated as quite sufficient. Men do not see that everything that relates to logic is summed up in this, and in similar characters of acts, that wherever we talk logically about 'presentations' and 'judgements' and about their manifold forms, acts of this sort alone determine our concepts. Men do not see that it is the immanent essence of such act-characters that makes them the consciousness of what is general, and that all types of intended generality which are of concern to pure logic, whether in its forms or its laws, only come to be given by way of corresponding forms of such intentional characters. Men also fail to see that while individual intuitions in a certain manner provide the basis for the novel acts of cogitative presentation that we build upon them + +- whether these be acts of 'symbolic' or of 'authentic' presentation - they themselves, with their own sensuous-intuitive intention, do not enter into the content of our thought at all, so that one simply does not have what talk of representation, in its prevailing sense, implies, the sense upheld by those + +who defend a theory of such representation. + +**§26 Continuation. The varying modifications of the consciousness of generality, and the sensuous** + +**intuition** + +A closer treatment will here be useful. Each new conception which gives to a name or an image a representative character is, we emphasized, a new type of presentative act; in the act of meaning (and not merely the act of general meaning) we achieve what, in relation to mere intuition, whether of 'outer' or 'inner sense', is a new mode of reference, with a sense, and also often with an object, quite different from those of the reference occurring in mere intuition. The content of this new reference varies (as we have already noted by the way);3 it undergoes multiple differentiation of its descriptive essence in accordance with the logical function of the general name, with the semantic context in which this name occurs, and which it helps to bring to expression. What is individually intuited is no longer simply referred to as it appears before us: but on one occasion we refer to the species in its ideal unity (the pitch C, the number 3, e.g.), on another, to the class as sum total of the individual items which share in a universal (all tones of this pitch, or, formally, all *A's),* on yet another, to an unspecified individual of this sort (an *A),* or coming from this class (one of the *A's),* and on yet another occasion to this intuited individual, but thought of as exhibiting the attribute (this *A* over here) etc. Each such modification alters the 'content' or 'sense' of our intention: there is, in other words, at each step, an alteration in our 'presentation' in the logical sense of this word, i.e. in the presented thing *as* it is logically grasped and meant. It does not matter whether our accompanying individual intuition remains constant or varies continually: the logical presentation changes if its meaning (the sense of our expression) changes, and stays the same as long as its meaning does so. We need scarcely stress the fact that the phenomenon which serves as basis for all this may + +drop out altogether. + +The distinction between the cogitative and the sensuous 'conception' is one of essence. It is not like a case where, e.g., we conceive 'the same object' as at one time a wax-figure and at another time (caught in illusion) as a living person, as if two individually-intuitive 'conceptions' were merely being exchanged. Nor should we be led astray by the fact that our presentative intention in the form of a cogitative individual presentation, of a presentation of plurality and one of totality, can likewise be directed to individual items (to one, to several, or to all of a kind). It is indeed evident that the character of the intention, and with it that of the semantic content, differs + +totally from that of any intuitive (sensuous) presentation. To refer to *an A* is a different thing from representing an *A* in simple intuition without the thought of *an A,* and a different thing again from referring to it in an act of direct meaning and naming, i.e. by way of proper names. The presentation *a man* differs from the presentation *Socrates,* and just so also the presentation *the man Socrates* differs from both of them. The presentation *some A's* is not a series of intuitions of these or those *A's,* not an act of collection which gathers previously presented individual intuitions together (though such a unification, with its objective correlate the aggregate, is an additional performance transcending the sphere of sensuous intuition). Where such a sum or collection of intuitions underlies our presentation and serves to exemplify it, we are not concerned with the individuals that appear before us, nor with the aggregate they form: what we mean is 'some *A's',* and this cannot be spied out by an external or even by an internal act of sense. The same naturally holds of other general meaning-forms, of number-forms, e.g., such as 'two' or 'three', or again of an exhaustively universal form such as 'all *A's'.* We have a presentation of exhaustive universality in the logical sense of this term whenever we understand the expression 'All *A's'* and apply it significantly. Exhaustive universality is therefore presented by way of a unitary thought; and it can only be brought to consciousness as exhaustive universality in this or in some corresponding 'authentic' form of thinking. For we can only intuit a this or a that. However many individual items we may run through, and however zealously we may collect them, we can at best - if we really have exhausted our concept's range of application - only have presentations of all *A's,* which would not mean that we had the presentation of *All A's,* that we had really achieved this logical presentation. If, however, we do achieve such a presentation, we may try to intuit its content, and may both hope for and achieve clarification by doing so. One sees, however, that a sensuous-intuitive assembling of the objects presented, in this case the sum total of the *A's,* cannot bring before us 'what we really meant'. Our thought-intention must rather, in virtue of the demands made by its form and its content, both relate to intuition and also fulfil itself in such intuition, thereby giving rise to a complex act, superior in clarity and insight, yet not dispensing with thought, nor replacing it with a mere picture. These provisional, more or less superficial indications will have to suffice at this point. We shall have to clear up the distinction between thought and intuition, between presentation of an 'authentic' and a 'non-authentic' sort, by instituting a comprehensive set of analyses in the last Investigation in this book. **In** the course of these analyses a new notion of intuition will present + +itself, differing from the usual notion of sensuous intuition. + +**§27 The justifiable sense of general representation** + +After these discussions we might feel little inclined to be kind to the longcherished talk of the representative function of general signs and intuitive + +pictures. This talk is so ambiguous that, especially in its common acceptation, it can contribute nothing toward an e1ucidatory characterization of the + +thought which is deployed in general forms. + +Generality of presentation *(Vorstellung)* consists, it is held, in generality of representation *(Repriisentation).* If we could interpret the latter as the new modes of consciousness which we build on an intuitive basis, varying modifications in which the consciousness of generality is characterized as consciousness of the Species, consciousness of *all* cases, or as indefinite consciousness of a case or of *cases* etc., all would be in order. Talk of the representative function of an intuitive picture would to this extent be applicable, that the intuitive picture presents only one single individual from the species in question, but serves as *point d'appui* for the conceptual consciousness built upon this, so that through it the intention towards the Species, towards the total objective range of the concept, towards an unspecified individual of the sort in question, comes into being. The intuitive object could then itself be regarded and spoken of as being a representative of the Species, of the class, of the unspecified intended + +individual etc. + +What holds of the illustrative intuitive picture holds also of names which function 'representatively' without illustrative aids. As the consciousness of meaning may be developed on an inadequate intuitive basis, which may be far from exemplifying properly, it may do so also on the basis of a mere name. That the name represents something, means only that its physical manifestation serves to carry the significant intention, in which the con- + +ceived object is intended. + +Such a conception would exclude nominalism. Thought in its view no longer reduces to any external manipulation of names and individual ideas, nor to unconscious associative mechanisms which cause individual items to jump up in their places, as numbers jump up from a computer. There exists for it a conceptual presentation which differs descriptively from an intuitive presentation (from a reference directly related to some phenomenal object before us): a reference of a fundamentally new sort, to which the forms *some X* or *some X's,* or *two* or *three,* or *something or other in general,* or *all* etc., essentially pertain. Among these forms is also one in which the *Species* is made to function as a *presented object,* and so as a subject for + +possible attributions and predications. + +**§28 Representation as substitution. Locke and** + +**Berkeley** + +Talk of general representation was not, however, given the sense expounded above - the only sense it can correctly have, though the name 'representation' does not fit it very well - in the historical treatment of abstraction. It + +Locke had already made such substitution play an essential role in his doctrine of abstract ideas, and the theory of abstraction held by Berkeley and his successors took this over from Locke. We read, e.g., in Locke:4 + +It is plain ... that general and universal belong not to the real existence of things; but are the inventions and creatures of the understanding, made by it for its own use, and concern only signs, whether words or ideas. Words are general ... when used for signs of general ideas, and so are applicable indifferently to many particular things: and ideas *are general when they are set up as the representatives of many particular* things ... their general nature being nothing but the capacity they are put into by the understanding, of *signifying or representing many particulars;* for the signification they have is nothing but a relation that by + +the mind of man is added to them. + +Berkeley's lively attacks on Locke's theory of abstraction concern these 'abstract ideas'; but he transfers the representative functions which Locke accords to such ideas to our individual ideas at the moment or to general names in their own right. Let me recall the following passages from the + +Introduction to the *Principles of Human Knowledge:* + +Now if we will annex a meaning to our words, and speak only of what we can conceive, I believe we shall acknowledge *that an idea which, considered in itself, is particular,* becomes general *by being made to represent or stand for all other particular ideas of the same sort.* To make this plain by an example, suppose a geometrician is demonstrating the method of cutting a line into two equal parts. He draws, for instance, a black line of an inch in length, this which in itself is a particular line is nevertheless *with regard to its signification general,* since, as it is there used, *it represents all particular lines whatsoever:* for what is there *demonstrated of it,* is demonstrated of all lines or, in other words, of a line in general. And as that particular line becomes general, by being *made a sign,* so the *name line* which taken absolutely is particular, by being a sign is made general. And as the former owes its generality, not to its being the sign of an abstract or general line, *but of all particular right lines that may possibly exist,* so the latter must be thought to derive its generality from the same cause, namely, the various particular lines which + +it indifferently denotes.s + +Universality, so far as I can comprehend, does not consist in the absolute, positive nature or conception of anything, but in the relation it bears to the particulars signified or represented by it: by virtue whereof it is that things, names or notions, being in their own nature particular, + +But it seems that a word becomes general by being made the sign, not of an abstract general idea, but of several particular ideas, *anyone of which it indifferently suggests to the mind.* For example, when it is said the *change of motion is proportional to the impressed force,* or that *whatever has extension is divisible,* these propositions are to be understood of motion and extension in general, and nevertheless it will not follow that they suggest to my thoughts an idea of motion without a body moved, or any determinate direction and velocity ... it is only implied that, whatever motion I consider, whether it be swift or slow, perpendicular, horizontal or oblique, or in whatever object, the axiom concerning it holds equally true. As does the other of every particular extension ... 7 + +**§29 Critique of Berkeley's doctrine of** + +**representationS** + +Against these contentions the following objections are in place. No acceptable sense can be given to Berkeley's assertion that an individual idea is used to represent all other individual ideas of the same kind, in view of the normal meaning of the word 'represent'. We speak of something representing another where one object takes over performances (or undergoes performances) which another object would otherwise perform (or undergo). Thus the attorney who has been granted full powers represents his clients and carries out their business, the ambassador represents the ruler, the symbolic abbreviation represents the complex algebraical expression etc. We may, however, ask, in our case, whether the individual idea in its momentary life likewise functions representatively, whether it takes over a performance, which another individual idea, or perhaps every individual idea in its class, could properly be called on to perform? This certainly fits in with the plain letter of what Berkeley says, but there can be no question of its being true. Obviously we can only maintain that the performance which our present individual idea carries out *could as well* have been carried out by any other individual idea; each could have served as well as a basis for our abstraction, as an intuitive foundation for our general meaning. The thought of representation first arises from the *reflection* that each individual idea is equivalent in respect of this function, and that when one has been chosen, any other could replace it, and conversely. Wherever a general meaning is carried out intuitively, such a thought is possible, but it is not for that reason actual, above all since it presupposes the general concept that it is designed to replace. Individual ideas are therefore merely possible, not actual, + +representatives for other similar individual ideas. + +But Berkeley takes representation seriously and takes his stand, on the one hand, on the sense of general assertions, on the other hand, on the part played by figures in geometrical proofs. The former applies to the above quotation from paragraph XI of the Introduction of his *Principles.* If we + +judge that 'whatever is extended is divisible' we mean that whatever extended thing we may deal with will show itself to be divisible. The general name (or possibly the accompanying individual idea) represents, in conformity with the simple sense of our sentence, every individual extended thing, no matter which - the individual idea in question therefore 'suggests indifferently to the mind' every other individual idea which belongs to the class of extended + +things. + +In all this Berkeley has confused two essentially different things: + +1. That the sign (name or individual idea) is a representative of each individual falling within our concept's range, whose presentation Berkeley + +says that it suggests. + +2. That the sign has as its meaning the sense *all A's* or *any A whatsoever.* In regard to the latter there can be no question of representation in the sense of replacement. One or more *A's* may be suggested or presented with intuitive fullness, but the individual I look at (without intending to look at it) refers me to no other individual for which it serves as a substitute, let alone to every individual of the same kind. *All A's,* or every *A* whatsoever, are represented in a wholly different sense: they are *presented in thought.* We achieve the consciousness of *all A's* in a single pulse, in a homogeneous, peculiar act, in an act which has no components directed to all the individual *A's,* and which can neither be reconstituted nor replaced by a sum or combination of individual acts or individual suggestions. This act refers to each member of its range in virtue of its 'content', in virtue of its ideally seizable sense; it does not do so in a real *(realer),* but in an ideal, i.e. in a logical manner. What we assert of all *A's,* i.e. what we assert in a unitary sentence of the form *'All A's* are *B's',* obviously holds with *a priori* force of every *A* that definitely comes before me. An inference from universal to singular can be carried out in each given case, and the predicate *B* ascribed with logical correctness to *A.* The universal judgement does not for this reason include the particular judgement in itself, nor the general presentation the individual presentation that falls under it, or it does not do so in a psychologically or phenomenologically 'real' *(reell)* manner, and so not in the fashion of a bundle of 'representations'. The mere infinity of the range of all pure general concepts, i.e. concepts unmixed with empirical assertions of existence, such as Number, Spatial Figure, Colour, Intensity, shows such + +a misinterpretation to be nonsensical. + +**§30 Continuation. Berkeley's argument from** + +**geometrical demonstrations** + +Berkeley appeals in the second place to the *instance of the drawn line,* which assists the geometer in his proof. He here allows himself to be misled by his empiricist tendency to give preference to the sensuous individual case (or rather to the sensuous analogon of such an individual case) over genuine + +objects of thought: this tendency shows itself, here as elsewhere, in his treatment of the sensuous individual case, which lends support to mathematical thought, as the subject of his proof. As if we went through the proof to apply it to the stroke on paper, to the triangle chalked up on the board, and not to the straight line or the triangle 'as such' or 'in general'. This error has already been corrected above;9 we have shown that the proof is not in reality conducted on behalf of the individual in the drawing, but has from the start a general application. It applies to all straight lines whatever, grasped in a single act of thought. Nothing is changed in all this by the geometer's mode of speech, when he enunciates his proposition generally and perhaps starts his proof with the words: 'Let *AB* be any straight line ... ' This does not at all mean that the proof is in the first instance performed for this single straight line *AB* (or for a particular ideal straight line that it represents), and that this single straight line then functions as representing every other straight line; it only says that *AB* must render presentable, through intuitive symbolism, an instance which then may serve to catch, as intuitively as possible, the thought of *a straight line in general,* which thought constitutes the true, + +the continuously pervasive theme of our logical context. + +How little 'representation' helps to clear up the nature of general thought, appears from the question: What is the position of the general presentations that would have to appear for *the straight line on the paper* in the given proof? The intuitive data which correspond to them are surely not to be taken as objects of our demonstrative thought? For we should otherwise fail to set up a single proposition: we should have only representative individual ideas, but no thinking. Does anyone think that a conglomeration of such individual items can give rise to a predication? The function of a general name in the predicate certainly differs from its function in the subject, and its function varies, as noted above, according to our logical forms, to the forms of the thought-combinations into which our general meanings are welded, keeping a selfsame semantic nucleus, but varying with their varied syntactical functions (cf. the note to p. 371). How could all these forms, in which the make-up of 'thought' is as such manifest, or in which (to use objective language) the ideal essence of meaning is unfolded *a priori* (as the essence of number is unfolded in the forms of the numbers), how could one hope to cover all these matters by the one blanket phrase of 'representing'? + +**§31 The main source of the errors that we** + +**have indicated** + +One would be going too far were one to reproach Locke and Berkeley for altogether overlooking the descriptive difference between an individual idea, as part of an individual intention, and the same idea as part of a general intention (as serving to found a conceptual consciousness). One is assured, with many turns of phrase, that it is the 'mind' which gives such ideas their + +representative function, that it is the 'mind' that applies individual appearances as representatives; that all these mental activities are conscious activities, and so fall into the sphere of reflection, would certainly have been admitted by these great thinkers. Their fundamental epistemological errors or obscurities spring from a source that we have already laid bare: 10 in their phenomenological analysis, they stick almost exclusively to the intuitive individual, to the palpable side, as it were, of our thought-experiences, to names and illustrative intuitions, while they are quite unable to do anything with 'act-characters', since these are not at all 'palpable'. They therefore go on in quest of further sensuous details, and of sensuously presentable manipulations of such details, so as to give thought the sort of reality that they favour, and that flatly refuses to show itself in the actual phenomenon. They cannot bring themselves to take acts of thought for what they show themselves in pure phenomenological examination; they cannot let them count as wholly new 'act-characters', as new modes of consciousness opposed to direct intuition. They cannot see what is quite plain to anyone who approaches the matter unconfused by traditional prejudices, that these 'actcharacters' are modes of meaning, modes having this or that significant content, behind which nothing whatever may be looked for that either differs + +or could differ from meaning, significant reference. + +What 'meaning' is, is a matter as immediately given to us as is the nature of colour and sound. It cannot be further defined, it is ultimate in description: whenever we perform or understand an act of expression, it means something to us, we have an actual consciousness of its sense. This understanding, meaning, enactment of sense, is not the hearing of the spoken word nor the experiencing of some contemporaneous image. Just as plainly as phenomenological differences between apparent sounds are self-evidently given to us, so are differences among meanings likewise self-evidently given. This is not of course the last word in the phenomenology of meanings, it is only its beginning. One will have, on the one hand, to pin down the distinction, fundamental for epistemology, between symbolical, 'empty' meanings and meanings having intuitive 'fulfilment', and one will have, on the other hand, to devote study to the essential kinds of meaning and to the modes in which meanings are combined. This is the sphere of actual meaning-analysis. Its problems are solved when we represent to ourselves the acts concerned and the things given in them. Pure phenomenological identification and distinction, combination and separation, as well as generalizing abstraction, will lead us on to the essential species and forms of meaning: one will get down, in other words, to the logically elementary concepts which are merely + +the idealized forms of primitive semantic differences. + +Instead, however, of analysing meanings phenomenologically in order to determine the basic forms of logic, or instead, conversely, of becoming clear that the basic forms of logic are merely the typical characters of our acts and their forms of combination (in the build-up of complex intentions), + +people engage in *logical analysis in the ordinary sense of the word,* they consider what these meanings objectively intend, and then seek what is thus objectively meant as something really present in the act. One thinks *in* meanings and not *about* meanings: one concerns oneself with states of affairs presented or judged about, not with their presentations and judgements (i.e. not with nominal and propositional meanings). One claims and thinks that one has carried out a descriptive analysis of acts, though the territory of reflection has been long left, and *objective* has been substituted for phenomenological analysis. Even purely logical analysis is objective when it investigates 'what is contained *in our mere concepts or meanings',* i.e. what must be attributed *a priori* to objects, in so far as these are thought of in such forms. The act-analysis of meaning investigates 'what is contained in our meanings' in a totally different sense. Here alone such a mode of expression is appropriate: meanings are reflected upon and made objects of investigation, their real *parts* and *forms* are enquired into, not what is true of their objects. The manner in which Locke arrives at his doctrine of general ideas and, among other things, at his doctrine of representation: the manner, likewise, in which Berkeley applies and defends this doctrine, and especially his approach to the meaning of general propositions - cf. his analyses of the examples quoted on p. 395 from paragraph XI of the Introduction to the + +*Principles* - merely confirm what we have said. + +**Phenomenological study of Hume's** + +**theory of abstraction** + +**§32 Hume's dependence on Berkeley** + +One need not nowadays stress the fact that Hume's conception of abstraction is not at all the same as Berkeley's.! Nonetheless, the two notions are so closely akin, that it is quite comprehensible that Hume at the start of his exposition in Part I, Section VII of the *Treatise,* should have gone so far as simply to attribute his thesis to Berkeley. 'A great philosopher,' he + +tells us, + +has disputed the received opinion ... and has asserted that all general ideas are nothing but particular ones annexed to a certain term which gives them a more extensive signification, and makes them recall upon occasion other individuals which are similar to them ... I look upon this to be one of the greatest and most valuable discoveries that has + +been made of late years in the republic of letters. + +This is plainly not quite Berkeley's view, who does not, like Hume, want to attribute to general names the primary power of making individual presentations that accompany them into representations of other individual presentations of the same class. On Berkeley's view, general names may function representatively in isolation from corresponding individual presentations, individual presentations may also function representatively without names, and both may, lastly, occur together, in which case, however, the name has no special advantage in its association with the representative presentation. Nonetheless the main point remains the same; generality consists in representation, and this is expressly conceived by Hume as a 'doing duty' by an individual item before us for other individual items, which, in Berkeley's mode of expression, are mentally 'suggested' by the former, or in Hume's + +straight phrase, are *'recalled to memory'.* + +Hume is accordingly hit by all our objections to Berkeley, and more severely hit, since in Berkeley the literal treatment of representation, and of the evocation of represented individual presentations, still floats in + +obscure suspense, whereas in Hume it appears with unveiled sharpness and + +clearness. + +**§33 Hume's critique of abstract ideas and its supposed outcome. His ignoring of pivotal** + +**phenomenological issues** + +The spirit of Berkeley's doctrine therefore lives on, as regards its main features, in Hume. Hume, however, does not merely reproduce this doctrine but extends it further: he tries to elaborate it more exactly and especially to deepen it *psychologically.* In this regard the arguments Hume directs against the doctrine of abstract ideas are not so important as the associationistpsychological discussion that he appends to them. The arguments in question do not go essentially beyond Berkeley's circle of ideas, and are, for one that fixes the aim of the proof correctly, quite irrefragable. The impossibility of abstract ideas *in the sense of Locke's philosophy,* i.e. of abstract images formed by disengaging ideas of properties from concrete images, has certainly been proved. Hume himself sums up his result in the proposition: 'Abstract ideas are therefore in themselves individual, however they may become general in their representation. The image in the mind is only that of a particular object; though the application of it in our reasoning be the same as if it were universal.'2 *These* propositions could naturally not be proved by Hume's critique which showed abstract images to be impossible, and which tried to conclude from this that, if we nonetheless speak of general ideas, ideas belonging to general names as their meanings or meaning-fulfilments, something must be added to our concrete images to create such generality of meaning. This added element - so the discussion *should* properly have continued - cannot consist in new concrete ideas, and therefore not in the ideas of names: a conglomeration of concrete images can do no more than present just those objects whose images it contains. We must not overlook the fact that generality of meaning - whether this be generality of meaning-intention or generality of meaning-fulfilment - is something *felt* as immanent in *each individual case* where a general name is understood, and is applied to intuition in accordance with its sense, and that it is something which, in immediately evident fashion, distinguishes such a case from an individual intuition. It only, therefore, remains to argue that it must be the *manner* of consciousness, the *manner* of our intention, that makes the difference. A new type of reference makes its appearance, in which we neither mean the intuitively apparent object as such, nor the object of our verbal idea, nor that of our accompanying thing-idea, but the quality or form exemplified in the latter, which we understand in general fashion as a unity in the sense of a Species. Hume, however, remains attached to Berkeley's thought of representation, and externalizes it completely. Instead of looking to the semantic character of meaning-intention and meaning-fulfilment, he loses himself in the genetic + +connections which give names an associative relation to the objects of a class. He quite fails to mention, and does not see with operative lucidity, that generality evinces itself in our subjective experience, and, as previously stressed, in each single enactment of a general meaning. Still less does he note, that what is here evinced exhibits sharp descriptive differences: that our consciousness of 'generality' at one time takes on a generic character, at another time a character of universal application, or that it becomes other- + +wise tinged in virtue of this or that 'logical form'. + +Modes of consciousness, acts in the sense of *intentional* experiences, certainly cause discomfort to a psychology and epistemology of 'ideas', which aims at reducing everything to 'impressions' (sensations), and associative concatenations of 'ideas' (images, the enfeebled shadows of 'impressions'). I recall here Hume's vain efforts over *belief,* and how he repeatedly has recourse to treating this character of our acts as an intensity, or as an analogue of intensity, in our ideas. 'Representation', likewise, must in some manner be reduced to something seizable. This is what a genetic-psychological analysis must achieve: it must show how, in our judgements, we come to apply the mere individual image that we experience, *'beyond its own nature',* and *'as if* + +it were general'. + +This last-mentioned turn of speech shows, to an extraordinary extent, the characteristic obscurity of Hume's position. With his 'as if', Hume fundamentally concedes to his great predecessor Locke that his theory of general ideas - *if* such ideas were possible - would achieve its purpose. He does not perceive that Locke's general ideas, as fragments torn from concrete contents, would themselves again be individual singulars, and that the fact that they were inseparable from other similar ideas (whether torn from or immanent in concrete ideas) would not yet endow them with the generality of thought. He does not perceive that peculiar acts, peculiar manners of referring or meaning, are necessary to do all this. Even if we accept Lockean abstracta, we still need the form of thought about 'all' in order to intend an infinite range of individual singulars not really presented. The self-identical unity of the genus was likewise first set up for consciousness by an act of generic thinking, and so on. An objective relation of exact similarity, that exists, yet is not subjectiv~ly revealed, will obviously not alter the single similar individual set before consciousness: only *thought* can give this indi- + +vidual a thought-relation to such a circle of similars. + +**§34 Reduction of Hume's investigation to** + +**two questions** + +If we now cast a glance at the content of Hume's psychological analyses, we can express what he hoped to achieve in the two following questions: + +1. How does the individual idea come by its representative function? Through what psychological processes does it become capable of functioning + +as a substitute for other similar ideas, and ultimately for every possible idea + +of the same class? + +2. The same individual idea fits into many circles of similarity, though in each *definite* thought-context it only represents ideas from *one* such circle. What circumstance picks out this circle of representation in a given context, what limits the representative function of the individual idea in this manner + +and so makes unity of sense possible? + +It is clear that these psychological questions retain their good sense if one here drops the guiding concept of representation, and substitutes for it the well-understood, genuine concept of a general presentation as being an act of general meaning or meaning-fulfilment (cf. general intuition in the sense of Investigation VI, *§S2).* That general presentations have emerged genetically out of intuitive, individual ones is generally accepted. But though the consciousness of the universal is repeatedly kindled by individual intuition, and derives clarity and self-evidence from the latter, it is not therefore a direct product of individual intuition. How then did we ever manage to go beyond individual intuition, to mean something quite other than the singular phenomenon before us, a universal instantiated in the latter, and yet not really contained in it? And how did we get all those forms which diversify the objective relations of the universal, and constitute differing logical kinds of presentation? If associative connections are now brought in to explain this, we are at once introduced to dispositional groups of similars and the signs we externally attach to them. This makes the second question a real one, how the circles of similars can maintain their fixed internal coherence, + +and not be mutually confounded in our thinking. + +In this situation we do not contradict ourselves if, on the one hand, we say Hume's treatment of abstraction was an extreme case of error, and yet vindicate for it the glory of having shown the way to a psychological theory of abstraction. It is an extreme case of error from the angle of logic and epistemology, for which it is important that experiences of knowing should be investigated in a purely phenomenological manner, that acts of thought should be treated as what they intrinsically are and contain in themselves, so that we may bring clearness to the fundamental concepts of knowledge. Hume's genetic analyses certainly cannot claim theoretical completeness and finality, since they lack a foundation in an adequate descriptive analysis. This does not, however, mean that they do not contain valuable trains of thought, which could not escape notice and have also had a fruitful effect. On his complete lack of a strictly descriptive analysis of thinking (or on his substitution of empirical-psychological for epistemological investigations) the further fact depends that Hume likewise imagines that to think of thought as having an economical function in knowledge yields a standpoint from which thought can be epistemologically illuminated. In this regard Hume is the true pupil of Locke and his philosophy. The objections to this point of + +**§35 The guiding principle and outcome of Hume's doctrine of abstraction and the main thoughts in** + +**which it is worked out** + +The *guiding* principle of Hume's psychological exposition is stated in the following words: 'If ideas be particular in their nature, and at the same time finite in number, 'tis only by custom they can become general in their representation, and contain an infinite number of other ideas under them.' Hume's conclusion runs as follows: 'A particular idea becomes general by being annexed to a general term, that is to a term which from a customary conjunction has a relation to many other particular ideas, and readily recalls + +them in the imagination.' + +The main thoughts in which this doctrine is worked out are set forth in + +the quotation: + +The application of ideas beyond their nature proceeds from our collecting all their possible degrees of quantity and quality in such an imperfect manner as may serve the purposes of life ... When we have found a resemblance among several objects that often occur to us, we apply the same name to all of them, whatever differences we may observe in the degrees of their quantity and quality, and whatever other differences may appear among them. After we have acquired a custom of this kind, the hearing of that name revives the idea of one of these objects, and makes the imagination conceive it with all its particular circumstances and proportions. But as the same word is supposed to have been frequently applied to other individuals, that are different in many respects from that idea which is immediately present to the mind, the word not being able to revive the idea of all these individuals, only touches the soul, if I may be allowed so to speak, and revives that custom which we have acquired by surveying them. They are not really and in fact present to the mind, but only in power: nor do we draw them all out distinctly in the imagination, but keep ourselves in a readiness to survey any of them, as we may be prompted by a present design or necessity. The word raises up an individual idea, along with a certain custom; and that custom produces any other individual one for which we may have occasion. But as the production of all the ideas, to which the name may be applied is in most cases impossible, we abridge that work by a more partial consideration, and find but few inconveniences to arise in our + +reasoning from that abridgement. 3 + +These quotations may serve to recall the gist of Hume's theory with sufficient completeness for our purposes. We need not here proceed to analyse them critically, since genetic problems fall outside the limits of + +**§36 Hume's doctrine of the d;st;nct;o rat;on;s in its** + +**moderate and its radical interpretation** + +Of particular interest for us is Hume's doctrine of the *distinctio ration is,* which also indirectly yields an answer to the second question formulated above. The question is how we are able to distinguish abstract 'moments' from intuitive objects: the former can of course be made into ideas in their own right, i.e. not through an abstraction in the Lockean sense of a separation. How do we rise to a distinction between the *white sphere* we have just intuited and *whiteness* (or sphericity), since 'whiteness' and 'sphericity' cannot count as ideas in the Lockean sense, which are contained in the concrete idea as particular parts separable from it. Berkeley had answered this question by pointing to the emphatic power of attention. Hume here attempts to + +penetrate further, and provides the following solution: + +If we compare a white sphere with a black sphere and on the other hand with a white cube, we notice two differing resemblances. Through repeated comparisons of this sort, objects sort themselves out for us into 'circles of resemblance' and ever strengthening habits teach us to *consider each object 'in different aspects',* according to the resemblances that permit its placing in different, but definite circles. That in one case we direct our gaze to colour only, does not mean that we have separated colour, but that we accompany what is in fact a unitary and indivisible presentation *'with a kind of reflection, of which custom renders us in a great measure insensible'.* In this obscure consciousness, a white cube perhaps floats before us, and so brings out a resemblance (i.e. that in respect of colour) to which we turn our inner gaze, so that the white sphere we perceive is only given a place in the resemblancecircle of colour. According to the manner of this reflection (or the resemblances that govern it), a different 'moment' in the same intuitive object is noted; or, what is in essence the same, the same intuition serves as a basis for the so-called abstraction of general presentations. With each circle of resemblance a particular name is associatively linked, so that the inner reflection, together with its characteristic 'angle' of treatment, also fixes the + +general name. + +We are not here engaged in psychological research, and it is not therefore for us to set forth critically what is good, and what is also crude, in such a theoretical attempt. Up to a point, however, we must consider it, in view of a paradoxical thought that seems to have inspired Hume's exposition, which modern Humeans have been the first to profess in undisguised crudity. This + +thought can be expressed as follows: + +Characters, inner properties, are not truly immanent in the objects that 'have' them. The distinct, mutually inseparable 'sides' or 'moments' of an intuitive content, e.g. its colour, form etc., that we think we apprehend as being 'there' *(vorhanden)* in it, are not really in it at all. There are rather only one kind of real parts, the parts, namely, that we can also isolate, in other + +words, the thing's *pieces.* So called abstract part-contents, of which it is said that they can indeed not *be* on their own account, (or be so intuited), but that they can be attended to by themselves, are to some extent a mere fiction *cum fundamento in reo* There is neither colour in a coloured thing, not form in a thing formed, but there are really only circles of resemblances in which the object in question has its place, and certain *habits* tied to our intuition of it. Considered more carefully, our doubt certainly is twofold; it is both objective and subjective. Objectively, it concerns the *objects* apparent before us in regard to their intrinsic *properties,* subjectively it concerns the *appearance itself* (taken as immanent experience) in relation to its inner load of sensation and sensuous content in general, i.e. to the contents which receive objectifying 'interpretation' (apperception) in our act of intuition. It is in the 'interpretation' that the appearance of the corresponding objective characters or properties is realized. On the one hand, therefore, we are concerned with the *sphere itself* and its inner properties, e.g. its uniform white colouring: on the other hand we are concerned with the *appearance of the sphere* and the complex of sensations immanent in it, among which is, e.g., the continuously graded sensation of white - the subjective correlate of the objective white which is uniformly apparent in perception. Here as elsewhere, Hume left this difference quite unnoticed; for him appearance and + +the apparent phenomenon coalesce. + +I am not really sure whether I have hit off Hume's own view in the theses formulated above; perhaps he only means, as against the Lockeans, that the concrete object is quite simple in respect of its characters, simple in the sense that *we cannot break it up into such characters,* though these characters as 'corresponding features' still are something really present in individual objects of the same sort. If this interpretation is right, Hume agrees with Berkeley on the matter, and only goes on to give a psychological elucidation + +of the manner in which the *distinctio rationis* comes into being. + +Plainly the problem has a good sense, even if one holds abstract 'moments' to be genuinely immanent. One may ask how individual properties, which can only appear in the most intimate mutual penetration, and never in isolation, can nonetheless become exclusive objects of intuitions or of thought-intentions. What explanation can there be in the former case of that preferential attention which dispenses its favouring notice to differing + +properties at different times? + +**§37 Objections to this doctrine in its radical** + +**interpretation** + +The objections raised by a moderate interpretation of Hume's statement need not be considered here: psychological interests should not lure us from our cause. We need only say that Hume's thoughts, suitably modified, provide a basis on which a workable theory may very well be built. One need + +not, above all, take his mythical 'inner reflection' seriously. G. E. Muller (in the dictated notes published by F. Schumann)4 has worked out the Humean theory more closely, with very great clearness and penetration, and though he himself prefers the radical interpretation, his restatement nonetheless + +plainly shows the fruitfulness of Hume's germinal suggestions. + +Let us now turn to criticism of the radical interpretation of Hume's doctrine. It occupies a central place in our sphere of epistemological interest. The difficulties in which consistent development involves it, are not small. If the abstract contents which correspond to the absolute properties are themselves simply 'nothing' in concrete intuition, associative and relational contents will even be more absolutely 'nothing' in our intuition of an aggregate with the corresponding form of unity. The problem of the *distinctio rationis,* and the principle of its solution, is plainly one and the same for *all* abstract contents. It is therefore the same for relational and associative contents as for absolute contents. One cannot therefore answer questions as to the way in which colour was seemingly found in, or distinguished in (or from) a coloured object, by having recourse to the finding of a similarity between the coloured object and other coloured objects. Since such a finding would, if the explanation is consistently pursued, lead to the finding of a similarity of this similarity with other similarities (in the case or colour, to a group of similar *similarities* such as subsist among coloured objects). The explanatory principle would again have to be applied to this further similar- + +ity, and so on. + +This argument carries over from abstract *contents,* understood as really experienced *(reell erlebte)* moments in the unity of a concrete intuition, to presentations of properties and modes of composition in 'external' objects. We therefore make use of a distinction which we emphasized against Hume, a distinction between concrete intuition, as the really *(reell)* present appearance or givenness of the object (as experience), and the *object* intuited (perceived, imagined etc.). We must here note that nothing scientifically or metaphysically transcendent should be substituted for this object; by 'the object' we meant the object as it *appears* in *this* intuition, as it *counts* (so to say) *for* this intuition. To the sphere's *appearance* or givenness the apparent *sphere* therefore stands opposed. Just so to the *sensed contents* of the sphere's appearance (moments phenomenologically discoverable by descriptive analysis), the perceived, or imagined parts or sides of the apparent *sphere* stand opposed: to the *sensation* of white, e.g., the sphere's apparent whiteness. All this having been granted, we may say: Should anyone wish to declare *all* talk of the intuitive presentation of abstract, objective determinations to be senseless, and to maintain that when we think we perceive, e.g., the property of white, we really only perceive, or otherwise present to ourselves, a resemblance between the apparent object and other objects, then such a man has involved himself in an infinite regress, since talk of this presented + +We here at once see the absurdity of the conception we are criticizing in the fact that, in the face of all self-evidence, an object self-evidently different from our intentional object has been substituted for it. The thing comprised in my intuition's intention, the thing I think that I am grasping perceptually or constructing imaginatively, stands by and large above all dispute. I may be deceived as to the existence of the object of perception, but not as to the fact that I do perceive it as determined in this or that way, that my percept's target is not some totally different object, a pine-tree, e.g., instead of a cockchafer. This *self-evidence in characterizing description (or in identification and distinction of intentional objects),* has, no doubt, its understandable limits, but it is true and genuine self-evidence. Without it even the far-famed self-evidence of *inner perception* (introspection), with which it is usually confused - wherever, that is, 'inner perception' is understood as the perception of intentional experience - would be wholly useless: when expressive talk begins, and the descriptive distinction of inwardly perceived experiences is carried out, this self-evidence is presupposed, since the distinction and description of intentional experiences without regard to their intentional objects is impossible.s This self-evidence helps us at this point. There is a self-evident difference between intuiting this object's redness and intuiting any relation of resemblance. If the latter intuition is relegated to the unnoticed or the unconscious, one merely adds to one's malaise, since one is sacrificing the self-evidently + +given intention in favour of what is unobservable. + +Our previous discussion runs over into our present discussion of apparent *objects,* to the extent that *contents* become perceived *objects* for reflective phenomenological analysis. Though we would not and should not call the appearance of the sphere *(qua* experience) a thing, nor call its abstract, immanent contents properties or characters, the descriptive situation as regards the points here relevant remains the same. The differences between thing and property are ontological differences, not characters of experience. They correspond to nothing in the phenomenon momentarily given, they are not real moments entering into this phenomenon and discoverable in it. They point rather to combinations of conscious experiences in which they appear conjointly, in which we have experience of them and can pin them + +down scientifically. + +Surveying this whole situation, we can appeal to the self-evidence which holds for the distinction of intentional objects in general in the special case of the intentional distinction of interior data. In this limiting case, where the object meant itself belongs to the real content of the experience (taken in its complete concreteness), the self-evidence of 'inner' perception comes into action; we do not merely have a self-evidence as to the difference of our intended data, but self-evidence as to their actual existence. When we direct our analytic interest not so much to the apparent sphere as to the sphere's appearance *(qua* experience), and distinguish parts or sides in *the latter,* while deliberately not noticing what such sensed contents mean, it is not + +merely self-evident that our colour-content, our total content etc. is perceived, it is also self-evident that it really exists. We may not always be successful in ignoring meaning, nor in carrying the analysis of experienced contents as far as one might wish; broadly and roughly, however, both may be achieved. Just as the self-evident difference of our intentional objects is not shaken by the fact that we may readily deceive ourselves regarding our intentions once we leave the sphere of grosser differences - just as the difference between a cockchafer and a pine-tree (both taken purely as they announce themselves to consciousness, intentional objects of our intentions) has genuine self-evidence - so there is a genuine self-evidence by which we often know that a colour-moment, a sensation, is really *there* in our unitary intuition, that it helps to build up the latter, and that it is quite different from the moment of shape that is likewise present. The situation is not affected by the fact that the separation of these moments, their independent + +being without inherence or being possessed, is unthinkable. + +One does not do justice to this self-evident situation if one says: 'Certain mental events exist in themselves, certain unnoticed arousals of series of similars, which impart a certain character to the absolutely simple concrete things in question, a certain colouring, a Jamesian "fringe".' In the first place such 'fringes' have their reality quite as much as the supposed unconscious events, which are in any case wholly irrelevant for pure phenomenology. In the second place, 'fringes' are mere appendages which may equally well be present or absent. If we therefore identify these supposed 'fringes' with the moments self-evidently noticed in the concrete thing, these 'fringes' would all become mere appendages of a carrier, a carrier quite of the type of the wonderful, + +featureless 'substance' that no one any longer takes seriously. + +The self-evident fact that the sensory moments, the colour-moment, the shape-moment and other immanent determinations, really belong to the unity of intuition, are moments making it up, cannot in any manner be interpreted away. One can no doubt explain them as the results of certain fusions, as products really but unnoticeably embracing their factors, but, however interesting this may be from the psychological standpoint, it does not affect our immediate descriptive findings, which alone have relevance for the clarification of our concepts and acts of knowing. Theoretically to conjure abstract contents, and with them abstract concepts, out of existence, is to try to expose as fictions, what we really presuppose in all insight, + +whether in our thoughts or our proofs. + +Possibly one may defer to hypercritical doubts, and object that a *distinctio rationis* is only given by way of a judgement. On one side stands the absolutely unitary phenomenon, to which our assertion accedes, attributing inner differences to it, which do not prove that the phenomenon really *has* + +inner differences. + +We should reply: obviously where we pass judgement on an experience, two things are present, the experience and our assertion. The assertion, + +however, may be correct, and it is correct when accompanied by *insight.* If one wants to approve a case as valid where containment is genuinely given and experienced, one can only do so on the basis of self-evidence. If ever self-evidence spoke for such a containment, it certainly does so in the present case. The notion of containment should not be unnecessarily restricted, not restricted, i.e. to the concept of articulation into discrete 'pieces'. If one keeps to this narrower concept the word is rendered inapplicable, but the + +fact is still clear. + +**Notes** + +1. We encountered a line of thought similar to the one just dealt with on a previous occasion.6 We there dealt with the question whether Species could be treated as objects, whether it was not more correct to say that there are in reality only individual objects, variously ordered according to their similarities. But in our last discussions we were not dealing with Species but with their instances. There is not merely a denial that one can speak of Red in general as an object of thought, but also that one can speak of an instance of red, of red as a 'moment' of an intuition which occurs here and now. We could not achieve the self-evident consciousness of generality, in which the Species is (as it were) given in person, if the instance, whose intuitive givenness is presupposed in the actual performance of abstraction, were reinterpreted in relativistic fashion. The parallel arguments are therefore + +essentially connected. + +2. I note subsequently that A. von Meinong, in his valuable essay 'Uber Gegenstande h6herer Ordnung und deren Verhaltnis zur inneren Wahrnehmung' (which unfortunately appeared too late to be of assistance to me in these *Logical Investigations)* has devoted some discussion to the relation between the self-evident recognition of immanent objects and inner perception *(Zeitsch. f Phil. u. Psych. d.* S. Bd. 21, Section 2, p. 205 *ff).* If I understand him rightly, Meinong makes the former case of self-evidence coincide with that of the inner perception relating *to the existence of the presentation concerned.* In that case he cannot have meant the self-evidence that we meant in the text. That the so-called immanent object is not in a serious sense an object in our presentation (as Twardowski still put it),? is naturally my definite opinion too: on the side of the presentation nothing exists but the reference-to-this-object, the significant scope *(Bedeutungsgehalt),* as it were, of the presentation. But the self-evidence of the fact that I mean a pine-tree in my presentation of *pine-tree,* a tree of a sort determined by such and such features, and not possibly a cockchafer or anything else is not what can be attributed to a mere percept, even to one relating to the mere experience of presentation. One is here dealing with the selfevidence of assertions, whose complex meaning-intention is fulfilled on a basis of numerous acts, of numerous presentations, and of identifications + +and differentiations which connect them. Even if we ignore the acts to be found on the intentional side, it is quite impossible to make do with mere acts of inner perception in the case of fulfilment. The inner perception of the acts of identification and differentiation just mentioned is obviously not adequate to account for the self-evident subsistence of identities and differences. + +**§38 Transference of our scepticism from abstract** + +**part-contents to all parts whatsoever** + +Scepticism in regard to abstract part-contents is paralleled by possible scepticism in regard to concrete part-contents, i.e. 'pieces'. A homogeneous white surface we take to be a divisible object; all parts that can be distinguished by us in actual division are treated as pre-existent parts in the surface. This practice we carryover to the case of sensation. The contents we actually experience in dealing with the white surface are bits analogously related to the total content as the objective bits of the surface are to the total surface. If it is pointed out that, in the intuitive presentation of the surface, we 'allow our glance to glide over it', thereby experiencing a multitude of continuously differing contents, we are not at a loss. We simply transfer our concep- + +tion to each such content. + +But how do we know that the content is really composite? If we imagine divisions in the unbroken white surface, the corresponding sense-content may really exhibit connected parts, but such imaginative intrusions do not leave our original content unaltered. The complex, discontinuously fragmented content we now have is not the same as the original, quite single, inwardly undivided one. The parts, into which one can think such a unity broken up, are fictitious parts.'8 Certain activities of imagination and judgement have been superimposed on an indivisible content of consciousness, + +and what the former produce we credit to the latter. + +Doubt grips us further, if we turn to consider a case, at first unassailed, where the intuitive content already exhibits divisions. Does our experience in such a case not first offer us a certain unitary content, that we afterwards say is compounded of parts, and is our saying this not due to a prior performance of certain novel operations? We pay attention, it is commonly said, now to one part, now to another, and now to yet another part of *the* content. But with each step our experience alters. Our tendency to confuse sense-contents with perceived or imagined objects, makes us substitute quite different contents for our original content at each step. The part we are attending to at the moment not merely lies in our focus of attention but also, more literally, in our focus of vision, and so yields sensations differing from those that it yields when remaining in the background. Keeping more strictly to contents, we may say that the content we momentarily pick out is surrounded only by an obscure, wholly chaotic mass, a fringe, a penumbra, or however one may wish to name the unnameable. It is not separated from + +the latter, but 'inwrought' with it. As one passes from part to part, the situation remains generally the same, though always differing in content: this is the case even when we do not let our glance wander. It would be a crude account of the descriptive situation were one to speak of this or that indirectly seen part (or of the corresponding experiential part) as if it were merely made individually noticeable in an identical unity of content, without suspicion of accompanying changes in the experience itself. Here, as in the case of abstract contents, genetic grounds point to certain connections in past experience which render selective notice possible, and whose effects are also shown in other facts of consciousness. What we see indirectly operates as a sign for anything coming from a sphere of similars bounded by past experience: the emphasis of attention involves, further, an interpretation, and with this, generally a change in content (an 'elaboration in fancy'). But if we object that repeated revival and comparison of experienced contents teaches us that it is right to talk of a division even in the case of such contents, the sceptic may well point to the abiding illusions to which such comparisons are subject, to the confusions between apparent things and experienced contents, between comparisons of objects and comparisons + +of contents etc. + +**§39 The extreme limit of scepticism and its refutation** If we persist in this sceptical direction, we shall have to doubt whether there are parts of any sort; and in consequence whether there is ever a plurality of concrete contents, since ultimately (if we may still presume to judge the matter) the contents which appear in co-existence and succession are always in a manner unified. Our scepticism would at length be crowned by the assertion: consciousness is something quite unitary, regarding which we can at least not *know,* whether it has partial contents at all, or whether it in any way unfolds itself in simultaneous or temporally successive experiences. Such a scepticism, it is plain, would render all psychologies impossible.9 How one must combat it need not be said after our previous explanations. Whatever the flux of immanent phenomena, it does not rule out the possibility of first grasping these phenomena in vague but quite clear concepts (clear because directly formed on an intuitive basis), and then, based on such concepts, of making many decisions, rough in fact but *self-evident,* + +which are quite enough to render psychological research possible. + +As regards the white surface - I am not here referring to the white surface itself, treated as a thing, but to the 'conscious content' - we see very well how it changes, but also how, despite all such changes, it stays alike, even identical. The boundaries added by imagination do not constitute its pieces originally; they merely *bound* them. It is self-evident to us that these pieces really were present in the unity of the content 'white surface'. The content, held without boundaries in an identical intention, coincides with the same + +content changed only by such imagined boundaries; the two coincide in respect of the outlined parts. The parts were, and always are, in the whole, not however as separated unities in their own right. A certain fluctuation and flux of contents, the uncertainty, even the impossibility, of keeping them just the same, does not destroy the self-evidence of these judgements. Like all *purely* descriptive judgements passed on intuitive data as such in a faithfully 'expressive' manner, they hold within a certain range of variability, with a certain index, therefore, of vagueness. 10 Naturally we only adduce examples where all relationships exhibit *gross* differences, and so really fall + +within the sphere of the gross self-evidence spoken of above. + +Self-evidence is also present if we proceed in the opposite direction, and remove in thought a fragmentation that is actually present. If a surface divides into a white and a red section, then, if there are merely qualitative changes, the identity of the two extended parts is maintained. If we now think of the white of the one, and the red of the other, as shading continuously into one another, both parts now coalesce in an inwardly undivided unity. But however this may come about, the result is evidently not an absolutely simple unity, but a homogeneous one, in which alone all inner separations have been blurred. The parts are self-evidently there, but, though each part has its own quality and every condition of concreteness, it still lacks qualitative discontinuity to set itself off, and with this the character of + +shutting itself off from the parts which melt into it. + +If we make empirical concepts and relations into precise ones, if we frame ideal concepts of extension, surface, qualitative alikeness and continuity etc., we arrive at exact, *a priori* propositions which set forth what is founded on the intentions of such strict concepts. Compared with these, merely descriptive assertions are inexact approximations. Though the vague sphere of singular phenomenal individuality in general, does not fall within the sphere of exact knowledge (which operates merely with ideals), it is none the less + +not at all excluded from the general sphere of knowledge. + +From this we see also the stand we must take up against doubts which go further, and which lead ultimately to the denial of all parts and differences. In individual cases the flux of sense-experiences, or also of specific mental experiences, may very well leave room for doubt: this is not possible in all cases. Where differences are gross, a self-evidence is attainable which renders + +all doubt unjustifiable. + +**Appendix** + +*Modern* **Humeanism** + +Hume's philosophy, with its richly brilliant psychological analyses, and its systematically applied psychologism in epistemology, corresponds so closely to tendencies dominant in our time, that it could scarcely fail to have a + +lively influence. One can perhaps even say that Hume has never been more influential than he is now, and one could even apply the name 'modern Humeans' to quite a fair number of contemporary thinkers. Here again one may note that, in this spread of historical influence, the errors have spread as much as, or more than, the good features. Particularly as regards the doctrine of the *distinctio rationis,* recent writings often offer us utterances or explanations which fit in with the radical sense of this doctrine. I I H. Cornelius has, however, taken up this doctrine in a peculiarly wholehearted, articulate manner: his *Psychologie* is an attempt to work out a fully-developed, psychologistic theory of knowledge, in the most extreme manner so far conceived, on the basis of modern psychology. To the extent that his work really is psychology, it contains many highly interesting, stimulating expositions of detail. To the extent, however, that it is epistemology, I think I may say that Cornelius confuses matters pertaining to the *intentional content* of knowledge (to knowledge's ideal sense, to what knowledge means and what is therefore necessarily posited along with it), with matters pertaining to the *intentional object* of knowledge, and both with matters pertaining to the mere *psychological constitution* of the knowledge-experience (perhaps only to mere phenomenal accompaniments of our intention, or to its unconscious, unnoticed genetic grounds). These confusions, I should say, have never been so richly represented in the literature, and have never stamped themselves so strongly on the whole treatment of problems of knowledge, as in the expositions of Cornelius. 12 This is particularly plain in the type of questions which here concern us. In the interests of truth, we shall here linger a little and prove our point by way of a few quotations, partly from the *Psychologie,* partly from a supplementary treatise of our author. To show that a scientific movement has gone astray, nothing is more instructive than to study its consequences as worked out by its adherents, and so to convince oneself that the final theory they think they have gained, has rather involved them + +in self-evident contradictions. + +In regard to the dictated notes of G. E. Muller, of whose content Cornelius + +wholly approves, he says:J3 + +the distinction of differing features ... is based ... on the fact that the contents are gathered into groups according to their similarities, and are named with common names. There is therefore nothing else that *we mean* when we talk of the varying features of a content, than the fact that this content belongs to various such groups of contents, all mentally + +similar and therefore called by the same name. + +Nothing so definite is to be found in Hume: the great thinker would probably have hesitated before accepting *this* proposition. 'What we mean' is surely our sense, and can one say even for an instant that the sense of the proposition 'This tone is faint' is the same as the sense of the proposition. + +'This tone belongs to a group (of whatever sort) of similars?' If someone says that, in order to speak of the tone's faintness, one must necessarily imagine tones similar in their faintness, we need not dispute what he says. It may be so. But do we *mean* that the tone belongs to this group, one consisting perhaps of *n* objects? And if the infinitely many similar objects could stand before our eyes as a single group, and actually did so stand, would the sense of our expression be the membership of this group? Naturally the utterances 'A tone is faint' and 'A tone belongs to the sum total of objects alike in their faintness' are semantically equivalent, but equivalence is not identity. If someone says that talk about faintness of tones could arise only if we had noticed similarities among faint tones, and that, further, the memory-traces of such previous experiences are somehow excited when we meaningfully speak of such tones, and that their dispositional after-effects determine the character of our present experience, he may well be right. But what has all this to do with our sense, with what we *mean* by our words? My reference is plainly an immediately given, present experience. How this experience, with its evident content, may have *arisen;* what may be necessarily true of it from the genetic standpoint; what may underlie it physiologically or psychologically, whether in the marginal or the unconscious - all these are interesting themes for enquiry. But it is absurd to seek information about our meaning along such paths. It is an error more or less analogous to the common materialism that seeks to assure us that tones really are air-vibrations, excitations of the acoustic nerve etc. Here, too, theoretical hypotheses which explain the given genetically, are substituted for the given. That we are not here dealing with a passing looseness of expression on + +Cornelius' part, is shown by his further statements. We read: + +We need hardly say that, on the theory just set forth, this 'common feature' of simple contents cannot be used generally to explain the similarity among these contents - as one is accustomed to reduce the similarity of two carpets to an exact match of colour. *For to assert such a match of colour is on the present theory nothing but to assert the similarity of both* + +*contents with other previously known contents.* + +The one assertion *is* the other (this is stressed by Cornelius), they are therefore the same assertion. It would therefore harmonize with the sense of our statement that the assertion of this colour-match had a different sense for each man, and a different sense at different times. It would depend on the 'otherwise known' contents, and thus on previously experienced contents, + +which plainly differ from man to man, and from time to time. + +When Cornelius adds that the 'meaning of predicates need not appear in the form of separate presentations on each occasion, but can be given in "rudimentary association",' we are not greatly helped: what actual associations cannot do, 'rudimentary' association, brought in as a substitute, + +cannot do either. Cornelius so darkens facts with theory that he even saysl4 that the expression 'abstract content' or 'abstract presentation' are 'abbreviations' for 'presentation of the similarity in a certain respect of one content to others'. *Which* of the various features of a content is spoken of at a time, in which *direction* or *respect* the content is treated, depends on 'which of these differing similarities will be brought to consciousness (will be + +"inwardly perceived" by us)'Y + +Cornelius will not permit us to call his conception 'nominalistic' . Yet extreme nominalism has always thought that similarity mediated the relation between a general name and the class it applies to, and for Cornelius, as for such nominalism, general names are in a manner equivocal. Psychological grounds (the theory maintains) limit the application of a name to a class, but the name's meaning consists in particular similarities experienced from moment to moment, and therefore varies from case to case. The ideal unity of the class sets bounds to this multiplicity of meanings, but it does not and cannot create the single meaning of the univocal concept. But how we should know anything of this ideal unity, of *the* group of objects which *one* similarity encompasses, remains, on the theory, mysterious. 16 The content of the + +theory liquidates its own presupposition. + +A certain sense that the consciousness of generality also makes itself felt descriptively and demands explanation, shows itself in several passages in Cornelius. We read, e.g., that a predicate-word, in virtue of its origin and meaning, does not stand for this or that individual content, nor for a certain number of particular contents, but rather for something common to all these contents. The general idea associated with the predicate, which determines its meaning, is the *memory of the similarity binding all those contents together,* a thing not further describable, but immediately known to internal perception.' Of course the 'thing not further describable but immediately known to internal perception' is the peculiar consciousness of meaning, the *act* of general meaning: but the words certainly manage to describe this indescribable, and, it seems to me, in an incorrect fashion, since they substitute a sense-content for an 'act-character', and a fictitious sense-content + +at that, one at least that eludes phenomenological scrutiny. + +If we do not take this passage quite literally, let us seek closer guidance in Cornelius' exposition of psychology, to see how Cornelius does justice to the meaning-conferring character of acts: this, as the thing really requiring explanation, should be sharply focused, distinguished in regard to its essential modifications, and set up in these fixed differences to illuminate genetic analysis. Here *two* fundamental confusions may be noted. The first is the confusion of the *objective* fact, that the general name is confined by associative connections to the circle of similarity, with the *subjective* fact, that we mean the universal in the individual act, and so refer ourselves in our intention to the class, or to an indefinite individual as member of that class, or to the unitary species etc. This is the confusion on which extreme nominalism + +is, as it were, nourished: it alone makes such nominalism possible, with it such nominalism stands and falls. Mixed up with this first confusion, there is a second confusion in Cornelius's *Psychologie* which runs basically different things together, the confusion of the *inexactness* of memory, of the *indistinctness* and fluidity of 'obscurely' reproduced images, with the *character of generality* which characterizes the consciousness of generality as its act-form, or with the *indefiniteness of content* in our intention which makes up the *definite* meaning of the *'indefinite'* article. The following quotations + +may serve to prove our point: + +'The more that similar contents have been experienced, the less will ... their memory images refer back to temporally *definite* contents, and the more will they achieve the character of *general* presentations, and so be able to serve as symbols of any content whatever within definite limits of similarity.'17 Next + +to this we put the following passage: + +A word heard for the first time cannot as yet be understood, but as soon as any of the other contents which occurred together with the verbal sound-complex we once heard, is recalled together with it, this word's *first meaning* is given ... 18 Corresponding to the ... inexactitude of recall,. the word's meaning will at first likewise be *inexact.* Since the memory presentation associated with the word does not merely serve to symbolize a *completely determined* experience, but *leaves its properties undetermined within certain limits,* the word likewise must be rendered ambiguous through its association with this memory presentation. A later content, conversely, will likewise be in a position to be associated with the word as long as its difference from the content previously bound up with this word, does not go beyond these limits ... When the meaning of a word thus emerges ... an *abstract,* ambiguous symbol is necessarily created, standing equally for a series of different contents alike in a particular respect. The word obtains *conceptual* meaning to the extent that, in virtue of the emergence of its meaning, it serves the individual as a symbol for all contents lying within certain limits in a definite similarity-series. 19 + +At the close of the same section we read further: 20 + +We find ... that not only words, but also presentations can be general (and are in fact always general within limits) in the sense in which conceptualism asserts such generality. This generality, however, remains bound within limits fixed by our acquired fineness of discrimination, whereas the generality of the word is in no way limited by the limited + +generality of the associated image. + +That there is no presentation of a triangle in which the properties of the acute-angled and obtuse-angled triangle are united, we can unconditionally grant to Berkeley as against Locke, but that *in every* + +*presentation of a triangle completely definite* relations of sides and angles are presented could be *denied* as definitely. We can as little frame the image of a triangle with a definite, wholly exact proportion of sides, as we are in a position to draw it. The presentation just spoken of is impossible since the differences of form between acute and obtuse-angled triangles are too gross and familiar, for us to be in any possible doubt regarding the corresponding properties in the case of a triangular form. The fully-executed presentation of a completely determinate triangle is also impossible for the reason that our discrimination of triangular forms can never be quite exact - small differences at least are lost in memory. + +The confusions noted above at once spring out in the above quotation. A symbol for a single item, which, through our regular confusion of this single item with similar singulars, stands for each member of a range of similars, and can presumably recall each such member, is, on the view of Cornelius, a general symbol. The indifference of the general concept towards such features of its object as do not fall within its content, is further identified with the vagueness of the memory-image. And, in his final passage, Cornelius thinks that he can mediate in the Berkeleyan-Lockean dispute over the general triangle, by substituting for a question about the sensuous presentability of a triangle having conflicting properties (Locke's idea of a triangle), the quite different question as to the possibility of framing a precise mental image of a geometrically definite triangle of given proportions, or of recognizing one so framed as corresponding to our geometrical ideal, and of distinguishing it from others slightly different. In this indefiniteness, taken as vagueness, seems confused with inexactness in the exemplification of an ideal. Cornelius thinks that a sensuous triangle can unite contradictory properties, infinitely many of these in fact: it must only avoid trying to unite large differences, like those between being obtuse-angled and being acuteangled. One would hardly care to accept such a psychologistic rehabilitation of Locke's idea of a triangle, even when confined to such finer differences. We cannot agree to believe something to be psychologically possible if it is + +logically and geometrically absurd. + +**Separation of varying concepts of** + +**abstraction and abstract** + +**§40 Confusion of concepts of abstraction and abstract concerned with non-independent part-contents, on** + +**the one hand, and Species on the other** + +The 'attentional' theory of abstraction presupposes, what the doctrine of the *distinctio* rejects, *that there is a certain difference in our contents themselves, corresponding to the difference between abstract and concrete,* On the *distinctio rationis* doctrine there are only one kind of parts, i.e. 'pieces', parts capable of separation or of being presented as separated. On the former view, however, one distinguishes between 'independent' parts (in Stumpf's terminology), on the one hand, and non-independent 'part-contents', on the other. Among the latter we count the inner determinations of a content (exclusive of its 'pieces'), and among these also the forms of unity discernible in this content (or, objectively regarded, present in it), through which its parts are combined to make up the unity of the whole. **In** relation to this same distinction, one speaks also of *concrete* and *abstract contents* or parts of contents. 1 **In** the theory of abstraction since Locke, the problem of *abstraction in the sense of an emphatic pointing to 'abstract contents'* has been mixed up with the problem of *abstraction in the sense of concept-formation.* **In** regard to the latter, we are concerned to give a descriptive analysis of the essence of the act in which we are self-evidently aware of a Species, or to clarify the meaning of general names by recourse to fulfilling intuitions. From an empirical, psychological viewpoint, we must try to explore the corresponding psychological facts in the context of human consciousness, the genetic origin of men's general presentations in the natural process of naIve, unconsidered living or in the artificial process of deliberate, logical concept-formation. The abstract presentations which are *here* in question, are presentations whose intention is to Species and not to non-independent or abstract contents. Should these intentions be intuitively fulfilled, concrete intuitions with (as it were) stressed part-contents will serve as their foundation. The intended Species are not, however, these latter part-contents; however much we may stress the latter in our consciousness of generality, they do not + +become our intended objects themselves, nor are they objects of separate contemplation. There is, however, a constant confusion, as can be seen from our present critical investigation, between abstract, non-independent moments *in the object,* and the *Species,* or between the corresponding *subjectively experienced* abstract contents and *abstract concepts* (the meanings of certain names), or also between the acts of emphasis or *regarding* of these abstract contents, and the *acts of general presentation.* Locke, e.g., wants abstract ideas to be general meanings, but they are described as features of objects, and psychologized as abstract sense-contents torn from concrete intuitions. The 'attentional' theory likewise points to the possibility of a peculiar notice paid to such abstract contents (without a tearing of them from their context), and thinks that it has thereby shed light on the origin of our general concepts (as meanings). **In** the same vein some deny the intuitive character of abstract contents,2 though, as aspects of concrete intuitions, they must be intuited with the latter: this error occurs since men are led astray by the inaccessibility of general concepts to sensuous intuition. **If** it is absurd to try to paint tones, or to represent colours by smells, or, generally, to represent one heterogeneous content by another, it is doubly absurd to + +try to represent what is essentially non-sensuous sensuously. + +We may say in general that there are differing concepts of abstract and abstraction that call for distinction: our present task is to pursue their + +distinctions. + +**§41 Separation of concepts grouped about the** + +**concept of the non-independent content** + +**If** we adhere to the talk of 'contents' favoured by recent theories of abstrac- + +tion, we may say: + +*(a) 'Abstract'* contents are *non-independent* contents, *'concrete'* contents are *independent.* We think of this difference as objectively determined, perhaps, as follows: concrete contents are by their nature such as to be capable of existing in and for themselves, whereas abstract contents are only possible + +in or attached to concrete contents. 3 + +It is plain that this talk about *contents* can and must be carried further than it is in the phenomenological sense of real *(reellen)* elements in consciousness. The phenomenal external object which appears, but which is not a real datum of consciousness - at least if one does not falsely interpret the 'intentional' or merely *intended* object, as a real constituent of the experience in which the intention takes place - is as a whole concrete: its immanent determinations, colour, form etc., understood as moments constituting its unity, are abstract. This *objective* distinction between abstract and concrete is the more general, since immanent contents are only a special class of objects (which naturally does not mean of *things).* The difference in question could therefore more suitably be called a difference between abstract and + +concrete *objects* or parts of objects. If I here still continue to talk of 'contents', I do so as not to give persistent offence to most of my readers. The distinction has arisen in the field of psychology, where intuitive illustration naturally grasps at sensuous examples. Here the interpretation of the word 'object' to mean a thing, is so dominant, that to call a colour or form an object might be felt disturbing or even confusing. We must, however, bear in mind that *talk about contents is not here at all restricted to the sphere of contents of consciousness in any real (reellen) sense, but embraces all individual objects and parts of objects as well.* We do not even restrict ourselves to the sphere of objects which are intuitive to us. The restriction has, rather, an ontological significance: objects are certainly possible, that in fact lie beyond the phenomena accessible to any human consciousness. The distinction, in short, concerns individual objects as such with unrestricted generality, its + +true place is in the framework of an *a priori* formal ontology. + +*(b)* Taking the objective (ontological) concept of 'abstract contents' as our foundation, we may mean by 'abstraction' the *act* through which an abstract content is distinguished, i.e. through which it is not prised loose, but none the less made the peculiar object of an intuitive presentation directed upon it. It appears in and with the relevant concretum, from which it is abstracted, but it is specially meant, and further not merely meant (as in 'indirect' merely symbolic presentation) but also intuitively given *as* what it + +is meant as being. + +*(c)* Here we must, however, take account of an important difference that has been more than once previously emphasized. 4 If we pay attention to one of the side-surfaces of a cube which appears before us, this surface is the 'abstract content' of our intuitive presentation. But the genuinely *experienced* content, which corresponds to this phenomenal side-surface, itself differs from the latter: it only forms the basis of an 'interpretation', through which, while it is sensed, a side of the cube differing from itself manages to appear. The sensed content is not in this case the object of our intuitive presentation: it first becomes such an object in psychological or phenomenological 'reflection'. Descriptive analysis none the less teaches us that it is not merely contained in the total concrete appearance of the cube, but that it is in a certain fashion set in relief, accented as against all other contents, which in *their* presentation of the side-surface in question do not function representatively. It naturally remains so emphasized, when it becomes *itself the object* of a presentative intuition peculiarly directed to *it,* except that then (in reflection) this intuition is added. This setting-in-relief of the content, which itself is *no act,* but a descriptive peculiarity of the phenomenal side of the acts in which the content becomes the bearer of its own intention, could likewise be called 'abstraction'. We should thus have laid down a totally + +new concept of abstraction. 5 + +*(d)* If one assumes that abstraction is a peculiar act or (in general) a descriptively peculiar experience, responsible for setting the abstract content + +in relief from its concrete background, or if one sees in the manner of such setting in relief the essence of the abstract content as such, one comes to yet another concept of the abstract. Its difference as against the concrete, is *not sought in the intrinsic nature of its contents,* but *in the manner in which they are given.* A content is said to be abstract, in so far *as it is abstracted,* + +concrete in so far as it is *not* abstracted. + +It will readily be noted that the tendency to characterize a difference in content by having recourse to acts, stems from a confusion with more advanced concepts of abstract and concrete, in which the essence of the + +matter certainly lies in the acts. + +*(e)* If one understands by abstraction, in the *positive* sense, the *preferential notice paid* to a content, by abstraction in the *negative* sense the *ignoring* of simultaneously given contents, the word loses its exclusive relation to abstract, in the sense of non-independent, contents. Even in the case of concrete contents one speaks, certainly only in a negative sense, of abstraction: one attends, e.g., to such contents 'in abstraction from their background'. + +**§42 Separation of the concepts that group themselves** + +**about the concept of the Species** + +*(a)* One distinguishes abstract and concrete *concepts:* by 'concepts' one understands the *meanings of names.* To this distinction there accordingly corresponds a distinction of names: in a nominalistic logic only this grammatical distinction tends to be drawn. We may very well start with grammar. Names can name individuals, e.g. 'man', 'Socrates', likewise attributes, e.g. 'virtue', 'whiteness', 'similarity'. The former are called 'concrete', the latter 'abstract' names. Predicative expressions corresponding to the latter, e.g. 'virtuous', 'white', 'similar', count as concrete names. More precisely we should have to say that they are concrete when the possible subjects to which they relate are concrete subjects. This is not always the case. Names like 'attribute', 'colour', 'number' etc., relate predicatively to attributes (as specific singulars) and not to individuals, or at least only mediately to indi- + +viduals, and with an alteration in predicative sense. + +Behind this grammatical distinction there is plainly a logical one, the distinction, namely, between *nominal meanings directed to attributes* and *nominal meanings directed to objects in so far as they share in such attributes.* If one follows Herbart in calling all logical presentations (this means, we hold, all nominal meanings) 'concepts', their concepts in this sense divide into abstract and concrete. But if one prefers to talk of concepts in *another* sense, which puts *concept* = *attribute,* we have a distinction among the meanings which present concepts as such, and which present the objects of concepts. This is a relative distinction in so far as objects of concepts can, in relation to certain new objects, have the character of concepts. This cannot, however, continue *in irifinitum,* and we necessarily come at last to the absolute + +distinction between concepts on the one hand, and those objects of concepts, that can no more function as concepts, on the other. On one side there will therefore be attributes, on the other side objects that 'have' attributes without themselves being attributes. To the distinction of meanings there accordingly corresponds a distinction in the field of objects, the distinction, in other words, between individual and specific (i.e. 'general') objects. General objects and general presentations or meanings, i.e. *direct* presentations of general-objects, are alike called concepts, but equivocally so. The concept of Redness is either Redness itself - as when its manifold objects, i.e. red things, are opposed to this concept - or it is the meaning of the name 'redness'. Both plainly stand in the same relation to one another as do the meaning *Socrates* and Socrates himself. The word 'meaning' is no doubt likewise equivocal, so that men do not hesitate at times to call the object of a presentation a 'meaning', and at times to say the same of its 'content' (the *sense* of its name). To the extent that a meaning is also called a 'concept', the relative talk of concept and object of concept likewise becomes ambiguous. At one time one is dealing with the relation, just now taken as basic, between the attribute (Redness) and the object to which this attribute belongs (the red house), at another time with the totally different relation between the logical presentation (the meaning, e.g., of the word 'redness', or of the proper name 'Thetis') and the presented object (the + +attribute Redness and the goddess Thetis). + +*(b)* The distinction between concrete and abstract presentations can also be interpreted in another fashion: *a presentation can be called concrete* when it directly *presents an individual object,* without the mediation of conceptual (attributive) presentations, abstract in the contrary case. On the one side, in the realm of meanings, we shall then have the *meanings of proper names,* on + +the other side *all other nominal meanings.* + +*(c)* To the above marked off meanings of the word 'abstract', there corresponds a new range of meanings for talk of 'abstraction'. This will include the acts through which abstract 'concepts' arise. Put more precisely, we are dealing with *the acts in which general names achieve their direct relation to specific unities,* and also with the acts which belong with these names in their attributive or predicative function, in which, therefore, forms like *an A, all A, some A,* S *which is A* etc., are constituted; and lastly with the acts in which the objects apprehended in these manifold forms of thought are selfevidently 'given', with the acts, in other words, in which our conceptual intentions are fulfilled, achieve self-evidence and clarity. Thus we directly apprehend the Specific Unity *Redness* on the basis of a singular intuition of something red. We look to its moment of red, but we perform a peculiar act, whose intention is directed to the 'Idea', the 'universal'. Abstraction in the sense of this act is wholly different from the mere attention to, or emphasis on, the moment of red; to indicate this difference we have repeatedly spoken of *ideational or generalizing abstraction.* This is the act aimed at by traditional + +talk of 'abstraction': through 'abstraction' in this sense we do not get at individual traits, but at general concepts (direct presentations of attributes as unities for thought). The same talk possibly extends to conceptual presentations of the more complex forms indicated; in the presentation *an A, several A's* etc., there is an abstraction from all other properties. The abstract presentation *A* takes on new 'forms', but acquires no new 'matter'. + +3 For the present question Mill's polemic against Hamilton is more relevant than + +his principal work on logic. Necessary references follow below. + +4 Sigwart, *Logik,* ed. 3, p. 10. + +5 Cf. Bain, *Logic,* I (1879), §50, p. 34 *f* + +6 Kant himself, though he opposes logical laws, as 'necessary rules' which say 'how the understanding should proceed in thought', to psychological laws which say 'what the understanding is like and how it thinks' (cf. *Vorlesungen tiber Logik,* Hart. ed. VIII, p. 14), did not ultimately wish to regard logic as a normative discipline (in the sense of one that measures adequacy in relation to set ends). This is decisively shown by his coordination of logic and aesthetic to accord with the two 'basic sources of the mind', the latter being the (rational) 'science of the rules of sensibility in general', the former the correlative 'science of the rules of the understanding in general'. Logic in this Kantian sense can, no more than Aesthetics, count as a regulative discipline guided by goals. (Cf. *Critique of Pure Reason,* Introduction to the Transcendental Logic **I,** end of paragraph 2.) + +**3 Psychologism, its arguments and its attitude to the usual** + +**counter-arguments** + +I use the expressions 'psychologist', 'psychologism', and so on, without any evaluative 'colouring', similar to Stumpf in his *Psychology and Theory of Knowledge.* 2 'Logic is a psychological discipline just as surely as knowing only arises in the mind, and as thinking which terminates in knowledge is a mental happening.' + +Lipps, *op. cit.* + +3 Cf., e.g. W. Hamilton's Lectures III, p. 78, Drobisch, *Neue Darstellung der Logik,* + +ed. IV, §2; cf. also B. Erdmann, *Logik* I, p. 18. + +*4 Logik,* vol. **I,** p. 10. Sigwart's own way of treating logic (as we shall see in Ch. VIII) + +is altogether on psychologistic lines. + +5 This point of view is expressed with increasing clearness in the works of Mill, Sigwart, Wundt, and H6fier-Meinong. Cf. on this the quotations and criticisms + +in Ch. VIII, §49 *f* + +6 Cf. Lotze's *Logik,* ed. II, §332, pp. 543-4; Natorp 'Uber objektive und subjektive Begriindungen der Erkenntnis', *Phi/os. Monatshefte* XXIII, p. 264; Erdmann's *Logik,* vol. I, p. 18. As against this cf. Stumpf 'Psychologie und Erkenntnistheorie', p. 5 *(Proceedings of Kais. Bay. Akad. d. Wiss.,* I Kl., vol. XIX, Section II, p. 469). That Stumpf is discussing epistemology, not logic, obviously makes no essential + +difference. + +**4 Empiricistic consequences of psychologism** + +I employ the term 'vague' in contrast to 'exact'. I do not in the least mean to express any depreciation of psychology by it; to pick holes in psychology is remote from my intention. Even natural science has vague 'laws' in many disciplines, particularly in such as are concrete. Meteorological laws, e.g., are vague yet + +very valuable. + +2 I mean by these the senses of the propositions *'A* and *B',* i.e. both hold, and *'A* or + +*B',* i.e. one holds -- which does not imply that *only* one holds. + +3 Cf. the systematic discussions of Ch. VIII of this work regarding the scepticalrelativistic absurdity of all conceptions which make logical principles depend on + +**S Psychological interpretations of basic logical principles** + +A general discussion of the main defects of empiricism, carried as far as seemed likely to help our idealistic intentions in logic, is given in the Appendix to this + +and the following section. *2 Logic,* Book II, ch. VII, §4. + +3 Mill, *An Examination,* ch. XXI, p. 491. Mill slips in not noticing that Spencer's reference is not to the law of contradiction but to that of excluded middle. 4 Mill, *op. cit.* p. 491. Cf. also p. 487: 'It is the generalization of a mental act, which is of continual occurrence, and which cannot be dispensed with in reasoning.' 5 In the pointed sense of 'scepticism' developed in ch. VII, empiricism is therefore called a sceptical theory. Windelband tellingly applies the Kantian term 'hopeless attempt' to empiricism - it is the hopeless attempt 'to establish by an empirical + +theory what is itself presupposed by every theory' *(Priiludien I ,* p. 261). 6 Formulations of Heymans *(Die Gesetze und Elemente des wissenschaftlichen Denkens,* II, §§19-20. Sigwart's formulation in Logik, 12, p. 419, resembles H's second formulation: 'It is impossible consciously to affirm and deny the same + +proposition. ' + +7 Cf. the end of our quotation from Mill's polemic against Hamilton in §25 above. On p. 484 *op. cit.* Mill likewise writes 'two assertions, one of which denies what the other affirms, cannot be thought together', in which 'thought' is immediately + +equated with 'believed'. + +8 It is well-known that Kant's theory of knowledge has sides in which it strives and successfully gets beyond the psychologism of mental faculties as sources of knowledge. Here it is enough to stress that it also has prominent sides which fall within this psychologism, which of course does not preclude lively polemics against other forms of the psychologistic founding of knowledge. Not merely Lange, but most Kantianizing philosophers, fall in the field of psychologizing epistemologists, however little they may fancy the name. For even transcendental psychology *also* + +is psychology. + +**6 Syllogistic inferences psychologistically considered. Syllogistic** + +**and chemical formulae** + +Heymans, *op. cit.* I, p. 70. F. A. Lange likewise said (cf. the last paragraph of the long citation from the *Logische Studien,* above, §28) that the *factual* elimination of contradictions in our judgements was the ultimate *ground* of logical rules. + +**7 Psychologism as a sceptical relativism** + +1 Please note that the term 'knowledge' is, in this work, not restricted, as it usually + +is restricted, to objects that are real. 2 See Ch. v, Appendix to §§25-6. + +3 His view should recommend itself to those who think to separate subjective from objective truths by denying an objective character to judgements of introspection. They assume that the being-for-me of a conscious content cannot at the same time be a being-in-itself, that subjectivity in the psychological sense excludes + +objectivity in the logical sense. + +4 Cf. *op. cit.* p. 411: 'These propositions must be *a priori* certainties in the sense that we only recognize in them *a constant and unavoidable function of our thought'.* 1 may quote this passage though in its context it does not refer to the laws of logic. I am justified by the whole sense of Sigwart's statements (see 12, §48), and + +by the fact that, on the same page I have quoted, the law of contradiction + +is expressly compared with the certainties in question. + +5 Can I ever say this with certainty? The irrevocability in question does not concern the actual, but the ideal. It is not the certainty of my judgement that is unchangeable (as Sigwart has just maintained) but its *validity* or its truth. 6 Cf. Sigwart's excellent distinction between the occasion of a connection and the + +ground of a decision *(op. cit.* p. 250). + +7 I am here thinking of all pure logical principles taken together. With the two or three 'laws of thought' in the traditional sense, the concept of formally consistent thought is not even defined, and everything traditionally said on this head I (and not only 1) regard as erroneous. Each formal absurdity can be reduced to a contradiction, but only through the mediation of many other formal principles, e.g. syllogistic, arithmetical etc. Even in syllogistics there are at least a dozen principles. They can all be wonderfully proved - in sham proofs that presuppose + +themselves or equivalent propositions. + +8 Cf. *op. cit.* Nr. 369, sub e, pp. 377-8. Once men had accustomed themselves to the notion of a change in logical thinking, the thought of its development was not far. According to G. Ferrero, *Les lois psychologiques du Symbolisme, Paris* 1895 - I read from a report by A. Larson in the *Zeitschr.j Philos. vol.* 113, *p. 85* - 'Logic should become positive and should present rules of inference in connection with the period and stage of a culture, since even logic alters with the development of the brain ... That pure logic and deductive methods were previously preferred, is due to mental laziness. Metaphysics has remained the colossal monument to this mental laziness up to this day, fortunately only operative + +among a few retarded thinkers.' + +**8 The** psycho logistic **prejudices** + +A mark of a mark is, generally speaking, plainly *not* a mark of the thing. If the principle meant what it literally says, we could infer: This blotting-paper is red, + +Red is a colour, therefore this blotting-paper is a colour. + +2 In this view, that the normative notion of 'ought' does not form part of the content of logical laws, I am glad to find myself in agreement with Natorp, who has recently made the brief and clear remark in his *Sozialpiidagogik* (Stuttgart, 1899), §4, that 'logical principles, we maintain, are as little about what people actually think in such and such circumstances, as they are about what they ought to think'. He says of the equational reasonings 'If *A* = Band *B* = C, *A* = C' that 'I perceive its truth when only the terms to be compared, and the relations given together with them, are before me, without having to think in the least of the actual or proper conduct of some corresponding act of thought' (pp. 20-1). There are certain other equally important *rapprochements* between these Prolegomena and the distinguished thinker's present work, which unhappily came too late to assist in forming and expounding these thoughts. Two previous writings of Natorp, the above quoted article from *Phil. Monatshefte,* XXIII and the *Einleitung in die Psychologie,* stimulated me, however - though other points in them provoked me to controversion. 3 'Pure' or 'formal' mathematics, as I use the term, includes all pure arithmetic and theory of manifolds, but not geometry. Geometry corresponds in pure mathematics to the theory of a three-dimensional Euclidean manifold. This manifold + +is the generic Idea of space, but not space itself. + +4 Elementary arithmetic provides good examples of this last. A being that could intuit three-dimensional arrangements (with difference of sign) as clearly and with as much practical mastery as men are able to intuit two-dimensional arrangements would possibly have quite different methods of calculation. My *Philosophie* + +*der Arithmetik* deals with such questions, and, in particular, with the influence of + +physical circumstances on methodical set-up, pp. 275 *f,* 312 *ff* + +5 The impossibility of theoretical connections between heterogeneous fields, and the nature of the heterogeneity in question, has of course not been sufficiently + +investigated in logic. + +6 See in addition the fine statement of Natorp 'Uber objektive und subjektive Begriindung der Erkenntnis', *Philos. Monatshefte,* XXIII, p. 265 *f* Cf. also G. Frege's stimulating work *Die Grundlagen der Arithmetik* (1884), p. vif (I need hardly say that I no longer approve of my own fundamental criticisms of Frege's antipsychologistic position set forth in my *Philosophie der Arithmetik,* I, pp. 129- 32). I may here take the opportunity, in relation to all of the discussions of these Prolegomena, to refer to the Preface of Frege's later work *Grundgesetze der* + +*Arithmetik,* vol. I (lena, 1893). + +7 The law of contradiction should not be confused with the normative proposition for judgements which is its evident consequence: 'Of two contradictory judgements, one is *correct.'* The concept of correctness is correlative with that of truth. A judgement is correct when it treats what is true as true, a judgement, therefore, whose 'content' is a true proposition. The logical predicates True and False, taken in their proper sense, only concern propositions in the sense of the ideal meanings of assertions. The concept of a contradictory judgement is again correlated with that of a contradictory proposition. Judgements are called 'contradictory' in the noetic sense, if their 'contents', their ideal meanings stand in the descriptively definite relation which, in the sense of formal logic, we call + +'contradiction' . + +8 Wundt, *Logik,* I, 2nd ed., p. 91. Wundt regularly couples inner evidence with universal validity in this passage. As regards the latter, he distinguishes between a subjective form of universal validity, a mere consequence of inner evidence, and an objective form, which also covers the postulate of the intelligibility of experience. But as the justification and adequate fulfilment of this postulate itself rests on inner evidence, it does not seem feasible to drag in 'universal validity' into + +discussions of basic principles. + +9 If we really had to interpret the theory of inner evidence in the manner of Hofler on p. 133, *op. cit.,* it would have been corrected by our previous critique of empiricistic misunderstandings of logical principles (see §23). Hofler's statement 'that an affirmative and a negative judgement about the same object are incompatible', is, as an exact statement, false, and can even less count as a statement of the logical principle. A similar mistake slips into the definition of the correlatives 'ground' and 'consequence': if it were correct, it would falsify all syllogistic rules. It runs: 'A judgement C is the consequence of a ground G, if the *belief* in the falsity of C is incompatible with the (imagined) *belief* in the truth of G' *(op. cit.* p. 136). Note that Hofler explains incompatibility in terms of evident non-coexistence *(op. cit.* p. 129). He plainly confuses the ideal non-coexistence (i.e. lack of joint truth) of the propositions in question, with the real non-coexistence + +of the corresponding acts of affirmation, presentation etc. + +**9 Logic and the principle of the economy of thought** + +My negative criticism, in this chapter, of one main tendency in Avenarius's philosophy, does not mean that I do not deeply respect him as a thinker torn all too early from the labours of science, and that I do not likewise respect the solid + +seriousness of his scientific works. + +2 E. Mach, *Die Mechanik in ihrer Entwicklung* (1883), p. 460. The passage is worth quoting in full. It goes on: 'Mathematics taught in this manner has barely more + +chemical formulae 72-4 circles of similars 243-4, 292 classification 23-4, 76, 246 Cloyne, Bishop of 267 cognition 106, 114, 168 + +communication 173, 187, 189-203 complexity 126, 128, 194; of + +expressions 23 Comte, A. 125 + +concepts 16,69,82,97,111-12,137, 151,153-4,168-9,175,224,230-42, 255, 264, 311; cogitative/sensuous 280-91; formation 258-9, 308 concrete: concepts 311-12; contents 308; idea 259, 269, 290; images 290; intuition 296, 308; things 298 + +conditions 119 + +connection 76, 114, 121, 153, 291; + +apodeictic 102, 106 connotation 203-5 + +consciousness 57, 59, 62, 67, 69, 77, 83,85,127, 177,214,247,249,252, 263, 266, 268, 269, 272, 279-81, + +290-1, 305 consequence 104, 108 constitution 80-1 + +content 108-15, 185, 199-200, 222, 228, 253, 265, 273, 275, 297, 300-1, 305, + +309; knowledge 150-2 + +contingency 41,42, 82, 83, 107, 146 contradiction 47, 56-8, 61-4, 70-1, 78-9,81,91,104,107,113; double status 64-7; Sigwart's doctrine 67-9 + +Cornelius, H. 123, 129, 303-7 + +deduction 126-8, 155 definite article 220-1 delusion 61-4 demonstration 184-6 demonstratives 219-20 Descartes, R. 161,208 + +descriptive: analysis 292, 310; assertion 302; distinction 297; psychology 175-6, 206; science 148 + +disbelief 56 disciplines 37-9, 45 + +dispersed multiplicity 242-4 *distinctio rationis* 294-5, 303, 308 doctrine of terms III Drobisch, W. 31, 32, 137 + +economy of thought 277-8; facts/ideal 131-3; justified ends of 126-8; meaninglessness of 129-31; scientific + +meaning 123-6 + +empiricism 30, 46-8, 55, 56-7, 58-9, 67,68,70,73,76,120,133,160-1, 166, 243-4, 262; defects 59-61 epistemology 14, 16, 29, 51, 86, 120, 129-31, 133, 141, 169, 263, 292 + +equivalence 213 equivocation 217 + +Erdmann,B.22, 31,83,90-100,134,255 error 98, 99, 107, 133, 251, 261, 262, + +266, 286-8, 292, 309 + +essence 94-5, 102, 147, 151-2, 154, 212, + +224-5, 246, 263, 279 essentially occasional expressions + +217-21 ethics 36 + +evidence 19, 177, 179 + +existence 90 + +experience 54, 56, 57, 63, 85, 92, 106, 118,130, 149, 166, 168, 177, 186-7, 212, 222, 263, 273, 298, 310 explanation 50, 60, 81, 131, 132, 147-8, + +161, 246 + +expression 172-3, 187-8, 194, 199, 206, 211, 213-15, 222-4, 228-9, 237,287; in communication 189-90; fluctuating 221-2; as ideal unity 194-6; objective correlate of 196-8; phenomenological/intentional distinctions 188-9; in solitary life + +190-1 extension 264-6 external objects 124, 296 + +facts 53-4,57,80,82-3,88,89-90,97, + +131-3,160-1 fallacies 73 + +falsehood 41, 43, 51, 58, 59, 71, 79-80, 82,92, 98, 101, 106, 113,240 + +familiarity 213 fields 12-13 + +fixation of aims 260-2 + +forms 21, 22, 264-6, 281, 286, 288, 312; of presentation 111-12; of theory + +155, 156-7 + +formulae 61, 70, 77; chemical 72-4 + +Frege, G. 201, 318 + +fulfilment 179, 199-200, 212, 246, 263, + +287,290 function 84 + +games-meaning 210-11 + +general: concepts 277-82; names 289; objects 312; presentation 312 generality 53, 55-6, 58-9, 67, 114, 169, 266, 271, 280-2, 289, 291, 305; of associative functioning 267; of ideas 262-4; as meaning-form 264-6; of psychological function 264-6 + +generic images 256-7 + +geometry 15, 147, 157-8, 176, 255, 270, + +285-7 good 35-7 + +grammar 172-3, 311 + +ground 97, 104, 108, 147, 154; logical + +88 + +grounded knowledge 146 + +Hamilton, Sir W. 12, 30-1,40, 57, 157, + +258,259-60 + +Herbart, J. 30, 32,42, 135, 136-8 + +Heymans, G. 66, 70, 72 Hoffding, H. 213 Hofler, A. 116 + +Hume, D. 60-1, 125, 226, 262, 289-99, + +302-3 + +hypostatization 248-57 + +Idea (ideation) 232, 240, 250-2, 262, 270, 293, 312; formal logic 141-2; general 262-4; individual 284; of Knowledge 149-50; of Manifolds 157; of method 24; of normative discipline 37; of Science 25; of Subjectivity 150; of System 104; of Theory 152; of truth 86; unified + +experience 130 ideal objects 250 ideal unity 242-4 idealism 106-7, 238 + +ideality 50-1, 65, 68-9, 75-6, 83, 87, 89,92,110-11,113-14,118, 119-22, + +131-3, 151-2, 230, 231 + +identity 67-8, 84, 87, 89, 230, 241-2, 244 + +image-contents 239 images, illustrative 203 imagination 151, 208 imagined objects 300 incapacity 63 incompatibility 63 + +indication 183-6; associative origin + +186-7 + +individual: idea 284; objects 239-40 + +individuality 271 induction 56, 58, 60 inference 46, 88, 225-6 + +inner eVIdence 17-18,63,81,82, 115-22, + +126, 150 + +insight 55, 61, 73, 86,95, 99, 127, 171, + +176,184-5 + +intention 35, 69, 193, 265, 290-1, 301, + +309 + +interconnections 144 + +interpretation 214, 239; basic principles + +56-69 + +intimation 189-90,192-3,195,216-17 intuition 54,81,96,140, 168, 170, 174, 193-4,196,203,209-15,229,243,248, 252-3, 261, 273-6, 277-8, 279, 282, 287, 292, 295, 308; of sense 280-1 + +intuitive representation 154 irrefragable necessity 73 + +is-ought 102 + +Jiische, 41, 135 + +judgements 12-13, 17, 19,21,42,43, 49, 58, 60-2, 63-4, 67, 71, 75, 78, 80-1, 84, 85, 86, 88-9, 91, 92, 93-4, 97, 100, 102-3, 115-22, 130, 145, 166-7, 174, 184, 195, 205, 212, 215, 224-5, 230, 260, 265, 274, 298; assertoric/apodeictic 89; normative + +35-6; universal 241 + +justification 75 + +Kant, I. 13, 14, 28-30, 32, 36,41-2, 65, + +74, 135-6 knowing 18, 204, 298 + +knowledge 16-19,21,22,26-7,29,39, 43, 49, 53, 54-5, 60, 64, 75, 88, 89, 98, 99, 101-7, 128, 130, 145, 149-50, 150-2,160-1,166,175,178-9,204, + +206, 246, 251, 292, 303 Kries, J. von 147-8 Kroman, K. 66 + +Lange, F. A. 64-6, 141-2 language 23, 165-6, 244, 245 + +laws 20, 22, 31, 33-4, 41, 42-4, 47-8, 57, 58, 64, 66-7, 70, 71, 77, 79, 81, 84, 89-90, 92, 97-8, 101-3, 105-6, 111-13, 116, 129, 150, 152,277-8; approximate 46-7; basic 146; of complication 153; of Contradiction 47; empirical 52; exact 52, 61; factual + +53; genuine 52-3; ideal 153; knowledge of 54-5; natural 31, 48-51, 68, 80; pure 51-2, 53, 54; of thought 48-51, 73-4,92,97; vague + +59,61 + +least action 123, 129 + +Leibniz, G. W. 29, 33, 89-90, 135, + +138-40, 161 Liebmann, O. 66 likeness 241-2, 243 Lipps, T. 40, 83, 90, 134 + +Locke, J. 248,250-1,252, 254-6, 262-4, 270, 277, 283-4, 292, 306, + +308 + +logic 40,43-4,47-8, 83, 115, 224-5; applied 28-9; definitions 11, 26-7, 30-1; demarcation 13-14; formal 14, 33, 106-7, 142; practical character + +28-33 + +Lotze, H. 47, 135, 138 + +Mach, E. 123, 124, 126, 129 manifolds 155-8, 167,220, 228, 254 mathematics 15-16, 22, 32,47, 95, 97, 108-11,117,127-8,138,139-40, 142-3,156,158-60,176,220 meaning 154,167-8,170,171,174,177, 188-9, 198-9, 211-12, 215, 217, 228-9, 231-2, 233, 240, 241, 261, 281,287-8, 306; connotation 203-5; equivocations 200-3; ideal 224-7; as + +object 232; occasional 217-21; unified 229-31; usual 221; variations 222-4 + +meaning simpliciter 199-200 meaning-content 170, 221 + +meaning-fulfilment 167, 192-4, 196, + +199-200, 290 + +meaning-intention 167, 192-4, 199, 202-3,206,210,211,227,229,252, + +279, 290 + +meaninglessness 200-3 + +Meinong, A. von 116, 186,299 + +memory 22, 124, 306 + +mental phenomena 48,95,96,97,98, 110,113,118-19,125,129,169,170, + +188 + +metaphysical hypostatization 248-9 + +metaphysics 16, 76-7, 179 + +method 24, 25-6, 33, 105, 111, 126, + +128, 158 + +Mill, J. S. 11,29,30,31,40,56-9,58, 83, 103, 115, 134, 135, 165, 203-5, 244-6, 258, 261, 263, 264, 266, 269, + +272 + +mind 49, 57, 66-7, 286-7 moments 294-5, 298, 299 + +morality 37 + +motivation 184, 186,232 Muller, G. E. 296, 303 + +names 197-8,203-5,216-17,228,240, 244-6,258, 260, 311; general 262-3 nature 48-51, 66, 87, 88-9, 98, 106 necessity 73, 88-91,94, 97, 108 negation 41, 57, 61, 68, 91, 93 noetic 76, 77, 150, 168 nomenclature 23 + +nominalism 248-9, 259-60, 282, 305-6; critique 266; objections to 260-2; + +origin of modern 262-4 nomological sciences 148 nomology 152, 224 nonsense 78 + +normativity 16-17, 19, 25-6, 31-2, 44-5, 50, 58,62,68, 83-4, 97, 101-3, 106,131,138, 149,230; concept 33-7; disciplines/technologies 37-8; + +foundation 38-9 norms 103-6 + +object -directedness 171 + +objective: analysis 247; categories 153; conditions 76, 77; correlate 196~8, 202; expression 217~21; laws 63; reference 198~9; validity 154 objectivity 86, 87, 104, 121, 145, 161, + +169,178,217,295,305 + +objects 169,212, 215, 230, 239~40, 250, 273,275, 297, 309; apparent 252~3 + +observation 57, 207 ontology 148 + +opposition 97, 106, 121, 238, 255 + +ought/is 43 + +particularity 41 parts 294~5, 300~1 Paul, H. 221 + +perception 57,121,171, 176, 189~90, 199, 222, 295, 296~7, 305 personal pronoun 218~ 19 phenomenological analysis 247 phenomenology 153, 165~8, 176~9, 193~4, 263, 272, 298; analytic 168~72 + +philosophy 129, 133, 158~60 + +pictures 206~9 Plato 256 positive mode 57 + +possibility 108, 151~2, 243, 246 predicate, predication 104, 260, 262, + +265, 269, 282, 304 + +prejudices 101~3; content 108~15; judgement 115~22; knowledge 101~7 + +prescription 31 + +presentation 111~12, 171, 174, 177,205, 213~15, 228, 230, 248, 252, 261, 264, 275, 289, 292, 306, 308; general 282 presupposition 44, 54, 177~9, 225 principles 46, 48, 60, 70~2, 91~2, 113 probability 48~9, 56, 88, 108, 114, 140, + +160~1, 186 + +proof 22,46,49, 53, 59~60, 71, 74, 82, 108, Ill, 114, 126, 146, 185, 225, + +285~6 + +proper names 260, 271, 281 properties 104, 252, 253, 297 propositions II, 16, 19~20, 25~6, 29, 38,46, 52, 57~8, 68~9, 77, 89, 92, 94~6, 97, 101~3, 104, 136, 155~6, + +179, 225, 265, 303~4; normative 33~7; transformation of 116~19 + +pseudo-problems 266 pseudo-theories 266 + +psychological hypostatization 248~57 + +psychological theory 291~2 + +psychologism II, 14, 29, 40, 129, 169, 302; anti- 106~7; consequences 46~54; empiricist consequences 46~8; gap in proof 44~5; interpretations 56~69; like relativism 82~3; line of proof 41; opposition to 41~4; prejudices 101~22; Sigwart's logic + +83~90 + +psychology II, 14, 29, 77, 88, 104, 106, 118, 129~31, 166, 170, 175,272,303 pure logic 14, 28, 29, 31~3, 41, 45, 55, 69,84, 97, 104~5, 107, 110~11, 113, 117, 131~3, 134, 136, 140~1, 165~6, 175, 224~7, 237, 279; achievements in 158~60; broadening of theory 160~1; + +ideal conditions 149~50; + +interconnections 144~5; knowledge content 150~2; manifolds 156~8; tasks 152~6; unity of theory 146~9 + +rationality 48~51, 83, 89, 131~2 + +realism 249 + +reality 50~1, 88, 94, 113, 114, 119~22, 151,171, 177, 184,249,250 reflection 170, 172, 196, 232, 310 + +reflective circle 107 relation 104 + +relativism 129, 133; critique 78~82; extended sense 82; individual 78; like psychologism 82~3; specific 77~82 + +relatum 104 + +representation 278~80, 289, 291~2; critique 284~6; general 281~2; as + +substitution 282~4 Riehl, A. 108, 213 + +rules 41, 44, 46, 70, 84, 97, 103 + +scepticism 17,49,61,83; limit 301~2; metaphysical sense 76~7; refutation 301~2; strict concept 75~6; transference 300~ 1 Schleiermacher, F. 26~ 7 + +scholasticism 33, 135, 138 Schopenhauer, A. 37 Schuppe, W. 31 + +science 30, 104-5, 128, 133, 134, 138, 141, 145, 169, 224; aims 12; fields 12-13; logic as 16-19; possibility of 21-3; theory of 16-19, 21-3, 24-5, + +27 + +science of science *(Wissenschafislehre)* + +16-19,21-3, 24-5, 27 second-order concepts 153 + +self-evidence 61, 72, 75, 77, 78, 81, 93, 102, 116, 118, 167-8, 171, 174, 208, 212, 223, 226, 230, 239, 246, 260-1, 265, 266, 292, 297-300, 301-2 + +self-identical 241 sensation 171 + +sense 200-1, 206, 209, 213-14, 250, 263, 264-6, 273, 280-1 sense-contents 124, 239, 300 shall-should 34-5, 102 + +sign(s) 183, 187-8, 193, 210-11, 214, + +261, 264, 281, 285 + +Sigwart, C. 29, 31,43, 51, 64, 67-9, + +83-90, 103, 115, 135 singulars 213, 240-1, 243, 265-6 space 64, 157-8, 222, 224 + +species 230,231-2,237-8,239,241-2, 243,247, 250, 265-6, 269, 271, 273, 282, 299, 308, 311-13; external to thought 248; as objects 240-1, 243-4; in thought 248; unity of + +241-2 + +specific unity 261, 270 Spencer, H. 57, 244-6 subjective conditions 75-6, 77 subjective incapacity 63 + +subjectivity 77-9, 89, 104, 149-50, 253, + +295, 305 + +substitution 23, 282-4 surrogative function 210-11 + +syllogism 15, 20, 21, 46, 48,51-2,84, 105,108,114,136,139,152,155, 224, 230; and chemical formulae + +72-4; principles 70-2 + +symbolic: intentions 254; meaning 261; presentation 280; thought 211 + +technology 25-6, 29-32, 37-8, 103, + +116, 126-8, 134 teleology 124, 128 + +theoretical disciplines 37, 38-9 + +theory 33-4,40,61, 75-6, 83, 107, 133, 147, 151-2, 153, 167,224,272; forms + +155-7; general 149-50 thing 77, 101,249, 275, 295, 297 + +thing in general 271 + +thinking 22, 23, 26,31,41-2,45,48, 50, 64, 71, 88-9, 91, 92, 95, 116, 125, + +127,232, 274-6 + +thought 22, 23, 26, 41, 48-51, 57, 59, 61-3,71,73-4,84,91-2,93,97, 98-9, 102, 111, 137, 153, 166, 177, 210-11, 212, 226, 263, 275, 286, 291 + +thought-acts 274 thought-content 246, 249 thought-intention 281 time 222, 224 Trendelenburg, A. 12 + +triangles 254-6, 264, 267, 268, 270, + +286, 306-7 + +truth(s) 17, 18, 19,20,21,28,31,32, 41, 43, 45, 48, 55, 58, 59, 62, 71-2, 73,77-82,85-7,92,94,97,98, 99-100, 102, 104, 108, 113, 117, 119, 131, 142, 196, 211-12, 215, 223, 250, 266; general 146, 149; individual146; + +interconnection 144-5 + +Uberweg, F. 31 + +unconscious 22, 65, 209, 271, 287 understanding 42, 51, 83, 96, 209-10, + +213, 228-9 uniformity 214 + +unity 76,86, 104, 138, 167,217,226, 269; of acts 193-4; essential! extra-essential 147-9; of experience 186-7; ideaI194-6, 229-31; of knowledge 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b/lit-marker2/edmund-husserl-logical-investigations-vol2/edmund-husserl-logical-investigations-vol2.md @@ -0,0 +1,6131 @@ +**.** + +Logical + +Investigations + +Volume 2 + +Edmund Husserl + +Logical Investigations + +Volume II + +International Library of Philosophy + +Edited by Jose Bermudez, Tim Crane and Peter Sullivan + +Advisory Board: Jonathan Barnes, Fred Dretske, Frances Kamm, + +Brian Leiter, Huw Price and Sydney Shoemaker + +Recent titles in the ILP: + +The Facts of Causation + +D. H. Mellor + +The Conceptual Roots of Mathematics + +j. R. Lucas + +Stream of Consciousness + +Barry Dainton + +Knowledge and Reference in Empirical Science + +jody Azzouni + +Reason without Freedom + +David Owens + +The Price of Doubt N. M. L Nathan + +Matters of Mind Scott Sturgeon + +Logic, Form and Grammar + +Peter Long + +The Metaphysicians of Meaning + +Gideon Makin + +Logical Investigations, Vols I & II + +Edmund Husserl + +First published in German as Logische Untersuchungen + +By M. Niemeyer. Halle 1900/1901 + +Second German edition. Vol. I. Part I. first published 1913 Second German edition. Vol. II. Part II. first published 1921 + +First published in English 1970 By Routledge & Kegan Paul Ltd Reprinted 1976. 1977. 1982 + +This paperback edition first published 200 I + +by Routledge + +2 Park Square. Milton Park. Abingdon. Oxon. OX14 4RN + +Simultaneously published in the USA and Canada + +by Routledge + +270 Madison Ave. New York NY 10016 + +Routledge is an imprint of the Taylor & Francis Group + +Transferred to Digital Printing 2006 Translation © 1970 J. N. Findlay Editorial matter © 200 I Dermot Moran + +Typeset in Times by Graphicraft Limited. Hong Kong + +All rights reserved. No part of this book may be reprinted or reproduced or utilised in any form or by any electronic. mechanical. or other means. now known or hereafter invented. including photocopying and recording. or in any information storage or retrieval system. without permission in + +writing from the publishers. + +British Ubrary Cataloguing in Publication Data + +A catalogue record for this book is available from the British Library + +Ubrary of Congress Cataloging in Publication Data A catalog record for this book has been requested + +ISBN 0-415-24189-8 (Vol. I) ISBN 0-415-24190-1 (Vol. II) + +Publisher's Note + +The publisher has gone to great lengths to ensure the quality of this reprint but pOints out that some Imperfections In the original may be apparent + +Contents + +VOLUME II, PART I OF THE GERMAN EDITIONS + +(CONTINUED) + +INVESTIGATION III + +ON THE THEORY OF WHOLES AND PARTS + +Introduction 3 + +CHAPTER ONE + +The difference between independent and non-independent objeas 4 + +§1 Complex and simple, articulated and unarticulated objects 4 + +§2 Introduction of the distinction between independent and + +non-independent objects (contents) 5 §3 The inseparability of non-independent contents 6 §4 Analyses of examples following Stumpf 7 §5 The objective determination of the concept of inseparability 9 + +§6 Continuation. Tie-up with a criticism of a much-favoured + +notional determination 10 + +§7 Further pointing up of our notional determination by + +introducing the concepts of pure law and pure genus 11 §7a Independent and non-independent Ideas 13 + +§8 Demarcation of the distinction of independent and non-independent contents and the distinction between + +intuitively emphatic and intuitively blended contents 13 + +§9 Continuation. Reference to the wider sphere of the + +phenomena of fusion 15 + +§1O The multiplicity of laws governing the various sorts of + +non-independent contents 17 + +§1 1 The difference between these 'material' laws and 'formal' or + +'analytic' laws 19 + +propositions 20 §13 Relative independence and non-independence 22 + +CHAPTER TWO + +Thoughts towards a theory of the pure forms of wholes and parts 25 §14 The concept of foundation and some relevant theorems 25 + +§15 Transition to the treatment of the more important + +part-relations 27 §16 Reciprocal and one-sided, mediate and immediate foundation 27 + +§17 Exact determination of the concepts of piece (portion), + +moment, physical part, abstractum, concretum 28 + +§18 The difference between the mediate and immediate + +parts of a whole 30 + +§19 A novel sense of this distinction: nearer and more remote parts + +of the whole 30 §20 Nearer and remoter parts relatively to one another 32 + +§2l Exact pinning down of the pregnant notions of whole and + +part, and of their essential species, by means of the notion of + +foundation 34 §22 Forms of sensuous unity and wholes 35 §23 Forms of categorial unity and wholes 38 + +§24 The pure formal types of wholes and parts. The postulate + +of an a priori theory 39 + +§25 Additions regarding the 'piecing' (fragmentation) of wholes + +through the 'piecing' of their 'moments' 41 + +INVESTIGATION IV + +THE DISTINCTION BETWEEN INDEPENDENT AND NON-INDEPENDENT MEANINGS AND THE + +IDEA OF PURE GRAMMAR 47 + +Introduction 49 §l Simple and complex meanings 50 + +§2 Whether complexity of meanings merely reflects complexity of + +objects 50 + +§3 Complexity of meanings and complexity of the concrete act of + +meaning. Implied meanings 51 + +§4 The question of the meaningfulness of 'syncategorematic' + +components of complex expressions 53 + +§5 Independent and non-independent meanings. The non- + +independence of the sensory and expressive parts of words 55 + +§6 Other opposed distinctions. Unclosed, abnormally abbreviated + +and defective expressions 56 + +§8 Difficulties of this conception. (a) Whether the + +non-independence of the meaning does not really only + +lie in the non-independence of the object meant 59 §9 (b) The understanding of isolated syncategorematica 60 §1O A priori laws governing combinations of meanings 61 + +§l l Objections. Modifications of meaning which are rooted in + +the essence of expressions or meanings 64 §12 Nonsense and absurdity 67 + +§13 The laws of the compounding of meanings and the pure + +logico-grammatical theory of forms 68 + +§14 Laws which discourage nonsense and laws which discourage + +absurdity. The Idea of a purely logical grammar 71 Notes 75 + +INVESTIGATION V + +ON INTENTIONAL EXPERIENCES AND + +THEIR 'CONTENTS' 77 + +Introduction 79 + +CHAPTER ONE + +Consciousness as the phenomenological subsistence of the ego + +and consciousness as inner perception 81 + +§l Varied ambiguity of the term 'consciousness' 81 + +§2 First sense: Consciousness as the real phenomenological + +unity of the ego's experiences. The concept of an experience 82 + +§3 The phenomenological and the popular concept of + +experience 84 + +§4 The relation between experiencing consciousness and experienced content is no phenomenologically peculiar + +type of relation 85 §5 Second sense. 'Inner' consciousness as inner perception 86 §6 Origin of the first concept of consciousness out of the second 87 + +§7 Reciprocal demarcation of psychology and natural science + +(First edition) 89 §8 The pure ego and awareness ('Bewusstheit') 91 Additional Note to the Second Edition 93 + +CHAPTER TWO + +Consciousness as intentional experience + +94 + +§10 Descriptive characterization of acts as 'intentional' + +experiences 95 + +§1 1 Avoidance of verbally tempting misunderstandings. + +(a) The 'mental' or 'immanent' object 97 + +§12 (b) The act and the relation of consciousness or the ego to + +the object 100 §13 The fixing of our terminology 101 + +§14 Difficulties which surround the assumption of acts as a + +descriptively founded class of experiences 102 + +§15 Whether experiences of one and the same phenomenological kind (of the genus feeling in particular) can consist partly of + +acts and partly of non-acts 106 (a) Are there any intentional feelings? 107 + +(b) Are there non-intentional feelings? Distinction between + +feeling-sensations and feeling-acts 109 §16 Distinction between descriptive and intentional content 11 2 + +§17 The intentional content in the sense of the intentional + +object 11 3 §18 Simple and complex, founding and founded acts 115 + +§19 The function of attention in complex acts. Instance of the + +phenomenological relation of verbal sound to sense 11 6 + +§20 The difference between the quality and the matter of + +an act + +§21 The intentional and the semantic essence + +Appendix to §11 and §20. Critique of the 'image-theory' and of the doctrine of the 'immanent' objects of acts + +CHAPTER THREE + +11 9 122 + +125 + +The matter of the ad and its underlying presentation 128 + +§22 The question of the relation between the matter and + +quality of an act 128 §23 The view of 'matter' as a founding act of 'mere presentation' 129 + +§24 Difficulties. The problem of the differentiation of + +qualitative kinds 131 §25 Closer analysis of our two possible solutions 132 §26 Consideration and rejection of the proposed conception 134 + +§27 The testimony of direct intuition. Perceptual presentation + +and perception 135 + +§28 Special investigation of the matter in the case of + +judgement 139 + +§29 Continuation: 'acceptance' or 'assent' given to the mere + +presentation of the state of affairs 140 Additional note 143 + +§30 The conception of the identical understanding of a word + +or a sentence as a case of 'mere presentation' 143 + +§3 1 A last objection to our view. Mere presentations and + +isolated 'matters' 144 + +CHAPTER FOUR + +Study of founding presentations with special regard to the + +theory of judgement 146 + +§32 An ambiguity in the word 'presentation', and the supposed self-evidence of the principle that every act is founded on + +an act of presentation 146 + +§33 Re-establishment of our proposition by means of a new + +notion of presentation. Naming and asserting 147 + +§34 Difficulties. The concept of the name. Positing and + +non-positing names 149 + +§35 Nominal positing and judgement. Where judgements as such + +can be parts of nominal acts 152 + +§36 Continuation. Whether assertions can function as complete + +names 155 + +CHAPTER FIVE + +Further contributions to the theory of judgement 'Presentation' as a + +qualitatively unitary genus of nominal and propositional acts 158 + +§37 The aim of the following investigation. The concept of an + +objectifying act 158 §38 Qualitative and material differentiation of objectifying acts 159 + +§39 Presentation in the sense of an objectifying act, and its + +qualitative modification 162 §40 Continuation. Qualitative and imaginative modification 165 + +§41 New interpretation of the principle that makes + +presentations the basis of all acts. The objectifying act as + +the primary bearer of 'matter' 167 §42 Further developments. Basic principles of complex acts 168 + +§43 Backward glance to our previous interpretation of the + +principle under discussion 169 + +CHAPTER SIX + +Summing-up of the most important ambiguities in the terms + +'presentation' and 'content' 171 + +§44 'Presentation' 171 §45 The 'presentational content' 175 Note 175 + +VOLUME II, PART 2 OF THE SECOND + +GERMAN EDITION 177 + +Foreword to the second edition 177 + +INVESTIGATION VI + +ELEMENTS OF A PHENOMENOLOGICAL + +ELUCIDATION OF KNOWLEDGE 181 + +Introduction 183 + +First section + +Objectifying intentions and their fulfilments: knowledge as a synthesis of fulfilment and its + +gradations 189 + +CHAPTER ONE + +Meaning-intention and meaning-fulfilment 191 + +§l Whether every type of mental act, or only certain types, + +can function as carriers of meaning 191 + +§2 That all acts may be expressed does not decide the issue. + +There are two senses to talk about expressing an act 192 + +§3 A third sense of talk about the 'expression' of acts. + +Formulation of our theme 193 + +§4 The expression of a percept ('judgement of perception'). Its meaning cannot lie in perception, but must lie in peculiar + +expressive acts 195 + +§5 Continuation. Perception as an act which determines + +meaning, without embodying it 196 Addendum 199 + +§6 The static unity of expressive thought and expressed + +intuition. Recognition (das Erkennen) 201 §7 Recognition as a character of acts, and the 'generality of words' 202 + +§8 The dynamic unity of expression and expressed intuition. + +The consciousness of fulfilment and that of identity 206 Addendum 208 + +§9 The differing character of an intention inside and outside + +the unity of fulfilment 209 + +§10 The wider class of experiences of fulfilment. Intuitions as + +intentions which require fulfilment 210 §l l Frustration and conflict. The synthesis of distinction 21 1 + +§12 Total and partial identification and distinction as the common phenomenological foundations of predicative + +and determining forms of expression 213 + +CHAPTER TWO + +Indirect characterization of objectifying intentions and their essential + +varieties through differences in the syntheses of fulfilment 21 6 + +§13 The synthesis of knowing (recognition) as the characteristic form of fulfilment for objectifying acts. Subsumption of + +acts of meaning under the class of objectifying acts 216 + +§14 Phenomenological characterization of the distinction between signitive and intuitive intentions through peculiarities of + +fulfilment. (a) Sign, image and self-presentation 218 + +(b) The perceptual and imaginative 'adumbration' of the + +object 220 + +§15 Signitive intentions beyond the limits of the + +meaning-function 222 + +CHAPTER THREE + +The phenomenology of the levels of knowledge 226 + +§16 Simple identification and fulfilment 226 + +§17 The question of the relation between fulfilment and intuitive + +illustration 228 §18 The gradations of mediate fulfilments. Mediate presentations 229 + +§19 Distinction between mediate presentations and presentations + +of presentations 230 + +§20 Genuine intuitive illustration in every fulfilment. Authentic + +and inauthentic intuitive illustration 23 1 §21 The 'fulness' of a presentation 233 §22 Fulness and 'intuitive substance' (Gehalt) 234 + +§23 Relations of weight between the intuitive and signitive + +'substance' (Gehalt) of one and the same act. Pure intuition and pure signification. Perceptual and imaginal content, pure + +perception and pure imagination. Gradations of fulness 235 §24 Graded series of fulfilments 238 §25 Fulness and intentional matter 240 + +§26 Continuation. Representation or interpretation (Auffassung). Matter as the interpretative sense, the interpretative form and the interpreted content. Differentiating characterization of + +intuitive and signitive interpretation 242 + +§27 Representations as the necessary bases of presentation in all acts. Final clarification of talk about the different modes of + +§28 Intentional essence and fulfilling sense. Epistemic essence. + +Intuitions in specie 245 + +§29 Complete and defective intuitions. Adequate and objectively + +complete intuitive illustrations. Essentia (Essenz) 246 + +CHAPTER FOUR + +ConSistency and inconsistency 250 + +§30 The ideal distinction of meanings into the possible or real + +(reale) and the impossible or imaginary 250 + +§3 1 Compatibility or consistency as an ideal relationship in the widest sphere of contents in general. Compatibility of + +'concepts' as meanings 252 §32 Incompatibility (conflict) of contents in general 253 + +§33 How conflict can also be a foundation for unity. Relativity + +of the talk of compatibility and conflict 254 §34 Some axioms 256 §35 Incompatibility of concepts as meanings 257 + +CHAPTER FIVE + +The ideal of adequation. Self-evidence and truth 259 + +§36 Introduction 259 + +§37 The fulfilling function of perception. The ideal of ultimate + +fulfilment 259 + +§38 Positing acts in the function of fulfilment. Self-evidence in + +the loose and strict sense 262 §39 Self-evidence and truth 263 + +Second section + +Sense and understanding 269 + +CHAPTER SIX + +Sensuous and categorial intuitions 271 + +§40 The problem of the fulfilment of categorial meaning-forms, + +with a thought leading towards its solution 271 §41 Continuation. Extension of our sphere of examples 274 + +§42 The distinction between sensuous stuff and categorial form + +throughout the whole realm of objectifying acts 275 + +§43 The objective correlates of categorial forms are not 'real' + +(realen) moments 277 + +§44 The origin of the concept of Being and of the remaining + +understanding. Their psychological meaning and normative + +function in relation to inadequate thought 314 §65 The senseless problem of the real meaning of the logical 316 + +§66 Distinction between the most important differences mixed + +up in the current opposition of 'intuiting' and 'thinking' 317 Additional note to the second edition 319 + +Third section + +Clarification of our introductory problem 32 1 + +CHAPTER NINE + +Non-objedifying acts as apparent fulfilments of meaning 323 + +§67 That not every act of meaning includes an act of knowing 323 + +§68 The controversy regarding the interpretation of the peculiar + +grammatical forms which express non-objectifying acts 325 §69 Arguments for and against the Aristotelian conception 327 §70 Decision 332 + +APPENDIX + +External and internal perception: physical and psychical phenomena 335 + +§1 The popular and the traditional philosophical concepts of + +external and internal perception 335 + +§§2 and 3 Epistemological and psychological motives for + +deepening the traditional division: Brentano's conception 336, 339 + +§4 Criticism. External and internal perception are, + +on a normal interpretation of the concepts, of the same + +epistemological character: Perception and apperception 340 §5 The equivocations of the term 'appearance' 341 §5a Excised passage from the First Edition 344 + +§6 There is for this reason confusion between the + +epistemologically meaningless opposition of inner and outer perception, and the epistemologically fundamental opposition + +of adequate and inadequate perception 344 §7 That the dispute is not verbal 346 + +§8 Confusion of two fundamentally different divisions of 'phenomena'. That 'physical' contents do not exist + +'in merely phenomenal fashion', but exist 'actually' 347 + +�otes 349 Index 359 Investigation III + +On the theory of wholes + +and parts + +Introduction I + +The difference between 'abstract' and 'concrete' contents, which is plainly the same as Stumpf's distinction between dependent (non-independent) and independent contents, is most important for all phenomenological investigations; we must, it seems, therefore, first of all submit it to a thorough analysis. As said in my previous Investigation, this distinction, which first showed up in the field of the descriptive psychology of sense-data, could be looked on as a special case of a universal distinction. It extends beyond the sphere of conscious contents and plays an extremely important role in the field of objects as such. The systematic place for its discussion should therefore be in the pure (a priori) theory of objects as such, in which we deal with ideas pertinent to the category of object, ideas such as Whole and Part, Subject and Quality, Individual and Species, Genus and Species, Relation and Collection, Unity, Number, Series, Ordinal Number, Magnitude etc., as well as the a priori truths which relate to these. Here again we cannot allow our analytic investigation to wait on the systematic development of our subjectmatter. Difficult notions employed by us in our clarificatory study of knowledge, and made to work rather in the manner of a lever, cannot be left unexamined, till they spontaneously emerge in the systematic fabric of the logical realm. For we are not here engaged on a systematic exposition of logic, but on an epistemological clarification, as well as on the prolegomena + +to any future exposition of logic. + +To plumb the difference between dependent and non-independent contents, therefore, points so directly to the fundamental questions of the Pure Theory of Wholes and Parts (which is a part of formal ontology) that we + +cannot avoid going into these questions in some detail. + +Chapter I + +The difference between + +independent and non-independent + +objects + +§ I Complex and simple, arti culated and + +unarticulated objects + +Since the Investigation which follows mainly concerns relations of Parts, we + +start off with a wholly general discussion of such relations. + +Objects can be related to one another as Wholes to Parts, they can also be related to one another as coordinated parts of a whole. These sorts of relations have an a priori foundation in the Idea of an object. Every object is either actually or possibly a part, i.e. there are actual or possible wholes that include it. Not every object, on the other hand, need perhaps have parts, and we have therefore the ideal division of objects into the simple and the + +complex. + +The terms 'complex' and 'simple' are therefore defined by the qualification of having parts or not having parts. They may, however, be understood in a second, possibly more natural sense, in which complexity, as the word's etymology suggests, points to a plurality of disjoined parts in the whole, so that we have to call simple whatever cannot be 'cut up' into a plurality of parts, i.e. that in which not even two disjoined parts can be distinguished. In the unity of a sensory phenomenon we can perhaps discover a wholly determinate 'moment' of redness as well as the generic 'moment' of colour. Colour and determinate redness are not, however, disjoined 'moments'. Redness on the other hand, and the extension that it covers, are such disjoined moments, since they have no community of content. They have, we may say, a mutual association in the widest sense of the word; we have here a general relation of parts which is that of disjoined parts in a whole, an association of such parts. It now seems appropriate to call the associated parts members of the association: but to give so wide a sense to talk about members of a whole, means to count colour and shape as the associated parts of a coloured expanse. That goes against linguistic usage. For in such wholes the parts have relative dependence as regards one another: we find them so closely united as to be called 'interpenetrating'. It is quite different in the case of wholes which are broken up, or could be broken up, into + +pieces: in their case talk of members or of articulated structure alone comes natural. The parts are here not merely disjoined from each other, but relatively independent, they have the character of mutually-put-together pieces. Even at the start of our discussion, we see that the relations of parts fall under characteristically different forms: these forms, we suspect, depend on the cardinal difference between independent and non-independent objects, + +which is our theme in the present section. + +§2 Introduction of the di sti nction between + +independent and non-independent objects (contents) We interpret the word 'part' in the widest sense: we may call anything a 'part' that can be distinguished 'in' an object, or, objectively phrased, that is 'present' in it. Everything is a part that is an object's real possession, not only in the sense of being a real thing, but also in the sense of being something really in something, that truly helps to make it Up: l an object in itself, considered in abstraction from all contexts to which it is tied, is likewise a part. Every non-relative 'real' (reale) predicate therefore points to a part of the object which is the predicate's subject: 'red' and 'round', e.g. , do so, but not 'existent' or 'something' . Every 'real' (rea/e) mode of association, e.g. the moment of spatial configuration, likewise counts as a proper part of the + +whole. + +The term 'part' is not used so widely in ordinary discourse. If we now try to pin down the limitations which mark off this ordinary, from our notion of part, we come up against the fundamental distinction called by us that of independent and non-independent parts. Where one talks of 'parts' without qualification, one generally has the independent parts (those referred to as 'pieces') in mind. Since each part can be made the specific object (or, as we also have frequently said, 'content') of a presentation directed upon it, and can therefore be called an object or 'content', the distinction of parts just mentioned points to a distinction in objects (or contents) as such. The term + +'object' is in this context always taken in its widest sense. + +In ordinary talk of objects or of parts, one of course involuntarily thinks of independent objects. The term 'content' is less restricted in this respect since 'abstract contents' are also commonly talked of. But talk of 'contents' tends to move in a purely psychological sphere, a limitation with which we may start investigating our distinction, but which must be dropped as we proceed.2 As a matter of history the distinction between independent and nonindependent contents arose in the psychological realm, more specifically in the field of the phenomenology of inner experience. In a polemic against Locke, Berkeley said:3 We have the ability to recall individual things previously seen, or to put them together or break them down in imagination. We can imagine a man with two heads, the trunk of a man tied to the body of a horse, or isolated pieces such as a separated head, nose, ear etc. As + +opposed to this, it is impossible to form 'abstract ideas', to separate the idea, e.g., of a movement from that of a moving body. We can only abstract, in the Lockean separative sense, such parts of a presented whole as are in fact unified with other parts, but as could also exist without them. Since esse for Berkeley here always means the same as percipi, this inability to exist means no more than an inability to be perceived. We must note, further, that for Berkeley ideas are the things perceived, i.e. contents of consciousness in + +the sense of things we really (reel!) live through. + +We may now make a statement that brings out the essential point of Berkeley's distinctions, making use of a readily understandable verbal + +change.4 + +Seen in their mutual interrelations, contents presented together on any occasion fall into two main classes: independent and non-independent contents.s We have independent contents wherever the elements of a presentational complex (complex of contents) by their very nature permit their separated presentation; we have dependent contents wherever this is not the case. + +§3 The inseparabil ity of non-i ndependent contents + +To be more precise in regard to this ability or inability-to-be-separatelypresented, we make use of some of Stumpf's observations - quite insufficiently + +noticed - and assert the following:6 + +It is self-evident, in regard to certain contents, that the modification or elimination of at least one of the contents given with them (but not contained in them), must modify or eliminate those contents themselves. In the case of other contents, this is not at all self-evident; it is not absurd to suppose them remaining unaffected despite the modification or elimination of all coexistent contents. Contents of the former sort can only be conceived as parts of more comprehensive wholes, whereas the latter appear possible, even if nothing whatever exists beside them, nothing therefore bound up + +with them to form a whole. + +In the sense just laid down every phenomenal thing and piece of a thing is separably presentable. The head of a horse can be presented 'on its own' or 'cut off', i.e. we can hold it in our fancy, while we allow the other parts of the horse, and its whole intuited setting, to alter and vanish at will. Strictly speaking, the phenomenal thing or its piece, i.e. the sensuous phenomenon as such, the spatial shape filled with sensuous qualities, never stays just the same in descriptive content: but the content of such a 'phenomenon' does not at least involve anything entailing a self-evident, necessary, functional dependence of its changes on those of coexistent phenomena. This holds, we may say, of phenomenal objects as such, as well as of the 'appearances', in the sense of the experiences, in which these things appear, as also in respect of the sensational complexes which are given an objective 'interpretation' in such experiences. Good examples in this field are the phenomena of tones + +and chords, of smells and other experiences, that we can readily think of + +apart from all relation to existent thinghood. + +§4 Analyses of exam ples fo llowing Stu mpf + +Let us now consider some instances of inseparable contents, e.g. the relation of visual quality to extension, or the relation of both to the figure which bounds them. It is doubtless true in a certain sense that these moments can be independently varied. Extension can stay the same while colour varies indefinitely, colour stay the same while extent and figure vary indefinitely. But, strictly speaking, such independent variability affects only the kinds of the 'moments' in their various genera. While the moment of colour remains constant in respect of its specific shade, extension and shape may vary indefinitely in their sub-species, and vice versa. Specifically the same quality, and nuance of quality, may be stretched or spread out over every extension, and, conversely, the same extension may be covered by every quality. Scope, however, remains for relations of functional dependence among the changes of such moments, which, be it noted, are not exhausted by the ideal content of their Species. The moment of colour, as immediate part-content of the intuited concrete thing, is not the same in the two concrete intuitions, even when the quality, the lowest differentiation of the genus colour, remains the + +same. Stumpf has made the powerful observation: + +Quality shares after a fashion in changes of extension. We express this verbally when we say that colour diminishes, becomes smaller, even to the vanishing point. Increase and diminution are names for quantitative + +changes. + +Quality is indeed affected in sympathy with changes in extent, although its own peculiar manner of change is independent of extent. It does not thereby become less green or less red: it has itself no degrees, only kinds, and can in itself neither increase nor diminish, only alter. But none the less, when we leave quality quite unchanged as regards its peculiar manner of change, e.g. let it stay green, it still is affected by quantitative change. And that this is perhaps not an improper or misleading verbal transfer, is shown by the fact that a quality can decrease to nothing, that in the end mere change of quantity can bring it to nought.7 + +We accept Stumpf's observation, only adding that it is not really the quality that is affected, but the immediate intuitive 'moment' falling under it. Quality must be looked on as a second-order abstraction, just like the figure and magnitude of an extension. But just on account of the law here under discussion, the moment in question can only be named by way of concepts determined by the genera of Quality and Extension. Quality is differentiated to the qualitative 'moment' now under consideration, by + +something not contained in the Genus Colour, since we rightly treat the quality, e.g. the determinate shade of red, as the Infima Species within this genus. Just so, a determinate figure is the last difference of the Genus Figure, though the corresponding immediate, intuitive 'moment' is further differentiated. But the combinations among the various last differences of the Genera Figure and Colour fully determine the 'moments' in question, determine whatever else may be like or unlike them. The dependence of the immediate 'moments' therefore means a certain necessary relationship among them, which is determined purely by their abstracta at the level just above them. + +Stumpf adds the following valuable remarks: + +From this (i.e. the above described functional dependence of the 'moments' of Quality and Extension), it follows that both are in their nature inseparable, that they in some manner compose a total content, of which they are merely part-contents. Were they merely items in a sum, one might possibly think that, absolutely treated, disappearance of Extension might mean the concomitant disappearance of Quality, that they did not exist apart; but that Quality should gradually diminish and vanish through the mere diminution and vanishing of Quantity, without changing in its own fashion as Quality, would be unintelligible ... they can in any case not be independent contents. Their nature forbids them to have an isolated and mutually independent existence in our ideas.8 + +The same sort of thing could be said of the relation of Intensity to Quality. The intensity of a tone is not something indifferent or so-to-speak alien to its quality. We cannot keep the intensity just as it is, while the quality varies at will, or is allowed to vanish. Eliminate quality and you unavoidably eliminate intensity, and vice versa. Evidently this is no mere empirical fact, but an a priori necessity, grounded in pure essence. In the response to change we have a further analogy to the previously mentioned case: if intensity steadily approaches the zero-limit, we feel our qualitative impression likewise reduced, even though the quality as such remains specifically unaltered. Further examples fully illustrate the 'moments' of unity in the intuitive contents, 'moments' built on the elements that we primarily distinguish, by which such elements are similarly or dissimilarly associated into sensuous intuitive wholes. The use of such examples gives us our first narrower concepts of a whole, of an association etc., and, further, our distinctive concepts of various kinds and sorts of wholes, whether present to outer or inner sense. These 'moments of unity' are of course the same as the contents called 'form-qualities' by von Ehrenfels, 'figural' moments by myself, and 'founded contents' by Meinong.9 But one needs here a supplementary distinction between the phenomenological moments of unity, which give unity to the experiences or parts of experiences (the real phenomenological data), and + +the objective moments of unity, which belong to the intentional objects and parts of objects, which in general transcend the experiential sphere. The expression 'moment of unity', incidentally recommended to me by Riehl, has such obvious advantages in virtue of its immediate intelligibility, that it + +might well be universally adopted. + +§S The objective determ ination of the concept of + +inseparabil ity + +Stumpf uses considerations of this sort to prove the mutual inseparability of Extension and Quality, and hence their non-independence: we shall rather make use of them to define inseparability or non-independence, or contrariwise separability or independence. Stumpf himself gives us the means to do this at the end of the last quoted passage. 1O What does it mean to say we can form an idea of a content 'by itself' or 'in isolation'? Does this mean, as regards the actually experienced contents of the phenomenological sphere, that such a content can be freed from all blending with coexistent contents, can therefore ultimately be torn out of the unity of consciousness? Obviously not. In this sense no contents are isolable, and the same holds of the phenomenal thing-contents in their relation to the total unity of the phenomenon as such. If we form an independent idea of the content head of a horse, we inescapably present it in a context, the content stands relieved from an objective background that appears with it, it is inescapably given with many other contents, and is also in a way united to them. How then can this content be isolable in idea? The only answer we can give is the following: Isolability means only that we can keep some content constant in idea despite boundless variation - variation that is free, though not excluded by a law rooted in the content's essence - of the contents associated with it, and, in general, given with it. This means that it is unaffected by the elimination + +of any given arrangement of compresent contents whatsoever. + +This self-evidently entails: that the existence of this content, to the extent that this depends on itself and its essence, is not at all conditioned by the existence of other contents, that it could exist as it is, through an a priori necessity of essence, even if nothing were there outside of it, even if all + +around were altered at will, i.e. without principle. + +Or what plainly amounts to the same: In the 'nature' of the content itself, in its ideal essence, no dependence on other contents is rooted; the essence that makes it what it is, also leaves it unconcerned with all other contents. It may as a matter of fact be that, with the existence of this content, other contents are given, and in accordance with empirical rules. In its ideally graspable essence, however, the content is independent; this essence by itself, i.e. considered in a priori fashion, requires no other essence to be interwoven + +with it. + +The sense of non-independence (Unselbstiindigkeit) lies likewise in the positive thought of dependence (Abhiingigkeit). The content is by its nature bound to other contents, it cannot be, if other contents are not there together with it. We need not emphasize the fact that they form a unity with it, for can there be essential coexistence without connection or 'blending' , however loose? Contents which lack self-sufficiency can accordingly only + +exist as partial contents. + +We need only say 'object' and 'partial object', instead of 'content' and 'partial content' - the term 'content' we regard as the narrower term, the one restricted to the sphere of phenomenology - to achieve an objective distinction freed from all relation to interpretative acts and to any phenomenological content that might be interpreted. No reference back to consciousness is therefore needed, no reference to differences in the 'mode of presentation', to determine the difference between 'abstract' and 'concrete' which is here in question. All determinations which make use of such a relation, either represent an incorrect, misguided confusion with other notions of 'abstract', or are merely subjectively slanted expressions of a purely objective, ideal state of affairs, a sort of slanting that we also feel natural + +and useful in other cases. + +§6 Conti nuation. Tie-up with a criticism of a + +much-favoured notional determ ination + +Occasionally one hears the difference between independent and nonindependent contents expressed in the attractive formula: Independent contents (part-contents) could be presented by themselves, non-independent contents only noticed by themselves, not presented by themselves. To this formula one may object that 'by themselves' functions vary differently in the two expressions to be distinguished: 'presented by themselves' and 'noticed by themselves'. A thing is 'noticed by itself' if it is an object of an act of notice specially directed upon it (a direct act of attending), a thing is 'presented by itself' if it is an object of a specially directed presentation - this at least if 'by itself' functions analogously in the two cases. On such a basis, however, we cannot sustain the opposition between what can only be noticed and what can only be presented by itself. Could emphatic notice perhaps conflict with presentation in a class of cases, and exclude it? But non-independent moments such as attributes and terms of relations are as much the objects of presentations (as stated above) as are independent contents like window, head etc. Otherwise we should not be able to talk of them. To attend to something by itself, and to represent it by itself (in the sense just presupposed) are so little mutually exclusive, that we find them together. In perceptual 'interpretation' the thing we attend to by itself is at the same time eo ipso presented; and the complete content presented by itself, e.g. head, is + +also attended to by itself. + +'By itself' in fact means something quite different in the case of a presentation from what we thought it did. The equivalent expression 'present in isolation' points plainly to this fact. What it plainly means is that it is possible to present the object as something existing by itself, as independently there in the face of all other objects. A thing or piece of a thing can be presented by itself - this means it would be what it is even if everything outside it were annihilated. If we form a presentation of it, we are not necessarily referred to something else, included in which, or attached to which, or associated with which, it has being, or on whose mercy it depends, as it were, for its existence. We can imagine it as existing by itself alone, and beyond it nothing else. If it is intuitively presented, a context, a whole including it, may nonetheless be presented with it, must inevitably be so presented. The visual content head cannot be presented without a visual background from which it stands relieved. This impossibility is, however, quite different from the impossibility used to define non-independent contents. If we let the visual content head count as independent, we think that, despite its inescapable, accompanying background, it could be presented as existing by itself, and could therefore be intuitively envisaged in isolation. We, however, cannot effect this, whether because of powerful original or acquired associations, or other purely factual connections. The 'logical' possibility remains unshaken, + +our visual field, e.g., 'could' shrink down to this single content etc. + +What we here express by the word 'present', could be better expressed by the word 'think' . An attribute, a form of association and the like, cannot be thought of as self-existent, as isolated from all else, as being all that exists: this only can happen with 'thinglike' contents. Wherever the word 'think' occurs in this peculiar sense, we detect one of those subjective slantings of an objective, nay of an a priori state of affairs, which we referred to above. Differences such as this, that one object - we again choose the wider term, which includes the contents of intuitive experience - can be 'in and for itself', while another can only have being in, or attached to some other object - are no mere contingencies of our subjective thinking. They are real differences, grounded in the pure essence of things, which, since they obtain, and since we know of them, prompt us to say that a thought which oversteps them is impossible, i.e. a judgement deviating from them is wrong. What cannot be thought, cannot be, what cannot be, cannot be thought - this equivalence fixes the differences between the pregnant notion of thinking + +and the ordinary subjective sense of presentation and thought. + +§7 Further pointing up of our notional determination + +by introd ucing the concepts of pure law and + +pure ge nus + +Wherever therefore the word 'can' occurs in conjunction with the pregnant use of 'think', there is a reference, not to a subjective necessity, i.e. to the + +subjective incapacity-to-represent-things-otherwise, but to the objectivelyideal necessity of an inability-to-be-otherwise. ll This is by its essence such as to be given in our consciousness of apodictic self-evidence. If we remain within the expressions of this consciousness, we must assert it to be of the essence of such an objective necessity that it is correlated with a definite pure law in each case. It is in the first place obvious in general that objective necessity is as such tantamount to a being that rests on an objective law. An individual matter of fact, considered as such, is contingent in its being: that it is necessary means that it stands in a context of law. What prevents its being otherwise is the law which says that it is not merely so here and now, but universally so, and with a lawful universality. Here we must note that, just as the 'necessity' relevant to our discussion of non-independent 'moments' stands for an ideal or a priori necessity rooted in the essences of things, so, correspondingly, our 'lawfulness' stands for a lawfulness of essence, a non-empirical, universal and unconditionally valid lawfulness. No relation to empirical existence may restrict the extension of our legal concepts, no empirical assertion of existence be inwoven into our consciousness of law, as occurs in the case of empirically general rules and laws. 'Natural laws', laws in the sense of the empirical sciences, are not laws of essence (ideal or a priori laws): empirical necessity is no necessity of essence. + +The inability-to-exist-by-itself of a non-independent part points therefore to a law of essence, according to which the existence of a content belonging to the part's pure Species (e.g. the Species of Colour, Form etc.) presupposes the existence of contents of certain pertinent pure Species, i.e. contents to which - if such an addition is still needed - the content in question can pertain as a part or an adjunct, an associate. Put more simply we can say: Nonindependent objects are objects belonging to such pure Species as are governed by a law of essence to the effect that they only exist (if at all) as parts of more inclusive wholes of a certain appropriate Species. This is what we mean by the terser expression that they are parts which only exist as parts, that cannot be thought of as existing by themselves. The colour of this paper is a non-independent 'moment' of the paper. It is not merely an actual part, but its essence, its pure Species, predestines it to partial being: a colour in general and purely as such can exist only as a 'moment' in a coloured thing. In the case of independent objects such a law is lacking: they may, but need + +not, enter into more comprehensive wholes. + +In clarifying what must be meant by the phrase 'presented by itself' in the formulation just criticized, we have therefore brought the essence of the difference to be pinned down into the sharpest focus. It has shown itself to be an objective difference, one rooted in the pure essence of the objects (or the partial contents) in question. We may now ask how it stands with the rest of the formula; how far does the statement that non-independent objects or 'moments' could 'only' be noticed by themselves, or singled out from their associates for exclusive attention, not presented by themselves, help us + +to pin down such objects? We can only answer: Not at all. For if the word 'only' is tied exclusively to the phrase 'presented by itself', such an exclusive opposition achieves everything for it that can be achieved. Strictly speaking our approach is positive in the case of what is non-independent, negative in the case of what is independent: when we say that the former cannot be presented by itself, we merely return in double negation to our real startingpoint. However this may be, we need not fall back on the high-lighting role of attention, and it is not clear how it can help us. A head can certainly be presented apart from the person that has it. A colour, form etc., is not presentable in this fashion, it needs a substrate, in which it can be exclusively noticed, but from which it cannot be taken out. But the head also, considered, e.g. visually, can only be noticed by itself, since it is unavoidably given as an element in a total visual field. If we do not treat it as such an element, if we abstract from the background as something really foreign and indifferent, this does not depend on the peculiarity of our content, but on + +the circumstances of our thing-directed thought. + +§7a Independent and non-i ndependent Ideas + +Our distinctions have first of all related to the being of particular individuals thought of in 'ideal universality' , i.e. of such individuals treated purely as instances of Ideas. But they obviously carry over to Ideas themselves, which can, in a corresponding, if somewhat modified sense, be spoken of as 'independent' and 'non-independent'. A lowest difference of some highest pure Genus may be called relatively independent in relation to the hierarchy of pure Species which lead up to the highest Genus, just as every lower Species counts as relatively independent as against higher Species. Genera, the existence of whose corresponding individualizations represents an a priori impossibility, unless they simultaneously belong to the individual, but purely conceived extensions of other Genera, are non-independent in regard to these latter, and so mutatis mutandis in the case of other fields of instances. + +§8 Demarcation of the disti nction of independent and non-i ndependent contents and the di st inction between intu itively emphatic and intu itive ly blended contents We must be prepared for a further objection. Some may perhaps point to the manner in which an independent content puts itself forward as a unity valid in its own right, and cut off from all around, while a non-independent content is contrariwise characterized as something only grounded on other, independent contents, and insist that we here have a phenomenological con- + +trast that our discussion has not taken full account of. + +We might deal, in the first place, with the following descriptive situation. The non-independent moments of an intuition, are not mere parts, but in a + +certain (notionally immediate) manner they must also be regarded as parts: they cannot be separately noticed unless all the concrete contents, in which they are contained, have been stressed as wholes: this does not mean that they become objects in the pregnant sense of the word. A figure or colour cannot be separately noticed unless the whole object, which has the figure or the colour, stands out in relief. A 'striking' colour or form may seem at times to impress us in isolation, but if we bring such an event back to mind we see that the whole object is here phenomenally emphatic, though it is so in respect of the peculiarity that strikes us, and which alone is objective in the strict sense of the word. The same relation obtains between an emphasized sensuous 'moment' of unity - the 'moment' , e.g. , of spatial configuration, which, together with other 'moments' of unity, underlies the internal closure of a sensory manifold, which makes it impressively one - and the apprehension of the sensuously-unified whole itself. 12 In this manner the setting in relief of one content is at times the basis for noticing another that intimately belongs to it.13 If we explore the deeper grounds of the matter, we note that a second distinction is mixed up with and crosses the previously discussed difference of independent and non-independent contents in the phenomenological field (or the field of intuitive data as such). This is the distinction between intuitively 'separated' contents, contents relievedfrom or cut apart from associated contents, on the one hand, and contents which blend with their associates, or whichftow undividedly over into them, on the other. Our terms are of course ambiguous, but to put them together makes plain that we really do have a + +new distinction before us. + +A content, accordingly, is intuitively separated in relation to other contents if it does not flow over into them without a point of difference: it can thus make itself count on its own, and stand forth independently. The intuitively unseparated content forms a whole with other coexistent contents, but is not cut off in this manner within the whole; it is not merely bound up with its associates, but blends with them. Independent contents in our previous sense, which are what they are no matter what goes on around them, need not have the quite different independence of separateness. The parts of an intuitive surface of a uniform or continuously shaded white are indepen- + +dent, but not separated. + +If we ask what is involved in intuitive separation, the image of a mutual overflow points to cases where contents are continuously graded. This holds mainly in the case of sensuous concreta (i.e. of independent contents in the sphere of outer sense). Here separation often rests on discontinuity. One may + +affirm that: + +Two contemporaneous sensuous concreta necessarily form an 'undiff erentiated whole' if all the immediately constitutive 'moments' of the one pass unbrokenly over into corresponding constitutive 'moments' of the other. The case of exact likeness of any such corresponding moments shall here count as a legitimate limiting case of continuity, i. e. as a continuous passing over into self'. + +We can apply this in readily understandable fashion to a mUltiplicity of concreta. Here each single concretum lacks separation, if the aggregated concreta form a series, at each step of which the items are continuously conjoined, i.e. if what we have described holds of each neighbouring pair of items. An individual item already lacks separation from all other items if there + +is a single item from which it does not stand forth in relief + +§9 Continuation. Reference to the wider sphere of + +the phenomena of fu sion + +These propositions are in a certain sense idealized expressions of facts. Continuity and discontinuity must of course not be taken in a mathematically exact sense. Points of discontinuity are not mathematical limits, and distances + +must not be 'too small'. + +One might draw a somewhat finer distinction between sharper and more confused separation or limitation, in the empirically vague sense in which, in ordinary life, one speaks of sharp points and corners as opposed to blunt or even rounded ones. Plainly the essential forms of all intuitive data are not in principle to be brought under 'exact' or 'ideal' notions, such as we have in mathematics. The spatial shape of the perceived tree as such, taken precisely as a 'moment' found in the relevant percept's intentional object, is no geometric shape, no ideal or exact shape in the sense of exact geometry. Just so a seen colour as such is no ideal colour, whose Species occupies an ideal point in the colour-pyramid. The essences which direct ideation elicits from intuitive data are 'inexact essences', they may not be confused with the 'exact' essences which are Ideas in the Kantian sense, and which (like an 'ideal point', an ideal surface or solid, or ideal Species of colour in the ideal colour-pyramid) arise through a peculiar 'idealization' . The descriptive concepts of all pure description, i.e. of description adapted to intuition immediately and with truth and so of all phenomenological description, differ in principle from those which dominate objective science. To clear up these matters is a phenomenological task never yet seriously undertaken and not + +carried out in relation to our present distinction. + +It is also clear that this separation through discontinuity (or this fusion + +through continuity) only covers a very restricted field. + +I recall Stumpf's instructive investigations into the remarkable facts of fusion,14 in whose sphere we are here plainly moving. The cases stressed by us would play a peculiar role in the field of the phenomena of fusion. Considering these cases more closely, we are led back from the concreta, the independent total sensa, to their immediate, non-independent 'moments', or to the Species under which these immediately fall. Discontinuity relates as such to the lowest specific differences within one and the same immediately superordinate pure Genus: to qualities of colour, e.g., as compared with qualities of colour. But we do not define discontinuity as the mere distance + +of coexistent contents in respect of such lowest differences. Simultaneous tones have distance, but they lack discontinuity in the pregnant sense of the word. This only relates to specifically differing moments in so far as they are 'spread out' with common boundaries over a continuously varying spatial or temporal 'moment'. It is 'at' a spatial or temporal boundary that one visual quality, e.g., leaps over into another. In our continuous progress from spatial part to part there is at the same time no continuous progress in the covering quality: in one place at least the neighbouring qualities are finitely (and not too minutely) distant. The same holds of a discontinuity in phenomenal order. Here not merely qualities, e.g., colours, achieve separation, but whole concreta set bounds to one another, the visual field is split up into parts. The colour-distance in such a context of 'covering' - without which there can be no talk of discontinuity - also wins separation for the 'moments' bound up with it, the covered spatial parts of our example. These could otherwise not be free from the fusion. Spatiality necessarily varies continuously. A piece of such variation can only become separately noticeable and primarily emphatic in consciousness,15 when a discontinuity is provided by the covering 'moment', and the whole concretum which corresponds to it + +has thus been separated. + +The first meaning we give to 'spatiality', is here the sensational 'moment' which, when objectively referred, first yields phenomenal spatiality properly so called. But we can also mean by it the spatiality which a given intuition helps us to apprehend in the phenomenal thing as such, spatiality therefore as the intentional moment in which the objective, and objectively measurable, spatial shape of the physical 'thing itself' is intuitively revealed to us, + +and is differently revealed in different intuitions. + +The concrete thing of sensuous intuition therefore owes its isolation to the qualitative gap between neighbouring 'moments', but the relief achieved by the whole concretum has priority over the relief of the mutually separated moments of its content. This depends on the peculiarly intimate fusion of the different 'moments' of the concretum, their mutual 'penetration', which reveals itself in a mutual dependence as regard change and destruction. This fusion is not a fading into one another in the manner of the continuous, nor does it remove all separateness, but it is nonetheless a sort of peculiarly intimate mutual interconnection which must at a stroke set the whole complex of interpenetrating moments in relief, if only once a single discontinuous + +moment has provided the right conditions. + +A profounder and more penetrating analysis could here lay bare a wealth of interesting descriptive differences; for our purposes these fairly rough treatments are enough. We have gone far enough to see that, in thus distinguishing stressed from unstressed contents, as was done above, or to employ a few readily suggested expressions, in distinguishing between contents that can, and contents that cannot be presented 'by themselves', or that are independent and non-independent respectively, we are dealing with differences + +of 'subjective', intuitive materials, which have their own remarkable peculiarities of essence, but which will not help us to grasp the universal, ontological difference between abstract and concrete contents, or, as we deliberately called them above, independent and non-independent contents. Our former distinction between contents separately singled out and confused background contents, pivots on the facts of analysis and fusion; the contents thus separated off, might as well be independent as non-independent. The two distinctions should not therefore be confused, as is done, e.g., when the non-independence of the separate parts of a uniformly coloured surface is put on a level with the descriptively quite different non-independence of an abstract 'moment' . It is also done when attempts are made to base the essence of the ontological difference between concrete and abstract on phenomenological facts which concern the sphere of acts, the fact, e.g., that the act which presents a concrete object is immediate, and is independent in not needing to be based on other presentations, whereas the act which apprehends an abstract content is mediate and non-independent, in that it must be based on the presentation of a suitable concretum. Our analyses show, however, that anything that holds water in this descriptive situation is mixed up with other quite alien matters, and is in any case unfitted to + +illuminate our ontological distinction. + +§ 10 The mul tiplic ity of laws governing the various + +sorts of non-independent contents + +Our discussions so far have shown that there is always an a priori law governing what is non-independent, having its conceptual roots in what is universal in the whole and part in question. But this law can be interpreted and expressed with more or less definiteness. To pin down the concept of non-independence, it is enough to say that a non-independent object can only be what it is (i.e. what it is in virtue of its essential properties) in a more comprehensive whole. At times, however, a non-independent object can vary in Species: this entails varying the kind of supplementation it requires for existence. If we say, for example, that the 'moment' of sensory quality, e.g. of sensory colour, is non-independent, and requires a whole in which it may be embodied, we have only laid down one side of our governing law, the side of a part which belongs to the Genus Sensory Quality. We have not, however, laid down the character of the whole, the manner in which such a 'quality' is its part, nor the sort of supplement it needs to achieve existence. It is different when we say that a sensory quality can only exist in a sense-field, and a sensory colour in a visual sense-field, or that it can only exist as qualifying an extension. Here the law lays down the other sides as well; the notion of a visual sense-field is given; and it means a particular, definite sort of whole among various possible sorts of whole. Just so, the notion of 'qualifying an extension' points to quite specific possibilities of law-governed inherence + +18 On the theory of wholes and parts + +that a non-independent 'moment' may have to a whole. The specific character of this inherence is fixed in general fashion both by the essence of Sensory Quality and the essence of Extension, but each is contained in its own manner in the essential unity of visual sensation, or of the visual field in which all such unities find their place. This manner cannot be further described. If we ask what differentiates the generic feature of being a sensory 'moment', so as to yield the specific feature of being a sensory quality, we can give no answer that helps us; we can point to no additional feature in which the concept of quality is not included. Just so, if we are asked what must be added to Colour to produce its Species Redness we can only answer 'Redness'. The notion of what is non-independent, with its indirectly, generally characterized definitory lawfulness, points to many factually determined, variable laws of essence. It is not a peculiarity of certain sorts of parts that they should only be parts in general, while it remains quite indifferent what they are conglomerated with, and into what sorts of connection they are fitted. There are fixed, necessary connections, pure laws definite in content, which vary with the pure Species of non-independent contents, and accordingly prescribe one sort of completion to one of them, another sort of completion to another. The Species associated in these laws, which mark off the spheres of contingent individuality presupposed by these laws - are occasionally, but not always, lowest specific differences. A law, for instance, may prescribe to contents of the Species Colour a connection with contents of the Species Extension, but it does not prescribe a definite extension to a definite colour, or vice versa. The values of the lowest differences are accordingly not functionally interrelated. The law only refers to lowest Species, i.e. Species having the multiplicity of ultimate specific differences immediately beneath them. On the other hand, if we consider the dependence of qualitative remoteness on the qualities on which it rests, we find it unambiguously determined by the lowest specific differences of these qualities, and so again determined + +as a lowest difference. + +The concept of non-independence accordingly amounts to that of ideal lawfulness in unified combinations. If a part stands in an ideally law-bound and not merely factual combination, it must lack independence; since such a law-bound combination merely means that a part whose pure essence is of one sort, can exist lawfully only in association with certain other parts of these or those suitable sorts. And even where a law tells us of the impossibility, rather than the necessity of an association, where it says, e.g., that the existence of a part A excludes the existence of a part B as incompatible with A, our case still reduces to one of non-independence. For an A can only exclude a B, if both exclusively require the same thing. A colour excludes another colour, but only if both aim to cover an identical piece of surface, and both cannot do so completely. To each essential, law-bound exclusion of a determinate characterization, there corresponds a positive law-bound + +§ I I The difference between these 'material' laws and + +'formal' or 'analytic' laws + +The necessities or laws which serve to define given types of non-independent contents rest, as we often have emphasized, on the specific essence of the contents, on their peculiar nature. More precisely, they rest on the pure Genera, Species, differentiae under which, as contingent singulars, nonindependent contents as well as their supplementing contents, fall. If we conceive of the totality of such ideal objects, we have with them the totality of pure essences, the essences of all ideally possible individual objects (existences). To these essences correspond the concepts or propositions which have content, which we sharply distinguish from purely formal concepts and propositions, which lack all 'matter' or 'content'. To the latter belong the categories of formal logic and the formal ontological categories mentioned in the last chapter of the Prolegomena, which are essentially related to these, as well as to all syntactical formations they engender. Concepts like Something, One, Object, Quality, Relation, Association, Plurality, Number, Order, Ordinal Number, Whole, Part, Magnitude etc., have a basically different character from concepts like House, Tree, Colour, Tone, Space, Sensation, Feeling etc., which for their part express genuine content. Whereas the former group themselves round the empty notion of Something or Object as such, and are associated with this through formal ontological axioms, the latter are disposed about various highest material Genera or Categories, in which material ontologies have their root. This cardinal division between the 'formal' and the 'material' spheres of Essence gives us the true distinction between the analytically a priori and the synthetically a priori disciplines (or laws and necessities). The next section will make systematic pronounce- + +ments on these matters. + +It is now immediately plain, that all the laws or necessities governing different sorts of non-independent items fall into the spheres of the synthetic a priori: one grasps completely what divides them from merely formal, contentless items. Laws of the type of the law of causation, which lay down the non-independence of changes in what is thinglike and real, or the laws generally imperfectly formulated - which assert the non-independence of mere qualities, intensities, extensions, boundaries, relational forms etc. w�uld not be put on a level with a purely 'analytic' generalization such as 'A whole cannot exist without parts' or with analytic necessities such as 'There cannot be a king (master, father) without subjects (servants, children) etc.'. We may say in general: correlatives mutually entail one another, they cannot be thought of, or cannot be, without each other. If we set beside these any definite propositions of the opposite sort, e.g., 'A colour cannot exist without something coloured' or 'A colour cannot exist without some space that it covers' etc. - the difference leaps into view. 'Colour' is not a relative expression, whose meaning includes the idea of a relation to something else. + +Though colour is 'unthinkable' without something coloured, the existence of the latter, and more definitely that of a space, is not 'analytically' founded + +on the notion of colour. + +The following discussion clears up the essence of the difference. + +A part as such cannot exist at all without a whole whose part it is. On the other hand we say, with an eye to independent parts: A part often can exist without a whole whose part it is. Obviously this involves no contradiction. What we mean is that, if the part is treated in respect of its internal content, its own essence, then a thing having this same content can exist without a whole in which it exists; it can exist by itself, not associated with anything else, and will not then be a part. Change in, or complete elimination of associations, does not here affect the part's own, peculiarly qualified content, and does not eliminate its existence: only its relations fall away, the fact that it is a part. The contrary holds of other sorts of parts: without any association, as non-parts, they are unthinkable, in virtue of their very content. These impossibilities or possibilities are rooted in the essential specificity of the contents. The case is quite different in regard to the analytic triviality that a part as such cannot exist without a whole whose part it is. It would be a 'contradiction', i.e. a 'formal', 'analytical' absurdity, to call X a part where there was no whole belonging to X. Here the inner content of the part is irrelevant, the underlying 'formal' lawfulness of our case has nothing in common with the material lawfulness of our above cases, and can accordingly + +not disturb them. + +That correlatives as such mutually condition one another certainly points to certain mutually requiring 'moments', it points to the mutually 'belonging' relationships and relative properties which we find in the case of every relation. But it does so only with formal indefiniteness. The legality which here obtains is one and the same for all relations as such: it is in fact a merely formal legality, rooted in mere analytic essences, here in fact in the essence of relation as a formal category. It takes over none of the material specificity of relations and of their members, and discourses merely of 'certain' relations and members. It will perhaps say in the simple case of dyadic relations: If a certain A stands in a certain relation to a certain B, this same B stands in a certain corresponding (converse) relation to that A; A and B + +are here quite freely variable. + +§ 12 Basic determinations in regard to analyti c and + +synthetic proposit ions + +We may give the following general definitions: + +Analytic Laws are unconditionally universal propositions, which are accordingly free from all explicit or implicit assertions of individual existence; they include none but formal concepts, and if we go back to such as are primitive, they contain only formal categories. Analytic Laws stand + +opposed to their specifications, which arise when we introduce concepts with content, and thoughts perhaps positing individual existence, e.g. this, the Kaiser. The specification of laws always yields necessary connections: specifications of analytic laws therefore yield analytically necessary connections. What are called 'analytic propositions' are in general analytically necessary connections. When they imply existential assertions (e.g. If this house is red, then redness pertains to this house) such analytic necessity relates to that content of the proposition in virtue of which it empirically specifies the + +analytic law, not to its empirical assertion of existence. + +We may define analytically necessary propositions as propositions whose truth is completely independent of the peculiar content of their objects (whether thought of with definite or indefinite universality) and of any possible existential assertions. They are propositions which permit of a complete 'formalization' and can be regarded as special cases or empirical applications of the formal, analytic laws whose validity appears in such formalization. In an analytic proposition it must be possible, without altering the proposition's logical form, to replace all material which has content, with an empty formal Something, and to eliminate every assertion of existence by giving all + +one's judgements the form of universal, unconditional laws. + +It is, e.g., an analytic proposition that the existence of this house includes that of its roof, its walls and its other parts. For the analytic formula holds that the existence of a whole W (A, B, C ... ) generally includes that of its parts A, B, C ... This law contains no meaning which gives expression to a material Genus or Species. The assertion of individual existence, implied by the this of our illustration, is seen to fall away by our passage into the pure law. This is an analytic law: it is built up exclusively out of formal-logical + +categories and categorial forms. + +Having formed the concept of an analytic law and of an analytic necessity, we also have eo ipso formed the concept of a synthetic a priori law, and of a synthetic a priori necessity. Each pure law, which includes material concepts, so as not to permit of a formalization of these concepts salva veritate - each such law, i.e., that is not analytically necessary - is a synthetic a priori law. Specifications of such laws are synthetic necessities: empirical specifications of course are so also, e.g. This red is diff erent from this green. What we have said should be enough to make plain the essential distinction between laws grounded in the specific nature of the contents to which non-independent factors belong, and analytic and formal laws, which, being founded purely on formal 'categories', are unaffected by all 'material of + +knowledge' . + +Note 1 The points here made may be compared with those of Kant, which in our view do not deserve to be called 'classical'. It seems to us that these points satisfactorily dispose of one of the most important problems in the theory of knowledge, and make a first, decisive step in the division of a + +priori ontologies. Future publications will carry the enquiry further. + +Note 2 It is readily seen that the main concepts dealt with by us in this section: Whole and Part, Independence and Non-independence, Necessity and Law, are essentially changed in sense when they are not understood in the sense of purely conceptual matters of essence, but are given an empirical interpretation. For the purpose of the investigations which follow, it is not, however, necessary fully to discuss these empirical concepts and their rela- + +tion to the pure ones. + +§ 13 Re lative independence and non-independence + +Independence we have so far conceived absolutely, as a lack of dependence on all associated contents: non-independence was its contradictory opposite, a corresponding dependence on at least one such content. It is, however, important to treat both concepts relatively also, in such a way, that is, that the absolute distinction then becomes a limiting case of the relative. In the sphere of mere sense-data (not that of the things represented or apparent in such sense-data) the 'moment' of visual extent, 16 with all its parts, counts as non-independent, but within this extent conceived in abstracto each of its pieces counts as relatively independent while each of its 'moments', e.g. the 'moment' of 'form' as opposed to that of position and magnitude, counts as relatively non-independent. Here we therefore have a relative sort of 'independence', which taken absolutely, or in some other relation, could have been a case of non-independence, it is an independence, relatively to a whole, whose total range of parts, together with the whole itself, constitutes a sphere within which the distinctions previously drawn unrestrictedly now + +must move. I? We can therefore define as follows: + +Non-independence in and relative to the whole W or to the total range of contents determined by W, characterizes each of W's partial contents which can only exist as parts, and as parts of a sort of whole represented in this range. Every partial content regarding which this is not true, is called independent in, and relative to, the whole W. We also speak briefly of nonindependent or dependent parts of the Whole, and in a corresponding sense of non-independent and independent parts of parts (i. e. of part-wholes) of the + +whole. + +Our determinations can plainly be further generalized. One can interpret our definition so that it does not merely relate a partial content to a more comprehensive whole, but, quite generally, a content to another content, even + +if both are separated off. We define accordingly: + +A content A is relatively non-independent in regard to a content B (or in regard to the total range of contents determined by B and all its parts), if a pure law, rooted in the peculiar character of the kinds of content in question, ensures that a content of the pure Genus A has an a priori incapacity to exist except in, or as associated with, other contents from the total ranges + +If such a law is absent, we say that A is relatively independent in regard to B. More simply we can say: A content A is non-independent relatively to a content B, if there is a law rooted in the Generic Essences A, B, which lays down a priori that a content of the pure Genus A can only exist in or associated with a content of the Genus B. We naturally leave open the possibility that the Genera A and B should be Genera of combinations, so that in the elements of such combinations several corresponding Genera should be woven together. Our definition entails that an A as such, taken in unconditional universality, requires to be accompanied by, and unified with some B or other: otherwise put, the pure Genus requires, in respect of the possible existence of individuals falling under it, the Genus B, or to be joined with connected instances from B's range. Briefly we may say that the being of an A is relatively independent or non-independent in regard to + +the Genus B. + +The necessary coexistence mentioned in our definition is either a coexistence relating to any point in time, or a coexistence for a certain stretch of time. In the latter case B is a temporal whole, and temporal determinations then play their part (as temporal relations or stretches) in the range of contents determined by B. A content K, e.g., which includes the timedetermination to, may thus require the existence of another content with the + +time-determination t + +1= to + 1::., and accordingly be non-independent. In + +the sphere of the phenomenological events of the 'stream of consciousness', a law of essence paradigmatically illustrates the non-independence just mentioned, the law, namely, that each actual, fulfilled now-consciousness necessarily and continuously passes over into one that has just existed, so that our present conscious state makes continuous demands on our conscious future. The law further requires that our retentive awareness of what has just been, which itself has the immanent character of being actually present, demands that the phenomenon we are aware of as having just existed should in fact just have existed. The time we are talking of in this context is of course the immanent temporality which belongs to the phenomenological + +stream of consciousness itself. + +In the sense of our definition, to take somewhat differently slanted examples, each bit of our visual field, each concretely filled section of it, is independent within, and relatively to, the concrete totality of a visual intuition of a moment, whereas each colour of such a portion, the colour-pattern of the whole etc., is non-independent. And again in, and relatively to, the whole of the momentary sensuous total intuition, the visual field with its contents, the tactual field with its contents etc., are independent, whereas the qualities, forms etc., whether attaching to whole fields, or their individual members, are non-independent. We observe at the same time that all that counted as non-independent or independent in relation to the whole of our previous example will count as such in relation to our present standard of reference. + +Whatever is independent or non-independent in relation to a B, also maintains this property in relation to every whole B' in relation to which B is independent or non-independent - a proposition, whose converse is of course invalid. Although therefore, relations (and with them relative conceptions) vary as boundaries are differently drawn, nonetheless our law entails a certain relation for the groups of contents in the context referred to. Such a relation obtains, e.g., when we compare a coexistent group belonging to each point of time with successive groups which include such coexistent groups, or perhaps even with the inclusive group of unending, fully occupied phenomenological time. What counts as an independent element in the latter group is what is the more comprehensive element, and so not everything that counts as independent in the order of coexistence must for that reason count as independent in the order of succession. The converse holds, however. An independent thing in the order of coexistence, e.g. a bounded portion of the visual sense-field in its concrete fulness, is non-independent relatively to the whole of occupied time, to the extent that its time-determination is treated as a mere instant. Following on what we have said, an instant of time is as such non-independent: it can be concretely occupied only as part of the concrete occupation of a time-stretch or duration. If we replace the instant by a duration, in which our concrete content is thought of as remaining quite constant, then such an enduring coexistence could count as + +independent even in this wider sphere. + +Chapter 2 + +Thoughts towards a theory of the + +pure forms of wholes and parts + +§ 14 The concept of foundation and some re l evant + +theorems + +The law stated and applied in the last paragraph of the previous section is not an empirical proposition, and yet not an immediate law of essence. Like many similar laws, it permits of a priori proof. Nothing can show up the worth of a strict statement more clearly than the possibility of giving a deductive proof of such propositions as are familiar to us in another guise. In view of the great scientific interest that the constitution of a deductive theoretical transformation claims in every field, we wish to linger here + +a little. + +Definitions. If a law of essence means that an A cannot as such exist except in a more comprehensive unity which connects it with an M, we say that an A as such requires foundation by an M or also that an A as such needs to be supplemented by an M. If accordingly Ao, Mo are determinate instances of the pure kinds A or M, actualized in a single whole, and standing in the relations mentioned, we say that Ao is founded upon Mo, and that it is exclusively founded on Mo, if Ao's need for supplementation is satisfied by Mo alone. This terminology can of course be carried over to the Species, by a quite harmless equivocation. We say further, more indefinitely, that the two contents or two pure Species, stand in a foundational relationship or in a relationship of necessary connection. This indeed leaves it open which of the two possible but not mutually exclusive relationships is meant. The indefinite expression: Ao requires supplementation by, is founded upon a certain moment, plainly means the same as the expression: 'Ao is non-independent'. + +Proposition 1 If an A as such requires to be founded on an M, every whole + +having an A, but not an M, as a part, requires a similar foundation. + +This proposition is axiomatically self-evident. If an A cannot be except when completed by M, a whole including an A but no M cannot satisfy A's need + +As a corollary we can assert the following, making use of the definition of + +our previous section. + +Proposition 2 A whole which includes a non-independent 'moment', without including, as its part, the supplement which that 'moment' demands, is likewise non-independent, and is so relatively to every superordinate independent whole + +in which that non-independent 'moment' is contained. + +Proposition 3 If W is an independent part of (and SO lalso relatively to) F, + +then every independent part w of Walso is an independent part of F. + +If w needed a supplement M relatively to F, and so had a foundation Mo in the range of F, this foundation would necessarily be included in W. For, if this were not so, W would require supplementation in respect of M in conformity with Prop. 1, and since Mo is a part of F, it would, on Prop. 2, be non-independent relatively to F, which contradicts the assumption. But in accordance with this assumption, w is an independent part of W, and so also independent relatively to W: there can therefore be nothing in the range of W which could serve as a foundation for w, and so also nothing in the + +whole range of F. + +The proposition before us can also, with suitable changes in symboliza- + +tion, be expressed as follows: + +If A is an independent part of B, and B an independent part of C, A is also an independent part of C or more briefly: An independent part of an inde- + +pendent part is an independent part of a whole. + +Proposition 4 If C is a non-independent part of a whole /Iv, it is also a non- + +independent part of every other whole of which W is a part. + +C is non-independent relatively to W, i.e. it possesses a foundation in an Mo belonging to the range of W. This Mo must naturally also appear in the range of every whole superordinate to W, i.e. every whole which includes W as a part. C must therefore also be non-independent relatively to each such whole. (On the other hand, we add, C may very well be independent relatively to a subordinate whole: we need only so draw its boundaries that the required supplement M is excluded therefrom. A 'piece' of an extended phenomenon in abstracto, but taken as a 'moment' , is independent relatively to such extension; this, however, itself lacks independence relatively to the + +concrete wholes of the occupied extension.) + +Our proposition permits an expression analogous to the previous one, i.e. if A is a non-independent part of B, and B a non-independent part of C, + +then A too is a non-independent part of C. + +A non-independent part of a non-independent part is a non-independent + +Proposition 5 A relatively non-independent object also is absolutely nonindependent, whereas a relatively independent object may be non-independent + +in an absolute sense. + +For a proof see the previous section. + +Proposition 6 If A and B are independent parts of some whole W, they are also independent relatively to one another. For if A required supplementation by B, or any part of B, there would be, in the range of parts determined by W, certain parts (those of B) in which A would be founded A would therefore not + +be independent relatively to its whole W. + +§ 15 Transiti on to the treatment of the more + +important part- relations + +We shall now deal with some of the most remarkable differences among the a priori relationships holding between Whole and Part, and among the Parts of one and the same whole. The generality of these relationships leaves plenty of room for the most manifold differences. Not every part is included in its whole in the same fashion, and not every part is woven together with every other, in the unity of a whole, in the same way. In comparing the relations among the parts of different wholes, or even among the parts of one and the same whole, we come upon striking differences, on which our common talk of different sorts of wholes and parts is founded. A hand, e.g., forms part of a person in quite a different way from the colour of his hand, from his body's total extent, from his mental acts, and from the internal 'moments' of such phenomena. The parts of the extension are otherwise united with each other than they each are united with their colours etc. We shall see at once that all these differences belong to the sphere of our present + +investigations. + +§ 16 Rec iprocal and one-sided, mediate and + +im mediate foundation + +If we consider any pair of parts of a whole, the following possibilities obtain: + +1. There is a relation of foundedness between both parts. 2. There is no such relation. In case I the foundedness can be: + +(a) reciprocal + +(b) one-sided, according as the law in question is convertible or not. Colour and extension accordingly are mutually founded in a unified intuition,2 since no colour is thinkable without a certain extension, and no extension without a certain colour. The character of being a judgement is, on the other hand, one-sidedly founded on underlying presentations, since these latter need not + +function as foundations of judgements. Brentano's distinctions of parts mutually isolable, and parts having one-sided isolability, agrees in extension, though not in definition, with the notion before us. Brentano's additional talk of 'mutual isolability' rules out every sort of foundational relation. There is some interest in asking how matters here stand in regard to the relative independence or non-independence of the parts, relatively, of course, to the whole in which they are considered. If there is a reciprocal relation of foundedness among two parts, their relative lack of independence is unquestionable, as is the case, e.g., in the unity of Quality and Place. The case differs when the relation is one-sided: in that case the foundational (though naturally not the founded) content can be independent. Thus in every extension the shape of a portion is founded on the portion in question: something non-independent relatively to the whole extension is accordingly founded on + +something which is independent in relation to this whole. The foundation of one part in another can further be: + +(a) an immediate foundation or + +(b) a mediate foundation, according as the two parts are immediately or mediately associated. This relationship, like the previous one, is naturally not bound to the individually present 'moments', but concerns the essential being of the foundational relationship. If Ao is immediately founded on Bo, but mediately on Co (in so far as Bo is immediately founded on Co), it holds universally and purely in virtue of essence that an A is in general immediately founded on a B, and mediately upon a C. This results from the fact that if an A and a B are associated at all, they are so immediately, and again that, if an A and a C are associated, they are only mediately associated. The order of mediacy and immediacy is based by law on the pure Genera involved. The generic 'moment' of Colour, for instance, and in quite different fashion the 'moment' of Brightness, can only be realized in and with a 'moment' of lowest difference such as Red, Blue etc., and the latter again only in combination with a certain definite extension. These associations and foundations, which are always immediate, condition the mediate associations and foundations between the 'moment' of Colour or Brightness and that of Determinate Extension. Plainly the laws of combination which concern such mediate foundations, are analytic, indeed syllogistic consequences of those which + +pertain to the immediate foundations. + +§ 17 Exact determination of the concepts of piece (portion), moment, physical part, abstractum, + +concretum + +We may now also reduce a further series of familiar, fundamental concepts to the above defined concepts, and so give them an exact definition. Some of these terms may, we note in advance, be open to objection; the concepts + +We first perform a fundamental division of the concept Part into Pieces, or Parts in the narrowest sense, and into Moments or Abstract Parts of the Whole. Each part that is independent relatively to a whole W we call a Piece (Portion), each part that is non-independent relatively to W we call a Moment ( an abstract part) of this same whole W. It makes no difference here whether the whole itself, considered absolutely, or in relation to a higher whole, is independent or not. Abstract parts can in their turn accordingly have pieces, and pieces in their turn abstract parts. We speak of the portions of a duration, although this is something abstract, just as we speak of the portions of an extension. The forms of these portions are their immanent, abstract parts. Pieces that have no piece identically in common are called exclusive (disjoined) pieces. The division of a whole into a plurality of mutually exclusive pieces we call a piecing or fragmentation (Zerstiickung) of the same. Two such pieces may still have a common identical 'moment': their common boundary, e.g., is an identical 'moment' of the adjoining pieces of a divided continuum. Pieces are said to be isolated when they are disjoined in the strict + +sense, when they therefore also have no identical 'moments'. + +Since an abstract part also is abstract in relation to each more comprehensive whole and, in general, to any range of objects embracing this whole,3 what is abstract, relatively considered, is eo ipso abstract when considered absolutely. The latter can be defined as the limiting case of relative treatment, where the relation is determined by the total range of objects in general. We therefore needed no preliminary definition of the abstract or non-independent in the absolute sense. An abstractum simpliciter is therefore an object, in relation to which there is some whole of which it is a non- + +independent part. + +When a whole permits the sort of 'piecing' in which the pieces essentially belong to the same lowest Genus as is determined by the undivided whole, we speak of it as an extended whole, and of its pieces as extended parts. Here belongs, e.g., the division of an extent into extents, in particular of a spatial stretch into spatial stretches, of a temporal stretch into temporal stretches etc. + +We may here further add the following definition: + +An object in relation to its abstract 'moments' is called a 'relative concretum', and in relation to its proximate 'moments', their 'proximate concretum'. (The difference here presupposed between remoter and nearer 'moments' will be more precisely pinned down in the following sections.) A concretum that itself is abstract in no direction can be called an 'absolute concretum'. Since the proposition holds that each absolutely independent content possesses abstract parts, each such content can also be looked on and spoken of as an absolute concretum. The two notions are thus of equal extent. For a similar reason one can also speak of a piece as a concrete part, whose concreteness is either to be understood as absolute or relative, according as the whole itself only has abstract parts, or is itself abstract. Where the word 'concretum' is used simply, an absolute concretum is usually intended. + +§ 18 The difference between the mediate and + +im mediate parts of a whole + +The distinction between pieces and abstract parts is intimately connected with the distinction between mediate and immediate parts, or, more clearly, the distinction between proximate and remote parts. For talk of immediacy and mediacy can be understood in two ways. We shall first discuss the most + +natural sense of such talk. + +If P(W) is a part of the whole W, then a part of this part, e.g. P (P(W) , is again a part of the whole, but a mediate part. P(W) may then be called a relatively immediate part of the whole. The distinction is a relative one, since P( W) may itself again be a mediate part, in relation to another part of the whole in which it is contained as a part. The relative distinction is transformed into an absolute one, if we understand by absolutely mediate parts such parts as themselves enter into other parts in the whole, whereas absolutely immediate parts will be such as may enter as parts into any part of the same whole. Every geometrical part of an extension is in this absolute sense mediate, for there are always other geometric parts that include it. It is harder to adduce suitable examples of absolutely immediate parts. Perhaps the following might do: if we emphasize in a visual intuition the unified combination formed by all such internal 'moments' as remain identical despite all change of place, we have a part of the whole that can have no superordinate part above it. The same would hold of the totality of their mere extension in regard to the geometric bodies congruent with them in all except position. If we limit our distinction to parts of one and the same sort, then the 'moment' of total coloration is an absolutely immediate part, since there is no like moment of the whole, of which such coloration could be reckoned a part. As opposed to this, the coloration of a piece of the whole can be treated as mediate, in so far as it contributes to the total coloration of the whole. The same holds, in relation to the Species Extension, of the total extension of an extended thing: this is an absolutely immediate part of that thing, whereas a portion of that extension is an absolutely mediate part + +of that thing. + +§ 19 A novel sense of this distinct ion: nearer and + +more remote parts of the whole + +Our talk of immediate and mediate parts acquires quite a different content if we attend to certain remarkable differences that force themselves on us when we compare the relations between wholes and mediate parts.4 If we think of an extensive whole as 'pieced together', its pieces in their turn permit of further 'piecings', the pieces of the pieces in their turn etc. Here the parts of the parts are parts of the whole in exactly the same sense as the original parts were. We do not merely observe this likeness in respect of + +the sort of partial relation which condition talk of 'the same sort of parts' in regard to the whole - the pieces of the pieces are in their tum pieces of the wholes - but we also observe a likeness of such relations between the whole and its mediate parts, on the one hand, and its relatively immediate parts, on the other. There are diverse possible divisions in which the same part comes up, sometimes earlier, sometimes later, so that we have no temptation to accord any privilege to one part over another as regards the way in which it is contained in the whole. The descending order of divisions here corresponds to no fixed, factually determined gradation in the relation of parts to wholes. This does not mean that talk about mediate and immediate parts is entirely arbitrary, and without objective foundation. The physical whole genuinely has the parts first dealt with, and these in their tum no less genuinely have the parts distinguished in them, which are therefore mediate parts in relation to the whole, and the same is true of each stage of the serial division. But in themselves the remotest of these parts are no further from the whole than the nearest. The parts in any case also owe their serial order to the serial order of our divisions, and these latter have no objective foundation. In an extended whole there is no division which is intrinsically primary, and no definitely delimited group of divisions forming the first grade in division; from a given division there is also no progress determined by the thing's nature to a new division or grade in division. We could begin with each division without violating an intrinsic prerogative. Each mediate part can, according to one's chosen mode of division, likewise count as an imme- + +diate part, each immediate part as a mediate one. + +The case is quite different if we bring in other examples. An intuitively unified tone-sequence, e.g. a melody, is a whole, in which we find individual tones as parts. Each of these tones has further parts, a 'moment' of quality, of intensity etc., which as parts of parts are also parts of the melody. But it is clear in this case that the mediacy with which the qualitative 'moment' of the individual tone enters the whole, cannot be attributed to our subjective series of divisions or to any other subjective ground. It is no doubt certain that if the individual tone's moment of quality is to be singly noticed, the tone itself must be 'stressed'. To single out the mediate part presupposes the singling out of the immediate one. But this phenomenological relationship must not be confused with the objective situation we are here concerned with. It is evident that the quality in itself only forms part of the melody in so far as it forms part of the single tone: it belongs immediately to the latter, and only mediately to the total tone-pattern. This mediacy is not therefore bound up with some arbitrary, or some psychologically compulsive preference for a certain order of division which first makes us hit on the tone, and then on its 'moment' of quality: the tone in itself is a prior part in the whole melody, and its quality a later, mediate part. The same holds of the tone's intensity: it would here seem even to take us a step further from the melodic whole, being as it were no immediate 'moment' of the tone, but one more + +directly of its quality, and so a secondary part in relation to this melody (no doubt a somewhat objectionable conception, which requires closer scrutiny). If we are right in holding that there is a part of the quality, e.g. the pitch C, of the tone in question, which represents its generic 'moment', what it has in common with all tones, then this 'moment' primarily inheres in the quality, secondarily in the tone, and at least tertiarily in the whole tonepattern etc. Just so the moment of colour or shape that inheres in an extended part of what is visually intuited as such, is primarily attached to this part, only secondarily to the intuited whole. It is even more mediately related to the whole voluminousness6 of the patterned extension, the magnitude that it primarily possesses. (yVe can of course not talk of a genuine quantitative pinning down in the sphere of mere data of intuition as such.) Mter these discussions, the novel and important sense of the distinction between mediate and immediate parts should be clear. The difference is, however, not merely relative: in every whole there are parts which belong directly to the whole, and not first to one of its parts. It is definite for the single part whether it is mediate or not in our sense, and, if it is mediate, whether it is so primarily, secondarily or more remotely. To make a terminological distinction one could here speak of nearer and remoter parts, or to fix things more exactly of primary, secondary ... parts of a whole; the terms mediate and immediate part we retain in the more general sense applicable to any parts. Secondary parts are primary parts of primary parts, tertiary parts, primary parts of secondary parts etc. The notions comprised in this series + +are obviously mutually exclusive. + +Primary parts may be, and in general also will be, absolutely mediate. But there are also primary parts that are absolutely immediate, i.e. that are not included as parts in any part of their whole. Each portion of an extension is primarily contained in it, although it can always be regarded as a mediate part of the same extension. Objectively there are always parts whose part it is. As against this, the form of an extension is not included as a part in any + +of that extension's parts. + +§20 Nearer and remoter parts re lative ly to + +one another + +We spoke above of mediate and immediate, of nearer and remoter parts, in relation to the whole to which they belong. But even when we are dealing with parts in relation to one another we usually employ these terms, though in quite a different sense: we talk of an immediate or mediate connection of the terms and, in the latter case, draw further distinctions. Some parts, we say, are closer to one another, other parts further. Here the following relations are relevant. It often happens that a mode of association peculiarly unites two parts A, B into a partial unity which excludes other parts, but in which, further, B and not A is associated in just this manner with C. In this + +situation A is also associated with C, in virtue, that is, of a complex form of unity constituted by the two associations AB and Be. The latter associations we then call immediate, while we say that the association of A and C, achieved in the form ABC, is mediate. If there are further peculiar associations CD, DE etc., we shall say that A is associated with their final terms D, E ... with progressively increased mediacy, D is a remoter part than C, E still more remote than D etc. We have obviously only characterized a simple special case. Each symbol A, B, C ... could have summed up a complex partial unity, a whole group of unified members; in this case also the concatenations tying the partial unities together into wholes, would make the members of the different groups appear in relations of nearer or remoter + +connection. + +As to whether other associations, and in particular other direct associations, subsist among the mediately associated members - and associations perhaps of the same kind as those among the immediately associated members - we have so far said nothing. We are considering the members exclusively in respect of the forms of the complex relationships determined by their elementary associations. Naturally the treatment of these forms will be of particular significance in that special class of cases, so frequently dealt with in theory and practice, whose peculiarity can readily be shown up in the relations of points in a straight line. If we select any series of points from a straight line, we observe that the immediate associations of the mediately associated members belong, with the associations of immediately neighbouring points, to one and the same lowest Genus of associations: they are further only different in respect of their lowest specific difference, whereas this difference itself is unambiguously determined by the differences of the varied mediating associations. This holds of time-sequences, of spatial configurations, in short of every case where associations can be characterized by directed stretches of one and the same Genus. In every case, to put it briefly, stretches are addible. But in our quite formal treatment we can pass all such + +matters by. + +The essence of the matter can be conceptually laid out in the following fashion. Two associations form a concatenation, when they have some but not all members in common (i.e. do not coincide as when, e.g., the same members are united by several associations). Each concatenation is on this showing a complex association. Associations now divide into those which include concatenations and those which do not: associations of the former are combinations of associations of the latter sort. The members of an association that is free from concatenations are said to be immediately associated or proximate. In every concatenation, and therefore in every whole containing concatenations, there must be immediately associated members, which belong to associations of parts which include no further concatenations. All other members of such a whole are said to be mediately associated with one another. The member common to a simple concatenation ABC (simple + +because it contains no concatenation as a part) is, in the sense of our rulings, immediately associated with its neighbours, while these are mediately associated with one another etc. Talk of nearer and remoter parts always relates to concatenations. The concepts next neighbour (=immediately associated member), next-neighbour of a next-neighbour etc., yield, by an easily determined formal completion, the requisite gradations of 'distance', and are then no different from ordinal numbers: first, second etc. The completion naturally tries to make these concepts unambiguous by fixing a 'direction of progress', e.g. by bringing in the asymmetry of a class of relations, in consequence of which we form conceptual structures like 'right next-neighbour of A' (first man right of A), 'right next-neighbour of right next-neighbour of A' ('second man right of A') etc. The essential purposes of the present investigation do not require us to go more deeply into this not intrinsically + +trivial point. + +§2 1 Exact pinning down of the pregnant not ions of whole and part, and of their essential species, + +by means of the notion of foundati on + +Our interest in the foregoing treatments was directed to the most general relations of essence between wholes and parts, or between parts among one another (i.e. of contents that combine into a whole). In our definitions and descriptions on these matters the notion of Whole was presupposed. It is however possible to dispense with this notion in all cases: for it can be substituted the simple coexistence of the contents that were denominated parts. + +One could, e.g., define as follows: + +A content of the species A is founded upon a content of the species B, if an A can by its essence (i.e. legally, in virtue of its specific nature) not exist, unless a B also exists: this leaves open whether the coexistence of a C, a D + +etc. is needed or not. + +One can proceed similarly with the other definitions. If all is taken thus generally, one could then give the following noteworthy definition of the + +pregnant concept of Whole by way of the notion of Foundation: + +By a Whole we understand a range of contents which are all covered by a single foundation without the help of further contents. The contents of such a range we call its parts. Talk of the singleness of the foundation implies that every content is foundationally connected, whether directly or indirectly, with every content. This can happen in that all these contents are immediately or mediately founded on each other without external assistance, or in that all together serve to found a new content, again without external assistance. In the latter case the possibility remains open that this unitary content is built up out of partial contents, which in their turn are founded on partial groups from the presupposed range of contents, just as the Whole content is founded on its total range. Intermediate cases are finally also possible, where the + +unity of foundation is so formed, e.g., that A founds a new content together with B, B one together with C, C one together with D etc. In such cases the + +formation of new unities is in short concatenated. + +One sees at once how such differences determine essential divisions of the whole. In the cases first referred to, the 'parts' (defined as members of the range in question) 'interpenetrated' , in the other cases they were 'mutually external', but, whether taken all together, or concatenated in pairs, they embodied real forms of association. Where one speaks of connections, associations etc. in the narrower sense, one means wholes of the second sort, i.e. wholes where contents relatively independent as regards one another - where the whole falls apart into its pieces - serve to found new contents as their 'combinatory forms'. Talk of wholes and parts tends in general to be + +oriented exclusively to such cases. + +The same whole can be interpenetrative in relation to certain parts, and combinatory in relation to others: the sensuous, phenomenal thing, the intuitively given spatial shape clothed with sensuous quality, is (just as it appears) interpenetrative in respect of reciprocally founded 'moments' such + +as colour and extension, and combinatory in respect of its 'pieces'. + +§22 Forms of sensuous unity and wholes + +Before we go further, it is well to indicate expressly that, in harmony with our definition, there need not be a peculiar form for every whole, in the sense of a specific 'moment' of unity which binds all the parts. If unity arises, e.g., by concatenation, so that each pair of next members founds a new content, the demands of our definition are satisfied, without the presence of a peculiar moment (i.e. one of unity) founded on all parts together. That such a moment must always be presumed can scarcely be maintained a priori. On our concept of a whole, it is not even requisite that the parts should be associated in groups or pairs by peculiar 'moments' of unity. Only if the whole is an extended whole, and in general one that can be broken down into 'pieces', + +are such moments obvious and indispensable a priori. + +It might, however, seem odd that we make do with this definition, and can even dare to think that all wholes, with the sole exception of these which break up into 'pieces', lack binding forms of unity. It is odd to hold that the unity, e.g., of extension and colour, of tone-quality and tone-intensity, or between the sensational stuff of our percept of a thing and the peculiar phenomenological 'moments' brought to it by our perceptual consciousness, and all other similar unities, rest merely on one-sided or two-sided relations of foundation, without the added foundation, by way of such coexistence, of a peculiar form-content or 'moment' of unity. It is nonetheless obvious that wherever associative forms can really be demonstrated as peculiar moments in intuition, the things associated are relatively independent parts, parts such as tones in the unity of a melody, colours picked out piecemeal in + +the unity of a colour-pattern, or partial shapes taken from the unity of a complete shape etc. Contrariwise, it is vain to look in the unity of the visual phenomenon for special form-contents in addition to those which unify its pieces, form-contents which will bring together non-independent 'moments' such as colour and extension, or which will bring together colour-tone and brightness in the former, and the 'moments' of form and size in the latter. We are of course far from wishing to tum the undiscovered into the nonexistent without more ado. But it is in any case most important to discuss the possibility of there being sensuous unities without abstractible sensuous + +form, and if this proves feasible, to clarify the notion. + +It may at first seem extraordinary in this respect that mere necessities of coexistence, demands for supplementation, consisting in no more than the fact that the existence of certain sorts of contents conditions the mere coexistence of contents of certain coordinated sorts, that requirements of this kind, I say, should serve to produce unity. One at once objects: could contents in such a situation be side by side in complete isolation, dependent on each other for their existence and yet entirely uncombined, without their 'foundation' amounting to a connected unity in the manner here supposed? Our answer is plain. Talk of separation implies a thought of the relative independence of the separated, which is just what we have excluded. The picture of side-by-side existence is revealing: it plainly presupposes relatively independent contents, which, since they are such, can serve to found this sensuous form of side-by-side existence. What recommends such an unsuitable picture - unsuitable since it tries to illustrate sensuous formlessness by a case of sensuous form - is the mutual indifference of the contents merely given together in space. The thought insinuates itself: where there is not even the loosest, but simply no unifying form, contents could really not have anything to do with each other: they could never therefore come together but would remain eternally isolated. Is it not absurd to want to bind contents together without any bond? This is no doubt quite right for the contents the image presupposes, but the contents of which we speak have plenty to do with each other, they are in fact 'founded' on one another, and for this reason they require no chains and bonds to chain or knit them together, or to bring them to one another. In their case all these expressions have in fact no sense at all. Where it makes nonsense to speak of isolation, the problem + +of overcoming such isolation is likewise nonsensical. + +This conception is naturally not limited in its application to the sphere of the intuitive objects (phenomenological contents in particular) which served as our illustrations, but applies to the sphere of objects in general. The only true unifying factors, we may roundly say, are relations of foundation '. The unity even of independent objects is in consequence brought about by 'foundation' . Since they are not, as independent objects, 'founded' on one another, it remains their lot to 'found' new contents themselves, and to 'found' them together; it is only in virtue of this situation that these latter + +are thought of as unifying contents in respect of their 'founding' members. But the contents 'founded' on one another (whether one-sidedly or reciprocally) likewise have unity, and a much more intimate unity since less mediated unity. Such 'intimacy' consists simply in the fact that unity is here not engendered by a novel content, which again only engenders unity since it is 'founded' on many members separate in themselves. If one calls such a content 'unity', then unity is indeed a 'real predicate', a 'positive' 'real' content, and other wholes have, in this sense, no unity, and we shall not even be able to say that their own moment of unity is unified with each of the united members. If we refuse however to adopt such a wrong-headed terminology, which necessitates double-talk in practice, we shall speak of unities and wholes wherever we have a unitary foundation. We shall be entitled to say of each range of contents united in this manner that it has unity, though the predicate thus attributed to it is no 'rea1' one, though there is no constituent called 'unity' anywhere in our whole which can be + +prised out. Unity is in fact a categorial predicate. + +One should also take into account the by no means small theoretical advantage which our notion promises as removing a long-known and troublesome difficulty in the theory of wholes. This concerns the endlessly complicated part-relations which seem required by the endlessly complicated 'moments' of unity in every whole. The view against which our objections are directed is based on the apparently plain truth that, wherever two contents form a real unity, there must be a peculiar part, a 'moment of unity', that binds them together. If then U is the moment of unity of A and B, there + +must be a new 'moment' of unity U1 + +, for A and U (since these two are + +unified) and again a new U2, for B and U; and just so new 'moments' ul and U�, for U and U1 , and for U and U2 respectively, and so on in infinitum. If no distinction is drawn between associations and relations, between differences of 'sense-materia1' and 'categorial form', and if one then takes the boundlessly varied conceptual differences that are possible a priori, and which ideal principles allow one to complicate indefinitely, and puts all such differences into objects as their real moments, one gets the analyses which Twardowski has offered us in his 'psychologica1' researches, and which are + +as subtle as they are queer. + +Our conception avoids these endless regresses of parts which are always splitting into further series. Nothing really exists - in the sense of being a possible object of sense-perception - beyond the aggregate of a whole's 'pieces', together with the sensuous forms of unity, which rest on these pieces conjointly. Unity is conferred on the 'moments' in the 'pieces', as also on the 'moments' of unity and the 'pieces', by the foundational relations in + +the sense of our definition. + +The notion of the moments of unity, which we still distinguish from that of the 'form' which gives unity to a whole, has, lastly, been defined above in passing. Expressly put, we mean by it a content founded on a plurality of + +contents, and on all of them together, and not on some of them simply. (All this naturally presupposes our notion of foundation.) If we keep within the phenomenal sphere, this content may as readily belong to outer as to inner + +sense, according to the nature of its foundational contents. + +Note. 'Moments' of unity, like all other abstract contents, fall into pure Genera and Species.? The Genus Spatial Figure differentiates itself into Triangular Figure, the latter into the lower Species of Definite Triangular Figure, in the sense in which we speak of the 'same' triangle however much we may shift or turn it. Such examples make clear that the Genus of 'Moments' of unity is determined by the Genus of the contents which found them, and that the lowest difference of the former is unambiguously determined by the lowest difference of the latter. One notes, further, that 'moments of unity' must be distinguished into 'moments' or forms of the first, second, third ... level, according as the form is immediately 'founded' upon absolute contents, or on forms of the first level, or on forms founded on forms of the first level, and so on. One sees further that the form-contents of higher level necessarily form a whole with the whole descending series of forms of lower level, and in such combination always represent complex forms relatively to the ultimately foundational elements. In the sphere of complex sensuous shapes, particularly visual and auditory ones, this can be readily illustrated, whereas the general fact can be seen a priori from concepts. + +§23 Forms of categorial un ity and wholes + +In the sense in which we are here trying to pin down the notion of a whole, a mere aggregate or mere coexistence of any contents is not to be called a whole, as little as a likeness (the being of the same sort) or a difference (the being of another sort, or, in another sense, the not being identical) are wholes.8 'Aggregate' is an expression for a categorial unity corresponding to the mere form of thought, it stands for the correlate of a certain unity of reference relating to all relevant objects. The objects themselves, being only held together in thought, do not succeed in founding a new content, whether taken as a group or together; no material form of association develops among them through this unity of intuition, they are possibly 'quite disconnected and intrinsically unrelated' . This is shown in the fact that the form of the aggregate is quite indifferent to its matter, i.e. it can persist in spite of wholly arbitrary variation in its comprised contents. A 'founded' content, however, depends on the specific 'nature' of its 'founding' contents: there is a pure law which renders the Genus of the 'founded' content dependent on the definitely indicated Genera of the 'founding' contents. A whole in the full and proper sense is, in general, a combination determined by the lowest Genera of the parts. A law corresponds to each material unity. There are different sorts of whole corresponding to these different laws, or, otherwise put, to the different sorts of contents that are to serve as parts. We cannot at + +will make the same content at one time part of one sort of whole, at another time part of another sort. To be a part, and, more exactly, to be a part of some determinate sort (a metaphysical, physical or logical part or whatever) is rooted in the pure generic nature of the contents in question, and is governed by laws which in our sense are a priori laws or 'laws of essence'. This is a fundamental insight whose meaning must be respected in all our treatments and formulations. And with this insight we have the foundation for a systematic theory of the relations of wholes and parts as regards their pure forms, the categorially definable types which abstract from the + +'sensuous' material of such wholes. + +Before we pursue these thoughts, we must remove a further difficulty. The form of an aggregate is a purely categorial form, in opposition to which the form of a whole, of a unity due to foundation, appeared to be a material form. But did we not say in the previous section that unity (and we were talking specifically of a unity based on foundation) was a categorial predicate? Here we must note that, on our doctrine, the Idea of unity or the Idea of a whole is based on the idea of 'Founding', and the latter Idea upon the Idea of a Pure Law; the Form of a Law is further as such categorial - a law is not thinglike, not therefore perceptible - and that to this extent the notion of a Founded Whole is a categorial notion. But the content of the law governing each such whole is determined by the material specificity of the 'founding' contents and consequently of the 'founded' types of content, and it is this law, definite in its content, which gives the whole its unity. For this reason we rightly call each ideally possible specification of the Idea of such + +unity a material or also a real (reale) unity. + +According to our previous assertions,9 the laws constitutive of the various sorts of whole are synthetically a priori, as opposed to laws which are analytically a priori, such as those governing pure categorial forms, e.g. the Form-Idea of a whole as such, and all merely formal specifications of this Idea. We prefer to dwell in what follows, on such formal specifications. + +§24 The pure fo rmal types of wholes and parts. + +The postu late of an a priori theory + +The pure forms of wholes and parts are determined by the pure forms of law. Only what is formally universal in the foundational relation, as expressed in our definition, is then relevant, together with the a priori combinations that it permits. We rise, in the case of any type of whole, to its pure form, its categorial type, by abstracting from the specificity of the sorts of content in question. More clearly expressed, this formalizing abstraction is something quite different from what is usually aimed at under the title of 'abstraction' : it is a quite different performance from the one which sets in relief the universal Redness in a concrete visual datum, or the generic 'moment' of Colour in the Redness previously abstracted. In formalization we replace + +the names standing for the sort of content in question by indefinite expressions such as a certain sort of content, a certain other sort of content etc. At the same time, on the semantic side, corresponding substitutions of purely + +categorial for material thoughts take place. + +10 + +The distinctions between abstract parts and 'pieces' are purely formal, being in this sense drawn in purely categorial fashion, as can be seen at once from our pronouncements above. These pronouncements had however to be suitably interpreted in accordance with our present leaning towards final formalization: the pure concept of the whole, in the sense of our last definition, had to be made their basis. The distinction likewise between nearer and remoter parts that we merely explained, in descriptive fashion, ll by means of illustrations, can now be reduced to the mere form of certain foundational + +relations, and so formalized. + +In our examples we saw above that, in the case of many intuitive wholes, a graded series of fragmentations of such wholes always results in fragments of these wholes themselves, fragments all equally close to the whole, and which could with equal justice count as results of a first fragmentation. The sequence of the 'piecings' was in these instances not prescribed by the essence of the wholes. What is here relevant is first the proposition that pieces of pieces of a whole are themselves pieces of the whole - a proposition that we formally proved abovel2 (in different words). But we were there dealing with 'pieces', for which the sequence of fragmentations was meaningless, since it corresponded to no graded series of 'foundations' . All pieces always stood to the whole in the same relation of 'foundation' . There were no differences in the form of the relation to the whole, all parts were 'contained in the whole' in the same fashion. The matter would be quite different were we to fragment aesthetic unities, e.g. a star-shape built out of star-shapes, which in their turn are composed of stretches and ultimately of points. The points serve to 'found' stretches, the stretches serve to 'found', as new aesthetic unities, the individual stars, and these in their turn serve to 'found' the starpattern, as the highest unity in the given case. The points, stretches, stars and the final star-pattern are not now coordinated as are partial stretches in a stretch. There is, in their case, a fixed order of 'foundations', in which what is founded at one level serves to 'found' the level next above, and in such a manner that at each level new forms, only reachable at that level, are + +involved. We may here add the universal proposition: + +'Pieces' are essentially mediate or remote parts of a whole whose 'pieces' they are, if combinatory forms unite them with other 'pieces' into wholes which + +in their turn constitute wholes of higher order by way of novel forms. + +The difference between the parts nearer or further in regard to the whole has accordingly its essential ground in the formally expressible diversity of + +foundational relations. + +The case is similar in regard to non-independent 'moments', if we take account of the essential formal distinction between such 'moments' as can + +only satisfy their need for supplementation in the complete whole, and such as can satisfy this need in pieces of this whole. This makes a difference to the mode of belonging, to the form of foundation: by it certain parts, e.g. the total extent of the intuited thing, belong exclusively to the thing as a whole, while other parts, e.g. the extent of a 'piece', belong specifically to this 'piece', and only more remotely to the whole. This mediacy is no longer inessential, as is that of second-level 'pieces' in the division of a stretch, but is an essential mediacy, to be characterized in terms of the formal nature of the relationship. Obviously similar reasons place 'pieces' of non-independent 'moments' which pertain directly to the whole, further from the whole than the 'moments' are: this at least is the case if the rule holds that we found valid in the field of intuition, that such 'pieces' can have their immediate foundation only in a 'piece' of the whole. The wider proposition also can be formally expressed: Abstract parts are further from the whole, are in essence mediate parts, if their need for supplement is satisfied in the sphere of a mere part. This part can then well either be a 'piece' of the whole, or be in need of further completion. The mediacy in the latter case consists in the fact that the law of supplementation in which the form of foundation resides, points, in the case of the originally mentioned abstract part, to a whole which, in virtue of a new law of supplementation is, and must be, a part of a more comprehensive whole, i.e. of the complete whole, which accordingly only includes the first part mediately. This permits us also to say that abstract parts of the whole that are not abstract parts of its 'pieces', are nearer to the whole than + +the abstract parts of the 'pieces'. + +These thoughts can only be meant, and are only meant, to count as mere indications of a future treatment of the theory of Wholes and Parts. A proper working out of the pure theory we here have in mind, would have to define all concepts with mathematical exactness and to deduce all theorems by argumenta in forma, i.e. mathematically. Thus would arise a complete law-determined survey of the a priori possibilities of complexity in the form of wholes and parts, and an exact knowledge of the relations possible in this sphere. That this end can be achieved, has been shown by the small beginnings of purely formal treatment in our present chapter. In any case the progress from vaguely formed, to mathematically exact, concepts and theories is, here as everywhere, the precondition for full insight into a priori + +connections and an inescapable demand of science. + +§25 Addi tions regard ing the 'pieci ng' (fragmentation) of wholes through the 'pieci ng' of their 'moments' + +We may end with an additional observation that is perhaps not without + +interest. + +It is an analytic proposition that 'pieces' considered in relation to the whole whose 'pieces' they are, cannot be founded on each other, either one-sidedly + +or reciprocally, and whether as wholes or in respect of their parts. But, on the other hand, we cannot at all conclude from the content of our basic definition that it is impossible that 'pieces' should enter into foundational relationships in regard to a more comprehensive whole in which they all count as non-independent 'moments' . In fact, however, we find no such example in the field of pure intuition and self-evidence that is open to us, and remarkable relationships among parts depend on this circumstance in precisely this field. We can in fact enunciate a proposition which is in a wider sense phenomenological. To each 'piece' in a relative abstraction there corresponds a 'piece' in each of its relative concreta, so that the mutually exclusive 'pieces' of the former serve to ground mutually exclusive pieces in each of the latter. In other words: the fragmentation of a non-independent 'moment' conditions a fragmentation of the concrete whole, in so far as the mutually exclusive 'pieces', without themselves entering into a foundational relation with one another, attract new 'moments' to themselves in virtue of + +which they are singly distributed to 'pieces' of the whole. + +A few examples will make this clear. The fragmentation of the quasispatial extensity of a visual content, which endures unchanged, but which is considered in abstraction from its temporality, also effects a 'piecing' of this visual content itself. The same holds of spatial data of intuition in respect of spatial 'piecing'. The separated spatial pieces serve to 'found' mutually independent complementary 'moments' . The colouring of one piece is not, e.g., 'founded' upon the colouring of any other. To this extent one may say, further, that the complementary moments are themselves fragmented by the fragmentation of the spatiality which serves to 'found' them, or that they divide themselves piecemeal over the spatial 'pieces'. The colourings of the 'pieces' stand in the same whole-part relations (exclusion, inclusion, intersection) as the 'pieces' themselves. This peculiar fact, that here the 'piecing' of a 'moment' simultaneously entails a 'piecing' of the whole, obviously rests on the fact that the 'pieces' of the 'moment' do not serve to 'found' one another even within the more inclusive whole, but that they need new 'moments' to 'found' them in each case: it also depends on the further fact that these new 'moments' themselves only find their needed foundation in the + +'pieces', not mutually in one another. + +The same is the case with intuitive time-wholes. If we fragment the duration of a concrete course of events, we have fragmented this course of events itself: to the segments Qf time, segments of movement correspond ('movement' being understood in the widest Aristotelian sense). The same holds in the case of rest: rest too has its segments that count as 'pieces' in the sense of our pronouncements, since rest during one lapse of time, and rest during any other lapse, do not stand in any evident foundational relation to each other. The case is quite different if, instead of limiting ourselves to the sphere of essential data to be studied by way of intuition, we rather bring our con- + +This transition, however, demands a widening of our notions. We have related all our conceptual constructions to the pure sphere of essence, the laws of foundation were subject to pure laws of essence, the parts were essentially one in the whole, as a result of a priori connections of the Ideas corresponding to the parts and 'moments'. But nature with all its thing-like contents certainly also has its a priori, whose systematic elaboration and development is the still unperformed task of an ontology of nature. It is no doubt clear from the start that natural laws in the ordinary sense do not belong to this a priori, this pure universal 'form' of nature, that they have the character, not of truths of essence, but of truths of fact. Their universality is not a 'pure' or 'unconditioned' universality, and just so the 'necessity' of all the thing-histories which fall under them is infected with 'contingency'. Nature with all its physical laws is a fact that could well have been otherwise. If we now treat natural laws, without regard to their infection with contingency, as true laws, and apply to them all the pure concepts we have formed, we arrive at modified Ideas of empirical 'foundation', of empirical wholes, empirical independence and non-independence. If, however, we conceive the Idea of a factual nature as such, of which our own nature is an individual specification, we arrive at universal Ideas, not bound down to our nature, of an empirical whole, empirical independence etc. These Ideas are plainly constitutive of the Idea of a nature in general, and must fit, together with the essential relations pertaining to them, into a universal ontology of + +nature. + +All this being presumed, we return to our specific question. While we found no example in the material sphere of essence where a fragmentation of a non-independent 'moment', e.g. of the spatial and temporal 'moment', did not entail a fragmentation of the concrete whole, the matter is different in the field of all empirically real connections of coexistence and succession. This is clear if we consider the sense of empirical relations of necessity, which associate things spatially and temporally separate. If a particular causal law involves that a concrete process of change in a time-segment t,-to, is necessarily succeeded by a certain new process in the neighbouring timesegment, t2-t" the former thereby loses independence in regard to the latter. Let us assume now that particular laws of this sort, whose essence it is only to be knowable empirically, belong ontologically, i.e. in virtue of the Idea of Nature as such, to each concrete process of change, to which they assign certain necessary, temporally contiguous consequences, and let us make the still stronger assumption that each such process must itself be a necessary consequence of previous antecedents. To assume all this is to hold that each concrete natural process of change lacks independence in respect of the more embracing temporal whole in which it is realized, and that no fragmentation of a time-stretch therefore conditions a fragmentation of the correlated concrete temporal whole. But the limitation to processes of change is unnecessary and, strictly speaking, not even allowable. As mechanics treats + +of rest and movement from a single viewpoint, and includes rest as a special limiting case of motion in its laws, so one should proceed analogously with concepts extended in the Aristotelian manner. Even the imaginary case of fixed rest isolated from the whole world is not immune from the properly formulated principle of causality. If we conceive of any time-lapse, however small, as filled with a rigidly unchanging concrete content (if indeed the Idea of Nature permits such a conceptual possibility) and if we conceive of the whole of reality as reduced, during this period to such a changeless being, then the causal principle certainly demands that such being should persist unchanged a parte post for all eternity (though, a parte ante, it may have arisen out of eternal rest or law-governed change). In regard to these causal connections, from which nothing temporal is immune, we may therefore say that a fragmentation of its time aspects never entails a fragmentation of a concrete temporal whole. The 'moments' needed to complete its timesections are indeed separated as these sections are, but such separation effects no fragmentation in the temporal concretum: this is prevented by the + +reciprocal causal 'foundation' of its temporally sundered contents. + +The case is of course similar at least in regard to the spatial fragmentation of those wholes in which spatial and temporal extension are coincident, so that each fragmentation of the one 'moment' is attended by a fragmentation of the other, and vice versa. The fragmentation of the spatial aspect of a movement is as little able, as is the fragmentation of its temporal aspect, to + +effect a fragmentation of the movement itself. + +These considerations also mean that in objective time, the time of nature, time-stretches that in abstracto had the character of 'pieces' in respect of each duration that embraced them, lose their mutual independence, if we treat them in relation to a concretely occupied temporal unity of which they are non-independent 'moments' . The proposition that each objective temporal duration is a mere part of time, which cannot only be extended in both directions in infinitum, but also has to be so, is, as one readily sees, a mere consequence of causality, and therefore related to the content of time. This consequence makes a temporal part non-independent, not merely in relation to its own filling, but also in relation to neighbouring parts of time and their contents. This non-independence of temporal parts, and their reciprocal 'foundation' , is governed by laws which not merely associate time-stretches with time-stretches, but associate concretely occupied temporal wholes with other similar temporal wholes. Since in these laws, among the variables representing 'moments' of time-occupying contents, times or time-stretches also figure as mutually dependent variables, such time-stretches likewise acquire a mediate relation of 'foundedness' in regard to a more inclusive concrete unity. The same of course holds of bits of space in relation to more embracing spatial unities, and ultimately to the whole infinite space of nature. The proposition that each bit of space requires to be extended in all directions, or, as we should put it more precisely, requires the real possibility + +of being so extended and as far as the one infinite space goes, is a consequence of certain causal laws, more precisely of certain natural laws. The fact that we freely extend spatial and temporal stretches in imagination, that we can put ourselves in imagination at each fancied boundary of space or time while ever new spaces and times emerge before our inward gaze - all this does not prove the relative 'foundedness' of bits of space and time, and so does not prove space and time to be really infinite, nor even that they can really be so. This can only be proved by a law of causation which presupposes, and so requires, the possibility of being extended beyond any given + +boundary. + +Investigation IV + +The distinction between + +independent and non- + +independent meanings and + +the idea of pure grammar + +Introduction + +In the following discussions we wish to turn our gaze to a fundamental difference in the field of meanings, a difference which lies hidden behind insignificant grammatical distinctions, such as those between categorematic and syncategorematic expressions, or between closed and unclosed expressions. To clear up such distinctions will enable us to apply our general distinction between independent and non-independent objects in the special field of meanings, so that the distinction treated in our present Investigation may be called that of independent and non-independent meanings. It yields the necessary foundation for the essential categories of meaning on which, as we shall briefly show, a large number of a priori laws of meaning rest, laws which abstract from the objective validity, from the real (real) or formal truth, or objectivity of such meanings. These law�, which govern the sphere of complex meanings, and whose role it is to divide sense from nonsense, are not yet the so-called laws of logic in the pregnant sense of this term: they provide pure logic with the possible meaning-forms, i.e. the a priori forms of complex meanings significant as wholes, whose 'formal' truth or 'objectivity' then depends on these pregnantly described 'logical laws'. The former laws guard against senselessness (Unsinn), the latter against formal or analytic nonsense (Widersinn) or formal absurdity. If the laws of pure logic establish what an object's possible unity requires in virtue of its pure form, the laws of complex meanings set forth the requirements of merely significant unity, i.e. the a priori patterns in which meanings belonging to different semantic categories can be united to form one meaning, instead of + +producing chaotic nonsense. + +Modern grammar thinks it should build exclusively on psychology and other empirical sciences. As against this, we see that the old idea of a universal, or even of an a priori grammar, has unquestionably acquired a foundation and a definite sphere of validity, from our pointing out that there are a priori laws which determine the possible forms of meaning. The extent to which there may be other discoverable fields of the grammatical a priori goes beyond our present field of interest. Within pure logic, there is a field of laws indifferent to all objectivity to which, in distinction from 'logical iaws' + +in the usual pregnant sense, the name of 'logico-grammatical laws' can be justifiably given. Even more aptly we can oppose the pure theory of semantic + +forms to the pure theory of validity which presupposes it. + +§ I Simple and complex meanings + +We start from the immediately obvious division of meanings into simple and complex, which corresponds to the grammatical distinction between simple and complex expressions or locutions. A complex expression is an expression, to the extent that it has one meaning; as a complex expression it is made up of parts which are themselves expressions, and which as such have their own meanings. If we read of 'a man of iron' or 'a king who wins the love of his subjects' etc., we are impressed by such part-expressions or + +part-meanings as those of man, iron, king, love etc. + +If we now find further part-meanings in such part-meanings, meanings may again come forward as parts of these, but this can obviously not go on in infinitum. Continued division must ultimately lead to simple, elementary meanings. That there really are such simple meanings is shown by the indubitable case of something. The presentative experience we have when we understand this word is undoubtedly complex, but its meaning shows no + +sign of complexity. + +§2 Wheth er complexity of mean i ngs merely reflects + +complexity of objects + +Clear as this seems, we are still beset by varied doubts and questions. + +We may ask first whether the complexity or simplicity of meanings' merely reflects the complexity or siinplicity of the objects which such meanings significantly present. One might at first imagine so: the presentation presents the object, and is its mental picture. Very little reflection will, however, show how deceptive such a picture-analogy is, both in this and in many other cases, and that its presumed parallelism holds from neither side. In the first place, complex meanings may present simple objects. An example as clear as it is decisive is the expression 'simple object' itself. It is quite indifferent + +whether there is, or is not, any such object.2 + +It is true, conversely, that simple meanings can 'present' complex objects, can refer to them in significant fashion. One might doubt (though I do not think correctly) whether the simple names in our above examples ('man', 'iron', 'king' etc.), really give expression to simple meanings, but we shall have to count names like 'one' and 'something' as doing so. It is clear that they, in their indefinite reference to all that is possible, will refer to every complex object, even if they refer to it quite indeterminately, or as a mere 'something'. It is clear, further, that even where a complex meaning refers to a complex object, no part of the object need correspond to each part of the meaning, + +let alone the other way round. Bolzano's noteworthy example, a land without mountains, has indeed been disputed by Twardowski, but this is due to his identification of meaning with the direct, intuitive presentation of the subject, and to his total disregard of that notion of meaning which alone is fundamental in logic. This leads him to take constituents of the meaning (without mountains) as 'auxiliary presentations which resemble linguistic + +roots'.3 + +§3 Complexity of meani ngs and complexity of the + +concrete act of meani ng. Impli ed meani ngs + +There are, on the other hand, wide ranges of cases where doubt arises whether a given meaning should count as complex or simple. If we wish, e.g., to treat the meanings of proper names as simple, we face the objection that in a certain obviously good sense, we can say that a name like 'Schultze', when used of a person known to us, helps to present a certain human being, a being possessed of all the parts and attributes that we think proper to human beings, as well as many individual peculiarities which distinguish him from others. On the other hand, we hesitate to assign partial meanings within such 'proper meaning' to the successively stressed attributes of the thing the name uniquely stands for, the more or less clearly presented object, or even to identify such a 'proper meaning' with a complex meaning of the form 'an A, which is a, b, c .. .' which we build up step by step as we + +analyse the content of the idea Schultze objectively. + +Closer consideration shows that we must here distinguish two senses of simplicity and complexity; simplicity in one sense does not exclude complexity in another. Undoubtedly we must refuse to look on a 'proper meaning' as an articulate, and so complex structure of meanings: we must nonetheless grant that our consciousness of meaning here shows a certain complexity, that surely stands in need of clarification. Everything that later explication and conceptualization coax out of the Schultze on whom we confer a name and a certain content, no doubt represents new meanings that were not really (reel!) implicit as under-emphasized parts in our original meaning. Without doubt, the 'proper meaning' of Schultze was simple. It is plain, further, that the presentative content with which Schultze is presented when we name him, can change in many ways, while his proper name goes on performing the same significant role, always naming the same Schultze 'directly' . On the other hand, we are not here dealing with some chance presentational addition to our consciousness of meaning, but with facts of presentation that are necessary, even though variable in content; without them our actual meaning could not point to the object it means, and so not really be a meaning at all. Using the proper name significantly, we must present to ourselves the subject named, in this case the definite person Schultze, and as endowed with some definite content or other. However + +impalpably, defectively, vaguely, indefinitely we may think of him, presentational content cannot be wholly lacking. The indefiniteness which is here to a large extent inevitable - for even the most intuitively vivid and rich presentation of a real thing (Dingrealen) must be in principle one-sided and incomplete - can never be entirely void of content. Its essence plainly involves possibilities of further determination, and these not in any direction whatsoever, but in connection with the identical man Schultze whom we mean, and no other. Or what is the same: our consciousness of meaning, taken in its full concreteness, has an essence which involves possibilities of fulfilment and coincidence with certain ranges of intuition and no others. This consciousness, even when wholly non-intuitive, must plainly have a certain intentional content, in virtue of which the individual is not given as a quite empty somewhat, but as somehow determinate and typically determinable determinable whether as a physical thing, an animal, a human being etc. + +- even if not meant in such capacities. + +The consciousness of meaning which attaches to proper names therefore has a certain double-sidedness: there are two directions in which one can here talk of complexity or simplicity. One side fixes the simplicity or complexity of the meaning itself, and here we have the pure essence of meaning as such; to it alone belongs the intentional essence of our concrete, complete meaning-consciousness which, regarded in specie, is the meaning. In our case of 'proper meanings' this side is simple. But it necessarily presupposes a wider intentional background of content, for the very reason that the same thing, referred to in the same sense (or univocally named by the same proper name) can be very differently presented, with a variable set of determining marks, and that it must be presented with some such set - while the vari- + +ation and complexity of this set do not touch the meaning itself. + +Here we have openings for expositions and for predicative interpretations of meaning, such as we give when we try to answer the question as to how, and as what, the object called 'Schultze' is presented in a given case. Such complicating developments stand in contrast with our original consciousness of meaning, and we must therefore first clarify the essence of our present distinction: the distinction between concrete, meaning-conferring experiences, which are complex or simple as regards their meaning conceived purely as meaning, and such experiences as are complex or simple only in a secondary respect, through the presentative content through which one is conscious of the object meant. Plainly, as pointed out above, the meanings which emerge in predicative expositions of what is presented as such, are newly conceived meanings, not in any way really (reell) implicit in our original meaning, in our intrinsically simple 'proper meanings'. The proper name P names the object, or its 'proper meaning' means the object, in a single 'ray' as it were, a 'ray' intrinsically uniform, and so not capable of differentiation in respect of the same intentional object. Explicative meanings such as E which is a, Ea which is b, Eb which is a etc., are many-rayed meanings, or are at least put + +together in several steps and in varying forms, so that they can 'head for' the same object with varying content. Their plurality of levels does not disturb their unity: they are unified, complex meanings. The corresponding consciousness of meaning is, on its purely meaning-side, a single act, but also an + +act that is complex. + +We assumed above that the proper name was that of a known person. This means that it is functioning normally, and not in the indirect sense of a certain person called Schultze. The latter meaning would, of course, be complex. A similar problem and a similar attempted solution occur in many other substantial meanings, and also in certain adjectival and similar meanings: e.g. human being, virtue, just etc. We must observe further that logical definition, in which bounds are set to the difficulties of articulate analysis, and above all to shifts in verbal meanings, is of course merely a practical logical artifice, through which meaning cannot properly be said to be demarcated or inwardly articulated. Here, rather, a new meaning, articulate in content, is set over against the existent meaning, as a standard to govern judgements which rely on the meaning in question. To avoid logical dangers, we forbid all judgements in which meanings cannot be replaced by such standard equivalents, and recommend also, as far as possible, the regular use of such standard word-meanings in the work of knowing, or the regulation of the effect on knowledge of our actual meanings, by frequently measuring these + +latter against such standards and by appropriate habits of use. + +Note. The duality of our meaning-intentions as treated in the first edition of this section has received a clearer, phenomenologically more profound treatment in the present edition. The writer had not plumbed the full sense and range of application of the distinction when he first conceived of this book. The careful reader will note that the Sixth Investigation does not give + +a proper account of it. + +§4 The question of the mean ingfu lness of 'syncategorematic' components of complex + +expressions + +The treatment of complex meanings leads at once to a new and fundamental division. Such meanings are, in general, only given to us as meanings of articulate word-complexes. Regarding these one may, however, ask whether each word in such a complex has its own correlated meaning, and whether all verbal articulation and form counts as expressing a corresponding semantic articulation and form. According to Bolzano, 'each word in speech stands for its own presentation, while some stand for entire propositions'.4 He therefore, without further ado, attributes a peculiar meaning to every conjunction or preposition. On the other hand, one frequently hears of words and expressions that are merely 'synsemantic' , i.e. that have no meaning by themselves, but acquire this only in conjunction with other meanings + +or expressions. One distinguishes between complete and incomplete expressions of presentations, and likewise between complete and incomplete expressions of judgements and of the phenomena of feeling and will, and one bases on such a distinction the notion of the categorematic or syncategorematic sign. Marty applies the expression 'categorematic sign' (or 'name') to 'all verbal means of designation, that are not merely synsemantic (as, e.g., "the father's", "around", "nonetheless" etc.) but which yet do not themselves completely express a judgement (an assertion), or a feeling or voluntary decision etc. (requests, commands, questions etc.), but merely express a presentation. "The founder of ethics", "a son who has insulted his father" are names'.5 Since Marty and other writers employ the terms 'syncategorematic' and 'synsemantic' in the same sense of signs 'which only have complete significance together with other parts of speech, whether they help to arouse concepts as mere parts of a name, or contribute to the expression of a judgement (Le. to a statement) or to that of an emotion or act of will (Le. to a request or command-sentence) etc.',6 it would have been more consistent to interpret the notion of categorematic expression equally widely. This notion should have been made to cover all independently significant or complete expressions of any intentional experience (any 'psychic phenomenon' in Brentano's sense), and a division should have been made then between the categorematic expressions of presentations (i.e. names), the categorematic expressions of judgements (Le. statements) etc. Whether such a coordination is justified, whether names, e.g., express presentations in the same sense that request-sentences express requests, wish-sentences express wishes etc., and likewise whether the things that names and sentences are said to 'express' are themselves experiences of meaning, or how they stand to meaning-intentions and meanings - all these are questions to which we shall have to devote earnest thought. However this may be, the distinction between categorematic and syncategorematic expressions, and the pleas for its introduction, certainly have justification, and so we are led to conceive syncategorematic words in a manner at variance with the above-mentioned doctrine of Bolzano. Since the distinction between categorematic and syncategorematic words is grammatical, it might seem that the situation underlying it is likewise 'merely grammatical'. We often use several words to express a 'presentation' - this, one might think, depends on chance peculiarities of one's language. The articulation of one's expression may bear no relation to the articulation of meaning. The syncategorematic words which help to build up this expression are, properly speaking, quite meaningless: + +only the whole expression really has a meaning. + +The grammatical distinction, however, permits another interpretation, provided one decides to view the completeness or incompleteness of expressions as reflecting a certain completeness or incompleteness of meanings, the grammatical distinction as reflecting a certain essential semantic distinction.? Language has not been led by chance or caprice to express presentations by + +names involving many words, but by the need to express suitably a plurality of mutually cohering part-presentations, and dependent presentational forms, within the enclosed self-sufficiency of a presentational unity.s Even a non-independent moment, an intentional form of combination through which, e.g., two presentations unite in a third, can find semantic expression, it can determine the peculiar meaning-intention of a word or complex of words. Clearly we may say that if presentations, expressible thoughts of any sort whatever, are to have their faithful reflections in the sphere of meaningintentions, then there must be a semantic form which corresponds to each presentational form. This is in fact an a priori truth. And if the verbal resources of language are to be a faithful mirror of all meanings possible a priori, then language must have grammatical forms at its disposal which give distinct expression, i.e. sensibly distinct symbolization, to all distinguish- + +able meaning-forms. + +§S Independent and non-i ndependent meanings. The non-independence of the sensory and expressive + +parts of words + +This conception is plainly the only right one. We must not merely distinguish between categorematic and syncategorematic expressions but also between categorematic and syncategorematic meanings.9 It is more significant to speak of independent and non-independent meanings. It is of course possible that meaning may so shift that an unarticulated meaning replaces one that was originally articulated, so that nothing in the meaning of the total expression now corresponds to its part-expressions. But in this case the expression has ceased to be genuinely complex, and tends, in developed speech, to be telescoped into one word. We no longer count its members as syncategorematic expressions, since we do not count them as expressions at all. We only call significant signs expressions, and we only call expressions complex when they are compounded out of expressions. No one would call the word 'king' a complex expression since it consists of several sounds and syllables. As opposed to this, many-worded expressions are admittedly complex, since it is part of the notion of a word to express something; the meaning of the word need not, however, be independent. Just as nonindependent meanings may occur only as 'moments' of certain independent ones, so the linguistic expression of non-independent meanings may function only as formal constituents in expressions of independent meanings: they therefore become linguistically non-independent, i.e. 'incomplete' expressions. Our first purely external impression of the difference between categorematic and syncategorematic expressions ranks the syncategorematic parts of expressions on a level with quite different parts of expressions, with the letters, sounds and syllables which are in general meaningless. I say 'in general', since there are many genuine syncategorematic expressions even among these, + +such as the prefixes and suffixes used in inflexion. But, in the vast majority of cases, they are not parts of an expression qua expression, i.e. not its significant parts; they are only parts of the expression as a sensuous phenomenon. Syncategorematic expressions are therefore understood, even when they occur in isolation; they are felt to carry definite 'moments' of meaningcontent, 'moments' that look forward to a certain completion which, though it may be indeterminate materially, is formally determined together with the content in question, and is circumscribed and governed by it. But where a syncategorematic expression functions normally, and occurs in the context of an independently complete expression, it has always, as illustration will testify, a determinate meaning-relation to our total thought; it has as its meaning a certain non-independent part of this thought, and so makes a definite contribution to the expression as such. That we are right becomes clear when we consider that the same syncategorematic expression can occur in countless compounds in which it always plays the same semantic role. For this reason, in cases of syncategorematic ambiguity, we can reasonably consider, doubt and dispute whether the same conjunction, predicate or relational expression has the same meaning in two contexts or not. To a conjunction like 'but', or to a genitive like 'father's', we can significantly attribute a meaning, but not to a verbal fragment like 'fu'. Both come before us as needing completion, but their needs of completion differ essentially: in the one case the need principally affects the thought rather than the mere expression, in the other case it affects the expression alone or rather the fragmentary expression. The hope is it may become an expression, a possible spur to thought. In the successive formation of a complex verbal structure its total meaning gradually gets built Up, 1O in the successive formation of a word, the word alone gets built up; only when the word is completed does it house the fleeting thought. In its own way, of course, the verbal fragment evokes thoughts: that it is, e.g., a verbal fragment, and how it may be completed; these are not, however, its meaning. And according as we complete it in differing ways (fu-futile, fuming, fugitive, furry, refuge etc.) the meaning alters, without thereby revealing an element common to this multitude of meanings, that could be taken to be the meaning of this common fragment. We search in vain also for a structuring of the individual word-meaning which might in part depend upon the significance of this + +verbal fragment. It is quite meaningless. + +§6 Other opposed distinctions. Unc losed, abnormally + +abbreviated and defective express ions + +We must go on to a much-needed clarification of the difference between independent and non-independent meanings, fixing its character more precisely in relation to more general concepts, and connecting with it the dominant fact, the presiding rule in the whole field of meaning. Before we do this, + +however, it will be useful to separate off the grammatical distinction that + +formed our starting point from other distinctions confused with it. + +Syncategorematic expressions, qua non-independent, require some sort of completion, and we therefore also call them 'incomplete expressions'. Talk of 'incompleteness' has, however, another sense, which is not to be confused with the need for completion which is here in question. To show this, we first observe that a division of meanings into independent and nonindependent crosses the division into simple and complex. Meanings such as, e.g., larger than a house; beneath God's own sky; in life's troubles; but, Lord, to give thy messengers due honour, are non-independent meanings, unitary despite their plurality of discernible parts. Several non-independent meanings, or meanings partly non-independent and partly independent, can be accordingly associated in relatively closed units, which yet manifest, as wholes, a character of non-independence. This fact of complex non-independent meanings is grammatically registered in the relatively closed unity of complex syncategorematic expressions. Each of these is a single expression, because expressive of a single meaning, and it is a complex expression, because expressive part by part of a complex meaning. It is in relation to this meaning that it is a complete expression. If nonetheless we call it incomplete, this depends on the fact that its meaning, despite its unity, is in need of completion. Since it can only exist in a wider semantic context, its linguistic expression likewise points to a wider linguistic context, to a completion in + +speech that shall be independent and closed. + +It is quite different in the case of an abnormally abbreviated expression, which gives to thought, whether independent or non-independent, an incomplete, though possibly in the circumstances quite intelligible, expression. We can here point to defective expressions, where syntactical members are omitted from a continuous sentential context, although a certain mutual belongingness of the disjecta membra remains recognizable. The need for completion of such defective utterances differs in kind from the need for the completion of the syncategorematica. Not because the pertinent meaning is non-independent, but because all unitary meaning is absent, such defective talk cannot serve as finished talk, not even as talk at all. If on deciphering a fragmentary inscription we read Caesar ... qui ... duabus, external indications may point to a certain sentential and semantic unity: this indirect thought is not, however, the meaning of the fragment before us. As it stands, it is without unitary meaning, and constitutes no expression: a loose assemblage of partially independent, partially non-independent meanings, together with a side-thought relative but also strange to them, that they may be part + +of a certain significant unity: that is all that is given. + +Talk about expressions that are unclosed, incomplete and requiring completion, therefore plainly covers quite different things. On the one hand, it covers syncategorematic expressions: on the other hand, abnormally abbreviated and, in the limit, defective expressions, which are not so much + +expressions as expressional fragments. These distinct notions cross one another. An abbreviated expression can be categorematic, a syncategorematic + +expression gapless etc., etc. + +§7 The con cepti on of non-i ndependent meani ngs as + +founded contents + +We have recognized that the seemingly indifferent distinction between categorematic and syncategorematic expressions corresponds to a fundamental division in the realm of meanings. We took the former as our starting-point, but the latter revealed itself as basic, as the prime foundation of the gram- + +matical distinction. + +The concept of the expression, or of the difference between the merely audible, or sensuous parts of an expression and its partial expressions in the true sense of the word, or, as we may say more pointedly, its syntactical parts (roots, prefixes, suffixes, ll words, conjoined complexes of words), can only be fixed by recurring to a distinction among meanings. If these divide into simple and complex meanings, the expressions which fit them must also be simple or complex, and this complexity necessarily leads back to final significant parts, to syntactical parts and so once more to expressions. On the other hand, the analysis of expressions as mere sensuous phenomena also always yields mere sensuous parts, ones that no longer signify. The same is true of the superimposed distinction of expressions into categorematic and syncategorematic. It can at least be described by holding the former to be capable of serving as complete expressions, finished locutions by themselves, whereas the latter cannot. But if one wishes to limit the vagueness of this characterization, and to pin down the sense that is here relevant, as well as the inner ground that enables some expressions, and not others, to stand as finished locutions, one must, as we saw, go back to the semantic realm, and point out there the need of completion that attaches to certain non- + +independent meanings. + +Having called syncategorematic meanings 'non-independent', we have already said where we think the essence of such meanings lies. In our enquiries into non-independent contents in general, we have given a general determination of the concept of non-independence: it is this same non-independence that we have to recognize in the field of meaning. Non-independent contents, we stated above (Inv. III, §§5-7), are contents not able to exist alone, but only as parts of more comprehensive wholes. This inability has its a priori governing ground in the specific essences of the contents in question. Each non-independence points to a law to the effect that a content of the sort in question, e.g. sort A, can exist only in the context of a whole W (AB ... M), where B ... M stand for determinate sorts of content. 'Determinate', we said, since no law merely asserts connection between the sort A, and any other sorts whatever, that an A only needs some completion, no matter + +what. Law involves specific determinateness of context: dependent and independent variables have spheres limited by fixed generic or specific characters. We have mainly employed as examples the concrete things of sensuous intuition. We could, however, have brought in other fields, those of act- + +experiences and their abstract contents. + +Here we are only interested in meanings. We conceived these as ideal unities, but our distinction naturally passed over from the real (real) to the ideal realm (see above Inv. III, §7a). In the concrete act of meaning something, there is a moment which corresponds to the meaning which makes up the essential character of this act, i.e. necessarily belongs to each concrete act in which the same meaning is 'realized'. In regard to the division of acts into simple and complex, a concrete act can involve several acts; such partial acts can live in the whole, whether as independent or non-independent parts. An act of meaning, in particular, can as such be complex, be made up of acts of meaning. A total meaning then belongs to the whole act, and to each partial act a partial meaning (a part of the meaning that is itself a meaning). A meaning, accordingly, may be called 'independent' when it can constitute the full, entire meaning of a concrete act of meaning, 'non-independent', when this is not the case. It can then only be realized in a non-independent partact in a concrete act of meaning, it can only achieve concreteness in relation to certain other complementary meanings, it can only exist in a meaningful whole. The non-independence of meaning qua meaning thus defined deter- + +mines, in our view, the essence of the syncategorematica. + +§8 Difficu lties of this concepti on. (0) Whether the non-i ndependence of the meaning does not real ly only + +lie in the non-i ndependence of the object meant + +We must now consider the difficulties of our conception. We shall first discuss the relation between independence and non-independence of meanings, and independence and non-independence of objects meant. One might for the moment think the former distinction reducible to the latter. 12 Acts which lend meaning refer as 'presentations', as 'intentional' experiences, to objects. If some constituent of an object is non-independent, it cannot be 'presented' in isolation; the corresponding meaning therefore demands a completion, it is itself non-independent. The seemingly obvious principle emerges: categorematic expressions are directed to independent objects, + +syncategorematic expressions to non-independent ones. + +Such a conception is readily seen to be erroneous. The very expression non-independent moment provides a decisive counter-example. It is a categorematic expression and yet presents a non-independent object. Every non-independent object whatever can be made the object of an independent meaning, and that directly, e.g. Redness, Figure, Likeness, Size, Unity, Being. These examples show that independent meanings correspond, not merely to + +material moments of objects, but also to their categorial forms, meanings peculiarly directed to these forms and making them their objects: the latter are not for that reason self-existent in the sense of being independent. The possibility of independent meanings directed to non-independent 'moments' is not at all remarkable, when we reflect on the fact that a meaning 'presents' an object, but does not therefore have the character of picturing it, that its essence consists rather in a certain intention, which can be intentionally 'directed' to anything and everything, to what is independent as much as what is non-independent. Anything, everything can be objectified as a thing + +meant, i.e. can become an intentional object. + +§9 (b) The understanding of isolated + +syncategorematica + +A serious difficulty is occasioned by our understanding of syncategorematic expressions torn from all context. If our notion is right, there can be no such thing: for us the non-independent elements of categorematically closed speech (Myos) cannot be isolated. How can we possibly treat such elements, as Aristotle treated them, apart from all connection? Under the headings of Tel aVEU crul.mAoKfis, Tel KOTel 1-11l5El-liov crUI-ITIAOKT]V AEY0I-IEVO he covers all + +classes of words, including the syncat�gorematica. + +This objection can first be met by pointing to the distinction between 'authentic' and 'so-to-speak' presentations, or what is here the same, the difference between merely intending and fulfilling meanings. We may in fact say: Isolated syncategorematica such as equals, together with, and, or can achieve no fulfilment of meaning, no intuitive understanding, except in the context of a wider meaning-whole. If we wish to 'be clear' what the word 'equals' means, we must turn to an intuitive equation, we must actually (genuinely) perform a comparison, and following upon this, bring to understanding and fulfilment a sentence of the form a = b. If we wish to be clear as to the meaning of the word 'and', we must actually carry out an act of collection, and bring to fulfilment in the aggregate thus genuinely presented a meaning of the form a and b. And so in every case. The non-independent status of the fulfilling meaning, which thus necessarily forms part of a fulfilling meaning of wider content, serves to base derived talk about the non-independent + +status of the intending meaning. 13 + +Undoubtedly we have here a correct and valuable thought. We can also express it by saying that no syncategorematic meaning, no act of nonindependent meaning-intention, can function in knowledge outside of the context of a categorematic meaning. Instead of 'meaning', we could of course say 'expression', in the normal sense of a unity of verbal sound and meaning or sense. But we have to ask whether, since there is a unity-of-coincidence between intending and fulfilling meaning in the state of fulfilment, we can look on a fulfilling meaning as non-independent, while an intending meaning + +is independent. Can we, in other words, hold that talk of non-independence in the case of intuitively unfulfilled meanings is merely loose, conditional on non-independence in possible fulfilment? This seems scarcely thinkable, and so we are pushed back to holding that even empty meaning-intentions - the 'non-authentic', 'symbolic' presentations which give sense to an expression apart from any knowledge-function - reveal a difference between independence and non-independence. How can we explain the indubitable fact that isolated syncategorematica, e.g. the isolated word 'and', are understood? They are non-independent as regards their meaning-intention, and this surely means that such intentions can exist only in categorematic contexts: the isolated 'and', the particle tom from its context, ought therefore to be a + +hollow noise. + +We can only resolve our difficulty in the following manner: + +A syncategorematic expression tom from context either has not got the meaning it has in categorematic contexts, or it has got it, but has also undergone a completion of meaning quite indefinite in content, so that it is an incomplete expression of this momentarily activated, completed meaning. We understand an isolated 'and' either because the indirect, verbally unexpressed thought of a certain familiar conjunction gives it an unusual meaning, or because vague, unverbalized presentations of things help us to form a thought of the type A and B. In the latter case, the word 'and' is functioning normally to the extent that it is really only an aspect in a complete, inwardly performed meaning-intention, the same aspect as in a combination of categorematic expressions standing for a collection. It is functioning abnormally only in not being connected with other expressions, which give normal utterance to the complementary parts of the meaning here in question. Our difficulties are thus removed. We may assume that the difference between independent and non-independent meanings affects the realm of meaning-intentions as it affects the realm of fulfilment. We have the situation which the possibility of an adequate fit between intention and fulfilment + +necessarily requires. + +§ lO Apriori laws governing combi nations of mean i ngs If we relate the distinction between independent and non-independent meanings to the more general distinction between independent and nonindependent objects, we are really covering one of the most fundamental facts in the realm of meaning: that meanings are subject to a priori laws regulating their combination into new meanings. To each case of non-independent meaning, a law of essence applies - following the principle discussed by us in relation to all non-independent objects whatever - a law regulating the meaning's need of completion by further meanings, and so pointing to the forms and kinds of context into which it must be fitted. Since meanings cannot be combined to form new meanings without the aid of connective forms, which + +are themselves meanings of a non-independent sort, there are obviously a priori laws of essence governing all meaning-combinations. The important fact here before us is not peculiar to the realm of meaning: it plays its part wherever combination occurs. All combinations whatever are subject to pure laws; this holds particularly of all material combinations limited to a single sphere of fact, where the results of combination must occupy the same sphere as the combining members. (This case is opposed to that of formal, 'analytic' combinations, e.g. collections, which are not bound up with the peculiarities of a sphere of fact, nor with the factual essence of their combining members.) In no sphere is it possible to combine items of any and every kind by way of any and every form: the sphere of items sets a priori limits to the number of combinatorial forms, and prescribes the general laws for filling them in. That this fact is general should not lessen our obligation to point out such general laws in each given field, and to pursue + +their unfolding into special laws. + +As regards the field of meaning, the briefest consideration will show up our unfreedom in binding meanings to meanings, so that we cannot juggle at will with the elements of a significantly given, connected unity. Meanings only fit together in antecedently definite ways, composing other significantly unified meanings, while other possibilities of combination are excluded by laws, and yield only a heap of meanings, never a single meaning. The impossibility of their combination rests on a law of essence, and is by no means merely subjective. It is not our mere factual incapacity, the compulsion of our 'mentai make-up', which puts it beyond us to realize such a unity. In the cases we here have in mind, the impossibility is rather objective, ideal, rooted in the pure essence of the meaning-realm, to be grasped, therefore, with apodictic self-evidence. The impossibility attaches, to be more precise, not to what is singular in the meanings to be combined, but to the essential kinds, the semantic categories, that they fall under. This or that meaning is, of course, itself a species, but, relative to a meaning-category, it only counts as an individual specification. In arithmetic, likewise, relatively to numerical forms and laws a numerically definite number is an individual specification. Wherever, therefore, we see the impossibility of combining given meanings, this impossibility points to an unconditionally general law to the effect that meanings belonging to corresponding meaning-categories, and conforming to the same pure forms, should lack a unified result. We have, in short, an + +a priori impossibility. + +What we have just said holds of course of the possibility of significant + +combinations as it holds of their impossibility. + +To consider an example. The expression 'This tree is green' has unified meaning. If we formalize this meaning (the independent logical proposition) and proceed to the corresponding pure form of meaning, we obtain 'This S is P', an ideal form whose range of values consists solely of independent (propositional) meanings. It is now plain that what we may call the + +'materialization' of this form, its specification in definite propositions, is possible in infinitely many ways, but that we are not completely free in such specification, but work confined within definite limits. We cannot substitute any meanings we like for the variables 'S' and 'P'. Within the framework of our form we can change our example 'This tree is green' into 'This gold .. .', 'This algebraic number .. .', 'This blue raven etc., is green': any nominal material - in a wide sense of 'nominal material' - can here be inserted, and so plainly can any adjectival material replace the 'P'. In each case we have once more a meaning unified in sense, i.e. an independent proposition of the prescribed form, but if we depart from the categories of our meaningmaterial, the unitary sense vanishes. Where nominal material stands, any nominal material can stand, but not adjectival, nor relational, nor completed propositional material. But where we have materials from such other categories, other material of the same kind can be put, i.e. always material from the same category and not from another. This holds of all meanings + +whatsoever, whatever the complexity of their form. + +In such free exchange of materials within each category, false, foolish, ridiculous meanings - complete propositions or elements of propositions may result, but such results will necessarily be unified meanings, or grammatical expressions whose sense can be unitarily realized. When we transgress the bounds of categories, this is no longer true. We can string together words like 'This careless is green', 'More intense is round', 'This house is just like'; we may substitute 'horse' for 'resembles' in a relational statement of the form 'a resembles b', but we achieve only a word-series, in which each word is as such significant, or points to a complete, significant context, but we do not, in principle, achieve a closed unity of sense. This is above all the case when we seek arbitrarily to exchange parts which are themselves formed units within an articulated unit of meaning, or when we replace such parts by others taken at random from other meanings, as, e.g., when we try to replace the antecedent in a hypothetical proposition (a mere element in the total unity that we call 'the hypothetical proposition') by a nominal element, or one of the members of a disjunction by a hypothetical consequent. Instead of doing this in the concrete, we may also attempt it in the corresponding pure forms of meaning, i.e. propositional forms. We are at once made aware, through a priori insight into law, that such intended combinations are ruled out by the very nature of the constituents of the pure patterns in question, that such constituents can only enter into definitely constituted + +meaning-patterns. + +It is plain, finally, that the pure elements of form in a concrete unity of meaning can never change places with the elements to which they give form, and which also give our meaning its relation to things. The specification of unified meaning-forms such as 'An Sis p', 'If S is p, Q is r' etc., cannot, in principle, so proceed that abstracted elements of form take the place of the 'terms', i.e. the materials in the meaning-pattern which relate to things. We + +can construct verbal strings such as 'if the or is green', 'A tree is and' etc., but such strings have no graspable single meanings. It is an analytic truth that the forms in a whole cannot function as its materials, nor vice-versa, + +and this obviously carries over into the sphere of meanings. + +In general we recognize, as we construct and think over such examples, that every concrete meaning represents a fitting together of materials and forms, that each such meaning falls under an ideal pattern that can be set forth in formal purity, and that to each such pattern an a priori law of meaning corresponds. This law governs the formation of unitary meanings out of syntactical materials falling under definite categories having an a priori place in the realm of meanings, a formation according to syntactical forms which are likewise fixed a priori, and which can be readily seen to constitute a fixed system of forms. Hence arises the great task equally fundamental for logic and for grammar, of setting forth the a priori constitution of the realm of meanings, of investigating the a priori system of the formal structures which leave open all material specificity of meaning, in + +a 'theory of the forms of meanings' . + +§ II Objecti ons. Mod ifications of meaning which are rooted in the essence of expressions or meani ngs + +We must now take account of possible objections. One must not be led astray by the fact that meanings of any category, even syncategorematic forms like and, can be put into the sUbject-position otherwise occupied by substantival meanings. If one looks closely, one sees that this happens by a modification of meaning, so that what replaces a name is itself really nominal: a meaning differing in syntactical type (an adjectival or merely formal meaning) has not been simply transplanted. We have such a case, e.g., in statements like 'If is a conjunction' , 'And is a non-independent meaning'. The words certainly occupy the subject-position, but their meaning is plainly not the same as they have in an ordinary context. That each word and expression can, by a change of meaning, come to occupy every place in a categorematic whole, is not remarkable. What we have in mind here is not a verbal but a semantic compounding, or a compounding of words in which meanings remain constant. Logically considered, all shifts of meaning are to be adjudged abnormal. Our logical interest, oriented towards unitary selfsameness of meaning, demands constancy in the meaning-function. It naturally happens, however, that certain meaning-transformations belong to the grammatically normal stock-in-trade of every language. Verbal context will at least make a modified meaning readily intelligible, and, if the motives for modification are pervasively general, rooted, e.g., in the general character of expressions, or in the pure essence of the realm of meanings, then such abnormalities will recur regularly, and their logical abnormality will win a + +Here belongs the suppositio materialis of scholastic parlance. Every expression, whether its normal meaning is categorematic or syncategorematic, can also function as its own name, i.e. it will name itself as a grammatical phenomenon. If we say ' "The earth is round" is a statement', our subjectpresentation is not the meaning of the statement, but a presentation of the statement as such. We do not judge about the state of affairs that the earth is round, but about the indicative sentence: this sentence itself functions abnormally as its own name. If we say ' "And" is a conjunction', the nuance of meaning normally corresponding to the word 'and' is not put into the position of subject: this is occupied by an independent meaning directed to the word 'and'. In this abnormal reading, 'and' is not really a syncategorematic, but a categorematic expression: it names itself as a word. We have an exact analogue of suppositio materialis when an expression has, instead of its normal meaning, a presentation of this meaning (i.e. a meaning directed to this meaning as object). This is the case, e.g., if we say 'And, but, greater than are non-independent meanings' . Here we should generally say that the meanings of the words 'and', 'but', 'greater than' are nonindependent. Just so in the utterance 'Man, table, house, are thing-concepts' , presentations of these concepts function as subjects, and not the concepts themselves. In these, as in the previous cases, the change of meaning regularly shows itself in our written expression: quotation marks, or what may be suitably called other hetero-grammatical modes of expression, are employed. All expressions to which 'modifying' rather than 'determining' predicates attach, function abnormally in the above described or some similar sense: the normal sense of our utterance is to be replaced by another, in a more or less complex fashion, so that, however it may otherwise be built up, its apparent subject (on a normal interpretation) is replaced by some sort of presentation of itself, an ideal presentation, perhaps, in the sense of pure logic, or an empirical-psychological one, or a purely phenomenological one. We say, e.g., 'The centaur is a poetic fiction'. With a little circumlocution we can instead say: 'Our ideas of centaurs, i.e. subjective presentations with the meaning-content centaur, are poetic fictions' . The predicates 'is', 'is not', 'is true', 'is false' modify meaning. They do not express properties of the apparent subject, but of the corresponding subject-meaning. 'That 2 + 2 = 5 is false' means that the thought is a false thought, the proposition a false + +proposition. + +Leaving aside the examples in the last paragraph, where the modifying presentation is sUbjective in a psychological or a phenomenological sense, and understanding our analogue of suppositio materialis with its previously stated limitations, we note that we are here dealing with alterations in the content, or rather act of meaning, that have their roots in the ideal nature of the meaning-realm itself. They have their roots in changes of meaning, in a certain other sense of 'meaning' that abstracts from expressions, but which is not unlike that of arithmetical talk of 'transforming' arithmetical patterns. + +In the realm of meaning there are a priori laws allowing meanings to be transformed into new meanings while preserving an essential kernel. Here belongs the transformation that any meaning can undergo, by an a priori rule, when there is a 'direct presentation' of it, i.e. an intrinsic reference to its original meaning. Its verbal expression will then function, with modified meaning, as a 'proper name' of its original meaning. This modification, having a priori universality, conditions a large class of equivocations in general grammar, changes in the verbal act of meaning which go far beyond the peculiarities of empirical languages. In our further Investigations we shall have more chances of meeting similar modifications rooted in the essence of meanings, the important cases, e.g., where whole statements are 'nominalized' so as to appear in the subject-position, and so too in any position that requires nominal members. We may point to cases where adjectival predicates or attributes are 'nominalized', so as to dispel any doubt aroused by things said in our previous section. An adjective has, as it were, a predicative and, in consequence, an attributive role; it functions normally, in its 'original', unmodified meaning in, e.g., our above example 'This tree is green' . It remains intrinsically unchanged - apart from its syntactical role if we say 'This green tree'. Such a change in form as opposed to the stuff of syntax, which occurs also when, e.g., a nominal presentation functioning as subject takes on the object-role, or a proposition functioning as antecedent takes on the role of a consequent, must first be pinned down: it is a central theme in describing pervasive structures in the meaning-realm. But an adjectival meaning, in the sense of syntactical material not affected by changing from a predicative to an attributive role, can yet undergo a modification when, from functioning merely as an attributive aspect of some nominal meaning, it is itself nominalized, i.e. made into a name, as, e.g., in 'Green is a colour' and 'Being green (Greenness) is a differentiation of Being coloured + +(of Colour), + +. These two modes of speech do not mean quite the same, de- + +spite shifting ambiguities, since in one case a non-independent side of a concrete object's content may be meant, while in the other case we mean a nominalization of the being which is the correlate of the predicativity attaching to the predicate member of a categorical predication and applied to its positing of the subject. The same word 'green' therefore changes its meaning in such nominalizations: its written expression [in German] with its initial capital, indicates what is common to such modifications, which capital is by no means logically or grammatically pointless. The original and the nominalized meaning (green and Green, is green and Being-green) plainly have an essential moment, an identical kernel, in common. This kernel is an abstractum having several forms qua kernel: these forms are to be distinguished from the syntactical forms which already presuppose kernels, together with their forms qua kernels, as their syntactical materials. If the form qua kernel of an adjectival kernel or kernel-content yields syntactical material of nominal type, then such determinately constructed nominal + +meanings can perfonn every syntactical function which requires nominal meanings for its syntactical materials in accordance with formal meaning-laws. This will suffice as an indication. Closer treatment belongs in a systematic + +setting forth of our theory of fonns. + +§ 12 Nonsense and abs urd ity + +One must, of course, distinguish the law-governed incompatibilities to which the study of syncategorematica has introduced us, from the other incompatibilities illustrated by the example of 'a round square'. As said in + +our First Investigation, + +14 one must not confound the senseless (or nonsen- + +sical) with the absurd (or 'counter-sensical'), though we tend to exaggerate and call the latter 'senseless', when it is rather a sub-species of the significant. The combination 'a round square' really yields a unified meaning, having its mode of 'existence' or being in the realm of ideal meanings, but it is apodictically evident that no existent object can correspond to such an existent meaning. But if we say 'a round or' , 'a man and is' etc., there exist no meanings which correspond to such verbal combinations as their expressed sense. The coordinated words give us the indirect idea of some unitary meaning they express, but it is apodictically clear that no such meaning can exist, that significant parts of these sorts, thus combined, cannot consist with each other in a unified meaning. This indirect notion would not itself be accepted as the meaning of such verbal complexes. When an expression functions nonnally, it evokes its meaning: when understanding fails, its sensuous similarity to understood, meaningful speech will evoke the inauthentic notion of a 'certain' pertinent meaning, since the meaning itself + +is what is precisely missing. + +The difference between the two incompatibilities is plain. In the one case certain partial meanings fail to assort together in a unity of meaning as far as the objectivity or truth of the total meaning is concerned. An object (e.g. a thing, state of affairs) which unites all that the unified meaning conceives as pertaining to it by way of its 'incompatible' meanings, neither exists nor can exist, though the meaning itself exists. Names such as 'wooden iron' and 'round square' or sentences such as 'All squares have five angles' are names or sentences as genuine as any. In the other case the possibility of a unitary meaning itself excludes the possible coexistence of certain partial meanings in itself. We have then only an indirect idea, directed upon the synthesis of such partial meanings in a single meaning, and at the same time see that no object can ever correspond to such an idea, i.e. that a meaning of the intended sort cannot exist. The judgement of incompatibility is in one case connected with presentations, in another with objects; presentations of presentations enter the fonner unity of judgement, whereas plain presentations enter the latter. The grammatical expression of the a priori incompatibilities and compatibilities here in question, as of the pertinent laws governing + +meaning-combinations, must in part be found in the grammatical rules governing the parts of speech. If we ask why our language allows certain verbal combinations and disallows others, we are to a large extent referred to contingent linguistic habits, to matters of mere fact concerning language, which develop in one way in one speech-community and another way in another. In part, however, we encounter the essential difference of independent and non-independent meanings and, closely involved therewith, the a priori laws of the combination and transformation of meanings, laws which must be more or less revealed in every developed language, both in its grammar of forms and in the related class of grammatical incompatibilities. + +§ 13 The laws of the compounding of meani ngs and + +the pure logico-gram mati cal theory of fo rms + +The task of an accomplished science of meanings would be to investigate the law-governed, essence-bound structure of meanings and the laws of combination and modification of meaning which depend upon these, also to reduce such laws to the least number of independent elementary laws. We should obviously also need to track down the primitive meaning-patterns and their inner structures, and, in connection with these, to fix the pure categories of meaning which circumscribe the sense and range of the indeterminates - the 'variables' in a sense quite close to that of mathematics - that occur in such laws. What formal laws of combination may achieve, can be made fairly plain by arithmetic. There are definite forms of synthesis, through which, quite in general or in certain definite conditions, two numbers give rise to new numbers. The 'direct operations' a + b, ab, a + +b yield + +resultant numbers unrestrictedly, the 'inverse operations, a - b, alb, bWi, bloga, only in certain conditions. That this is the case must be laid down by an assertion or rather a law of existence, and perhaps proved from certain primitive axioms. The little we have so far been able to indicate has made plain that there are similar laws governing the existence or non-existence of meanings in the semantic sphere, and that in these laws meanings are not free variables, but are bound down to the range of varying categories, all + +arising out of the nature of the sphere in question. + +In the pure logic of meanings, whose higher aim is the laws of objective validity for meanings (to the extent that such validity depends purely on semantic form), the theory of the essential meaning-structures, and the laws of their formal constitution, provide the needed foundation. Traditional logic, with its theories of concepts and judgements, offers us a few isolated starting-points, without being clear as to the end to be aimed at, either in general or in respect of the pure Idea of meaning. Plainly the theory of the elementary structures and the concrete patterns of 'judgement' - here understood as 'propositions' - will comprise the whole form-theory of meanings, each concrete meaning-pattern being either a proposition or a possible element + +in propositions. We must note that the exclusion of the 'material of knowledge', to which pure logic is by its very sense committed, obliges us to keep out everything which could give semantic forms (types, patterns) a definite relation to factual spheres of being. Everywhere indefinitely general presentations of factual material, definitely determined only in respect of semantic category, e.g. nominal, adjectival, propositional etc., must do duty for contentful concepts and even for the highest of such concepts, e.g. physical thing, + +spatial thing, mental thing etc. + +Our first task, therefore, in a purely logical form-theory of meanings, is to lay down the primitive forms of meaning with the requisite purity just described. We must fix the primitive forms of independent meanings, of complete propositions with their internal articulations, and the structures contained in such articulations. We must fix, too, the primitive forms of compounding and modification permitted by the essence of different categories of possible elements. (We must note that complete propositions can become members of other propositions.) Mter this, we must systematically survey a boundless multitude of further forms, all derivable by way of repeated compounding + +or modification. + +The forms to be established are naturally 'valid', which here means that, however specified, they will yield real meanings, meanings real as meanings. To each such primitive form there belongs, therefore, an a priori law of existence, to the effect that each meaning-combination conforming to such a form genuinely yields a unified meaning, provided only that its terms, the Form's indeterminates or variables, belong to certain semantic categories. The deduction of derived forms must also pro tanto be a deduction of their validity, and laws of existence will, therefore, also relate to these, but they will be deduced from those relating to the primitive forms. Any two propositions yield, when combined in the form M and N, another proposition, any two adjectives another adjective (again one meaning that can stand as a complex but unitary attribute or predicate). To any two propositions, M, N, there belong, likewise, the primitive connective forms If M then N, M or N, so that the result again is a proposition. To any nominal meaning S, and any adjectival meaning p, there belongs the primitive form Sp (e.g. red house), the result being a new meaning fixed by law in the category of nominal meaning. We could in this manner give many other examples of primitive connective forms. We must remember, in stating all the laws that hold here, and in conceiving categorial Ideas of proposition, nominal presentation, adjectival presentation, which determine the variables of the laws, to abstract from the changing syntactical forms that such meanings have in given cases, and that they have to have in some determinate form. We speak of the same name, whether it occupies the subject-position or serves as a correlated object, of the same adjective, whether used predicatively or attributively, of the same proposition, whether used as a free unit or as a conjunctive, disjunctive, or hypothetical antecedent or consequent, or whether + +occupying this or that place as a member in a complex propositional unity. We thus fix plainly the much used, but never scientifically clarified, talk about terms in traditional logic. In the formal laws which enter the purview of this logic, 15 as in our own laws of structures, such 'terms' function as variables; the categories circumscribing the range of their variability are categories of terms. The scientific pinning down of these categories is plainly + +one of the first tasks of our doctrine of forms. + +If we now make gradual substitutions in the primitive forms set forth, and for a simple term repeatedly substitute a combination exemplifying the same forms, and if we always reapply our primitive existential law, we arrive at ever new forms, of deductively proven validity, encapsulated in one another with any degree of complexity. Thus for the conjunctive combination of pro- + +positions one can substitute: + +(M and N) and P + +(M and N) and (P and Q) {(M and N) and P} and Q etc., etc., and so for the disjunctive and hypothetical combination of propositions, and for other modes of combinations in any other semantic categories. We see at once that the compoundings go on in infinitum, in a manner permitting comprehensive oversight, that each new form remains tied to the same semantic category, the same field of variability as its terms, and that, as long as we stay in this field, all framable combinations of meanings necessarily exist, i.e. must represent a unified sense. We see also that the relevant existential propositions are obvious deductive consequences of an existential proposition with the primitive form. Instead of constantly reapplying the same mode of combination, we can plainly vary our procedure at will, and combine different forms of combination in our construction, always within legally allowed limits, and so conceive an infinity of complex forms legally engendered. As we formulate these facts in consciousness, we gain insight into the a priori constitution of the meaning-realm in respect of + +all those forms which have their a priori origin in its basic forms. + +This insight, and the final comprehensive insight into the formal constitution of the whole semantic realm, is, of course, the one aim of such investigations. It would be stupid to hope for worthwhile rules for the compounding of meanings (or rules for the grammatical compounding of expressions) from the formulation of semantic types, and the existential laws relating to them. There is no temptation here to depart from the line of correctness, hence no practical interest in determining it scientifically. Nonsense stands so immediately revealed, with each deviation from normal forms, that we hardly fall into such deviations in the practice of thought and speech. The theoretical interest of the systematic investigation of all possible meaningforms and primitive structures, is all the greater. We, in fact, rise to the insight that all possible meanings are subject to a fixed typic of categorial + +structures built, in a priori fashion, into the general Idea of meaning, that a priori laws govern the realm of meaning, whereby all possible concrete meaning-patterns systematically depend on a small number of primitive forms, fixed by laws of existence, out of which they flow by pure construction. This last generalization, through its a priori, purely categorial character, brings to scientific awareness a basic chapter in the constitution of 'theoretical reason'. Additional note. I talked above of compounding and modification. The rules of modification also have a place in the sphere we must define. What we mean is shown by the analogue of suppositio materialis considered above. Other instances are differences of contextual functioning, of a priori syntactical position, as when a name functioning as subject shifts to the objectplace. These differences are not easy to elucidate: they are mixed up with empirical factors, and terminate in case-forms and syntactical forms of grammar. The difference between the attributive and predicative functioning of adjectival meanings, as well as similar matters, have here their place. (The investigations of the form-doctrine of meanings announced in our First Edition, and since expounded with many improvements in my lectures at Gottingen since 1901, will shortly, I hope, be laid before a wider public in + +my Jahrbuch fur Philosophie und phiinomenologische Forschung.) + +§ 14 Laws wh ich discourage nonsense and laws which di sco urage absurd ity. The Idea of a purely logical + +gram mar + +The formal laws of meaning just discussed, which serve merely to separate the realms of sense and nonsense, must in an extended sense certainly count as laws of formal logic. They will, however, be the last things one will think of where 'logical laws' are in question: this term only suggests the quite different laws, infinitely more interesting in our cognitive practice, that are concerned only with significant (i.e. not-nonsensical) meanings, and with their objective possibility and truth. Let us look into the relation of these + +two types of law. + +The a priori laws pertinent to the constitution of the essential forms of meaning, leave quite open whether meanings built on such forms have objects or not, or whether (when they are propositional forms) they yield possible truth or not. As said above, these laws have the mere function of separating sense from nonsense. The word 'nonsense' - let us stress it again - must be understood in its literal, strict sense. A heap of words like 'King but or like and' cannot be understood as a unit: each word has sense in isolation, but the compound is senseless. These laws of sense, or, normatively put, laws of the avoidance of nonsense, direct logic to the abstractly possible forms of meaning, whose objective value it then becomes its first task to determine. This logic does by setting up the wholly diff erent laws which distinguish a formally + +consistent from a formally inconsistent, i.e. absurd, sense. + +The consistency or absurdity of meanings expresses objective, i.e. a priori, possibility (consistency, compatibility) as opposed to objective impossibility (incompatibility); it expresses, in other words, the possibility or impossibility of the being of the objects meant (compatibility or incompatibility of the objective determinations meant) to the extent that this depends on the intrinsic essence of meanings, and is seen from this essence with apodictic evidence. This contrast between objectively, semantically consistent sense and absurdity, has been notionally opposed and set apart from the contrast between sense and nonsense, but we must observe that, in loose, common speech, the two contrasts are confused, and every absurdity, even every affront to empirical truth, is readily called 'nonsense'. We have also to draw a line between material (synthetic) absurdity and formal, analytic absurdity. In the former case, concepts with content (first-order material kernels of meaning) must be given, as is the case, e.g., in the proposition 'A square is round' and in all false propositions of pure geometry, while the latter covers every purely formal, objective incompatibility, grounded in the pure essence of the semantic categories, without regard to any material content of knowledge. (There is an analogous division within the contrasted concept of a consistent sense.) Laws such as that of Contradiction, Double Negation or the Modus Ponens are, normatively restated, laws of the avoidance of formal absurdity. They show us what holds for objects in general in virtue of their pure 'thought-form', i.e. what can be said regarding the objective validity of meanings on a basis purely of the meaningful form in which we think them, and in advance of all objective matters signified. These laws may not be violated if falsehood is not to result, even before objects in their factual particularity have been taken into account. They are, in the sense of our Third Investigation (I ll , §§ 11 f) 'analytic' laws, as opposed to the synthetic a priori laws which contain non-formal concepts, and depend on these for their validity. In the sphere of analytic laws as such, these formal laws, with their objective validity reposing on pure categories of meaning, are distinct from ontological-analytic laws, which rest on formal-ontological categories (such as object, property, plurality etc.) and they define sharply a second, narrower notion of the analytic. We may call it the apophantic analytic, the analytic of apophantic logic. In part, but only in part, relations of equivalence link the two sets of laws, but we cannot go into this further here. If we now abstract from all questions of objective validity, and confine ourselves to the a priori which has its roots purely in the generic essence of meaning as such, if we confine ourselves to the discipline that our present Investigation has illuminated, in its probing of primitive meaning-structures, primitive articulations and combinations, as well as in the operational laws of meaning-compounding and meaning-modification which rest on these we recognize the undoubted soundness of the idea of a universal grammar conceived by the rationalists of the seventeenth and eighteenth century. What has been hinted at in this regard in our Introduction, scarcely needs + +fuller exposition. The older grammarians instinctively concentrated attention on this sphere of laws, even if they were unable to bring it to full clarity. Even in the sphere of grammar there are fixed standards, a priori norms that may not be transgressed. As in the proper sphere of logic, the a priori element separates itself off from the empirically and practically logical, so in the grammatical sphere the so-called purely grammatical, i.e. the a priori element or 'idealized form of speech', as it is well called, separates itself off from the empirical element. In both cases the empirical element is in fact determined by universal, yet merely factual traits of human nature, partly by chance peculiarities of race, nationality and national history, or by peculiarities of the individual and his life-experience. The a priori in either case is, at least in its primitive forms, obvious, even trivial, but its systematic demonstration, theoretical pursuit and phenomenological clarification remains of supreme scientific and philosophical interest, and is by no + +means easy. + +The notion of universal grammar can of course be carried beyond the a priori sphere, if the somewhat vague sphere of the universally human (in the empirical sense) is brought in. There can, and must, be a universal grammar in this widest of senses, and that this extended sphere is 'rich in important and well-established findings' (as A. Marty observes on page 61 of his Untersuchungen z. Grundlegung etc., under the strange impression that he is contradicting me) is something I do not, and never did, doubt. But here, as elsewhere where philosophical interests are concerned, it is important to separate the a priori sharply from the empirical, and to recognize that, within this widely conceived discipline, the findings of formal semantics relevant for grammarians have a peculiar character: they belong to an a priori discipline that should be kept apart in its purity. Here as elsewhere, one must subscribe to a great Kantian insight, and steep oneself in its sense: that one does not enrich, but rather subverts, the sciences if one blurs their boundaries. One must realize that a universal grammar in this widest sense is a concrete science which, like all concrete sciences, frequently brings together for explanatory purposes findings whose theoretical place lies in essentially different theoretical sciences, in empirical sciences, on the one hand, and in a priori sciences, on the other. Our age, oriented towards natural science, sees to it that generalizing, empirical investigations are not neglected in the grammatical field, nor in any other. What is a priori is not so favoured; even though all basic insights lead back to the a priori, our age's sense for it almost threatens to wither away. I therefore fairly take up the cudgels for the old doctrine of a grammaire generale et raisonnee, a philosophical grammar, for its obscure, undeveloped intention aiming at the 'rational' in speech, in the true sense of the word, and in particular at the + +'logic' of speech or its semantic a priori. 16 + +If I am right, it is of basic importance for linguistic investigations that they should become clear as to the distinctions provisionally shadowed forth + +here. They should possess themselves of the insight that the foundations of speech are not only to be found in physiology, psychology and the history of culture, but also in the a priori. The latter deals with the essential meaning-forms and their a priori laws of compounding or modification, and no speech is conceivable that is not in part essentially determined by this a priori. Every investigator of language operates with notions stemming + +from this field, whether he is clear on the matter or not. + +We may finally say: within pure logic one must separate off what, considered in itself, forms a first, basic sphere, the pure theory of meaning-forms. Considered from the standpoint of grammar, it must lay bare an ideal framework which each actual language will fill up and clothe differently, in deference either to common human motives or to empirical motives that vary at random. To whatever extent the actual content and grammatical forms of historical languages are thus empirically determined, each is bound to this ideal framework: theoretical research into this framework must accordingly be one of the foundations of the final scientific clarification of all language as such. The main point to be kept in mind is this: all semantic types set forth in pure, formal semantics, and systematically explored in their articulations and structures - the basic forms of propositions, the categorical proposition with its many particular patterns and forms of members, the primitive types of propositionally complex propositions, e.g. the conjunctive, disjunctive and hypothetical propositional unities, the differences of universality and particularity, on the one hand, and of singularity, on the other, the syntactical forms of plurality, negation, the modalities etc. - all these matters are entirely a priori, rooted in the ideal essence of meanings as such. The same applies to the semantic formations to be conjured up by operational laws of compounding and modification out of these primitive forms. They hold prime place over against their empirical-grammatical expressions, and resemble an absolutely fixed ideal framework, more or less perfectly revealed in empirical disguises. One must have this in mind in order to be able to ask significantly: How does German, Latin, Chinese etc., express 'the' existential proposition, 'the' categorical proposition, 'the' antecedent of a hypothetical, 'the' plural, 'the' modalities of possibility and probability, 'the' negative etc? It is no matter of indifference whether the grammarian is content with a prescientific personal opinion on meaningforms, or with notions empirically contaminated by historical, e.g. by Latin grammar, or whether he keeps his eyes on a scientifically fixed, theoretically coherent system of pure meaning-forms, i.e. on our own form-theory of + +meanings. + +Considering the fact that in this lowest field of logic questions of truth, objectivity, objective possibility are not yet relevant, and considering too its just described role of rendering intelligible the ideal essence of all speech as such, one might give this basic field of pure logic the name of pure logical + +Note 1 In the First Edition I spoke of 'pure grammar', a name conceived and expressly devised to be analogous to Kant's 'pure science of nature'. Since it cannot, however, be said that pure formal semantic theory comprehends the entire a priori of general grammar - there is, e.g., a peculiar a priori governing relations of mutual understanding among minded persons, relations very important for grammar - talk of pure logical grammar is to + +be preferred. + +Note 2 After what has been said, no one will imagine that there could be a universal grammar in the sense of a universal science comprehending all particular grammars as contingent specifications, just as a universal mathematical theory contains all possible cases a priori in itself, and settles them all 'in one go'. Naturally we speak of a general or purely logical grammar in a sense analogous to that in which we speak of general linguistic science. Just as the latter deals with the universal principles that can be placed before the sciences of particular languages, and mainly, therefore, with the presuppositions and foundations equally relevant to all such languages, so pure logical grammar in its narrower sense explores only one of these foundations, which has pure logic for its theoretical home-territory. Its inclusion in linguistic science naturally only serves interests of application just as, in another direction, linguistic science itself satisfied similar interests in many + +chapters of psychology. + +Marty of course disagrees with me on these points, as also generally in regard to a theoretical classification into a priori and empirical researches (cf. loco cit. §21, pp. 63 ff). In the note to page 67, he holds that the logicogrammatical findings I credit to pure logic 'have, theoretically, their natural home in the psychology of language. Logic, and the nomothetic part of linguistic psychology, borrow from this what serves and suits their purpose'. To me Marty's conception is basically mistaken. On it, we should ultimately have to class arithmetic, as well as all other formal disciplines in mathematics in - psychology, if not in linguistic psychology. For pure logic in the narrower sense, i.e. the doctrine of the validity of meanings, and the connected pure theory of meaning-forms, is, I hold, essentially one with these disciplines (cf. the final chapter of the Prolegomena). In the essential unity of a mathesis universalis all these sciences must be treated, and certainly be kept quite apart from all empirical sciences, whether styled 'physics' or 'psychology'. Mathematicians in fact do this, even if in naively dogmatic fashion, turning their back on specifically philosophical problems, and not worrying about philosophical objections - to the great profit, in my view, of their science. + +Note 3 Nothing has so much confused discussions of the question of the right relation of logic to grammar, as the constant confusion of two logical + +spheres, sharply distinguished by us as lower and upper, and characterized by way of their negative counterparts - the spheres of nonsense and of formal absurdity respectively. The logical sphere, in the sense of the upper sphere oriented towards formal truth and objectivity, is certainly irrelevant to grammar. This is not true of all logic whatever. If, however, one tried to discredit the lower logical sphere on account of its supposed narrow obviousness and practical uselessness, one would have to say that it ill befits the philosopher, the dedicated representative of purely theoretical interests, to let himself be guided by considerations of practical use. He must surely also know that it is precisely behind the obvious that the hardest problems lie hidden, that this is so much so, in fact, that philosophy may be paradoxically, but not unprofoundly, called the science of the trivial. In the present case at least what seems at first quite trivial, reveals itself, on closer examination, as the source of deep-lying, widely ramifying problems. These problems, though intrinsically prior in the sense of Aristotle, are not the first to make themselves felt by logicians, concerned as these are with objective validity: it is not, therefore, remarkable that, till this day, no logicians, not even Bolzano, have even formulated these problems scientifically, have formed the idea of a purely logical theory of forms. Logic accordingly lacks its prime foundation; it lacks a scientifically strict, phenomenologically clarified distinction of primitive meaning-elements and structures, and a knowledge of relevant laws of essence. We may thus explain how, in particular, the many theories of 'the concept' or 'the judgement', which in certain of their aspects belong in this field, have produced so few tenable results. This is to a large extent due to a lack of correct aims and viewpoints, to confusions of radically distinct layers of problems, and to a psychologism operative openly or in manifold disguises. Since the eye of the logician is ever on form, these defects also point to difficulties inherent in these matters + +themselves. + +Note 4 For related but opposed conceptions one may refer to H. Steinthal's Einleitung in die Psychologie und Sprachwissenschaft (Introduction IV, 'Sprechen und Denken, Grammatik und Logik', pp. 44 ff). I refer especially to his beautifully precise statement of the notion ofW. v. Humboldt (loc. cit. pp. 63 ff), from which it would seem that the views stated here are in some points close to those of the great thinker, whom Steinthal also respects. Steinthal himself sides against us, and raises many objections to our views, but our distinctions would seem to have disposed of these all so clearly, that + +no thoroughgoing criticism is required here. + +Investigation V + +On intentional experiences + +and their 'contents' + +Introduction + +In our Second Investigation we clarified the general sense of the ideality of the Species and, together with it, the sense of the ideality of meanings with which pure logic is concerned. As with all ideal unities, there are here real possibilities, and perhaps actualities, which correspond to meanings: to meanings in specie correspond acts of meaning, the former being nothing but ideally apprehended aspects of the latter. New questions now arise regarding the kind of experiences in which the supreme genus Meaning has its originative source, and likewise regarding the various sorts of experiences in which essentially different sorts of meaning unfold. We wish to enquire into the originative source of the concept of Meaning and its essential specifications, so as to achieve a deeper-going, more widely ranging answer to our question than our investigations have so far given us. In very close connection with this question, certain other questions arise: meanings have to be present in meaning-intentions that can come into a certain relation to intuition. We have often spoken of the fulfilment of a meaning-intention through a corresponding intuition, and have said that the highest form of such fulfilment was that of self-evidence. It is therefore our task to describe this remarkable phenomenological relationship, and to lay down its role, and so to clarify the notions of knowledge which presuppose it. For an analytical investigation these tasks are not really separable from our earlier work on the essence of meaning (particularly as this last relates to the logical presenta- + +tion and the logical judgement). + +The present investigation will not yet embark on these tasks, since we cannot enter upon them without first performing a much more general phenomenological investigation. Experiences of meaning are classifiable as 'acts', and the meaningful element in each such single act must be sought in the act-experience, and not in its object; it must lie in that element which makes the act an 'intentional' experience, one 'directed' to objects. The essence of the fulfilling intuition likewise consists in acts, for thinking and intuiting must be different qua acts. Naturally, too, self-fulfilment must be reckoned a relation especially bound up with the characters of acts. No term in descriptive psychology is, however, more controversial than the term + +'act', and doubt, if not quick rejection, may have been aroused by all passages in our previous Investigations where we made use of the notion of 'act' to characterize or express our conception. It is therefore important, and a precondition for carrying out all our tasks, that this concept should be clarified before all others. It will appear that the concept of act, in the sense of an intentional experience, circumscribes an important generic unity in the sphere of experiences (apprehended in its phenomenological purity), and that to put meaning-experiences into this genus enables us to charac- + +terize them in a truly worthwhile manner. + +It is of course part of phenomenological research into the essence of acts as such, that we should clear up the difference between the character and the content of acts, and that, as regards the latter, we should point out the fundamentally different senses in which the 'content' of an act has been + +talked about. + +The nature of acts as such cannot be satisfactorily discussed unless one goes fairly fully into the phenomenology of 'presentations'. The intimate relevance of this topic is recalled by the well-known statement, that every act is either a presentation or is founded upon presentations. We must, however, ask which of the very many concepts of 'presentation' is here the required one: to separate the closely confused phenomena underlying the ambiguities of this word thus becomes an essential part of our task. + +The treatment of the problems thus roughly outlined (to which certain others will be intimately linked) is suitably connected by us with the many concepts of consciousness which are always being distinguished, and are always shading into one another in descriptive psychology. Mental acts are often called 'activities of consciousness', 'relations of consciousness to a content (object)', and 'consciousness' is, in fact, at times defined as a com- + +prehensive expression covering mental acts of all sorts. + +Chapter I + +Consciousness as the + +phenomenological su bsistence of + +the ego and consciousness as inner + +perception + +§ I Varied ambigu ity of the term 'consciousness' + +In psychology there is much talk of 'consciousness', and likewise of 'conscious contents' and 'conscious experiences': the latter are generally abbreviated to 'contents' and 'experiences'. This talk is mainly connected with the division between psychical and physical phenomena; the former being those phenomena which belong to the sphere of psychology, the latter to the sphere of the natural sciences. Our problem, that of circumscribing the concept of 'mental act' in its phenomenological essence, is closely connected with this problem of division, since the concept arose precisely in this context, as supposedly marking off the psychological sphere. One concept of consciousness is justifiably employed in effecting this demarcation correctly, another yields us the definition of a mental act. We must, in either case, distinguish between + +several thematically cognate, and so readily confounded, notions. + +We shall, in what follows, discuss three concepts of consciousness, as + +having interest for our purposes: + +1. Consciousness as the entire, real (reelle) phenomenological being of the empirical ego, as the interweaving of psychic experiences in the unified + +stream of consciousness. + +2. Consciousness as the inner awareness of one's own psychic experiences. 3. 'Consciousness as a comprehensive designation for 'mental acts', or 'in- + +tentional experiences', of all sorts. + +It need hardly be said that we have not exhausted all ambiguities of the term in question. I particularly recall, e.g. , modes of speech current in non-scientific parlance such as 'entering consciousness', 'coming to consciousness', 'heightened' or 'reduced' self-consciousness, the 'awakening of self-consciousness' (the last expression quite differently used in psychology + +from the sense given it in ordinary life), and so forth. + +Since all terms at all relevant for terminological differentiation are ambiguous, an unambiguous fixing of the concepts which here distinguish themselves can only be done indirectly: we must put together equivalent + +expressions, and oppose them to expressions to be kept apart from them, and we must employ suitable paraphrases and explanations. We shall therefore + +have to make use of these aids. + +§2 First sense: Consciousness as the real + +phenomeno logical un ity of the ego's experien ces. + +The concept of an expe rience + +We begin with the following summary statement. The modern psychologist defines (or could define) his science as the science of 'psychic individuals' considered as concrete conscious unities, or as the science of the conscious experiences of experiencing individuals; the juxtaposition of these terms in this context determines a certain concept of consciousness and, at the same time, certain concepts of experience and content. These latter terms, 'experience' and 'content', mean for the modern psychologist the real occurrences (Wundt rightly calls them 'events') which, in flux from one moment to the next, and interconnected and interpenetrating in manifold ways, compose the real unity-of-consciousness of the individual mind. In this sense, percepts, imaginative and pictorial presentations, acts of conceptual thinking, surmises and doubts, joys and griefs, hopes and fears, wishes and acts of will etc., are, just as they flourish in our consciousness, 'experiences' or 'contents of consciousness' . And, with these experiences in their total and concrete fulness, their component parts and abstract aspects are also experienced: they are real contents of consciousness. Naturally, it is irrelevant whether these parts are in some manner inwardly articulated, whether they are marked off by special acts directed upon themselves, and whether, in particular, they are themselves objects of an 'inner' perception, which seizes them as they are in consciousness, and even whether they can be such objects or not. + +We may now point out that this concept of consciousness can be seen in a purely phenomenological manner, i.e. a manner which cuts out all relation to empirically real existence (to persons or animals in nature): experience in the descriptive-psychological or empirically-phenomenological sense then becomes experience in the sense of pure phenomenology. l The clarifying illustrations that we now append may and must lead to the conviction that the required exclusion lies always in our power, and that the descriptivepsychological treatments that we have first applied or might first apply to such illustrations, are to be interpreted 'purely' in the manner sketched above, and to be understood in what follows as pure, a priori insights into + +essence. The same, of course, holds in all parallel cases. + +The sensational moment of colour, e.g., which in outer perception forms a real constituent of my concrete seeing (in the phenomenological sense of a visual perceiving or appearing) is as much an 'experienced' or 'conscious' content, as is the character of perceiving, or as the full perceptual appearing of the coloured object. As opposed to this, however, this object, though + +perceived, is not itself experienced nor conscious, and the same applies to the colouring perceived in it. If the object is non-existent, if the percept is open to criticism as delusive, hallucinatory, illusory etc., then the visually perceived colour, that of the object, does not exist either. Such differences of normal and abnormal, of veridical and delusive perception, do not affect the internal, purely descriptive (or phenomenological) character of perception. While the seen colour, i.e. the colour appearing upon and with the appearing object of visual perception, and seen as its property, and one with it in its present being - while this colour certainly does not exist as an experience, there is a real part (reelles Bestandstiick) of our experience, of this appearing to perception, which corresponds to it. Our colour-sensation corresponds to it, that qualitatively determinate phenomenological colour-aspect, which receives an 'objectifying interpretation' in perception, or in an intrinsic aspect of such perception (the 'appearance of the object's colouring'). These two, the colour-sensation and the object's objective colouring, are often confounded. In our time people have favoured a form of words according to which both are the same thing, only seen from a different standpoint, or with a different interest: psychologically or subjectively speaking, one has a sensation, physically or objectively speaking, one has a property of an external thing. Here it is enough to point to the readily grasped difference between the red of this ball, objectively seen as uniform, and the indubitable, unavoidable projective differences among the subjective colour-sensations in our percept, a difference repeated in all sorts of objective properties and the + +sensational complexes which correspond to them. + +What we have said about single properties carries over to concrete wholes. It is phenomenologically false to say that the difference between a conscious content in perception, and the external object perceived (or perceptually intended) in it, is a mere difference in mode of treatment, the same appearance being at one time dealt with in a subjective connection (in connection with appearances which relate to an ego), and at another time in an objective connection (in connection with the things themselves). We cannot too sharply stress the equivocation which allows us to use the word 'appearance' both of the experience in which the object's appearing consists (the concrete perceptual experience, in which the object itself seems present to us) and of the object which appears as such. The deceptive spell of this equivocation vanishes as soon as one takes phenomenological account as to how little of the object which appears is as such to be found in the experience of its appearing. The appearing of the thing (the experience) is not the thing which appears (that seems to stand before us in propria persona). As belonging in a conscious connection, the appearing of things is experienced by us, as belonging in the phenomenal world, things appear before us. The appear- + +ing of the things does not itself appear to us, we live through it. + +If we ourselves appear to ourselves as members of the phenomenal world,z physical and mental things (bodies and persons) appear in physical and + +mental relation to our phenomenal ego. This relation of the phenomenal object (that we also like to call a 'conscious content') to the phenomenal subject (myself as an empirical person, a thing) must naturally be kept apart from the relation of a conscious content, in the sense of an experience, to consciousness in the sense of a unity of such conscious contents (the phenomenological subsistence of an empirical ego). There we were concerned with the relation of two appearing things, here with the relation of a single experience to a complex of experiences. Just so, conversely, we must of course distinguish the relation of the appearing person I to the externally appearing thing, from the relation of the thing's appearing ('qua' experience) to the thing which appears. If we speak of the latter relation, we only make clear to ourselves that the experience is not itself what is intentionally present 'in' it: we can, e.g., make plain that what is predicated of a thing's appearing is not also predicated of the thing that appears in it. And yet another relation is the objectifying relation ascribed by us to the sense-complex experienced by us when something appears to us, a relation in which the complex stands to the object which appears to us. We concede that such a complex is experienced in the act of appearing, but say that it is in a certain manner 'interpreted' or 'apperceived', and hold that it is in the phenomenological character of such an animating interpretation of sensation that what we call the appearing of + +the object consists.3 + +Similar distinctions of essence to those needed by us in the case of perception, when we sought to separate off what is really 'experience' in it and really composes it, from what is only 'in' it in an 'improper' or intentional sense, will have soon to be drawn in the case of other 'acts' as well. We shall soon have to deal with such distinctions more generally. Here it is only important to guard from the start against certain misleading thought-tendencies, which might obscure the plain sense of the notions to be elucidated. + +§3 The phenomenologi cal and the popu lar concept + +of experi ence + +A similar aim leads us to point out that our concept of experience does not tally with the popular notion; here the distinction just sketched, between + +real (reellem) and intentional content, has its part to play. + +If someone says he 'experienced' the wars of 1866 and 1870, then what he has been said to have 'experienced' in this sense, is a complex of outer events, and 'experiencing' consists here in perceptions, judgements and other acts, in which these events appear as objects, and often as objects of certain assertions which relate them to the empirical ego. The experiencing ego, in the phenomenologically paradigmatic sense, has naturally not got these events in itself as things mentally lived through, as its real constituents or contents, in the way in which these events are in the things concerned in them. What it finds in itself, what are present in it as realities, are the relevant acts of + +perceiving, judging etc., with their variable sense-material, their interpretative content, their assertive characters etc. Experiencing in the latter sense is quite different from experiencing in the former sense. To experience outer events meant to have certain acts of perception, of this or that type of knowledge, directed upon them. This 'having' at once furnishes an instance of the quite different 'experiencing' in the sense of phenomenology. This merely means that certain contents help to constitute a unity of consciousness, enter into the phenomenologically unified stream of consciousness of an empirical ego. This itself is a real whole, in reality made up of manifold parts, each of which may be said to be 'experienced' . It is in this sense that what the ego or consciousness experiences, are its experience: there is no difference between the experience or conscious content and the experience itself. What is sensed is, e.g., no different from the sensation. If, however, an experience 'directs itself' to an object distinguishable from itself, as, e.g., external perception directs itself to a perceived object, a nominal presentation to an object named etc. , such an object is not experienced or conscious + +in the sense to be established here, but perceived, named etc. + +The situation justifies talk of 'contents' , which is here entirely proper. The normal sense of the word 'content' is relative: it refers quite generally to a comprehensive unity which has its content in the sum total of its component parts. Whatever can be regarded as a part of a whole, and as truly constituting it in real fashion (reell), belongs to the content of that whole. In our current descriptive-psychological talk of contents, the tactitly assumed relational focus, i.e. the corresponding whole, is the real unity of consciousness. Its content is the sum total of present experiences, and 'contents' in the plural means these experiences themselves, i.e. all that as real parts consti- + +tute any phenomenological stream of consciousness. + +§4 The relation between experiencing consciousness and experi enced content is no phenomeno logi cal ly + +pecul iar type of re lation + +The foregoing exposition has made clear that the relation in which experiences are thought to stand to an experiencing consciousness (or to an experiencing 'phenomenological ego')4 points to no peculiar phenomenological situation. The ego in the sense of common discourse is an empirical object, one's own ego as much as someone else's, and each ego as much as any physical thing, a house or a tree etc. Scientific elaboration may alter our ego-concept as much as it will, but, if it avoids fiction, the ego remains an individual, thinglike object, which, like all such objects, has phenomenally no other unity than that given it through its unified phenomenal properties, and which in them has its own internal make-up. If we cut out the ego-body from the empirical ego, and limit the purely mental ego to its phenomenological content, the latter reduces to a unity of consciousness, to a real + +experiential complex, which we (i.e. each man for his own ego) find in part evidently present, and for the rest postulate on good grounds. The phenomenologically reduced ego is therefore nothing peculiar, floating above many experiences: it is simply identical with their own interconnected unity. In the nature of its contents, and the laws they obey, certain forms of connection are grounded. They run in diverse fashions from content to content, from complex of contents to complex of contents, till in the end a unified sum total of content is constituted, which does not differ from the phenomenologically reduced ego itself. These contents have, as contents generally have, their own law-bound ways of coming together, of losing themselves in more comprehensive unities and, in so far as they thus become and are one, the phenomenological ego or unity of consciousness is already constituted, without need of an additional, peculiar ego-principle which supports all contents and unites them all once again. Here as elsewhere it is + +not clear what such a principle would effect.s + +§S Second sense. 'Inn er' consciousness as + +inner perception + +Our sense of the terms 'consciousness', 'experience', 'content', has been fixed in the treatments of the last three sections, a descriptive-psychological sense which, with phenomenological 'purification', becomes purely phenomenological. We wish to adhere to this sense in future, but only when other concepts + +have been expressly indicated. + +A second concept of consciousness is expressed by talk of 'inner consciousness' . This is that 'inner perception' thought to accompany actually present experiences, whether in general, or in certain classes of cases, and to relate to them as its objects. The 'self-evidence' usually attributed to inner perception, shows it to be taken to be an adequate perception, one ascribing nothing to its objects that is not intuitively presented, and given as a real part (reel!) of the perceptual experience, and one which, conversely, intuitively presents and posits its objects just as they are in fact experienced in and with their perception. Every perception is characterized by the intention of grasping its object as present, and in propria persona. To this intention perception corresponds with complete perfection, achieves adequacy, if the object in it is itself actually present, and in the strictest sense present in propria persona, is exhaustively apprehended as that which it is, and is therefore itself a real (reel!) factor in our perceiving of it. It is accordingly clear, and evident from the mere essence of perception, that adequate perception can only be 'inner' perception, that it can only be trained upon experiences simultaneously given, and belonging to a single experience with itself. This holds, precisely stated, only for experiences in the purely phenomenological sense. One cannot, however, at all concur with the converse opinion and say, in psychological language, that each percept directed upon one's own + +inner experience (which would be called an 'inner' percept in the natural sense of the word) need be adequate. In view of the just exposed ambiguity of the expression 'inner perception', it would be best to have different terms for inner perception, as the perception of one's own experiences, and adequate or evident perception. The epistemologically confused and psychologically misused distinction of inner and outer perception would then vanish; it has been put in the place of the genuine contrast between adequate and inadequate perception which has its roots in the pure phenomenological essences of such experiences. [On this point, see the Appendix on internal + +and external perception.] + +Many thinkers, as, e.g., Brentano, are led to posit a close connection between the two concepts of consciousness so far discussed, because they think that they may regard the consciousness, or the being-experienced, of contents, in the first sense, as at the same time a consciousness in the second sense. The equivocation which pushes us to treat consciousness as a sort of knowing, and in fact of intuitive knowing, may here have recommended a conception fraught with too many grave difficulties. I recall the infinite regress which sprung from the circumstance that inner perception is itself another experience, which requires a new percept, to which the same again applies etc., a regress which Brentano sought to avoid by distinguishing between a primary and a secondary direction of perception. Since our concern is here with purely phenomenological asseverations, we must leave theories of this sort on one side, so long, that is, as the need to assume the unbroken activity of + +inner perception cannot be phenomenologically demonstrated. + +§6 Origin of the fi rst concept of consciousness + +out of the second + +Undeniably the second concept of consciousness is the more 'primitive': it has an 'intrinsic priority'. The following considerations would enable us to pass in scientific order from this last narrower concept to our former, broader one. If we consider the self-evidence of the Cogito, ergo sum, or rather of its simple sum, as one that can be sustained against all doubts, then it is plain that what here passes as ego cannot be the empirical ego. But since, on the other hand, we cannot allow the self-evidence of the proposition 'I am' to depend on the knowledge and acceptance of philosophical ideas about the ego which have always remained questionable, we can at best say: In the judgement 'I am' self-evidence attaches to a certain central kernel of our empirical ego-notion which is not bounded by a perfectly clear concept. If we now ask what could belong to this conceptually undemarcated and therefore unutterable kernel, what may constitute the self-evidently certain, given element in the empirical ego at each moment, it comes easy to refer to judgements of inner (i.e. adequate) perception. Not only is it self-evident that I am: self-evidence also attaches to countless judgements of the form + +I perceive this or that, where I not merely think, but am also self-evidently assured, that what I perceive is given as I think of it, that I apprehend the thing itself, and for what it is - this pleasure, e.g. , that fills me, this phantasm of the mind that float before me etc. All these judgements share the lot of the judgement 'I am', they elude complete conceptualization and expression, they are evident only in their living intention, which cannot be adequately imparted in words. What is adequately perceived, whether expressed thus vaguely or left unexpressed, constitutes the epistemologically primary, absolutely certain focus yielded by the reduction, at any given moment, of the phenomenal empirical ego to such of its content as can be grasped by the pure phenomenologist. It is also true, conversely, that in the judgement 'I am', it is the kernel of what is adequately perceived which, ranged under the ego, first makes possible and provides a ground for this 'I am's' evidence.6 To this primary focus more territory is added when we reduce to its past phenomenological content all that retention, essentially attached to perception, reports as having been recently present, and also all that recollection reports as having belonged to our earlier actual experience, and when we then go back through reflection to what 'in' retention and remembrance is reproductively phenomenological. We proceed similarly with what can be assumed on empirical grounds to coexist with what at each instant we adequately perceive, or with what can be assumed to have coexisted with what now forms the reflective substance of retention and recollection, and can be assumed to have cohered continuously with it in unity. When I say 'cohered continuously with it in unity', I refer to the unity of the concrete phenomenological whole, whose parts are either abstract aspects, mutually founded upon, and requiring each other in their coexistence, or pieces from whose nature spring forms of coexistent unity, forms which actually contribute to the content of the whole as real indwelling aspects. These 'unities of coexistence' pass continuously into one another from one moment to the next, composing a unity of change, of the stream of consciousness, which in its turn demands the continuous persistence, or no continuous change, of at least one aspect essential for its total unity, and so inseparable from it as a whole. This part is played by the presentative form of time which is immanent in the stream of consciousness, which latter appears as a unity in time (not in the time of the world of things, but in the time which appears together with the stream of consciousness itself, and in which the stream flows). Each instant of this time is given in a continuous projective series of (so-to-speak) 'time-sensations'; in each actual phase of the stream of consciousness the whole time-horizon of the stream is presented, and it thereby possesses a form overreaching all its contents, which remains the same form + +continuously, though its content steadily alters. + +This accordingly forms the phenomenological content of the ego, of the empirical ego in the sense of the psychic subject. Phenomenological reduction yields the really self-enclosed, temporally growing unity of the stream of + +experience. The notion of experience has widened out from what is inwardly perceived, and that is in this sense conscious, to the notion of the 'phenomenological ego', by which the empirical ego is intentionally constituted. + +§7 Reciprocal demarcation of psyc hology and + +natu ral science (fi rs,t edition) + +(Paragraph from the First Edition, excised by Husserl from the Second + +Edition as being unclear and irrelevant.) + +Psychology's task - descriptively - is to study the ego-experiences (or conscious contents) in their essential species and forms of combination, in order to explore - genetically - their origin and perishing, and the causal patterns and laws of their formation and transformation. For psychology, conscious contents are contents of an ego, and so its task is to explore the real essence of the ego (no mystical thing-in-itself but one only to be demonstrated empirically), to explore the interweaving of psychic elements in the ego, and + +their subsequent development and degeneration. + +To empirical egos stand opposed empirical, physical things, non-egos, unities of coexistence and succession, having a claim to exist as things. To us, who are egos, they are only given as intentional unities, as things referred to in psychical experiences, as unities presented or judged about. They are not for this reason themselves mere presentations, any more than the same is true of the egos alien to ourselves. Physical things are given to us, they stand before us, they are objects - this means that we have certain percepts and judgements fitted to them which are 'directed to these objects'. To the system of all such percepts and judgements corresponds its intentional correlate, the physical world. As we deal with the system of such judgements in individuals, or as the common judgement-system of a community of individuals, or in the unity of science, we should draw more precise distinctions between the world of the individual, the world of the empirical, social community, and perhaps the world of an ideal community of knowers, the world of (ideally perfected) science, the world in itself. Psychical experiences and the ego likewise document their being and their law-governed connections only in science as a system of objectively valid presentations and judgements, and they are given only as targets of intentional acts in the ego. But they are given, truly and as what they are, though in a somewhat narrower sphere than that of their being, while this never happens in the case of physical things. The doctrine of Berkeley and Hume, which reduces phenomenal bodies to bundles of ideas, fails to do justice to the fact that, even if the elementary ideas in these bundles are psychically realizable, the bundle itself, the intended complexes of elements, are never present in real fashion (reell gegenwiirtig) in any human consciousness and never will be. No body can be inwardly perceived - not because it is 'physical', + +but because, e.g., its three-dimensional spatiality cannot be adequately intuited in any consciousness. But adequate intuition is the same as internal perception. It is the fundamental defect of phenomenalistic theories that they draw no distinction between appearance (Erscheinung) as intentional experience, and the apparent object (the subject of the objective predicates), and therefore identify the experienced complex of sensation with the complex of objective features. In any case the objective unities of psychology and those of natural science are not identical, at least not, as in the position of first data, they await scientific elaboration. Whether the two sciences in their full development will still be separated, depends on whether they really concern separate, or at least relatively self-sufficient realities in their mutual relation. (Such self-sufficiency does not of course entail necessary separation of the two realities by any mystical abysses.) We can turn the matter round and say: If there is such a separation, we can only learn of it as both sciences develop. It is sure, at least, that their points of origin, the original spheres of facts that they attempt to elaborate, are to a large extent mutually independent, and that this is true, further, as regards their advancing growth. We can indeed not exclude the possibility which is presented by phenomenalism as a proven theory - to me phenomenalism has not advanced beyond vague, if by no means worthless lines of thought - that the objective bases of all talk of physical things and happenings lie merely in lawgoverned correlations established among the psychical experiences of many consciousnesses. The acceptance of such a theory would not, however, remove the separation of the sciences. The distinction between lived experiences, conscious contents, and the non-experiences presented in such experiences (and perceived in them or judged to exist) would remain as before the foundation for the division of the sciences as departments of reason. It would therefore be the foundation for the sort of division that alone is in question at the present stage of development of the sciences. With the demand of a 'psychology without a soul', i.e. a psychology that abandons all metaphysical presumptions in regard to the soul - and does so because they could only become insights when science was perfected - corresponds the demand of a 'natural science without bodies', i.e. a natural science that begins by rejecting all theories as to the metaphysical nature of the physical. Such a theory which puts metaphysics in bondage from the outset, is what we have in phenomenalism. But it ought not to anticipate the answer to the question as to the division of the two sciences. The division must rest on purely phenomenological ground, and I think that, in this respect, our discussions above were well suited to resolve the much-debated question in a satisfactory manner. They only make use of the most fundamental phenomenological distinctions, those between the descriptive content and + +the intended object of our percepts and of our 'acts' in general. + +This distinction has naturally not escaped the psychologists. We find it in Hobbes, Descartes and Locke. One can say that all the greater modern thinkers have at times touched on it or treated of it. It is only a pity that + +they merely do so at times, instead of starting with the distinction, and taking the closest account of it at every step, instead, that is, of making it the foundation of scientific epistemology and psychology. Only in this manner can there be scientific correctness in our way of speech and thought, al- + +though it may make this last very prolix and inconvenient. + +What we are conscious of, in the narrower sense, is something apparent and, if one wishes to speak of such a thing, in the usual way, as a 'phenomenon', a psychic phenomenon. As against this, far the greater part of what we are conscious of, in the wider sense of the word, is not, properly speaking, apparent. For one would certainly not wish to assert that all psychic being is perceived, or is even perceptible (i.e. in the sense of a real possibility). The definition of psychology as the science of psychic phenomena must therefore be understood just as we understand the definition of natural science as the science of physical phenomena. The phenomena in question do not mean an objective scientific field which they are to exhaust, but only the nearest points of attack for our scientific researches. So understood, these definitions raise no objections. + +§8 The pure ego and aware ness ('Bewussth eit') + +We have not so far referred to the pure ego (the ego of 'pure apperception') which for many Kantians, and likewise for many empirical investigators, provides the unitary centre of relation, to which all conscious content is as such referred in a wholly peculiar fashion. To the fact of 'subjective experience' or consciousness, this pure ego is accordingly held to pertain essentially. 'Consciousness is relation to the ego', and whatever stands in this relation is a content of consciousness. 'We call anything content if it is related to an ego in consciousness: its other properties are irrelevant.' 'This relation is plainly one and the same despite manifold variation of content: it constitutes, in fact, what is common and specific to consciousness. We mark it off' , says Natorp (whom we are continuously quoting)/ 'by the special expression "awareness" (Bewusstheit) to distinguish it from the total fact of + +consciousness. ' + +The ego as subjective centre of relation for all contents in my consciousness, cannot be compared to what are contrasted with it, it is not relative to them as they are to it, it is not consciously given to its contents as they are given to it. It reveals itself as sui generis in its incapacity to be in anything else's consciousness, while other things are in its consciousness. It cannot itself be a content, and resembles nothing that could be a content of consciousness. For this reason, it can be no further described, since all descriptive terms we might seek to employ, could be drawn only from the content of consciousness, and could not therefore hit off the ego, or a relation to the ego. Otherwise put: each idea we could make of the ego would tum it into an object, but we have ceased + +to think of it as an ego, if we think of it as an object. To be an ego is not to be an object, but to be something opposed to all objects, for which they are objects. The same holds of their relation to the ego. Beingin-consciousness means being-objective for an ego: such being-objective + +cannot in its turn be made into an object. + +The fact of awareness, while it is the basic fact of psychology, can be acknowledged and specially emphasized, but it can neither be defined + +nor deduced from anything else. + +These statements are impressive, but closer consideration fails to substantiate them. How can we assert such a 'basic fact of psychology', if we are unable to think it, and how can we think it, if not by making the ego and consciousness, both subject-matters of our assertion, into 'objects'? This might be done if we thought of this fact only in indirect, symbolic fashion. Natorp, however, wants it to be a 'basic fact', which must as such surely be given in direct intuition. He in fact tells us that it 'can be acknowledged and specially emphasized' . Surely what is acknowledged or emphasized will be content? Surely it will be made into an object? Perhaps, indeed, some narrower concept of object is excluded, but the wider concept is here relevant. A taking note of a thought, a sensation, a stirring of displeasure etc., makes these experiences objects of inner perception, without making them objects in the sense of things, just so, the ego as relational centre, and any particular relation of the ego to some content, will, if taken note of, be objectively given. I must frankly confess, however, that I am quite unable to find this ego, this primitive, necessary centre of relations.8 The only thing I can take note of, and therefore perceive, are the empirical ego and its empirical relations to its own experiences, or to such external objects as are receiving special attention at the moment, while much remains, whether 'without' or 'within', + +which has no such relation to the ego. + +I can only clarify this situation by subjecting the empirical ego, with its empirical relation to objects, to phenomenological analysis, from which the above conception necessarily results. We excluded the body-ego, whose appearances resemble those of any other physical thing, and dealt with the mind-ego, which is empirically bound up with the former, and appears as belonging to it. Reduced to data that are phenomenologically actual, this yields us the complex of reflectively graspable experiences described above, a complex which stands in the same sort of relation to the mental ego as the side of a perceived external thing open to perception stands to the whole thing. The conscious intentional relation of the ego to its objects means for me simply that intentional experiences whose intentional objects are the egobody, the personal ego-mind and therefore the entire empirical ego-subject or human person, are included in the total phenomenological being of a unity of consciousness, and that such intentional experiences also constitute + +This brings us to our third concept of consciousness, defined in terms of 'acts' or 'intentional experiences', which will be analysed in our next chapter. If the peculiar character of intentional experiences is contested, if one refuses to admit, what for us is most certain, that being-an-object consists phenomenologically in certain acts in which something appears, or is thought of as our object, it will not be intelligible how being-an-object can itself be objective to us. For us the "matter is quite clear: there are acts 'trained upon' the character of acts in which something appears, or there are acts trained upon the empirical ego and its relation to the object. The phenomenological kernel of the empirical ego here consists of acts which bring objects to its + +notice, acts in which the ego directs itself to the appropriate object. + +I am unable, further, to grasp the view that the relation of the ego to conscious content is bare of all difference. For if by 'content' we mean the experience which forms the real side of the phenomenological ego, surely the way in which contents enter the unity of experience will depend throughout on their specific nature, which is true of all parts that enter into wholes? But, if by 'content' we mean some object upon which consciousness 'directs itself', whether perceivingly, imaginingly, retrospectively, expectantly, conceptually or predicatively etc., then it plainly involves many differences, + +obvious even in running through the expressions just used. + +Objection may be raised to our previous assertion that the ego appears to itself, enjoys a consciousness and, in particular, a perception of itself. Selfperception of the empirical ego is, however, a daily business, which involves no difficulty for understanding. We perceive the ego, just as we perceive an external thing. That the object does not offer all its parts and sides to perception is as irrelevant in this case as in that. For perception is essentially the presumptive apprehension of some object, not its adequate intuition. Perception itself, though part of the ego's phenomenological being, naturally falls, like so much else in consciousness that evades notice, beyond the glance of perception, much as ungrasped, yet apparent, aspects of a perceived external thing are not themselves perceived. Ego and thing are in either case said to be perceived, and perceived they indeed are, and in full, 'bodily' presence. + +Additional Note to the Second Edition. I must expressly emphasize that the attitude here taken up to the question of the pure ego - an attitude I no longer endorse, as remarked before - is irrelevant to the investigations of this volume. Important as this question may be, phenomenologically or in other respects, there remain wide fields of phenomenological problems, relating more or less generally to the real content of intentional experiences, and to their relation of essence to intentional objects, which can be systematically explored without taking up any stance on the ego-issue. The present investigations are entirely confined to such problems. But since such an important work as volume I of P. Natorp's Second Edition of his Einleitung in die Psychologie concerns itself with what I have said above, I have not simply struck it out. Chapter 2 + +Consciousness as intentional + +• experience + +We must now embark upon a fuller analytic discussion of our third concept of consciousness, which ranges over the same phenomenological field as the concept of 'mental act'. In connection with this, talk of conscious contents, talk in particular concerning contents of presentations, judgements etc. , gains a variety of meanings, which it is all-important to sort out and to subject to + +the sharpest scrutiny. + +§9 The meaning of Brentan o's demarcation of + +'psychic phenomena' + +Among the demarcations of classes in descriptive psychology, there is none more remarkable nor more important philosophically than the one offered by Brentano under his title of 'psychical phenomena', and used by him in his well-known division of phenomena into psychical and physical. Not that I can approve of the great thinker's guiding conviction, plain from the very terms that he uses, that he had achieved an exhaustive classification of 'phenomena' through which the field of psychological research could be kept apart from that of natural science, and through which the vexed question of the right delimitation of the fields of these disciplines could be very simply solved. Possibly a good sense can be given to defining psychology as the science of psychical phenomena, and to the coordinated definition of natural science as the science of physical phenomena, but there are good reasons for disputing the view that the 'Concepts which occur in Brentano's division are those found under like names in the definitions in question. It can be shown that not all 'psychical phenomena' in the sense of a possible definition of psychology, are psychical phenomena (i.e. mental acts) in Brentano's sense, and that, on the other hand, many genuine 'psychical phenomena' fall under Brentano's ambiguous rubric of 'physical phenomena'.' The value of Brentano's conception of a 'psychical phenomenon' is, however, quite independent of the aims that inspired it. A sharply defined class of experiences is here brought before us, comprising all that enjoys mental, conscious existence in a certain pregnant sense of these words. A real being deprived of + +such experiences, merely having2 contents inside it such as the experiences of sensation, but unable to interpret these objectively, or otherwise use them to make objects present to itself, quite incapable, therefore, of referring to objects in further acts of judgement, joy, grief, love, hatred, desire and loathing - such a being would not be called 'psychical' by anyone. If one doubts whether it is at all possible to conceive of such a being, a mere complex of sensations, one has but to point to external phenomenal things, present to consciousness through sensational complexes, but not appearing as such themselves, and called by us 'bodies' or 'inanimate things', since they lack all psychical experiences in the sense of our examples. Turning aside from psychology, and entering the field of the philosophical disciplines proper, we perceive the fundamental importance of our class of experiences, since only its members are relevant in the highest ranks of the normative sciences. They alone, seized in their phenomenological purity, furnish concrete bases for abstracting the fundamental notions that function systematically in logic, ethics and aesthetics, and that enter into the ideal laws of these sciences. Our mention of logic recalls the particular interest which has + +inspired our whole probing into such experiences. + +§ I 0 Descri ptive characte rization of acts as + +'i ntentional' experiences + +We must now dig down to the essence of Brentano's demarcation of ph en omenal classes, of his concept of consciousness in the sense of psychical act. Moved by the interest in classification just mentioned, Brentano conducts his enquiry in the form of a two-edged separation of the two main classes of 'phenomena' that he recognizes, the psychical and the physical. He arrives at a sixfold differentiation in which only two heads are relevant for our purpose, since in all the others misleading ambiguities do their destructive work, rendering untenable his notion of 'phenomenon' in general and of 'physical phenomenon' in particular, as well as his concepts of internal and + +external perception. 3 + +Of his two principal differentiations, one directly reveals the essence of psychical phenomena or acts. This strikes us unmistakably in any illustration we choose. In perception something is perceived, in imagination, something imagined, in a statement something stated, in love something loved, in hate hated, in desire desired etc. Brentano looks to what is graspably common to such instances, and says that 'every mental phenomenon is characterized by what the mediaeval schoolmen called the intentional (or mental) inexistence of an object, and by what we, not without ambiguity, call the relation to a content, the direction to an object (by which a reality is not to be understood) or an immanent objectivity. Each mental phenomenon contains something as object in itself, though not all in the same manner'.4 This 'manner in which consciousness refers to an object' (an expression used by Brentano + +in other passages) is presentative in a presentation, judicial in a judgement etc. etc. Brentano's attempted classification of mental phenomena into presentations, judgements and emotions ('phenomena of love and hate') is plainly based upon this 'manner of reference', of which three basically different kinds are distinguished (each admitting of many further specifications). Whether we think Brentano's classification of 'psychical' phenomena successful, and whether we think it basically significant for the whole treatment of psychology, as Brentano claims it is, does not matter here. Only one point has importance for us: that there are essential, specific differences of intentional relation or intention (the generic descriptive character of 'acts'). The manner in which a 'mere presentation' refers to its object, differs from the manner of a judgement, which treats the same state of affairs as true or false. Quite different again is the manner of a surmise or doubt, the manner of a hope or a fear, of approval or disapproval, of desire or aversion; of the resolution of a theoretical doubt (judgemental decision) or of a practical doubt (voluntary decision in the case of deliberate choice); of the confirmation of a theoretical opinion (fulfilment of a judgemental intention), or of a voluntary intention (fulfilment of what we mean to do). Most, if not all, acts are complex experiences, very often involving intentions which are themselves multiple. Emotional intentions are built upon presentative or judging intentions etc. We cannot, however, doubt that to resolve such complexes is always to come down on primitive intentional characters whose descriptive essence precludes reduction into other types of experience, and that the unity of the descriptive genus 'intention' ('act-character') displays specific differences, flowing from its pure essence, which take a priori precedence over empirical, psychological matters-of-fact. There are essentially different species and subspecies of intention. We cannot, in particular, reduce all differences in acts into differences in the presentations or judgements they involve, with help only from elements not of an intentional kind. Aesthetic approval or disapproval, e.g., is evidently and essentially a peculiar mode of intentional relation as opposed to the mere presentation or theoretical assessment of the aesthetic object. Aesthetic approval and aesthetic predicates may be asserted, and their assertion is a judgement, and as such includes presentations. But the aesthetic intention and its objects are then objects of presentations and judgements: it remains essentially distinct from these theoretical acts. To evaluate a judgement as valid, an emotional experience as elevated etc., presupposes analogous, closely related, not specifically identical intentions. Just so in comparisons of judgemental with voluntary + +decisions etc. + +We take intentional relation, understood in purely descriptive fashion as an inward peculiarity of certain experiences, to be the essential feature of 'psychical phenomena' or 'acts', seeing in Brentano's definition of them as 'phenomena intentionally containing objects in themselves' a circumscription of essence, whose 'reality' (in the traditional sense) is of course ensured + +by examples.5 Differently put in terms of pure phenomenology: Ideation performed in exemplary cases of such experiences - and so performed as to leave empirical-psychological conception and existential affirmation of being out of account, and to deal only with the real phenomenological content of these experiences - yields us the pure, phenomenological generic Idea of intentional experience or act, and of its various pure species.6 That not all experiences are intentional is proved by sensations and sensational complexes. Any piece of a sensed visual field, full as it is of visual contents, is an experience containing many part-contents, which are neither referred to, nor + +intentionally objective, in the whole. + +The discussions which follow will give precision and clarity to the fundamentally different uses of the word 'content'. Everywhere it will appear that what one grasped in the analysis and comparison of instances of the two sorts of contents, can be ideationally seen as a pure distinction of essence. The phenomenological assertions we aim at, are all meant by us (even without + +special pointing) as assertions of essence. + +A second characterization of mental phenomena by Brentano that has value for us is the formula 'that they are either presentations or founded upon presentations'.7 'Nothing can be judged about, nothing can likewise be desired, nothing can be hoped or feared, if it is not presented.'s In this characterization the term 'presentation' does not of course mean the presented + +content or object, but the act of presenting this. + +This characterization does not seem a suitable starting-point for our researches, since it presupposes a concept of 'presentation' that has yet to be worked out: it is hard to draw distinctions among the word's highly ambiguous uses. The discussion of the concept of 'act' will lead us naturally on to this. But the characterization is an important utterance, whose content prompts further investigations: we shall have to come back to it later. + +§ I I Avoidance of verbally tempting misunderstandi ngs. + +(0) The 'mental' or 'im mane nt' object + +While we adhere to Brentano's essential characterization, our departures from his opinions force us to abandon his terminology. It will be as well to drop talk of 'psychical phenomena', or of 'phenomena' at all, where we are dealing with experiences of the class in question. 'Psychical phenomena' is a justifiable phrase only on Brentano's view that it fairly circumscribes the psychological field of research: on our view all experiences are in this respect on a level. The term 'phenomenon' is likewise fraught with most dangerous ambiguities, and insinuates a quite doubtful theoretical persuasion, expressly professed by Brentano, that each intentional experience is a phenomenon. As 'phenomenon' in its dominant use (which is also Brentano's) means an appearing object as such, this implies that each intentional experience is not only directed upon objects, but is itself the object of certain intentional + +experiences. One thinks here, mainly, of the experiences in which things 'appear' in the most special sense, i.e. perceptions: 'every psychical phenomenon is an object of inner consciousness' . We have already mentioned the + +grave misgivings that keep us from assenting to this. + +Further objections surround the expressions used by Brentano as parallel with, or roughly circumscribing, his term 'psychical phenomenon', and which are also in general use. It is always quite questionable, and frequently misleading, to say that perceived, imagined, asserted or desired objects etc., 'enter consciousness' (or do so in perceptual, presentative fashion etc.), or to say conversely that 'consciousness', 'the ego' enters into this or that sort of relation to them, or to say that such objects 'are taken up into consciousness' in this or that way, or to say, similarly, that intentional experiences 'contain something as their object in themselves' etc. etc.9 Such expressions promote two misunderstandings: first, that we are dealing with a real (realen) event or a real (reales) relationship, taking place between 'consciousness' or 'the ego', on the one hand, and the thing of which there is consciousness, on the other; secondly, that we are dealing with a relation between two things, both present in equally real fashion (reell) in consciousness, an act and an intentional object, or with a sort of box-within-box structure of mental contents. If talk of a relation is here inescapable, we must avoid expressions which tempt us to regard such a relation as having psychological reality (Realitat), as belonging to the real (reellen) content of an + +experience. + +Let us first discuss our second misunderstanding more closely. It is particularly suggested by the expression 'immanent objectivity' used to name the essential peculiarity of intentional experiences, and likewise by the equivalent scholastic expressions 'intentional' or 'mental inexistence' of an object. Intentional experiences have the peculiarity of directing themselves in varying fashion to presented objects, but they do so in an intentional sense. An object is 'referred to' lO or 'aimed at' in them, and in presentative or judging or other fashion. This means no more than that certain experiences are present, intentional in character and, more specifically, presentatively, judgingly, desiringly or othe�ise intentional. There are (to ignore certain exceptions) not two things present in experience, we do not experience the object and beside it the intentional experience directed upon it, there are not even two things present in the sense of a part and a whole which contains it: only one thing is present, the intentional experience, whose essential descriptive character is the intention in question. According to its particular specification, it constitutes the full and sole presentation, judgement etc. etc., of this object. If this experience is present, then, eo ipso and through its own essence (we must insist), the intentional 'relation' to an object is achieved, and an object is 'intentionally present'; these two phrases mean precisely the same. And of course such an experience may be present in consciousness together with its intention, although its object does not exist at all, and is + +perhaps incapable of existence. The object is 'meant', i.e. to 'mean' it is an experience, but it is then merely entertained in thought, and is nothing in + +reality. + +If I have an idea of the god Jupiter, this god is my presented object, he is 'immanently present' in my act, he has 'mental inexistence' in the latter, or whatever expression we may use to disguise our true meaning. I have an idea of the god Jupiter: this means that I have a certain presentative experience, the presentation-of-the-god-Jupiter is realized in my consciousness. This intentional experience may be dismembered as one chooses in descriptive analysis, but the god Jupiter naturally will not be found in it. The 'immanent', 'mental object' is not therefore part of the descriptive or real make-up (deskriptiven reel/en Bestand) of the experience, it is in truth not really immanent or mental. But it also does not exist extramentally, it does not exist at all. This does not prevent our-idea-of-the-god-Jupiter from being actual, a particular sort of experience or particular mode of mindedness (Zumutesein), such that he who experiences it may rightly say that the mythical king of the gods is present to him, concerning whom there are such and such stories. If, however, the intended object exists, nothing becomes phenomenologically different. It makes no essential difference to an object presented and given to consciousness whether it exists, or is fictitious, or is perhaps completely absurd. I think of Jupiter as I think of Bismarck, of the tower of Babel as I think of Cologne Cathedral, of a regular thousand-sided + +polygon as of a regular thousand-faced solid. ll + +These so-called immanent contents are therefore merely intended or intentional, while truly immanent contents, which belong to the real make-up (reellen Bestande) of the intentional experiences, are not intentional: they constitute the act, provide necessary points d'appui which render possible an intention, but are not themselves intended, not the objects presented in the act. I do not see colour-sensations but coloured things, I do not hear tone- + +sensations but the singer's song, etc. etc. 12 + +What is true of presentations is true also of other intentional experiences that are built upon them. To represent an object, e.g. the Schloss at Berlin, to oneself, is, we said, to be minded in this or that descriptively determinate fashion. To judge about this Schloss, to delight in its architectural beauty, to cherish the wish that one could do so etc. etc., are new experiences, characterized in novel phenomenological terms. All have this in common, that they are modes of objective intention, which cannot be otherwise expressed than by saying that the Schloss is perceived, imagined, pictorially repres- + +ented, judged about, delighted in, wished for etc. etc. + +We shall need more elaborate investigation to determine the justification of talking figuratively about the object presented in a presentation, judged in a judgement etc., as well as the full sense of talk about the relation of acts to objects. It is dear, at least, as far as we now have penetrated, that it will be well to avoid all talk of immanent objectivity. It is readily dispensed with, + +since we have the expression 'intentional object' which is not exposed to + +similar objections. + +As regards misleading talk of the intentional 'containment' of objects in acts, it is undeniable that the parallel, equivalent locutions - 'the object is a conscious datum', 'is in consciousness', 'is immanent in consciousness' etc. suffer from a most damaging ambiguity; 'being conscious' (bewusst) here means something quite different from the possible senses given to it in the two previously discussed meanings of 'consciousness'. All modern psychology and epistemology have been confused by these and similar equivocations. With psychological thought and terminology as influential as they are now, it would be ill-advised to set up our own terms in opposition to those of contemporary psychology. Our first concept of consciousness, given an empirical-psychological slant, covers the whole stream of experience which makes up the individual mind's real unity, together with all aspects that enter into the constitution of this stream. This conception shows signs of spreading to psychology, and we therefore decided in our last chapter to give the preference to it, though we did so in phenomenological purity and not from a properly psychological angle. We must therefore exercise some necessary care in talking of consciousness as inner perception, or in talking of it as intentional relation, even if we do not altogether avoid such 'uses', + +which would scarcely be practicable. + +§ 12 (b) The act and the re lation of consciousness or + +the ego to the object + +The situation is similar as regards the first misunderstanding we mentioned, where it is imagined that consciousness, on the one hand, and the 'matter in consciousness' on the other, become related to one another in a real sense. ('The ego' is here often put in the place of 'consciousness' .) In natural reflection, in fact, it is not the single act which appears, but the ego as one pole of the relation in question, while the other pole is the object. If one then studies an act-experience, which last tempts one to make of the ego an essential, selfsame point of unity in every act. This would, however, bring us back to the view of the ego as a relational centre which we repudiated before. + +But if we simply 'live' in the act in question, become absorbed, e.g., in the perceptual 'taking in' of some event happening before us, in some play of fancy, in reading a story, in carrying out a mathematical proof etc., the ego as relational centre of our performances becomes quite elusive. The idea of the ego may be specially ready to come to the fore, or rather to be recreated anew, but only when it is really so recreated, and built into our act, do we refer to the object in a manner to which something descriptively ostensible corresponds. We have here, in the actual experience described, a correspondingly complex act which presents the ego, on the one hand, and the presentation, judgement, wish etc., of the moment, with its relevant + +subject-matter, on the other. From an objective standpoint (and so, too, from the standpoint of natural reflection) it is doubtless the case that in each act the ego is intentionally directed to some object. This is quite obvious since the ego is either no more than the 'conscious unity', or contemporary 'bundle', of experiences, or, in a more natural empirically-real (realer) perspective, the continuous thing-like unity, constituted in the unity of consciousness as the personal subject of our experiences, the ego whose mental states these experiences are, that performs the intention, percept, or judgement in question. If such and such an intentional experience is present, the + +ego eo ipso has the corresponding intention. + +The sentences 'The ego represents an object to itself', 'The ego refers presentatively to an object', 'The ego has something as an intentional object of its presentation' therefore mean the same as 'In the phenomenological ego, a concrete complex of experiences, a certain experience said, in virtue of its specific nature, to be a presentation of object X, is really (reel!) present.' Just so the sentence 'The ego judges about the object' means the same as 'such and such an experience of judging is present in the ego' etc. etc. In our description relation to an experiencing ego is inescapable, but the experience described is not itself an experiential complex having the ego-presentation as its part. We perform the description after an objectifying act of reflection, in which reflection on the ego is combined with reflection on the experienced act to yield a relational act, in which the ego appears as itself related to its act's object through its act. Plainly an essential descriptive change has occurred. The original act is no longer simply there, we no longer live in it, + +but we attend to it and pass judgement on it. + +We must therefore avoid the misunderstanding which our present discussion has just ruled out, that of treating relation to an ego as of the essence of + +an intentional experience itself. 13 + +§ 13 The fixing of our term inol ogy + +After these critical prolegomena, we shall now fix our own terminology, excluding as far as we can, and in their light, all conflicting assumptions and confusing ambiguities. We shall avoid the term 'psychical phenomenon' entirely, and shall talk of 'intentional experiences' wherever accuracy requires it. 'Experience' must be understood in the phenomenological sense fixed above. The qualifying adjective 'intentional' names the essence common to the class of experiences we wish to mark off, the peculiarity of intending, of referring to what is objective, in a presentative or other analogous fashion. As a briefer expression, in harmony with our own and foreign + +verbal usage, we shall use the term 'act' . + +These expressions certainly have their defects. We speak of 'intending' [not, of course, in English: Trans.] in the sense of specially noticing, or attending to something. An intentional object need not, however, always be + +noticed or attended to. Several acts may be present and interwoven with one another, but attention is emphatically active in one of them. We experience them all together, but we 'go all out' (as it were) in this particular one. But it is not unfitting, in view of the traditional use of the term 'intentional object', to which Brentano has given renewed currency, to speak in a correlative sense of 'intention' , especially when we have the term 'attending' to do the work of 'intention' in the other sense; we shall find reason to hold that attention does not involve a peculiar act. 14 Another ambiguity, however, confronts us. The term 'intention' hits off the peculiarity of acts by imagining them to aim at something, and so fits the numerous cases that are naturally and understandably ranked as cases of theoretical aiming. But the metaphor does not fit all acts equally, and if we study the examples enumerated in §10, we cannot avoid distinguishing a narrower and a wider concept of intention. In our metaphor an act of hitting the mark corresponds to that of aiming, and just so certain acts correspond as 'achievements' or 'fulfilments' to other acts as 'intentions' (whether of the judging or the desiring sort). The image therefore fits these latter acts quite perfectly; fulfilments are, however, themselves acts, i.e. 'intentions', though they are not intentions at least not in general - in that narrower sense which points to corresponding fulfilments. This ambiguity, once recognized, becomes harmless. But of course, where the narrower concept is wanted, this must be expressly stated. The equivalent term 'act-character' will also help to avoid misunderstandings. In talking of 'acts', on the other hand, we must steer clear of the word's original meaning: all thought of activity must be rigidly excluded. 15 The term 'act' is so firmly fixed in the usage of many psychologists, and so wellworn and loosed from its original sense that, after these express reservations, we can go on using it without concern. If we do not wish to introduce artificial novelties, strange alike to our living speech-sense and to historical tradition, + +we can hardly avoid inconvenience of the just-mentioned sort. + +§ 14 Difficu lties which su rround the assumption of acts as a descri ptively founded class of experiences In all these terminological discussions, we have gone deep into descriptive analyses of a sort required by our interests in logic and epistemology. Before we go deeper, however, we shall have to consider some objections which + +affect the bases of our descriptions. + +There are a group of thinkers who absolutely reject any marking-off of a class of experiences which have been described by us as 'acts' or 'intentional experiences'. In this connection Brentano's original introduction of the distinction, and his aims in introducing it, have, with some surreptitious misunderstandings, produced confusion: they have kept the distinction's extraordinarily valuable descriptive content from being rightly assessed. Natorp, e.g., rejects it decisively. But when this distinguished thinker objects + +by saying that16 'I can deal with a tone by itself or in relation to other contents of consciousness, without also paying regard to its being for an ego, but I cannot deal with myself and my hearing by themselves, without thinking of the tone', we find nothing in this that could confuse. Hearing certainly cannot be torn out of the hearing of a tone, as if it were something apart from the tone it hears. But this does not mean that two things are not to be distinguished: the tone heard, the object of perception, and the hearing of the tone, the perceptual act. Natorp is quite right in saying of the former: 'Its existence for me is my consciousness of it. If anyone can catch his consciousness in anything else than the existence of a content for him, I am unable to follow him.' It seems to me, however, that the 'existence of something for me', is a thing both permitting and requiring further phenomenological analysis. Consider, first, differences in the mode of attention. A content is differently present to me, according as I note it implicitly, not relieved in some whole, or see it in relief, according as I see it marginally, or have specially turned my focussing gaze upon it. More important still are differences between the existence of a content in consciousness in the sense in which a sensation so exists, without being itself made a perceptual object, and of a content which is made such an object. The choice of a tone as an instance slightly obscures the distinction without altogether removing it. 'I hear' can mean in psychology 'I am having sensations': in ordinary speech it means 'I am perceiving'; I hear the adagio of the violin, the twittering of the birds etc. Different acts can perceive the same object and yet involve quite different sensations. The same tone is at one moment heard close at hand, at another far away. The same sensational contents are likewise 'taken' now in this, and now in that manner. What is most emphasized in the doctrine of apperception is generally the fact that consistency of stimulus does not involve constancy of sensational content; what the stimulus really provokes is overlaid by features springing from actualized dispositions left behind them by previous experiences. Such notions are, however, inadequate and, above all, phenomenologically irrelevant. Whatever the origin of the experienced contents now present in consciousness, we can think that the same sensational contents should be present with a differing interpretation, i.e. that the same contents should serve to ground perceptions of different objects. Interpretation itself can never be reduced to an influx of new sensations; it is an act-character, a mode of consciousness, of 'rnindedness' (Zumuteseins). We call the experiencing of sensations in this conscious manner the perception of the object in question. What has here been made plain, in a context of natural existence, and by methods appropriate to psychology and natural science, will yield up its phenomenological substance if we abstract from the empirically real (Realen). If we consider pure experiences and their own essential content, we form Ideas of pure species and specific situations, in this case the pure species of Sensation, Interpretation, Perception in relation to its perceptum, and the relations of + +essence among these. We then see it to be a fact of essence that the being of a sensational content differs from that of the perceived object presented by + +it, which is not a reality in consciousness (reel! bewusst). + +17 + +All this becomes clear if we change our field of illustration for that of vision. Let us lay the following considerations before a sceptic. I see a thing, e.g. this box, but I do not see my sensations. I always see one and the same box, however it may be turned and tilted. I have always the same 'content of consciousness' - if I care to call the perceived object a content of consciousness. But each turn yields a new 'content of consciousness', if I call experienced contents 'contents of consciousness', in a much more appropriate use of words. Very different contents are therefore experienced, though the same object is perceived. The experienced content, generally speaking, is not the perceived object. We must note, further, that the object's real being or nonbeing is irrelevant to the true essence of the perceptual experience, and to its essence as a perceiving of an object as thus and thus appearing, and as thus and thus thought of. In the flux of experienced content, we imagine ourselves to be in perceptual touch with one and the same object; this itself belongs to the sphere of what we experience. For we experience a 'consciousness of identity', i.e. a claim to apprehend identity. On what does this consciousness depend? Must we not reply that different sensational contents are given, but that we apperceive or 'take' them 'in the same sense', and that to take them in this sense is an experienced character through which the 'being of the object for me' is first constituted. Must we not say, further, that the consciousness of identity is framed on a basis of these two sorts of experienced characters, as the immediate consciousness that they mean the same? And is this consciousness not again an act in our defined sense, whose objective correlate lies in the identity it refers to? These questions, I think, call for an affirmative and evident answer. I find nothing more plain than the distinction here apparent between contents and acts, between perceptual contents in the sense of presentative sensations, and perceptual acts in the sense of interpretative intentions overlaid with various additional characters. Such intentions, united with the sensations they interpret, make up the full concrete act of perception. Intentional characters and complete intentional acts are, of course, contents of consciousness in the widest descriptive sense of experiences: all differences predicable at all, are in this sense eo ipso differences of content. But within this widest sphere of what can be experienced, we believe we have found an evident difference between intentional experiences, in whose case objective intentions arise through immanent characters of the experiences in question, and experiences in whose case this does not occur, contents that may serve as the building-stones of acts without + +being acts themselves. + +Examples that will serve to elucidate this distinction, and also to show up various characters of acts, are provided by comparing perception with memory, or comparing either with presentations by means of physical images + +(paintings, statues etc.), or of signs. Verbal expressions yield the best examples of all. Let us imaginel8 that certain arabesques or figures have affected us aesthetically, and that we then suddenly see that we are dealing with symbols or verbal signs. In what does this difference consist? Or let us take the case of an attentive man hearing some totally strange word as a soundcomplex without even dreaming it is a word, and compare this with the case of the same man afterwards hearing the word, in the course of conversation, and now acquainted with its meaning, but not illustrating it intuitively? What in general is the surplus element distinguishing the understanding of a symbolically functioning expression from the uncomprehended verbal sound? What is the difference between simply looking at a concrete object A, and treating it as representative of 'any A whatsoever'? In this and countless similar cases it is act-characters that differ. All logical differences, and differences in categorial form, are constituted in logical acts in the sense of + +intentions. + +In analysing such cases the inadequacies of the modem theory of apperception become plain: it overlooks points decisive from a logical or epistemological standpoint. It does not do justice to phenomenological fact; it does not even attempt to analyse or describe it. Differences of interpretation are above all descriptive differences, and these alone, rather than obscure, hypothetical events in the soul's unconscious depths, or in the sphere of physiological happenings, concern the epistemologist. These alone permit of a purely phenomenological treatment, excluding all transcendent affirmations, such as the critique of knowledge presupposes. Apperception is our surplus, which is found in experience itself, in its descriptive content as opposed to the raw existence of sense: it is the act-character which as it were ensouls sense, and is in essence such as to make us perceive this or that object, see this tree, e.g., hear this ringing, smell this scent of flowers etc. etc. Sensations, and the acts 'interpreting' them or apperceiving them, are alike experienced, but they do not appear as objects: they are not seen, heard or perceived by any sense. Objects on the other hand, appear and are perceived, but they are not + +experienced. Naturally we exclude the case of adequate perception. + +The same holds in other cases: it holds, e.g., in the case of the 'sensations' (or however we choose to call contents serving as bases to interpretation) which are found in acts of simple or representative imagining. It is an imaging interpretation that sets an imagined rather than a perceptual appearance before us, where experienced sensations mediate the appearance of a pic- + +torially presented object (e.g. a centaur in a painting). + +19 One sees at once that + +the very same thing which, in relation to the intentional object, is called its presentation, i.e. the perceiving, remembering, picturing, symbolizing intention directed towards it, is also called an interpretation, conception, apper- + +ception in relation to the sensations really present in this act. + +I also regard it as relevantly evident, in regard to the examples just cited, that there are different 'manners of consciousness', different intentional relations + +to objects: the character of our intention is specifically different in the case of perceiving, of direct 'reproductive' recall, of pictorial representation (in the ordinary sense of the interpretation of statues, pictures etc.), and again in the case of a presentation through signs. Each logically distinct way of entertaining an object in thought corresponds to a difference in intention. To me it seems irrefragable that we only know of such differences because we envisage them in particular cases (apprehend them adequately and immediately), can then compare them and range them under concepts, and can thus make them into objects of varying acts of intuition and thought. From such 'seeing' we can, through abstract Ideation, progress toward an adequate grasp of the pure species they exemplify, and of the connections of essence among these latter. When Natorp remarks that 'all richness, all multiplicity of consciousness pertains rather to contents alone. Consciousness of a simple sensation does not differ, qua consciousness, from consciousness of a world: the "being in consciousness" is entirely the same in both; their difference lies solely in their content', he seems to me not to be keeping apart quite distinct notions of consciousness and content, and to be erecting his identification into an epistemological principle. We have explained the sense in which we too teach that all multiplicity of consciousness depends on content. Content must mean experience, a real part of consciousness: consciousness itself must be the complex formed by experiences. The world, however, never is a thinker's experience. To refer to the world may be an experience, but the world itself is the object intended. It is immaterial, from the point of view of our distinction, what attitude one takes up to the question of the make-up of objective being, of the true, real inner being of the world or of any other object, or of the relation of objective being, as a 'unity', to our 'manifold' thought-approaches, or of the sense in which one may metaphysically oppose immanent to transcendent being. The distinction in question is prior to all metaphysics, and lies at the very gates of the theory of knowledge: it presupposes no answers to the questions that + +this theory must be the first to provide. + +§ 15 Whether experi en ces of one and the same phenomenologi cal ki nd (of the ge nus feeling in particular) can consist partly of acts and partly + +of non -acts + +A new difficulty arises in regard to the generic unity of intentional experiences. It might be thought that the standpoint from which we divide experiences into intentional and non-intentional, is a merely external one, that the same experiences, or experiences of the same phenomenological class, may at times have an intentional relation to some object, and at times have none. The examples used to attest either concept, and also, in part, the attempted solutions of the problem, have already been discussed in literary fashion in + +regard to the debated issue as to whether the 'intentional relation' suffices to demarcate 'psychical phenomena' (the domain of psychology) or not. The debate centred chiefly in phenomena from the sphere of feeling. Since the intentionality of other feelings seemed obvious, two doubts were possible: one wondered whether intentionality might not perhaps attach loosely to the acts of feeling in question, belonging really to the presentations fused with them, or whether intentionality could be essential to the class of feelings, since one allowed it to some feelings while denying it to others. The connection between this commonly debated question and our present question + +has thus been made clear. + +We must first see whether any sorts of feeling-experience are essentially intentional, and then whether other sorts of feeling-experience lack this property. + +(a) Are there any intentional feelings? + +Many experiences commonly classed as 'feelings' have an undeniable, real relation to something objective. This is the case, e.g., when we are pleased by a melody, displeased at a shrill blast etc. etc. It seems obvious, in general, that every joy or sorrow, that is joy or sorrow about something we think of, is a directed act. Instead of joy we can speak of pleased delight in something, instead of sorrow we can speak of displeased or painful dislike of it, + +aversion from it etc. etc. + +Those who question the intentionality of feeling say: Feelings are mere states, not acts, intentions. Where they relate to objects, they owe their + +relation to a complication with presentations. + +No intrinsic objection is involved in this last position. Brentano who defends the intentionality of feelings, also maintains without inconsistency that feelings, like all acts that are not themselves presentations, have presentations as their foundations.20 We can only direct ourselves feelingly to objects that are presented to us by inwoven presentations. No difference emerges between the disputing parties until someone is really prepared to maintain that feeling, considered in itself, involves nothing intentional, that it does not point beyond itself to a felt object, that only its union with a presentation gives it a certain relation to an object, a relation only intentional by way of this connection and not intrinsically so. This is just what the other + +party disputes. + +Brentano thinks we have here two intentions built on one another: the underlying, founding intention gives us the presented object, the founded intention the feZt object. The former is separable from the latter, the latter inseparable from the former. His opponents think there is only one intention + +here, the presenting one. + +Ifwe subject the situation to a careful phenomenological review, Brentano's conception seems definitely to be preferred. Whether we tum with pleasure to something, or whether its unpleasantness repels us, an object is presented. + +But we do not merely have a presentation, with an added feeling associatively tacked on to it, and not intrinsically related to it, but pleasure or distaste direct themselves to the presented object, and could not exist without such a direction. If two psychical experiences, e.g. two presentations, are associated in an objective-psychological sense, there is a phenomenologically discernible type of associative unity among the reproduced experiences which corresponds to the objective dispositions which govern them. Side by side with the intentional elation which each has to its object, there is also a phenomenological mode of connection: one idea, e.g. that of Naples, carries with it the idea of Vesuvius, the one is peculiarly bound up with the other, so that we say in regard to the objects presented - the mode of their presentation here essentially requires further description - that the one reminds us of the other. (This sentence is being used to express a phenomenological situation.) It is easily seen, however, that though all this in a sense constitutes a new intentional relationship, it does not tum each associated member into an object of the other's intention. The intentional relationships remain unconfused in their association. How indeed could they furnish an object, borrowed from an associated intention, to something not itself intentional? It is clear, further, that such a phenomenologically associative relation is extrinsic, not at all to be put on a level with the relation of pleasure to the pleasant. The presentation which reproduces is quite possible without such a reproductive function. But pleasure without anything pleasant is unthinkable. And it is unthinkable, not because we are here dealing with correlative expressions, as when we say, e.g. , that a cause without an effect, or a father without a child, is unthinkable, but because the specific essence of pleasure demands a relation to something pleasing. Just so the feature known as conviction is unthinkable apart from something of which we are convinced. There is, similarly, no desire whose specific character can do without something desired, no agreement or approval without something agreed on or approved etc. etc. These are all intentions, genuine acts in our sense. They all 'owe' their intentional relation to certain underlying presentations. But it is part of what we mean by such 'owing' that they themselves + +really now have what they owe to something else. + +It is plain, too, that the relation between founding (underlying) presentation and founded act cannot be correctly described by saying that the former produces the latter. We say that the object arouses our pleasure, just as we say in other cases that some circumstance inspires doubt, compels agreement, provokes desire etc. But the result of such apparent causation, the pleasure, doubt or agreement provoked, is itself through and through intentional. We are not dealing with an external causal relation where the effect conceivably could be what it intrinsically is without the cause, or where the cause brings something forth that could have existed independently. + +Closer consideration shows it to be absurd in principle, here or in like cases, to treat an intentional as a causal relation, to give it the sense of an + +empirical, substantial-causal case of necessary connection. For the intentional object, here thought of as ' provocative', is only in question as an intentional, not as an external reality, which really and psycho-physically determines my mental life. A battle of centaurs, seen in a picture or framed in fancy, 'provokes' my approval just like some beautiful, real landscape: if I look on the latter psycho-physically as the real cause of my mentally provoked state of pleasure, this 'causation' is altogether different from the causation we have when we see the visible landscape - in virtue of such and such a mode of appearing and such and such pictured colours and forms - as the 'source', 'ground' or 'cause' of my pleasure. Pleasantness or pleasure do not belong as effect to this landscape considered as a physical reality, but only to it as appearing in this or that manner, perhaps as thus and thus judged of or as reminding us of this or that, in the conscious act here in question: it is as such that the landscape 'demands', 'arouses' such + +feelings.21 + +(b) Are there non-intentional feelings? Distinction between + +feeling-sensations and feeling-acts + +We may now ask more generally whether, in addition to the intentional varieties of feeling, there are not other non-intentional species. It may seem at first that an obvious 'Yes' is the right answer. In the wide field of socalled sensory feelings, no intentional characters can be found. The sensible pain of a burn can certainly not be classed beside a conviction, a surmise, a volition etc. etc., but beside sensory contents like rough or smooth, red or blue etc. If we recall such pains, or any sensory pleasures (the fragrance of a rose, the relish of certain foods etc. etc.), we find that our sensory feelings are blended with the sensations from the various sense-fields, just as these + +latter are blended with one another. + +Every sensory feeling, e.g. the pain of burning oneself or of being burnt, is no doubt after a fashion referred to an object: it is referred, on the one hand, to the ego and its burnt bodily member, on the other hand, to the object which inflicts the burn. In all these respects there is conformity with other sensations: tactual sensations, e.g., are referred in just this manner to the bodily member which touches, and to the external body which is touched. And though this reference is realized in intentional experiences, no one would think of calling the referred sensations intentional. It is rather the case that our sensations are here functioning as presentative contents in perceptual acts, or (to use a possibly misleading phrase) that our sensations here receive an objective 'interpretation' or 'taking-up'. They themselves are not acts, but acts are constituted through them, wherever, that is, intentional characters like a perceptual interpretation lay hold of them, and as it were animate them. In just this manner it seems that a burning, piercing, boring pain, fused as it is from the start with certain tactual sensations, must + +itself count as a sensation. It functions at least as other sensations do, in + +providing a foothold for empirical, objective interpretations. + +All this seems unobjectionable, and the whole question disposed of. We seem to have shown that some feelings are to he reckoned among intentional + +experiences, while others are non-intentional. + +But we are led to doubt, then, whether two such sorts of 'feelings' really form a single class. We spoke previously of 'feelings' of liking and dislike, of approval and disapproval, of valuation and disvaluation - experiences obviously akin to theoretical acts of assent and rejection, of taking something to be probable or improbable, or to deliberative acts of judgemental or voluntary decision etc. Here we have a kind, a plain unity of essence, which included nothing but acts, where such sensations of pain and pleasure have no place: descriptively the latter belong, in virtue of their specific essence, among tactual, gustatory, olfactory and other sensations. Being at best presentative contents of objects of intention, but not themselves intentions, they manifest descriptive differences so essential, that we cannot seriously believe in the unity of a genuine class. In both cases of course, we speak of 'feelings', i.e. in the case of the above-mentioned acts of liking as in the case of the above-mentioned sensations. This fact need not perplex, any more than our ordinary talk of 'feeling' , in the sense of touching, need lead us + +astray in the case of tactile sensations. + +Brentano has already pointed to the ambiguity here dealt with, in discussing the intentionality of feelings. He draws a distinction, in sense if not in words, between sensations of pain and pleasure (feeling-sensations) and pain and pleasure in the sense of feelings. The contents of the former - or, as I should simply say, the former22 - are in this terminology 'physical', while the latter are 'psychical phenomena' , and they belong therefore to essentially different genera. This notion I regard as quite correct, but only doubt, whether the meaning of the word 'feeling' does not lean predominantly towards 'feeling-sensation', and whether the many acts we call 'feelings' do not owe their name to the feeling-sensations with which they are essentially interwoven. One must of course not mix up questions of suitable terminology with questions regarding the factual correctness of Brentano's distinction. Our distinction should constantly be kept in mind and fruitfully applied in analysing all complexes of feeling-sensations and feeling-acts. Joy, e.g., concerning some happy event, is certainly an act. But this act, which is not merely an intentional character, but a concrete and therefore complex experience, does not merely hold in its unity an idea of the happy event and an act-character of liking which relates to it: a sensation of pleasure attaches to the idea, a sensation at once seen and located as an emotional excitement in the psycho-physical feeling-subject, and also as an objective property - the event seems as if bathed in a rosy gleam. The event thus pleasingly painted now serves as the first foundation for the joyful approach, the liking for, the being charmed, or however one's state may be described. A sad event, + +likewise, is not merely seen in its thinglike content and context, in the respects which make it an event: it seems clothed and coloured with sadness. The same unpleasing sensations which the empirical ego refers to and locates in itself - the pang in the heart - are referred in one's emotional conception to the thing itself. These relations are purely presentational: we first have an essentially new type of intention in hostile repugnance, in active dislike etc. Sensations of pleasure and pain may continue, though the act-characters built upon them may lapse. When the facts which provoke pleasure sink into the background, are no longer apperceived as emotionally coloured, and perhaps cease to be intentional objects at all, the pleasurable excitement may linger on for a while: it may itself be felt as agreeable. Instead of representing a pleasant property of the object, it is referred merely to the + +feeling-subject, or is itself presented and pleases. + +Much the same holds in the sphere of desire and volition.23 If difficulty is felt in the fact that desire does not always seem to require conscious reference to what is desired, that we are often moved by obscure drives or pressures towards unrepresented goals, and if one points especially to the wide sphere of natural instinct, where goal-consciousness is at least absent at the start, one may say: This is a case of mere sensations - we may speak analogically of 'desire-sensations' - without needing to affirm the existence of an essentially new class of sensations - i.e. of experiences really lacking intentional reference, and so also remote in kind from the essential character of intentional desire. Alternatively one may say: Here we are dealing with intentional experiences, but with such as are characterized by indeterminateness of objective direction, an 'indeterminateness' which does not amount to a privation, but which stands for a descriptive character of one's presentation. The idea we have when 'something' stirs, when there is a rustling, a ring at the door, etc. , an idea had before we give it verbal expression, has indeterminateness of direction, and this indeterminateness is of the intention's essence, it is determined as presenting an indeterminate + +'something' . + +Our one concept of desire might fit many cases, and our other concept others, and we might have to allow, not a relation of generic community between intentional and non-intentional urges or desires, but one of mere + +equivocation. + +We must observe, also, that our classification is oriented to the concretely complex, and that the total character of such unities may at one time seem to depend on sensational features (e.g. pleasure on urge-sensations), at another on act-intentions which rest on these. The formation and use of our expressions will at times therefore point to sensory contents, at times to + +act-intentions, so giving rise to the equivocations in question. + +Additional Note. The obvious tendency of our conception is to attribute primary, genuine differences in intensity to underlying sensations, and to concrete acts only in a secondary manner, in so far as their concrete total + +character involves differences of intensity in their sensational basis. Actintentions, the inseparable aspects which give acts their essential distinctive peculiarities, or which characterize them severally as judgements, feelings etc., must be without intrinsic intensity. Deeper analyses are, however, re- + +quired here. + +§ 16 Distinction between descri ptive and + +intentional content + +We have buttressed our notion of the essence of acts against objection, and given them a generic unity of essence in their character as intentions, as consciousnesses in the unique descriptive sense. We now introduce an important phenomenological distinction, obvious after our previous discussions, between + +the real (reellen)24 and the intentional content of an act. + +By the real phenomenological content of an act we mean the sum total of its concrete or abstract parts, in other words, the sum total of the partial experiences that really constitute it. To point out and describe such parts is the task of pure descriptive psychological analysis operating from an empirical, natural-scientific point of view. Such analysis is in all cases concerned to dismember what we inwardly experience as it in itself is, and as it is really (reell) given in experience, without regard either to genetic connections, or to extrinsic meaning and valid application. Purely descriptive psychological analysis of an articulated sound-pattern finds only sounds and abstract parts or unifying forms of sounds, it finds no sound-vibrations or organs of hearing etc.; it also never finds anything that resembles the ideal sense that makes the sound-pattern to be a name, nor the person to whom the name may apply. Our example suffices to make our intention clear. The real (reell) contents of acts are of course only known through descriptive analyses of this kind. That obscurities of intuition or inadequacies of descriptive conception - faults, in short, of method - may lead to much 'manufacture' of sensations (to use Volkelt's phrase) cannot be denied. This, however, only concerns the legitimacy of particular cases of descriptive analysis. It is clear, if anything is clear, that intentional experiences contain distinguishable parts and aspects, and this alone is of importance here. Let us now shift from our natural-scientific, psychological standpoint to an ideal-scientific, phenomenological one. We must exclude all empirical interpretations and existential affirmations, we must take what is inwardly experienced or otherwise inwardly intuited (e.g. in pure fancy) as pure experiences, as our exemplary basis for acts of Ideation. We must ideate universal essences and essential connections in such experiences - ideal Species of experiencing of differing levels of generality, and ideally valid truths of essence which apply a priori, and with unlimited generality, to possible experiences of these species. We thus achieve insights in a pure phenomenology which is here oriented to real (reellen) constituents, whose descriptions are + +in every way 'ideal' and free from 'experience', i.e. from presupposition of real existence. When we speak simply of the real (reellen), and in general of the phenomenological analysis and description of experiences, the tie-up of our discussions to psychological material is (we must keep on stressing) merely transitional, since none of its empirically real (reellen) conceptions and assertions of existence (e.g. of experiences as states of animal beings having experiences in a real (realen), space-time world) are at all operative, that pure phenomenological validity of essence is aimed at and claimed.2s Content in the real (reellen) sense is the mere application of the most general notion of content, valid in all fields to intentional experiences. If we now oppose intentionaP6 to real (reell) content, the word shows that the peculiarity of intentional experiences (or acts) is now in question. Here, however, there are several concepts, all grounded in the specific nature of acts, which may be equally covered by the rubric 'intentional content', and are often so covered. We shall first have to distinguish three concepts of the intentional content: the intentional object of the act, its intentional material (as opposed to its intentional quality) and, lastly its intentional essence. These distinctions will become familiar in the course of the following very general analyses, which are also essential to the more restricted aim of clarifying the + +essence of knowledge. + +§ 17 The intentional content in the sense of the + +intentional object + +Our first concept of intentional content needs no elaborate preliminaries. It concerns the intentional object, e.g. a house when a house is presented. That the intentional object does not generally fall within the real (reellen) content of an act, but rather differs completely from this, has been already discussed. This is not only true of acts pointing intentionally to 'outer' things; it is also true in part of acts that point to our own present experiences, as when I speak of, e.g., my actually present, but 'background' conscious experiences. Partial coincidence is only found where an intuition actually points to something 'lived through' in the intentional act itself, as, e.g., in acts of + +adequate perception. + +We must distinguish, in relation to the intentional content taken as object of the act, between the object as it is intended, and the object (period) which is intended. In each act an object is presented as determined in this or that manner, and as such it may be the target of varying intentions, judgemental, emotional, desiderative etc. Known connections, actual or possible, entirely external to the reality of the act, may be so cemented with it in intentional unity as to be held to attribute objective properties to the same presented object, properties not in the scope of the intention in question. Many new presentations may arise, all claiming, in virtue of an objective unity of knowledge, to be presenting the same object. In all of them the object which we + +intend is the same, but in each our intention differs, each means the object in a different way. The idea, e.g., of the German Emperor, presents its object as an Emperor, and as the Emperor of Germany. The man himself is the son of the Emperor Frederick III, the grandson of Queen Victoria, and has many other properties neither named nor presented. One can therefore quite consistently speak of the intentional and extra-intentional content of the object of some presentation, and one can use many other suitable, nontechnical expressions, e.g. what we intend in the object, that would not lead + +to misunderstandings. + +Another, yet more important, distinction goes with the distinction just drawn, that between the objective reference of the act, taken in its entirety, and the objects to which its various partial, constituent acts refer. Each act has its own appropriate, intentional, objective reference: this is as true of complex as of simple acts. Whatever the composition of an act out of partial acts way be, if it is an act at all, it must have a single objective correlate, to which we say it is 'directed', in the full, primary sense of the world. Its partial acts (if they really are acts entering the complex act as parts, and not mere parts of this act) likewise point to objects, which will, in general, not be the same as the object of the whole act, though they may occasionally be the same. In a secondary sense, no doubt, the whole act may be said to refer to these objects also, but its intention only terminates on them inasmuch as its constituent acts primarily intend them. Or, seen from the other side, they are only the act's objects in so far as they help to make up its true object, in the manner in which this is intended. They function as terms of relations in which the primary object is seen as the correlated term. The act, e.g., corresponding to the name 'the knife on the table' is plainly complex: the object of the whole act is a knife, of one of its part-acts, a table. But, as the whole nominal act refers to the knife as on the table, presents it in this relative position to the latter, one can say that the table is in a secondary sense an intentional object of the whole act. Again, to illustrate another important class of cases, the knife is the object about which we judge or make a statement, when we say that the knife is on the table; the knife is not, however, the primary or full object of the judgement, but only the object of its subject. The full and entire object corresponding to the whole judgement is the state of affairs judged: the same state of affairs is presented in a mere presentation, wished in a wish, asked after in a question, doubted in a doubt etc. The wish that the knife were on the table, which coincides (in object) with the judgement, is concerned with the knife, but we don't in it wish the knife, but that the knife should be on the table, that this should be so. The state of affairs must obviously not be confused with the judging of it, nor with the presentation of this judgement: I plainly do not wish for a judgement, nor for any presentation. Just so there is a corresponding question regarding the knife, but the knife is not (nonsensically) what we ask; we ask regarding the knife's position on the table, whether this actually is the case. + +So much for the first sense in which we speak of intentional contents. Since such talk is so highly ambiguous, we shall do well never to speak of an intentional content where an intentional object is meant, but to call the latter the + +intentional object of the act in question. + +§ 18 Simple and complex, founding and founded acts We have so far only learnt to attach one meaning to the term 'intentional contents'. Further meanings will develop in our ensuing investigations, where we shall attempt to seize on certain important peculiarities of the phenomenological essence of acts, and to throw light on the ideal unities rooted in these. We start with the difference, previously noted, between simple and compound acts. Not every unitary experience compounded out of acts is for that reason a compound act, just as every concatenation of machines is not a compound machine. Our comparison illuminates our further requirements. A compound machine is a machine compounded out of machines, but so compounded, that it has a total performance into which the performances of the partial machines flow, and the like is the case in regard to compounded acts. Each partial act has its particular intentional reference, each its unitary object, and its way of referring to it. These manifold part-acts are, however, summed up in one total act, whose total achievement lies in the unity of its intentional reference. To this the individual acts contribute their individual performances: the unity of what is objectively presented, and the whole manner of the intentional reference to it, are not set up alongside of the partial acts, but in them, in the way in which they are combined, a way which realizes a unity of act, and not merely a unity of experience. The object of this total act could not appear as it does, unless the partial acts presented their objects in their fashion: their general function is to present parts, or to present externally related terms, or to present relational forms of the object etc. The same is true of the non-presentative aspects of the act that make out of the unified qualities in the partial acts the quality of whole acts, and so determine the specifically different ways in which the objects concerned in either sort of act are 'taken up into + +consciousness' . + +We may take as an example the unity of categorical or hypothetical predication, where the total acts are plainly put together out of partial acts. The subject-member of a categorical assertion is an underlying act, a positing of a subject, on which the positing of a predicate, its attribution or denial, reposes. Just so the antecedent of a hypothetical assertion is constituent in a clearly demarcated part-act, upon which the conditional assertion is built. The total experience is in each case plainly one act, one judgement, whose single, total object is a single state of affairs. As the judgement does not exist alongside of, or between, the subject-positing and the predicating acts, but exists in them as their dominant unity, so, on the correlative side, the + +objective unity is the state of affairs judged, an appearance emergent out of + +subject and predicate, or out of antecedent and consequent. + +The situation may be yet more complex. On such a structured act (whose members may themselves be further structured) a new act may be built, e.g. a joy may be built on the assertion of a state of affairs, a joy in that state of affairs. The joy is not a concrete act in its own right, and the judgement an act set up beside it: the judgement rather underlies the joy, fixes its content, realizes its abstract possibility for, without some such foundation, there could be no joy at all.27 Judgements may similarly serve as foundations for surmises, doubts, questions, wishes, acts of will etc., and the latter acts may likewise serve to found other acts in their turn. There are therefore manifold ways in which acts may be combined into total acts. The briefest consideration makes plain that there are deep differences in the ways in which acts are concretely woven into other acts, or based upon underlying acts, and made possible by such concretion: the systematic investigation of such ways, even in descriptive, psychological fashion, is as yet hardly in its beginnings. + +§ 19 The fu nction of attention in complex acts. Instance of the phenomenological re lation of verbal + +sound to sense + +How far differences go in this direction will be plain from an example previously considered: the whole which is formed by expression and sense.28 This will be quite as interesting as the examples just analysed. Further considerations will also illustrate the obvious to anyone, the fact that there are great differences in the energy, so to speak, with which acts assert themselves in an act-complex. Generally the greatest energy will be displayed by the act-character which comprehends and subsumes all partial acts in its unity - whether it be a particular act-intention like joy, or a form of unity that pervades all parts of the whole act. In this act, we live, as it were, principally; in the subordinate acts only in proportion to the importance of their achievements for the whole act and its intention. But plainly to talk of such differences of importance, is just to use other words to cover the 'preferential living' in question, which some acts enjoy and others not. Let us now consider our example. It concerns a union of the acts in which an expression, treated as a sensuous verbal sound, is constituted, with the quite different act constitutive of its meaning, an essentially different connection, we may note, to that of the last-mentioned acts with the acts in which they have an immediate or a more remote intuitive fulfilment. Not only is the mode of union here essentially different, but also the energy with which certain acts are performed. The expression is indeed perceived, but our interest does not live in this perception; we attend, when not distracted, to the signified rather than the signs. Dominant energy resides in the sensegiving acts. The intuitive acts which perhaps accompany, and are inwoven + +into the total act's unity, lending it evidence, or illustrating it, or otherwise functioning in it, absorb our dominant interest in varying degree. They may be prominent, as in the perceptual judgement, or the analogously constituted picture-judgement, where our one wish is to express the perception or imagination in which we live, and likewise in the completely evident judgement of necessary law. They may recede and come to seem quite subsidiary, as in cases of imperfect or wholly unsuitable illustration of some dominant thought. They may then be a vanishing phantasm, to which practically no interest attaches. (In extreme cases one may even doubt whether accompanying picture-ideas really enter the unity of the expressive act at all, whether they are not mere accompaniments; coexisting with the acts in question but + +not forming a single act with them.) + +For us it is especially important to get as much clarity as we can on this situation of expressions: we shall therefore dwell on some points in more + +detail. + +Expression and sense are two objective unities, laid before us by certain acts. An expression itself, e.g. a written word, is, as our First Investigation showed,29 as much a physical object as any penscratch or ink-blot on paper. It is 'given' to us in the same sense as a physical object, i.e. it appears, and that it appears merely means, as it means elsewhere, that a certain act is experienced, in which certain sensory experiences are 'apperceived' in a certain manner. The acts in question are naturally perceptual or imaginative presentations: in these the expression (as physically meant) is constituted. What make the expression an expression are, we know, the acts attaching to it. These are not outside of it or beside it, or merely simultaneous in consciousness; they are one with it, and so one, that we can scarce avoid regarding them all as making up a unitary total act. (By the word 'expression' we mean, with natural and convenient looseness, the act-unity which presents it.) A statement, an assertion, e.g., we should at once say, is a strictly unitary experience, which belongs to the genus Judgement. We do not find in ourselves a mere sum of acts, but a single act in which, as it were, a bodily and spiritual side are distinct. Just so an expressed wish is no mere ensemble of expression and wish - with perhaps an additional, debatable judgement regarding the wish - but a whole, an act, which we unhesitatingly call a wish. The physical expression, the verbal sound, may seem unessential to this unity, and it is unessential inasmuch as any other verbal sound might have replaced it and done duty for it: it could even have been wholly dispensed with. But if it is there, and serves as a verbal sound, it will be fused with the accompanying acts in a single act. Plainly the connection is in a certain sense extrinsic, since the expression as such, i.e. the manifest verbal sound or written sign etc., is not seen as part of the object meant in the whole act, nor even as really determining it, nor as having really to do with it. The contribution made by the acts constituting the verbal sound of a statement, differs characteristically from the contribution of the underlying + +acts illustrated and discussed above, or of the partial acts which pertain to the predicative members of complete predications. We must not, however, despite all this, question the presence of a certain intentional linkage between word and thing. Inasmuch, e.g., as the word names the thing, it once more appears as in some sense one with it, as belonging to it, even if not as materially part of it, or one of its material properties. Its material unrelatedness does not exclude a certain intentional unity, correlated with the interconnection of the corresponding acts to form a single act. This is confirmed if we recall the deep-set tendency to exaggerate the bond between word and thing, to invest it with objectivity, perhaps even to insinuate some- + +thing of mystic unity into it. [Cf. Inv. VI, §6 ff] + +In the compound act which includes both appearing-expression and sensegiving acts, it is plainly the latter, or the act-unity which dominates both, which essentially fixes the character of the whole act. It is for this reason that we call experiences, whether expressed or unexpressed, by the same names: i.e., 'judgement', 'wish', etc. Certain acts in the compound are therefore peculiarly prominent, a fact incidentally noted when we said that, when we normally express something, we do not, qua expressing it, live in the acts constituting the expression as a physical object - we are not interested in this object - but we live in the acts which give it sense: we are exclusively turned to the object that appears in such acts, we aim at it, we mean it in the special, pregnant sense. We pointed out, also, that, while a special orientation to the physical expression is possible, it essentially changes the character of our experience: this no longer is 'expressive' in the ordinary sense of the word. Plainly we are here concerned with a case of the general fact of attention, + +to which long effort has not yet brought sufficient clearness.3 + +o Nothing has + +so hindered right views in this field as the by-passing of the fact that attention is an emphatic function which belongs among acts in the above defined sense of intentional experiences, and which is not descriptively graspable as long as 'being experienced', in the sense of the mere existence of a content in consciousness, is confused with intentional objectivity. Acts must be present, before we can live in them or be absorbed in performing them, and when we are so absorbed (in various manners requiring further description) we mind the objects of these acts, we are primarily or secondarily oriented towards them, perhaps thematically concerned with them. Absorption in acts and + +minding objects are the same thing expressed from different angles. + +As opposed to this, men speak of attention as if it were a name for modes of special relief imparted to experienced contents. At the same time there is still talk of these contents (the contemporary experiences themselves) as if they were the things to which we ordinarily say we are attending. We do not of course dispute the possibility of attending to experienced contents, but when this happens, such contents become objects of internal perception: such perception is not the mere being of the content in a conscious setting, but an act in which the content is rendered objective. Intentional objects of + +acts, and only intentional objects, are the things to which we are at any time attentive, and to which we can be so attentive. This accords with ordinary usage, whose true sense should be plain on the briefest reflection. To ordinary usage the objects of attention are always objects of inward or outward perception, objects of memory, of expectation, perhaps states of affairs in a scientific discussion, etc. Certainly we can only speak of attention where what we attend to is 'in consciousness' . What is not a 'content of consciousness' cannot attract or hold attention nor become a theme of consciousness. The danger of this obvious truth lies in the equivocal term 'content of consciousness'. For the obvious truth does not mean that attention is necessarily directed to conscious contents in the sense of experiences, as if no one could attend to things, and to other real (reale) or ideal objects, which are not experiences. It means, rather, that there must be a basic act in which what we attend to becomes objective, becomes presented in the widest sense of this word. Such presentation can be non-intuitive as well as intuitive, can be utterly inadequate as much as adequate. One might, however, consider, from another angle, whether the preference an act enjoys over its fellows when we 'live' in it, when we are primarily or secondarily 'turned' towards its objects, are perhaps 'specially concerned' with them, should itself be reckoned as an act. Such a view would make all dominant facts eo ipso complex. Should we not rather regard the phenomena of attention as mere ways requiring much more detailed description of their several varieties - in which + +acts may be carried out? This would seem to be undoubtedly right. + +But we do not wish to work out a 'theory' of attention here, but to discuss the important role played by it in complex acts, in putting certain actcharacters into relief, and so essentially influencing the phenomenological + +pattern of these acts. + +§20 The difference between the qual ity and the + +matter of an act + +We now turn from the distinction between the acts in which we 'live' and the acts which proceed 'on the side', to another extremely important, seemingly plain distinction lying in a quite different direction. This is the distinction between the general act-character, which stamps an act as merely presentative, judgemental, emotional, desiderative etc., and its 'content' which stamps it as presenting this, as judging that etc. etc. The two assertions '2 x 2 = 4' and 'Ibsen is the principal founder of modern dramatic realism', are both, qua assertions, of one kind; each is qualified as an assertion, and their common feature is their judgement-quality. The one, however, judges one content and the other another content. To distinguish such 'contents' from other notions of 'content' we shall speak here of the matter (material) of judgements. We shall draw similar distinctions between quality and matter + +in the case of all acts. + +Under the rubric of 'matter' we shall not divide, and then reassemble in unity, constituents of an act such as the subject-act, the predicate-act etc.: this would make the unified total content the act itself. What we here have in mind is something totally different. Content in the sense of 'matter' is a component of the concrete act-experience, which it may share with acts of quite different quality. It comes out most clearly if we set up a series of identical utterances, where the act-qualities change, while the matter remains identical. All this is not hard to provide. We recall familiar talk to the effect that the same content may now be the content of a mere presentation, now of a judgement, now of a question, now of a doubt, a wish etc. etc. A man who frames the presentation 'There are intelligent beings on Mars' frames the same presentation as the man who asserts 'There are intelligent beings on Mars', and the same as the man who asks 'Are there intelligent beings on Mars?', or the man who wishes 'If only there are intelligent beings on Mars!' etc. etc. We have deliberately written out the closely correspondent expressions in full. To be alike in 'content', while differing in act-quality has its visible grammatical expression; the harmony of grammatical forms + +points the way to our analysis. + +What do we mean by the 'same content'? Plainly the intentional objectivity of the various acts is the same. One and the same state of affairs is presented in the presentation, put as valid in the judgement, wished for in the wish, asked about in the question. This observation does not, however, go far enough, as we shall now show. In real (reell) phenomenological treatment, objectivity counts as nothing: in general, it transcends the act. It makes no difference what sort of being we give our object, or with what sense or justification we do so, whether this being is real (real) or ideal, genuine, possible or impossible, the act remains 'directed upon' its object. If one now asks how something non-existent or transcendent can be the intentional object in an act in which it has no being, one can only give the answer we gave above, which is also a wholly sufficient one. The object is an intentional object: this means there is an act having a determinate intention, and determinate in a way which makes it an intention towards this object. This 'reference to an object' belongs peculiarly and intrinsically to an actexperience, and the experiences manifesting it are by definition intentional experiences or acts.31 All differences in mode of objective reference are descrip- + +tive differences in intentional experiences. + +We must note, however, that this peculiarity revealed in the phenomenological essence of acts, of directing themselves to a certain object and not another, will not exhaust the phenomenological essence in question. We spoke of differences in mode of objective reference, but this lumps together totally distinct, independently variable differences. Some are differences in act-quality, as when we speak of such different ways of being intentional as being presented, being judged, being asked etc. Such variation intersects with the other, wholly independent variation in objective reference: one act + +may point to this, another to that object, regardless as to whether the acts are alike or different in quality. Every quality can be combined with every objective reference. This second variation therefore points to a second side in + +the phenomenological content of acts, differing from their quality. + +In the case of this latter variation, which concerns the changing direction to objects, one does not speak of different 'manners of objective reference', + +though the differentia of this direction lies in the act itself. + +Looking more closely, we see another possibility of variation independent of quality which certainly prompts talk of different ways of referring to objects. We see, too, that the twofold variation just distinguished is not quite in a position to effect a neat separation of what must be defined as 'matter' from quality. Our distinction posited two sides in every act: its quality, which stamped it as, e.g., presentation or judgement, and its matter, that lent it direction to an object, which made a presentation, e.g., present this object and no other. This is quite right, and yet is to some extent misleading. For one is at first tempted to interpret the situation simply: matter is that part of an act which gives it direction to this object and no other. Acts are therefore unambiguously determined by their quality, on the one hand, and by the object they will intend, on the other. This seeming obviousness is, however, delusive. One can readily see, in fact, that even if quality and objective direction are both fixed at the same time, certain variations remain possible. Two identically qualified acts, e.g. two presentations, may appear directed, and evidently directed, to the same object, without full agreement in intentional essence. The ideas equilateral triangle and equiangular triangle differ in content, though both are directed, and evidently directed, to the same object: they present the same object, although 'in a different fashion'. The same is true of such presentations as a length of a + b units and a length of b + a units; it is also true of statements, in other respects synonymous, which differ only in 'equivalent' concepts. The same holds if we compare other types of equivalent assertions, e.g. We shall have rain and The weather is becoming rainy. If we consider a series of acts like the judgement It will rain today, the surmise It may well rain today, the question Will it rain today? and the wish Oh that it would rain today!, we see that it exemplified identity not only as regards objective reference in general, but also as regards a new sense of objective reference, a sense not fixed by the + +quality of the act. + +Quality only determines whether what is already presented in definite fashion is intentionally present as wished, asked, posited in judgement etc. The matter, therefore, must be that element in an act whichfirst gives it reference to an object, and reference so wholly definite that it not merely fixes the object meant in a general way, but also the precise way in which it is meant.3 + +2 + +The matter - to carry clearness a little further - is that peculiar side of an act's phenomenological content that not only determines that it grasps the object but also as what it grasps it, the properties, relations, categorial forms, + +that it itself attributes to it. It is the act's matter that makes its object count as this object and no other, it is the objective, the interpretative sense (Sinn der gegenstiindlichen Auffassung, Auffassungssinn) which serves as basis for the act's quality (while indifferent to such qualitative differences). Identical matters can never yield distinct objective references, as the above examples prove. Differences of equivalent, but not tautologically equivalent expressions, certainly affect matter. Such differences must not be thought to correspond to any fragmentation of matter: there is not one piece of matter corresponding to an identical object, another to the differing mode of presenting it. Reference to objects is possible a priori only as being a definite + +manner of reference: it arises only if the matter is fully determined. + +To this we may add an observation: act-quality is undoubtedly an abstract aspect of acts, unthinkable apart from all matter. Could we hold an experience possible which was a judging without definite subject-matter? This would take from the judgement its character as intentional experience, + +which is evidently part of its essence. + +The same holds of matter. A matter that was not matter for presentation, nor for judgement, nor for ... etc. etc., would be held to be unthinkable. Talk about the manner of objective reference is ambiguous: at times it points to differences of quality, at times to differences of matter. We shall henceforth counteract such ambiguity by suitable locutions involving the + +terms 'quality' and 'matter' . That such' + +talk has yet other important mean- + +ings will appear in due course. [Cf. the enumeration in Inv. VI, §27 below] + +§2 1 The intent ional and the semantic esse nce + +We shall postpone investigation of the difficult problems here involved, to treat of a new distinction, in which a new concept of intentional content arises, which has to be separated off from the full descriptive content of + +the act. + +In each act's descriptive content we have distinguished quality and matter as two mutually dependent aspects. If both are taken together, it would at first seem, the act in question will merely have been reconstituted. Looked at more closely, however, another conception distinguishes itself from whose point of view the two aspects, brought to unity, do not make up the concrete, complete act. Two acts may in fact agree in respect of their quality and their matter, and yet differ descriptively. In so far as quality and matter now count for us (as will be shown later) as the wholly essential, and so never to be dispensed with, constituents of an act, it would be suitable to call the union of both, forming one part of the complete act, the act's intentional essence. To pin down this term, and the conception of the matter it goes with, we simultaneously introduce a second term. To the extent that we deal with acts, functioning in expressions in sense-giving fashion, or capable of so functioning - whether all acts are so capable must be considered later - + +we shall speak more specifically of the semantic essence of the act. The ideational abstraction of this essence yields a 'meaning' in our ideal sense. In justification of our conceptual ruling, we may point to the following new series of identifications. We may say generally, and with good sense, that a man may, at different times, and that several men may, at the same or different times, have the same presentation, memory, expectation, perception, utter the same assertion or wish, cherish the same hope etc. etc.33 To have the same presentation means, but does not mean as much as, having a presentation of the same object. The presentation I have of Greenland's icy wastes certainly differs from the presentation Nansen has of it, yet the object is the same. Just so the ideal objects straight line and shortest line are identical, but the presentations - 'straight' being suitably defined - + +different. + +Talk about the same presentation, judgement etc. points to no individual sameness of acts, as if my consciousness were in some way conjoined with someone else's. It also means no relation of perfect likeness, of indiscernibility as regards inner constituents, as if the one act merely duplicated the other. We have the same presentation of a thing, when we have presentations in which the thing is not merely presented, but presented as exactly the same: following our previous treatment we may add 'presented with the same interpretative sense' or 'based on the same matter'. In our 'essence' we really have the same presentation despite other phenomenological differences. Such essential identity comes out most clearly when we reflect how presentations function in forming higher acts. For essential identity can be equivalently defined if we say: Two presentations are in essence the same, if exactly the same statements, and no others, can be made on the basis of either regarding the presented thing (either presentation being taken alone, i.e. analytically). The same holds in regard to other species of acts. Two judgements are essentially the same judgement when (in virtue of their content alone) everything that the one judgement tells us of the state of affairs judged, would also be told us by the other, and nothing more is told us by either. Their truth-value is identical, and this is clear to us when 'the' judgement, the intentional essence uniting judgement-quality and judgement-matter, is + +the same. + +Let us now be quite clear that the intentional essence does not exhaust the act phenomenologically. An imaginative presentation, qualified as merely imaginative, is unessentially altered in manner, if the fulness and vividness of the sensuous contents helping to build it up is increased or decreased, or, objectively put, if the object now appears with greater clearness and definiteness, now becomes lost in a mist, now becomes paler in colour etc. Whether or not one here assumes intensive differences, whether one concedes or denies a basic likeness between the sensory phantasms here present and the sensational elements in perception, all this makes little difference to the absolute qualities, forms etc. of the act, in so far as the act's intention, its + +meaning, stays unchanged, identically determined (identity of matter). We attribute these changes, not to the object, but to its 'appearance'; we 'mean' the object as constant and persistent, and we 'mean' this in merely 'feigning' fashion (identity of quality). As opposed to this, the matter of a unitary presentation changes if its object is given as changing (despite any overreaching form of unity to which the intentional object's identity-in-variety corresponds). The same is true when new features enrich our conception of an object, which is constantly before consciousness, features not previously part of the object's intentional content, of the object of our presentation as such. The case of perception is similar. If many persons share the 'same' percept, or repeat a previous one, we have merely an identity of matter, of intentional essence, which does not at all exclude change in the descriptive content of the experience. The same holds of the variable part played, or that can be played, by imagination in perception, in the putting of a perceived object before us. Whether or not images of the back of the cigarette-box float in front of me, with this or that degree of fulness, steadiness and vividness, is quite irrelevant to the essential content, the interpretative sense of my percept, to that side of it, in short which, suitably understood, explains and justifies talk of the 'same percept' in opposition to a multiplicity of phenomenologically distinct perceptual acts. In each of such cases the object is presupposed as identical, is seen clothed with the same array of properties: it is 'meant' or 'apprehended' and posited in perceptual fashion. A percept may, further, have the same matter as a flight of fancy: the latter may present an object or state of affairs in imagination as being 'just the same' as it is perceptually apprehended in the percept. Nothing may be objectively ascribed in the one case which is not likewise ascribed in the other. Since the quality of the presentation may be identical (e.g. in the case of memory), we see that the specific differences of intuitive acts do not + +depend on their intentional essence. + +Much the same may be said of any sort of act. Many persons cherish the same wish, when their optative intention is the same. This wish may in one person be fully expressed, in another unexpressed, in one person it may bring to full intuitive clarity its basic presentative content, in another it may be more or less 'notional' etc. In each case the identity of essence plainly lies in the two aspects distinguished above, in an identity of act-quality and of matter. The same may be claimed for expressive acts, for the acts in particular which lend meaning to expressions: as said above by anticipation, their semantic essence, i.e. the really present (reel!) phenomenological correlate of + +their meaning, coincides with their intentional essence. + +We may confirm our notion of semantic essence (the act of meaning in concreto) by recalling the series of identities used above in Investigation I (§1 2) in order to draw a distinction between a unity of meaning and a unity of object, and the numerous examples of expressive experience which there illustrated our general notion of intentional essence. The identity of 'the' + +judgement or of 'the' statement consists in an identity of meaning repeated as the same in the many individual acts, and represented in them by their semantic essence. This leaves room for important descriptive difference in regard to other constituents of these acts, as we have pointed out in detail.34 + +Appendix to § I I and §20 + +Critique of the =0'. A sign, whether it depicts or names, is called the + +'representation' ('presentation') of what it stands for. + +Our present talk of representation (which we do not wish to erect into a fixed terminology) relates to objects. These 'representative objects' are constituted in certain acts, and acquire a representative character for new objects in certain new acts of transcendent (hinausdeutenden) presentation. Another, more primitive sense of 'representation' was mentioned under (1): this made 'representatives' experienced contents receiving an objectifying interpretation in such representation, and in this manner helping to present + +objects, without becoming objective themselves. + +This leads to a new ambiguity. + +9. The distinction between perception and imagination (which latter itself shows important descriptive differences) is always confused with the distinction between sensations and images. The former is a distinction of acts, the latter of non-acts, which receive interpretation in acts of perception or imagination. (If one wishes to call all contents which are in this sense 'representative', 'sensations', we shall have to have the distinct terms 'impressional' and 'reproductive sensations'.) If there are essential descriptive differences between sensations and images, if the usually mentioned + +differences of liveliness, constancy, elusiveness etc., are sufficient, or if a varying mode of consciousness must be brought in, cannot be discussed here. Anyhow we are sure that possible distinctions of content do not make up the difference between perception and imagination, which analysis shows, with indubitable clarity, to be a difference of acts qua acts. We cannot regard what is descriptively given in perception or imagination as a mere complex of experienced sensations or images. The all too common confusion between them is, however, grounded in the fact that at one time a 'presentation' is understood as an imaginative idea (in the sense of (6) and (7)), at another time as a corresponding image (the complex of represen- + +tative contents or imagery), so that a new ambiguity arises. + +10. The confusion between an appearance (e.g., a concrete imaginative experience or a 'mental picture'), and what appears in it, leads us to call the presented object a presentation (idea). This applies to perceptions, and generally to presentations in the sense of mere intuitions or logically interpreted + +intuitions, e.g. 'The world is my idea' . + +II. The notion that all conscious experiences (contents in the real (reellen)4 phenomenological sense) are 'in consciousness', in the sense of inner perception or some other inner orientation (consciousness, original apperception), and that with this orientation a presentation is eo ipso given (consciousness or the ego represents the content to itself), led to all contents of consciousness being called 'presentations'. These are the 'ideas' of the English empiricist philosophy since Locke. (Hume calls them 'perceptions'.) To have an experience and to experience a content: these expressions are often used as + +equivalent. + +In logic it is very important to separate the specifically logical concepts of presentation (idea) from other concepts of it. That there are several such concepts has already been indicated in passing. We may again mention one not included in our list so far, Bolzano's notion of the 'presentation in itself', which we interpreted as equal to every independent or dependent + +part-meaning within a complete assertion. + +In connection with all purely logical concepts of presentation, we must, on the one hand, distinguish the ideal presentation from the real (realen)4 one, e.g. the nominal presentation in the purely logical sense and the acts in which it is realized. And, on the other hand, we must distinguish between the mere meaning-intentions and the experiences which fulfil them more or + +less adequately, i.e. presentations in the sense of intuitions. + +13. Beside the aforementioned ambiguities, whose danger is obvious to all who seriously absorb themselves in the phenomenology of the thoughtexperiences, there are others which are in part less important. We may for instance mention talk of presentation (idea) in the sense of Opinion (56�a). This is an ambiguity which arose through gradual transformations as occurs in all similar terms. I recall the verbally manifold, but always equivalent + +§45 The 'presentational content' + +Expressions correlative to 'presentation' naturally have a correspondent ambiguity. This is particularly the case in regard to talk about 'what is presented in a presentation' , i.e. about the 'content' of a presentation. That a mere distinction between content and object of presentations, like the one recommended by Twardowski following Zimmerman, will not remotely suffice - however meritorious it may have been to dig down to any formdifferences in this field - is clear from our analyses up to this point. In the logical sphere - to which these authors limit themselves without being aware of their limitation - there is not one thing which can be distinguished as 'content' from the object named; there are several things which can and must be so distinguished. Above all, we can mean by 'content', in the case, e.g., of a nominal presentation, its meaning as an ideal unity: the presentation in the sense of pure logic. To this corresponds, as a real (reelles) moment in the real (reellen) content of the presentative act, the intentional essence with its presentative quality and matter. We can further distinguish, in this real (reellen) content, the separable contents not belonging to the intentional essence: the 'contents' which receive their interpretation in the act-consciousness (in the intentional essence), i.e. the sensations and images. To these are again added, in the case of many presentations, variously meant differences of form and content: particularly important is here the difference of matter (in a totally new sense) and categorial form, with which we shall have to concern ourselves a great deal. With this is connected the by no means univocal talk concerning the content of concepts: content = sum total of 'properties', in distinction from their mode of combination. How dubious 'blanket' talk about 'content' can be, when we merely oppose act, content and object, is shown by the difficulties and confusions into which Twardowski fell, and which have in part been exposed above. We may point particularly to his talk of 'presentative activity moving in two directions', his complete ignoring of meaning in the ideal sense, his psychologistic elimination of plain differences· of meaning by recourse to etymological distinctions and, lastly, his treatment of the doctrine of 'intentional inexistence' and the doc- + +trine of universal objects. + +Note. In recent times a view has often been expressed which denies the difference between presentation and presented content, or at least denies its phenomenological ostensibility. One's attitude to this rejection naturally depends on one's interpretation of the words 'presentation' and 'content'. If these are interpreted as the mere having of sensations and images, and the phenomenological moment of interpretation is ignored or discounted, it is right to deny a distinct act of presentation: presentation and presented are one and the same. The mere having of the content, as a mere experiencing of an experience, is no intentional experience, directing itself upon an object + +by way of an interpretative sense: it is, in particular, not an introspective percept. For this reason we identified a sensation with a sensational content. But can anyone doubt, once he has distinguished the various concepts of presentation, that a concept so delimited is impossible to sustain, and has arisen merely through a misinterpretation of original, intentional notions of presentation? However the notion of presentation is defined, it is universally seen as a pivotal concept, not only for psychology, but also for epistemology and logic, and particularly for pure logic. A man who admits this, and yet bases himself on the above rejection, has eo ipso involved himself in confusion. For this concept has no part to play in epistemology and pure + +logic. + +Only through this confusion can I explain how a thinker as pentrating as v. Ehrenfels, on occasion maintained (Zeitschr. f Psychologie u. Physiologie der Sinnesorgane, XVI, 1898) that we cannot dispense with a distinction between act and content of presentation since without it we should be unable to state the psychological difference between the presentation of an object A, and the presentation of a presentation of this object. For the rest, he informs us, he has no direct assurance of the existence of such a phenomenon. I myself should say that an act of presentation is as such directly intuited, precisely where this distinction between a presentation and a presentation of this presentation is phenomenologically drawn. Were there no such cases, no earthly argument could possibly provide an indirect justification of the distinction in question. Just so, I believe, we have directly established the existence of an act of presentation in becoming clear as to the difference between a mere sound-pattern and the same pattern understood + +as a name etc. + +Volume II, Part 2 of the Second German Edition + +Fo rewo rd to the second edition + +The present new edition of the final part of my Logical Investigations does not correspond, unfortunately, with the notice in the Preface added in 1913 to the first volume of the Second Edition. I was forced to a decision to publish the old text, only essentially improved in a few sections, instead of the radical revision of which a considerable portion was already in print at the time. Once again the old proverb came true: that books have their destinies. The exhaustion naturally consequent on a period of overwork first forced me to interrupt the printing. Theoretical difficulties that had made themselves felt as the printing progressed, called for revolutionary transformations of the newly planned text, for which fresher mental powers were necessary. In the war years which followed, I was unable to muster, on behalf of the phenomenology of logic, that passionate engagement without which fruitful work is impossible for me. I could only bear the war and the ensuing 'peace' by absorption in the most general philosophical reflections, and by again taking up my works devoted to the methodological and material elaboration of the Idea of a phenomenological philosophy, to the systematic sketch of its foundations, to the arrangement of its work-problems and the continuation of such concrete investigations as were in these connections indispensable. My new teaching activity at Freiburg favoured a direction of my interest to dominant generalities and to system. Only very recently have these systematic studies led me back into the territories where my phenomenological researches originated, and have recalled me to my old work on the foundations of pure logic which has so long awaited completion and publication. Divided as I am between intensive teaching and research, it is uncertain when I shall be in a position to adapt my oid writings to the advances since made, and to recast their literary form. It is also uncertain whether I shall use the text of the Sixth Investigation for this purpose, or shall give my plans, whose content already goes far beyond the + +text, the form of an entirely new book. + +As things stand, I have yielded to the pressures of the friends of the present work, and have decided to make its last part once more accessible, + +The First Section, that I could not revise in detail without endangering the style of the whole, I have allowed to be reprinted practically verbatim. But in the Second Section on Sensibility and Understanding by which I set particular store, I have, on the other hand, continually intervened to improve the form of the text. I remain of the opinion that the chapter on 'Sensuous and Categorial Intuition', together with the preparatory arguments of the preceding chapters, has opened the way for a phenomenological clarification of logical self-evidence (and eo ipso of its parallels in the axiological and practical sphere). Many misunderstandings of my Ideas towards a Pure Phenomenology would not have been possible had these chapters been attended to. Quite obviously, the immediacy of the vision of universal essences spoken of in the Ideas, implies, like the immediacy of any other categorial intuition, an opposition to the mediacy of a non-intuitive, e.g. an emptily symbolic thought. But people have substituted for this immediacy, the immediacy of intuition in the ordinary sense of the word, just because they were unacquainted with the distinction, fundamental to any theory of reason, of sensible and categorial intuition. I think it shows something about the contemporary state of philosophical science that straightforward statements of such incisive meaning, presented in a work that for nearly two decades has been much attacked, but also much used, should have remained + +without noticeable literary effect. + +The position is similar in the case of the textually improved chapter on 'The A Priori Laws of Authentic and Inauthentic Thinking'. It at least offers a blueprint for the first radical worsting of psychologism in the theory of Reason. This blueprint makes its 'breakthrough' within the framework of an Investigation exclusively concerned with formal logic, and is therefore restricted to the Reason of formal logic. With how little deep attention this chapter is read, is shown by the often heard, but to my mind grotesque reproach, that I may have rejected psychologism sharply in the first volume of my work, but that I fell back into psychologism in the second. It does not affect what I have said to add that, after twenty years of further work, I should not write at many points as I then wrote, and that I do not approve of much that I then wrote, e.g. the doctrine of categorial representation. Nonetheless, I think I can say that even the immature and misguided elements in my work deserve a close pondering. For everything and all that is there said, derives from a research which actually reaches up to the things themselves, which orients itself towards their intuitive self-givenness, and which also has that eidetic-phenomenological attitude to pure consciousness through which alone a fruitful theory of reason becomes possible. Anyone who here, as also in the Ideas, wishes to grasp the sense of my arguments, must not be afraid of considerable efforts, including the efforts of 'bracketing' his own notions and convictions upon the same, or the putatively same, themes. These efforts are demanded by the nature of the things themselves. + +One who is not afraid, will find sufficient opportunity for improving on my positions and, if he cares to, for censuring their imperfections. Only if he entrenches himself in a superficial reading drawn from an extraphenomenological sphere of thought, will he refuse to attempt this, if he is not to be disavowed by all who truly understand the matter. How readily many authors employ critical rejections, with what conscientiousness they read my writings, what nonsense they have the audacity to attribute to me and to phenomenology, are shown in the Allgemeine Erkenntnislehre of Moritz Schlick. On page 121 of this work it is said that my Ideas 'asserts the existence of a peculiar intuition, that is not a real psychical act, and that if someone fails to find such an "experience ", which does not fall within the domain of psychology, this indicates that he has not understood the doctrine, that he has not yet penetrated to the correct attitude of experience and thought, for this requires "peculiar, strenuous studies" '. The total impossibility that I should have been able to utter so insane an assertion as that attributed to me by Schlick in the above italicized sentences, and the falsity of the rest of his exposition of the meaning of phenomenology, must be plain to anyone familiar with this meaning. Of course I have always repeated my demand for 'strenuous studies' . But not otherwise than, e.g., the mathematician demands them of anyone who wishes to share in talk of mathematical matters, or who even presumes to criticize the value of mathematical science. In any case, to devote less study to a doctrine than is necessary to master its meaning, and yet to criticize it, surely violates the eternal laws of the literary conscience. No amount of learning in natural science or psychology or historical philosophies, will make it unnecessary to make these efforts in penetrating into phenomenology, or can do more than lighten them. Everyone, however, who has made these efforts, and who has risen to a very seldom exercised lack of prejudice, has achieved an indubitable certainty regarding the givenness of its scientific foundation and the inherent justification of the method demanded by it, a method which here, as in other sciences, renders possible a common set of conceptually definite work-problems, as well as definite decisions as to truth or falsehood. I must expressly observe that, in the case of M. Schlick, one is not dealing with irrelevant slips, but with sense-distorting substitutions on which all his criti- + +cism is built up. + +Mter these words of defence, I must also observe, in regard to Section 111, that I changed my position on the problem of the phenomenological interpretation of interrogative and optative sentences shortly after the first edition of the work, and that there would be no place for small revisions, which were all that could be undertaken at the time. The text therefore remained unaltered. I could be less conservative as regards the much used Appendix on 'External and Internal Perception' . Though the text's essential content has been preserved, it now appears in a considerably improved form. + +The desideratum of an Index for the whole work could unfortunately not be realized, since my promising pupil, Dr Rudolf Clemens, who had under- + +taken to prepare it, had died for his country. + +E. HUSSERL + +Freiburg-im-Breisgau, October 1920 + +Investigation VI + +Elements of a + +phenomenological + +elucidation of knowledge + +Introduction + +Our last Investigation may have seemed at first to lose itself in remote questions of descriptive psychology: it has, however, been of considerable help in our attempted elucidation of knowledge. All thought, and in particular all theoretical thought and knowledge, is carried on by way of certain 'acts', which occur in a context of expressive discourse. In these acts lies the source of all those unities-of-validity which confront the thinker as objects of thought and knowledge, or as the explanatory grounds and principles, the theories or sciences of the latter. In these acts, therefore, lies the source, also, of the pure, universal Ideas connected with such objects, whose ideally governed combinations pure logic attempts to set forth, and whose elucidation is the supreme aim of epistemological criticism. Plainly we shall have gone far in our elucidation of knowledge, once we have established the phenomenological peculiarities of acts as such, that much debated, little understood class of experiences. By putting our logical experiences into this class, we shall have taken an important step towards the demarcation of an analysis which will 'make sense' of the logical sphere and of the fundamental concepts which concern knowledge. In the course of our Investigation we were led to distinguish various concepts of content which tend to become confusedly mixed up whenever acts, and the ideal unities pertaining to acts, are in question. Differences which had already struck us in our First Investigation, in the narrower context of meanings and of acts conferring meaning, appeared once more in a wider context and in the most general forms. Even the highly noteworthy notion of content, that of 'intentional essence', which emerged as a novel gain from our last Investigation, was not without this relation to the logical sphere: for the same series of identities, previously employed to illustrate the unity of meaning, now yielded, suitably generalized, a certain identity, that of 'intentional essence', which applied to all acts whatsoever. By thus linking up, or subordinating, the ideal unities and phenomenological characters of the logical realm, to the quite general characters and unities of the sphere of acts, we importantly deepened our phenomenological and critical understanding of the former. + +The investigations carried out in the last chapter, basing themselves on the distinction of act-quality and act-material within the unity of intentional essence, again led us far into the zone of logical interest. We were forced to enquire into the relation of such intentional material to the presentational foundation essential to every act, and were compelled to hold apart several important, constantly confounded concepts of presentation, and so to work out a fundamental part of the 'theory of judgement'. Here as elsewhere a vast amount remains to be done: we have barely made a beginning. + +We have not yet even been successful in our more immediate task, that of laying bare the source of the Idea of Meaning. Undeniably and importantly, the meaning of expressions must lie in the intentional essence of the relevant acts, but we have not at all considered the sorts of acts that can thus function in meaning, and whether all types of acts may not be in this respect on a level. But when we seek to tackle this question, we at once encounter as the next paragraphs will demonstrate - the relation between meaningintention and meaning-fulfilment, or to speak traditionally, and in fact ambiguously, the relation between 'concept' or 'thought' on the one hand, understood as mere meaning without intuitive fulfilment, and 'correspond- + +ing intuition', on the other. + +It is most important that this distinction, touched on even in our First Investigation, should be most minutely explored. In carrying out the appropriate analyses and, in the first instance, attaching them to the simplest naming-intentions, we at once perceive that our whole treatment calls for a natural extension and general circumscription. The widest class of acts, in which we meet with distinctions between intention and intention-fulfilment (or intention-frustration), extends far beyond the logical sphere. This is itself demarcated by a peculiarity in the relation of fulfilment. A class of acts - those known as 'objectifying' - are in fact marked off from all others, in that the fulfilment-syntheses appropriate to their sphere have the character of knowings, of identifications, of a 'putting-together' of things congruent, while their syntheses of frustration, similarly, have the correlative character of a setting apart of things conflicting. Within this widest sphere of objectifying acts, we shall have to study all the relations relevant to the unity of knowledge. We shall not have to limit ourselves to the fulfilment of such peculiar meaning-intentions as attach to our verbal expressions, since similar intentions also turn up without grammatical support. Our intuitions, further, themselves mostly have the character of intentions, which + +both require, and very often sustain a further fulfilment. + +We shall provide a phenomenological characterization of the quite general notions of signification and intuition in relation to the phenomena of fulfilment, and we shall pursue the analysis of various sorts of intuition, starting with sensuous intuition, an enquiry basic to the elucidation of knowledge. We shall then embark upon the phenomenology of the varying degrees of knowledge, giving clearness and definite form to a related series + +of fundamental epistemological concepts. Here certain novel notions of content, barely glanced at in our previous analyses, will take the centre of the stage: the concept of intuitive content and the concept of representing (interpreted) content. We shall range the notion of epistemic essence alongside of our previous notion of intentional essence, and within the former we shall draw a distinction between intentional quality and intentional matter, the latter being divided into interpretative sense, interpretative form and interpreted (apperceived, or representing) content. We shall thereby pin down the concept of Interpretation (Auffassung) or Representation, as the unity of + +material and representing content by way of interpretative form. + +In connection with the graded transition from intention to fulfilment, we shall recognize distinctions of greater or less mediacy in an intention itself, which exclude straightforward fulfilment, and which require rather a graded sequence of fulfilments: this will lead to an understanding of the allimportant, hitherto unclarified sense of talk about 'indirect presentations'. We then follow up the differences of greater or lesser adequacy of intention to the intuitive experiences which fuse with it, and which fulfil it in knowledge, and point to the case of an objectively complete adequacy of the one to the others. In this connection we strive towards an ultimate phenomenological clarification of the concepts of Possibility and Impossibility (harmony, compatibility - conflict, incompatibility), and of the ideal axioms relating to these. Bringing back into consideration the act-qualities that we have for a while neglected, we then deal with the distinction, applicable to thetic acts, of a provisional and a final fulfilment. This final fulfilment represents an ideal of perfection. It always consists in a corresponding percept (we of course take for granted a necessary widening of the notion of perception beyond the bounds of sense). The synthesis of fulfilment achieved in this limiting case is self-evidence or knowledge in the pregnant sense of the word. Here we have being in the sense of truth, 'correspondence' rightly understood, the adaequatio rei ac intellectus: here this adaequatio is itself given, to be directly seized and gazed upon. The varying notions of truth, which all must be built up on one single, selfsame phenomenological situation, here reach complete clearness. The same holds of the correlative ideal of imperfection and therefore of the case of absurdity, and as regards the 'conflict' and the non-being, + +experienced therewith, of falsehood. + +The natural course of our Investigation, which at first only concerns itself with such intentions as are meanings, has as a consequence that our treatments all begin with the simplest meanings, and in so doing abstract from formal differences among such meanings. The complementary Investigations of our Second Section will then make these differences their main theme, and will at once lead to a totally new concept of matter or material, to a basic contrast between sensuous stuff and categorial form or - abandoning an objective for a phenomenological stance - to a contrast between sensuous and categorial acts. In close connection with this last, we have the important + +distinction between sensuous (real) and categorial objects, determinations, combinations etc., regarding which last it becomes clear that they can only be 'perceptually' given in acts which are founded upon other acts, and in the last resort, on acts of sensibility. In general we may say that the intuitive, and accordingly likewise the imaginative, fulfilment of categorial acts, is founded on acts of sense. Mere sense, however, never fulfils categorial acts, or intentions which include categorial forms: fulfilment lies rather, in every case, in a sensibility structured by categorial acts. With this goes an unavoidable extension of the originally sense-turned concepts of intuition and perception, which permits us to speak of categorial and, in particular, of universal intuition. The distinction between sensuous and purely categorial abstraction then leads to a distinction between sensuous concepts and categories. The old epistemological contrast between sensibility and understanding achieves a much-needed clarity through a distinction between straightforward or sensuous, and founded or categorial intuition. The same is true of the contrast between thinking and seeing (intuiting), which confuses philosophical parlance by confounding the relations of signification to fulfilling intuition, on the one hand, with the relations of sensuous and categorial acts, on the other. All talk of logical form concerns what is purely categorial in the meanings and meaning-fulfilments in question. But the 'matter' of logic, the 'intention' of terms, itself admits, through a graded superimposition of categorial intentions, of distinctions of matter and form, so that the logical antithesis of matter and form points the way to a readily understandable + +'relativization' of our absolute distinction. + +We shall end the main body of this Investigation by discussing the factors which limit freedom in the actual categorial shaping of given matter. We shall become aware of the analytic rules of authentic thinking which, grounded in pure categories, do not depend on the specificity of their materials. Similar factors limit thought in the inauthentic sense, i.e. pure acts of meaning to the extent that they might lend themselves to authentic cases of expression, resting on a priori principles and not dependent on subject-matters to be expressed. From this demand springs the function of the laws of authentic + +thinking to provide norms for our acts of mere meaning. + +We raised a question at the beginning of this Investigation as to the natural circumscription of sense-giving and sense-fulfilling acts: this is answered by ranging such acts under objectifying acts, and by subdividing the latter into acts of signification and acts of intuition. Having successfully clarified the phenomenological relations which concern fulfilment, we are at last in a position to evaluate the arguments for, and the arguments against, Aristotle's view of optative and imperative sentences as special cases of predication. The last section of the present Investigation is devoted to clearing + +up this controversial issue. + +The aims just sketched are not the final, highest aims of a phenomenological elucidation of knowledge in general. Our analyses, comprehensive as they + +are, leave untilled the extremely fruitful field of mediate thought and knowledge: the nature of mediate evidence, and of its correlated idealia, remains insufficiently illuminated. We consider, however, that our aims have not been too trivial, and we hope that we may have dug down to the genuinely first, underlying foundations of a critique of knowledge. Even such a critique demands of us an exercise of the modesty essential to all strict, scientific research. If this last aims at a real, full completion of the tasks at hand, if it has given up the dream of solving the great problems of knowledge by merely criticizing traditional philosophemes or by probable argumentation, if it has at last seen that matters can be advanced and transformed only by getting to close grips with them, it must then also reconcile itself to tackling the problems of knowledge, not in their higher or their highest, and therefore their most interesting developments, but in their comparatively simplest forms, in the lowest grades of development accessible to us. That even such a modest epistemological enquiry has vastly many difficulties to surmount, that it has in fact still got all its achievements ahead of it, will become clear + +in the course of the ensuing analyses. + +First Section + +Objectifyi ng intentions and + +their fu lfilments: knowledge as + +a synthesis of fu lfilment and its + +gradations + +Chapter I + +Meaning-intention and + +mean i ng-fu Ifil ment + +§ I Whether eve ry type of me ntal act, or only certai n + +types, can fu nction as carri ers of meaning + +We shall now go on with the question raised in our Introduction: whether meaning-something is exclusively the prerogative of certain restricted sorts of mental acts. It might seem at first plain that no such restrictions can exist, and that any and every act might operate in sense-giving fashion. For it seems plain that we can verbally express acts of every kind - whether presentations, judgements, surmises, questions, wishes etc. - and that, when we do this, they yield us the meanings of the forms of speech in question, the meanings of names, of statements, of interrogative or optative sentences etc. The opposite view can, however, lay claim to the same obviousness, particularly in a form that restricts meanings to a single, narrow class of acts. All acts are certainly expressible, if language is sufficiently rich, each has its own appropriate speech-form: sentence-forms, e.g., differentiate themselves into indicative, interrogative, imperative etc., and among the first of these we have categorical, hypothetical, disjunctive and other sentence-forms. In each case the act, in so far as it achieves expression in this or that speechform, must be known for the sort of act it is, the question as a question, the wish as a wish, the judgement as a judgement etc. This will apply also to the partial acts constitutive of such acts, in so far as these too are expressed. Acts cannot, it seems, find their own appropriate expressive forms till their form and content have been apperceived and known. The expressive role in speech lies, accordingly, not in mere words, but in expressive acts: these create for the correlated acts to be expressed by them a new expressive material in which they can be given thinking expression, the general essence + +of which constitutes the meaning of the speech-form in question. + +A striking confirmation of this view seems to lie in the possibility of a purely symbolic functioning of expressions. The mental (geistige) expression, the thinking counterpart of the act to be expressed, attaches to the verbal expression, and can be brought to life by the latter even when the act itself is not performed by the person who understands the expression. We + +understand the expression of an act of perception without ourselves perceiving anything, of a question without ourselves asking anything etc. We experience more than the mere words, we enjoy the thought-forms or the expressions. In the opposed case, where the intended acts are themselves actually present, the expression comes to coincidence with what it has to express, the meaning which clings to the words fits itself into what it means, + +its thought-intention finds in the latter its fulfilling intuition. + +It is plainly in close connection with these opposed viewpoints that we have the old dispute as to whether or not the peculiar forms of interrogative, optative, imperative and similar sentences are to count as statements, and their meanings aS judgements. Aristotle's doctrine places the meaning of all complete sentences in the varied array of psychic experiences, experiences of judging, wishing, commanding and so forth. As against this, another more modem and increasingly influential doctrine locates meaning exclusively in our judgements (or in their purely presentative modifications). An interrogative sentence in a sense expresses a question, but only in so far as this question is realized to be a question, in so far as it is referred in thought to a speaker, and so judged to be his experience. And so similarly in other cases. Each meaning is, on this view, either a name-meaning or a propositional meaning, i.e. either the meaning of a complete indicative sentence or a possible part of such a meaning. Indicative sentences are here to be understood as predicative sentences, since judgements are, on this view, generally thought of as predicative acts: we shall see, however, that the controversy still has a sense even when judgements are looked on as positing acts in general. + +To find the right stance towards the questions here raised would call for more exact discussion than the above, superficial argumentations have attempted. It will become plain, when we look at the matter more closely, that the appeals to sheer obviousness on one side or the other conceal obscurity + +and even error. + +§2 That al l acts may be expressed does not decide the issue. There are two senses to tal k about + +express ing an act + +All acts it has been agreed are expressible. This cannot, of course, be questioned, but it does not therefore follow, as might be surreptitiously suggested, that all acts for that reason also function as carriers of meaning. Talk of 'expressing' is, as we argued earlier, I ambiguous, and it remains so even when we connect it with the acts to be expressed. What are expressed may be, on the one hand, said to be the sense-giving acts, to which, in the narrower sense, 'voice' is given. But' there are other acts which can also be said to be expressed, though this is the case, naturally, in a different sense. I refer here to the very frequent cases in which we name acts we are now experiencing, and through such naming manage to say that we are experiencing + +them. In this sense I 'express' a wish through the words 'I wish that ... ', a question through the words 'I am asking whether ... ', a judgement through the words 'I judge that .. .', and so on. Naturally we can pass judgement on our own inner experiences just as we can pass judgement on outward things and, when we do the former, the meanings of the relevant sentences will reside in our judgements upon such experiences, and not in the experiences themselves, our wishes, questions etc. Just so, the meanings of statements about external things do not reside in these things (the horses, houses etc.), but in the judgements we inwardly pass upon them (or in the presentations that help to build up such judgements). That the objects judged about in one case transcend consciousness (or purport to do so), in another case are taken to be immanent in consciousness, makes no real difference. Naturally when I express the wish that now fills me, it is concretely one with my act of judgement, but it does not really contribute to the latter. The wish is apprehended in an act of reflex perception, subsumed under the concept of wishing, and named by way of this concept and of the further determining presentation of the wish-content. Thus the conceptual presentation makes the same sort of direct contribution to the judgement about the wish (and the corresponding wish-name to the wish-statement), that the presentation of Man makes to a judgement about Man (or the name 'Man' to a statement about Man). Substitute for the subject word '1' in the sentence 'I wish that .. .' the relevant proper name, and the sense of the sentence remains unaffected in its remaining parts. It is, however, undeniable that the wishstatement can now be understood without change of sense by someone who hears it, and can be imitatively re-judged by him, even though he does not share the wish at all. We see, therefore, that, even when a wish chances to form a unity with an act of judgement directed upon it, it does not really form part of the meaning of the latter. A truly sense-giving experience can never be absent if the living sense of the expression is to survive change. It becomes clear, therefore, that the expressibility of all acts is without relevance to the question whether all acts can function in sense-giving fashion, so far, that is, as such 'expressibility' means no more than the possibility of making certain statements about such acts. For in this connection acts are + +just not functioning as carriers of meaning at all. + +§3 A third sense of tal k about the 'expression' of + +acts. Formulation of our theme + +We have just distinguished two senses in which there can be talk about 'acts expressed'. Either they are acts in which the sense, the meaning of the relevant expression is constituted, or they are acts that the speaker attributes to himself as items in his recent experience. This latter conception may be appropriately widened. Plainly the situation that it covers would not differ in any essential respect, were an expressed act not to be attributed to the + +experiencing ego, but to other objects, and it would not differ for any conceivable form of expression that really (reel!) named this act as something experienced, even if it did not do it so as to mark the act off as the subjector object-member of a predication. The main point is that the act, whether directly named or otherwise 'expressed', should appear as the actually present object of discourse (or of the objectifying, positing activity behind discourse), + +whereas this is not the case in regard to our sense-giving acts. + +There is a third sense of the same talk of 'expression' in which we deal, as in our second sense, with a judgement or other objectification related to the acts in question, but not with a judgement about the latter - not, therefore, with an objectification of these acts by way of presentations and namingacts which refer to them; we have rather a judgement grounded upon such acts, which does not demand their objectification. That I express my percept of something may, e.g. , mean that I attribute this or that content to it: it may also mean that I derive my judgement from my percept, that I do not merely assert but also perceive the matter of fact in question, and that I assert it as I perceive it. My judgement is not here concerned with the perceiving but with the thing perceived. By 'judgements of perception' tout + +court we generally mean judgements belonging to this last class. + +In a similar manner we can give expression to other intuitive acts, whether + +imaginings, remembering or expectations. + +In the case of utterances grounded on imagination we may indeed doubt whether a genuine judgement is present: it is in fact plain that this is not then present. We are here thinking of cases where we allow our imagination to 'run away' with us, and where we employ ordinary statements, appropriate to things perceived, in giving a name to what then appears to us, or of the narrative form in which story-tellers, novelists etc., 'express', not real circumstances, but the creations of their artistic fancy. As we saw in our last Investigation, we are here dealing with conformably modified acts which serve as counterparts which correspond to the actual judgements that might be expressed in the same words, just as intuitive imaginations correspond to perceptions, and perhaps also to rememberings and expectations. We shall + +leave aside all such distinctions for the present. + +In connection with the above class of cases, and in connection with the thereby defined new sense of 'expressed act', we wish to make clear the whole relation between meaning and expressed intuition. We wish to consider whether such an intuition may not itself be the act constitutive of meaning, or if this is not the case, how the relation between them may be best understood and systematically classified. We are now heading towards a more general question: Do the acts which give expression in general, and the acts which in general are capable of receiving expression, belong to essentially different spheres, and thereby to firmly delimited act-species? And do they nonetheless take their tone from an overarching, unifying genus of acts, in which all acts capable of functioning 'meaningfully', in the widest sense of the + +word - whether as meanings proper, or as 'fulfilments' of meanings - can be brought together and set apart, so that all other genera of acts can eo ipso, in law-governed fashion, be excluded from such functions? This, we may say, is the immediate aim of our Investigation. And as our considerations advance, there will be an obvious widening of our sphere of treatment so as to render self-evident the relation of the questions here raised to a general 'sensemaking' of knowledge. New and higher aims will then enter our field of view. + +§4 The express ion of a percept (,j udgement of perception'). Its meaning can not lie in perception, + +but must lie in pecul iar expressive acts + +Let us consider an example. I have just looked out into the garden and now give expression to my percept in the words: 'There flies a blackbird!' What is here the act in which my meaning resides? I think we may say, in harmony with points established in our First Investigation, that it does not reside in perception, at least not in perception alone. It seems plain that we cannot describe the situation before us as if there were nothing else in it - apart from the sound of the words - which decides the meaningfulness of the expression, but the percept to which it attaches. For we could base different statements on the same percept, and thereby unfold quite diff erent senses. I could, e.g., have remarked: 'That is black!', 'That is a black bird!', 'There flies that black bird!', 'There it soars!', and so forth. And conversely, the sound of my words and their sense might have remained the same, though my percept varied in a number of ways. Every chance alteration of the perceiver's relative position alters his percept, and different persons, who perceive the same object simultaneously, never have exactly the same percepts. No such differences are relevant to the meaning of a perceptual statement. One may at times pay special attention to them, but one's statement + +will then be correspondingly different. + +One might, however, maintain that this objection only showed meaning to be unaffected by such differences in individual percepts: it might still be held to reside in something common to the whole multitude of perceptual + +acts which centre in a single object. + +To this we reply, that percepts may not only vary, but may also vanish altogether, without causing an expression to lose all its meaning. A listener may understand my words, and my sentence as a whole, without looking into the garden: confident in my veracity, he may bring forth the same judgement without the percept. Possibly he is helped by an imaginative re-enactment, but perhaps this too is absent, or occurs in so mutilated, so inadequate a form, as to be no fit counterpart of what appears perceptually, + +at least not in respect of the features 'expressed' in my statement. + +But if the sense of a statement survives the elimination of perception, and is the same sense as before, we cannot suppose that perception is the act in + +which the sense of a perceptual statement, its expressive intention, is achieved. The acts which are united with the sound of our words are phenomenologically quite different according as these words have a purely symbolic, or an intuitively fulfilled significance, or according as they have a merely fancied or a perceptually realizing basis: we cannot believe that signification is now achieved in this sort of act, and now in that. We shall rather have to conceive that the function of meaning pertains in all cases to one and the same sort of act, a type of act free from the limitations of the perception or the imagination which so often fail us, and which, in all cases where an expression authentically 'expresses', merely becomes one with the act expressed. It remains, of course, incontestable that, in 'judgements of perception' , perception is internally related to our statements' sense. We have good reason to say: the statement expresses the percept, i.e. brings out what is perceptually 'given'. The same percept may serve as a foundation for several statements, but, however the sense of such statements may vary, it addresses itself to the phenomenal content of perception. It is now one, now another, part of our unified, total percept - a part, no doubt, in a non-independent, attributive sense - which gives our judgement its specific basis, without thereby becoming the true carrier of its meaning, as the possibility of eliminating percepts + +has just shown us. + +We must accordingly say: This 'expression ' of a percept - more objectively phrased, of a perceived thing as such - is no affair of the sound of words, but of certain expressive acts. 'Expression' in this context means verbal expression informed with its full sense, which is here put in a certain relation to perception, through which relation the latter is in its tum said to be 'expressed'. This means, at the same time, that between percept and sound of words another act (or pattern of acts) is intercalated. I call it an act, since the expressive experience, whether or not accompanied by a percept, always has an intentional direction to something objective. This mediating act must be the true giver of meaning, must pertain to the significantly functioning expression as its essential constituent, and must determine its possession of an identical sense, whether or not this is associated with a confirming percept. The rest of our investigation will show ever more clearly that our concep- + +tion is workable. + +§5 Contin uation. Percepti on as an act which determ ines meani ng, without embodyi ng it + +We can go no further without discussing a doubt which crops up at this point. Our treatment seems to demand a definite narrowing down: it appears to cover more than can be fully justified. If perception never constitutes the full meaning of a statement grounded on perception, it seems nonetheless to make a contribution to this meaning, and to do so in cases of the sort just dealt with. This will become clearer if we slightly modify our + +example, and instead of speaking quite indefinitely of a blackbird, proceed to speak of this blackbird. 'This' is an essentially occasional expression which only becomes fully significant when we have regard to the circumstances of utterance, in this case to an actually performed percept. The perceived object, as it is given in perception, is what the word 'this' signifies. The present tense in the grammatic form of a verb likewise expresses a relation to what is actually present, and so again to perception. Plainly the same holds of our original example: to say 'There flies a blackbird' is not to say that some blackbird in general is flying by, but that a blackbird is flying by + +here and now. + +It is clear, of course, that the meaning in question is not attached to the word-sound of 'this'; it does not belong among the meanings firmly and generally bound up with this word. We must, however, allow that the sense of a unified statement is to be found in the total act of meaning which in a given case underlies it - whether or not this may be completely expressed through the universal meanings of its words. It seems, therefore, that we must allow that perception contributes to the significant content of a judgement, in all cases where such perception gives intuitive presence to the fact to which our statement gives judgemental expression. It is of course a contribution that can perhaps also be made by other acts, in an essentially similar manner. The listener does not perceive the garden, but he is perhaps acquainted with it, has an intuitive idea of it, places the imagined blackbird and reported event in it, and so, through the mere picture-work of fantasy, achieves an understanding which follows the intention and which agrees in + +sense with the speaker's. + +The situation permits, however, of another reading. Intuition may indeed be allowed to contribute to the meaning of a perceptual statement, but only in the sense that the meaning could not acquire a determinate relation to the object it means without some intuitive aid. But this does not imply that the intuitive act is itself a carrier of meaning, or that it really makes contributions to this meaning, contributions discoverable among the constituents of the completed meaning. Genuinely occasional expressions have no doubt a meaning which varies from case to case, but in all such changes a common element is left over, which distinguishes their ambiguity from that of a casual equivocation.2 The addition of intuition has as effect that this common element of meaning, indeterminate in its abstraction, can determine itself. Intuition in fact gives it complete determinateness of objective reference, and thereby its last difference. This achievement does not entail that a part + +of the meaning must itself lie in the intuitive sphere. + +I say 'this', and now mean the paper lying before me. Perception is responsible for the relation of my word to this object, but my meaning does not lie in perception. When I say 'this' , I do not merely perceive, but a new act of pointing (of this-meaning) builds itself on my perception, an act directed upon the latter and dependent on it, despite its diff erence. In this pointing + +reference, and in it alone, our meaning resides. Without a percept - or some correspondingly functioning act - the pointing would be empty, without definite differentiation, impossible in the concrete. For of course the indeterminate thought of the speaker as pointing to something - which the hearer may entertain before he knows what object we wish to indicate by our 'this' - is not the thought we enact in the actual pointing, with which the determinate thought of the thing pointed to has been merely associated. One should not confuse the general character of actual pointing as such with the + +indefinite presentation of 'a certain' act of pointing. + +Perception accordingly realizes the possibility of an unfolding of my act of this-meaning with its definite relation to the object, e.g. to this paper before my eyes. But it does not, on our view, itself constitute this meaning, nor + +even part of it. + +In so far as the act-character of a pointing act is oriented to intuition, it achieves a definiteness of intention which fulfils itself in intuition, in accordance with a general feature of acts which may be called their intentional essence. For a pointing reference remains the same, whichever out of a multitude of mutually belonging percepts may underlie it, in all of which the same, and recognizably the same, object appears. The meaning of 'this' is again the same when, instead of a percept, some act from our range of imaginative presentation is substituted for it, an act presenting the same object through a picture in a recognizably identical manner. It changes, however, when intuitions from other perceptual or imaginative spheres are substituted. We are once more referring to a this, but the general character of the reference which obtains here, that of direct, attributively unmediated aiming at an object, is otherwise differentiated: the intention to another object attaches to it, just as physical pointing becomes spatially different + +with each change in spatial direction. + +We hold, therefore, that perception is an act which determines, but does not embody meaning. This view is confirmed by the fact that essentially occasional expressions like 'this' can often be used and understood without an appropriate intuitive foundation. Once the intention to an object has been formed on a suitable intuitive basis, it can be revived and exactly reproduced without the help of a suitable act of perception or imagination. Genuinely occasional expressions are accordingly much like proper names, in so far as the latter function with their authentic meaning. For a proper name also names an object 'directly' . It refers to it, not attributively, as the bearer of these or those properties, but without such 'conceptual' mediation, as what it itself is, just as perception might set it before our eyes. The meaning of a proper name lies accordingly in a direct reference-to-thisobject, a reference that perception only fulfils, as imagination does provisionally and illustratively, but which is not identical with these intuitive acts. It is just in this manner that perception gives an object to the word 'this' (where it is directed to objects of possible perception): our reference to 'this' + +is fulfilled in perception, but is not perception itself. And naturally the meaning of both types of directly naming expressions has an intuitive origin, from which their naming intentions first orient themselves towards an individual object. In other respects they are different. As 'this' is infected with the thought of a pointing, it imports (as we showed) a mediation and a complication, i.e. a peculiar form absent from the proper name. The proper name also belongs as a fixed appellation to its object; to this constant pertinence corresponds something in the manner of its relation to that object. This is shown in the fact of our knowing a person or thing by name, as something called so-and-so: I know Hans as Hans, Berlin as Berlin. We have, in our treatment, no doubt ignored the case of all those proper names which are significant in derivative fashion. When proper names have once been formed in direct application (and so on a basis of intuitions which give things to us), we can, by employing the concept of 'being called', itself formed by reflection on the use of proper names, give proper names to objects, or take cognizance of their proper names, even though such objects are not directly given or known to us, but are only described indirectly as the bearers of certain properties. The capital of Spain, e.g., is called (i.e. has the proper name) 'Madrid'. A person unacquainted with the town Madrid itself, thereby achieves both knowledge of its name and the power to name it correctly, and yet not thereby the individual meaning of the word 'Madrid'. Instead of the direct reference, which only an actual seeing of the city could arouse, he must make do with an indirect pointing to this reference, operating through characteristic ideas of properties and the conception of 'being + +called' such and such. + +If we may trust our arguments, we must not only draw a general distinction between the perceptual and the significant element in the statement of perception; we must also locate no part of the meaning in the percept itself. The percept, which presents the object, and the statement which, by way of the judgement (or by the thought-act inwoven into the unity of the judgement) thinks and expresses it, must be rigorously kept apart, even though, in the case of the perceptual judgement now being considered, they stand to each other in the most intimate relation of mutual coincidence, or in the unity of fulfilment. We need not dwell on the fact that a like result applies also to other intuitive judgements, and thus also to statements which, in a sense analogous to that which applies to perceptual judgements, 'express' the intuitive + +content of an imagination, a remembering, an expectation etc. + +Addendum. In the exposition of §26 of Investigation I we began with the understanding of the hearer, and drew a distinction between the 'indicating' (anzeigende) and the 'indicated' (angezeigte) meaning of an essentially occasional expression and, in particular, of the word 'this' . For the hearer, in whose momentary field of vision the thing that we wish to point out is perhaps not present, only this indefinitely general thought is at first aroused: + +Something is being pointed out. Only when a presentation is added (an intuitive presentation if the thing dealt with demands an intuitive pointing out), is a definite reference constituted for him, and so a full, authentic meaning for the demonstrative pronoun. For the speaker there is no such sequence: he has no need of the indefinitely referential idea which functions as 'index' for the hearer. Not the idea of an indication, but an indication itself, is given in his case, and it is eo ipso determinately directed thingward: from the first the speaker enjoys the 'indicated' meaning, and enjoys it in a presentative intention immediately oriented towards intuition. If the thing meant cannot be intuitively picked out, as in a reference to a theorem in a mathematical proof, the conceptual thought in question plays the part of an intuition: the indicative intuition could derive fulfilment from an actual re-living of this past thought. In each case we observe a duplicity in the indicative intention: the character of the indication seems in the first case to espouse the directly objective intention, as a result of which we have an intention directed upon a definite object that we are intuiting here and now. Our other case does not differ. If the previous conceptual thought is not now being performed, an intention which corresponds to it survives in memory; this attaches itself to the act-character of the indication, thereby lending it + +definiteness of direction. + +What we have just said about indicating and indicated meaning can have two meanings. It can mean (1) the two mutually resolving thoughts which characterize the hearer's successive understanding: first the indeterminate idea of something or other referred to by 'this', then the act of definitely directed indication into which a completing presentation transforms it. In the latter act we have the indicated, in the former the indicating meaning. (2) If we confine ourselves to the complete, definitely directed indication which the speaker has from the beginning, we can again see something double about it: the general character of indication as such, and the feature which determines this, which narrows it down to an indication of 'this thing there'. The former can again be called an indicating meaning, or rather the indicating element in the indissoluble unity of meaning, in so far as it is what the hearer can immediately grasp by virtue of its expressive generality, and can use to indicate what is referred to. If I say 'this', the hearer at least knows that something is being pointed at. (Just so in the case of other essentially occasional expressions. If I say 'here', I have to do with something in my nearer or further spatial environment, etc.) On the other hand, the true aim of my talk lies not in this general element, but in the direct intending of the object in question. Towards it and its fulness of content I am directed, and these empty generalities do little or nothing towards determining the latter. In this sense a direct intention is the primary, indicated + +meaning. + +This second distinction is the one laid down by our definition in our previous exposition. (Inv. 1, §26). The distinctions achieved in this section, + +and our much clearer treatment, will probably have helped towards a fur- + +ther clarification of this difficult matter. + +§6 The static un ity of expressive thought and expressed intuition. Recogn ition (dos Erkennen) + +We shall now absorb ourselves in a closer investigation of the relations holding among intuitive acts, on the one hand, and expressive acts, on the other. We shall confine ourselves, in the present section entirely, to the range of the simplest possible cases, and so naturally to expressions and significant intentions which belong to the sphere of naming. We shall make, for the rest, no claim to treat this field exhaustively. We are concerned with nominal expressions, which refer themselves in the most perspicuous of possible fashions to + +'corresponding' percepts and other forms of intuition. + +Let us first glance in this field at a relationship of static union, where a sense-giving thought has based itself on intuition, and is thereby related to its object. I speak, e.g., of my ink pot, and my inkpot also stands before me: I see it. The name names the object of my percept, and is enabled to name it by the significant act which expresses its character and its form in the form of the name. The relation between name and thing named, has, in this state of union, a certain descriptive character, that we previously noticed: the name 'my inkpot' seems to overlay the perceived object, to belong sensibly to it. This belonging is of a peculiar kind. The words do not belong to the objective context of physical thinghood that they express: in this context they have no place, they are not referred to as something in or attaching to the things that they name. If we turn to the experiences involved, we have, on the one hand, as said before/ the acts in which the words appear, on the other hand, the similar acts in which the things appear. As regards the latter, the inkpot confronts us in perception. Following our repeated demonstration of the descriptive essence of perception, this means no more phenomenologically then that we undergo a certain sequence of experiences of the class of sensations, sensuously unified in a peculiar serial pattern, and informed by a certain act-character of 'interpretation' (Auffassung), which endows it with an objective sense. This act-character is responsible for the fact that an object, i.e. this inkpot, is perceptually apparent to us. In similar fashion, the appearing word is constituted for us in an act of perception or + +imaginative presentation. + +Not word and inkpot, therefore, but the act-experiences just described, in which they make their appearance, are here brought into relation: in these word and inkpot appear, while yet being nothing whatever in the acts in question. But how does this happen? What brings these acts into unity? The answer seems clear. The relation, as one of naming, is mediated, not merely by acts of meaning, but by acts of recognition (Erkennen), which are here also acts of classification. The perceived object is recognized for an inkpot, + +known as one, and in so far as the act of meaning is most intimately one with an act of classification, and this latter, as recognition of the perceived object, is again intimately one with the act of perception, the expression seems to be + +applied to the thing and to clothe it like a garment. + +Ordinarily we speak of recognizing and classifying the object of perception, as if our act busied itself with this object. But we have seen that there is no object in the experience, only a perception, a thus and thus determinate mindedness (Zumutesein): the recognitive act in the experience must accordingly base itself on the act of perception. One must not of course misunderstand the matter, and raise the objection that we are putting the matter as if perception was classified rather than its object. We are not doing this at all. Such a performance would involve acts of a quite different, much more complex constitution, expressible through expressions of corresponding complexity, e.g. 'the perception of the inkpot' . It follows that the recognitive experience of this thing as 'my inkpot', is nothing but a recognition which, in a definite and direct fashion, fuses an expressive experience, + +on the one hand, with the relevant percept, on the other. + +The same holds of cases in which picture-presentations serve in place of percepts. The imaginatively apparent object, e.g. the identical inkpot in memory or in fancy, is felt to bear the expression which names it. This means, phenomenologically speaking, that a recognitive act in union with an expressive experience is so related to an imaginative act as to be, in objective parlance, spoken of as the recognition of an imaginatively presented object as, e.g., our inkpot. The imagined object, too, is absolutely nothing in our presentation of it, our experience is rather a certain blend of images, fancied sensations, informed by a certain interpretative act-character. To live through this act, and to have an imaginative presentation of the object, are one and the same. If we therefore express the situation in the words 'I have before me an image, the image of an inkpot', we have plainly coupled new acts with our expressions and, in particular, a recognitive act which is + +intimately one with our act of imagining. + +§7 Recogn ition as a character of acts, and the + +'generality of words' + +The following more exact argument would seem to show conclusively that, in all cases where a name is applied to a thing intuitively given, we may presume the presence of a recognitive act-character mediating between the appearance of the word-sounds, on the one hand (or the complete senseinformed word), and the intuition of the thing on the other. One often hears of the generality of words, and usually understands by this highly ambiguous phrase that a word is not bound to an individual intuition, but belongs + +rather to an endless array of possible intuitions. In what, however, does this belonging consist? + +Let us deal with an extremely simple example, that of the name 'red' . In so far as it names an appearing object as red, it belongs to this object in virtue of the moment of red that appears in this object. And each object that bears a moment of like sort in itself, justifies the same appellation: the same + +name belongs to each, and does so by way of an identical sense. + +But in what does this appellation by way of an identical sense consist? We observe first that the word does not attach externally, and merely through hidden mental mechanisms, to the individual, specifically similar traits of our intuitions. It is not enough, manifestly, to acknowledge the bare fact that, wherever such and such an individual trait appears in our intuition, the word also accompanies it as a mere pattern of sound. A mere concomitance, a mere external going with or following on one another would not forge any internal bond among them, and certainly not an intentional bond. Yet plainly we have here such an intentional bond, and one of quite peculiar phenomenological character. The word calls the red thing red. The red appearing before us is what is referred to by the name, and is referred to as 'red'. In this mode of naming reference, the name appears as belonging to + +the named and as one with it. + +On the other hand, however, the word has its sense quite apart from an attachment to this intuition, and without attachment to any 'corresponding' intuition. Since this sense is everywhere the same, it is plain that it is not the mere phoneme, rather the true, complete word, endowed on all occasions with the constant character of its sense, that must be held to underlie the naming relation. Even then it will not be enough to describe the union of meaningful word and corresponding intuition in terms of mere concomitance. Take the word, present in consciousness and understood as a mere symbol without being actually used to name anything, and set the corresponding intuition beside it: these two phenomena may at once, for genetic reasons, be brought together in the phenomenological unity of naming. Their mere togetherness is, however, not as yet this unity, which grows out of it with plain novelty. It is conceivable, a priori, that no such unity should emerge, that the coexistent phenomena should be phenomenologically disjoined, that the object before us should not be the thing meant or named by the meaningful -word, and that the word should not belong to the object + +as its name, and so name it. + +Phenomenologically we find before us no mere aggregate, but an intimate, in fact intentional, unity: we can rightly say that the two acts, the one setting up the complete word, and the other the thing, are intentionally combined in a single unity of act. What here lies before us can be naturally described, with equal correctness, by saying that the name 'red' calls the object red, or that the red object is recognized (known) as red, and called 'red' as a result of this recognition. To 'call something red' - in the fully actual sense of 'calling' which presupposes an underlying intuition of the thing so called - and to 'recognize something as red', are in reality synonymous expressions: they + +only differ in so far as the latter brings out more clearly that we have here no mere duality, but a unity engineered by a single act-character. In the intimacy of this fusion, we must nonetheless admit, the various factors implicit in our unity - the physical word-phenomenon with its ensouling meaning, the aspect of recognition and the intuiting of what one names - do not separate themselves off clearly, but our discussion compels us to presume them all to be there. We shall have more to say on this point later on. It is plain that the recognitive character of certain acts, which gives them their significant relation to objects of intuition, does not pertain to words as noises, but to words in their meaningful, their semantic (bedeutungsmiissigen) essence. Very different verbal sounds, e.g. the 'same' word in different languages, may involve an identical recognitive relation: the object is essentially known for the same, though with the aid of quite different noises. Naturally the complete recognition of something red, being equivalent to the actually used name, must include the noise 'red' as a part. The members of different speech-communities feel different verbal sounds to be fitting, and include these in the unity of 'knowing something'. But the meaning attaching to such words, and the recognitive act actually attaching this meaning to its object, remains everywhere the same, so that these verbal differences are rightly + +regarded as irrelevant. + +The 'generality of the word' means, therefore, that the unified sense of one and the same word covers (or, in the case of a nonsense-word, purports to cover) an ideally delimited manifold of possible intuitions, each of which could serve as the basis for an act of recognitive naming endowed with the same sense. To the word 'red', e.g., corresponds the possibility of both knowing as, and calling 'red', all red objects that might be given in possible intuitions. This possibility leads on, with an a priori guarantee, to the further possibility of becoming aware, through an identifying synthesis of all such naming recognitions, of a sameness of meaning of one with the other: this A is red, and that A is the same, i.e. also red: the two intuited singulars + +belong under the same 'concept'. + +A dubious point emerges here. We said above that a word could be understood even if not actually used to name anything. Must we not, however, grant that a word must at least have the possibility of functioning as the actual name of something and so of achieving an actual recognitive relation to corresponding intuition? Must we not say that without such a possibility it could not be a word at all? The answer, of course, is that this possibility depends on the possibility of the recognitions, the 'knowings', in question. Not all intended knowing is possible, not all nominal meaning can be realized. 'Imaginary' names may be names, but they cannot actually be used to name anything, they have, properly speaking, no extension, they are without generality in the sense o/the possible and the true. Their generality is empty pretension. But how these last forms of speech are themselves to be made clear, what phenomenological + +What we have said applies to all expressions, and not merely to such as have generality of meaning in the manner of a class-concept. It applies also to expressions having individual reference, such as proper names. The fact spoken of as the 'generality of verbal meaning' does not point to the generality accorded to generic, as opposed to individual concepts, but, on the contrary, embraces either indifferently. The 'recognition', the 'knowing', of which we speak when a significantly functioning expression encounters corresponding intuition, must not, therefore, be conceived as an actual classification, the ranging of an intuitively or cogitatively presented object in a class, a ranging necessarily based on general concepts and verbally mediated by general names. Proper names, too, have their generality, though, when actually used to name anything, they can eo ipso not be said to classify it. Proper names, like other names, cannot name anything, without thereby also 'knowing' it. That their relation to corresponding intuition is, in fact, as indirect as that of any other expression, can be shown by a treatment exactly analogous to the one conducted above. Each and every name obviously belongs to no definite percept, nor to a definite imagination nor to any other pictorial illustration. The same person can make his appearance in countless possible intuitions, and all these appearances have no merely intuitive but also a recognitive unity. Each appearance from such an intuitive manifold will justify a precisely synonymous use of the proper name. Whichever appearance is given, the man using the name means one and the same person or thing. And he means this not merely in being intuitively oriented to it, as when he deals with an object personally strange to him; he knows it as this definite person or thing. He knows Hans as Hans, Berlin as Berlin. To recognize a person as this person, or a city as this city, is again an act not tied to the particular sensuous content of this or that word-appearance. It is identically the same act in the case of a variety (in possibility of an infinite variety) of verbal noises, as, e.g., when several different proper names apply + +to the same thing. + +This generality of the proper name, and of the peculiar meaning which corresponds to it, is plainly quite different in kind from that of the general + +name. + +The former consists in the fact that a synthesis of possible intuitions belongs to a single individual object, intuitions made one by the common intentional character imparted by every relation to the same object, despite all phenomenal differences among individual intuitions. On this unified basis, the particular unity of recognitive knowing reposes, which belongs to the 'generality of verbal meaning', to its range of ideally possible realizations. In this way the naming word has a recognitive relation to a boundless multitude of + +intuitions, whose identical object it both knows and thereby names. + +The case of the class-name is quite different. Its generality covers a range of objects, to each of which, considered apart, a possible synthesis of percepts, a possible individual meaning and proper name belongs. The general + +name 'covers' this range through being able to name each item in the whole range in general fashion, i.e. not by individually recognizing it in the manner of the proper name, but by classifying it, in the manner of the common name. The thing that is either directly given, or known in its authentic self-being (Eigenheit), or known through its properties, is now known as an A and + +named accordingly. + +§8 The dynam ic un ity of exp ress ion and expressed intuit ion. The consciousness of fu lfil ment and that + +of ide ntity + +From the tranquil, as it were static coincidence of meaning and intuition, we now turn to that dynamic coincidence where an expression first functions in merely symbolic fashion, and then is accompanied by a 'more or less' corresponding intuition. Where this happens, we experience a descriptively peculiar consciousness of fuljilment:4 the act of pure meaning, like a goal-seeking intention, finds its fulfilment in the act which renders the matter intuitive. In this transitional experience, the mutual belongingness of the two acts, the act of meaning, on the one hand, and the intuition which more or less corresponds to it, on the other, reveals its phenomenological roots. We experience how the same objective item which was 'merely thought of' in symbol is now presented in intuition, and that it is intuited as being precisely the determinate so-and-so that it was at first merely thought or meant to be. We are merely expressing the same fact if we say that the intentional essence of the act of intuition gets more or less perfectly fitted into the semantic essence + +of the act of expression. + +In the previously considered static relation among acts of meaning and intuition, we spoke of a recognition, a knowing. This represents the senseinformed relation of the name to the intuitive datum that it names. But the element of meaning is not here itself the act of recognition. In the purely symbolic understanding of a word, an act of meaning is performed (the word means something to us) but nothing is thereby known, recognized. The difference lies, as the foregoing paragraphs have established, not in the mere accompanying presence of the intuition of the thing named, but in the phenomenologically peculiar form of unity. What is characteristic about this unity of knowing, of recognition, is now shown up by the dynamic relationship before us. In it there is at first the meaning-intention, quite on its own: then the corresponding intuition comes to join it. At the same time we have the phenomenological unity which is now stamped as a consciousness of fulfilment. Talk about recognizing objects, and talk about fulfilling a meaning-intention, therefore express the same fact, merely from differing standpoints. The former adopts the standpoint of the object meant, while the latter has the two acts as its foci of interest. Phenomenologically the acts are always present, while the objects are sometimes non-existent. Talk of + +fulfilment therefore characterizes the phenomenological essence of the recognitive relation more satisfactorily. It is a primitive phenomenological fact, that acts of significationS and acts of intuition can enter into this peculiar relation. Where they do so, where some act of meaning-intention fulfils itself in an intuition, we also say: 'The object of intuition is known through its concept' or 'The correct name has been applied to the object appearing + +before us'. + +We can readily do justice to the obvious phenomenological difference between the static and the dynamic fulfilment or recognition. In the dynamic relationship the members of the relation, and the act of recognition which relates them, are disjoined in time: they unfold themselves in a temporal pattern. In the static relationship, which represents the lasting outcome of this temporal transaction, they occur in temporal and material (sachlicher) coincidence. There we have a first stage of mere thought (of pure conception or mere signification), a meaning-intention wholly unsatisfied, to which a second stage of more or less adequate fulfilment is added, where thoughts repose as if satisfied in the sight of their object, which presents itself, in virtue of this consciousness of unity, as what is thought of in this thought, what it refers to, as the more or less perfectly attained goal of thinking. In the static relationship, on the other hand, we have this consciousness of unity alone, perhaps with no noticeably marked-off, precedent stage of unfulfilled intention. The fulfilment of the intention is not here an event of self-fulfilment, but a tranquil state of being-fulfilled, not a coming into + +coincidence, but a being coincident. + +From an objective point of view we may here also speak of a unity of identity. If we compare both components of a unity of fulfilment - whether treating them in dynamic transition into one another, or holding them apart analytically in their static unity, only to see them at once flowing back into one another - we assert their objective identity. For we said, and said with self-evidence, that the object of intuition is the same as the object of the thought which fulfils itself in it and, where the fit is exact, that the object is seen as being exactly the same as it is thought of or (what always says the same in this context) meant. Identity, it is plain, is not first dragged in through comparative, cogitatively mediated reflection: it is there from the start as experience, as unexpressed, unconceptualized experience. In other words, the thing which, from the point of view of our acts is phenomenologically described as fulfilment, will also, from the point of view of the two objects involved in it, the intuited object, on the one hand, and the thought object, on the other, be expressively styled 'experience of identity', 'consciousness of identity', or 'act of identification' . A more or less complete identity is the objective datum which corresponds to the act of fulfilment, which 'appears in it' . This means that, not only signification and intuition, but also their mutual adequation, their union of fulfilment, can be called an act, since it has its own peculiar intentional correlate, an objective + +something to which it is 'directed' . Another side of the same situation is again, we saw above, expressed in talk about recognizing or knowing. The fact that our meaning-intention is united with intuition in a fulfilling manner, gives to the object which appears in such intuition, when it primarily concerns us, the character of a thing known. If we try to say more exactly 'as what' we recognize something, our objective reflection points, not to our act of meaning (Bedeutens), but to the meaning (Bedeutung), the selfidentical 'concept' itself; talk of recognition therefore expresses our view of the same unified state from the standpoint of the object of intuition (or of the fulfilling act), in its relations to the meaning-concept of the signitive act. Conversely we say, though perhaps in more special contexts, that our thought 'grasps' (begreife) the matter, that it is the latter's concept (Begriff) or 'grasp'. After our exposition it is obvious that recognition, like fulfilment the former is in fact only another name for the latter - can be called an act + +of identification. + +Addendum. I cannot here suppress a difficulty connected with the otherwise illuminating notion of the unity of identity or recognition, as an act of identification or recognition. This is particularly the case, since this difficulty will reveal itself as a serious one as our clarifications proceed and progress, and will inspire fruitful discussions. Closer analysis makes it plain that, in the cases detailed above, where a name is actually applied to an object of intuition, we refer to the intuited and named object, but not to the identity of this object, as something at once intuited and named. Shall we say that an emphasis of attention decides the matter? Or ought we not rather to grant that there is not here a fully constituted act of identification: the nucleus of this act, the connective union of significant intention and corresponding intuition is really present, but it 'represents' no objectifying interpretation (Auffassung). On the experienced unity of coincidence no act of relational identification is founded, no intentional consciousness of identity, in which identity, as a unity referred to, first gains objective status. In our reflection on the unity of fulfilment, in analysing and opposing its mutually connected acts, we naturally, and indeed necessarily, also framed that relational interpretation which the form of its union, with a priori necessity, permits. Our second section will deal with this question in its widest form which concerns the categorial characters of acts (see Chapter VI, §48, and the whole of Chapter VII). Meanwhile we shall continue to treat the sort of unity in question as a full act, or we shall at least not differentiate it expressly from a full act. This will not affect the essential point in our treatment, in so far as the passage from a consciousness of unity to a relational identification always remains open, has a possibility guaranteed a priori, so that we are entitled to say that an identifying coincidence has been experienced, even if there is no conscious intention directed to identity, and + +no relational identification. + +§9 The differing character of an intention inside and + +outside the un ity of fu lfilme nt + +Our introduction of dynamic fulfilment, o r o f fulfilment strung out in an articulated process, to help interpret the static act of recognition, removes a difficulty which threatens to blur our clear grasp of the relation between significant intention and the full act of recognition. Can we really say that all these factors can be distinguished in the unity of recognition, the verbal expression, the acts of meaning and intuition and, finally, the overarching character of recognitive unity or fulfilment? One might hold that analysis only lays bare verbal expressions, particularly names, on the one hand, and intuition, on the other, both unified through the character of recognitive naming. One might reject the idea of an act of meaning bound up with the verbal expression, an element distinct from recognitive character and fulfilling intuition, and identifiable with the 'understanding' as opposed to the 'knowing' character of the expression: this would seem, at least, to be an + +unnecessary assumption. + +This doubt affects, therefore, the central conception which in §4 we took to be most intelligible, before we embarked on our analysis of the unity of recognition. We must accordingly re-emphasize the following points in our + +discussion: + +1. If we compare expressions used in recognizing objects with those used outside of such recognition, it is plain that both have the very same meaning. Whether I understand the word 'tree' as a mere symbol, or use it in connection with my intuition of a tree, it is plain that I mean something + +by the word, and mean the same thing on both occasions. + +2. It is plain that it is the significant intention of the expression that 'fulfils' itself in the process of fulfilment, and so achieves 'coincidence' with an intuition, and that the recognition which stems from this process of coincidence is itself this unity of coincidence. The notion of this unity of coincidence plainly involves that we are not here concerned with a divided duality but with a seamless unity, which only acquires articulation when drawn out in time. We must, therefore, maintain that the same act of meaning-intention which occurs in an empty symbolic presentation is also part of the complex act of recognition, but that a meaning-intention that was 'free', is now 'bound' and 'neutralized' in the stage of coincidence. It is so peculiarly inwrought and infused in this combination that, while its semantic essence remains intact, it nonetheless undergoes a certain change + +of character. + +The same holds wherever contents are first studied apart, and then seen in their connection with other contents, as parts knit into wholes. Connections would not connect if they made no difference to what they connected. Certain changes necessarily occur, and these are naturally such specific connectednesses as constitute the phenomenological correlatives of what + +are objectively relational properties. Consider, for example, a line set apart, perhaps on a bare white background, and the same line as part of a figure. In the latter case, it impinges on other lines, is touched, cut by them etc. If we turn from mathematical ideals to empirically intuited linear stretches, these are phenomenological characters that help determine the appearance of linearity. The same stretch - 'same' in internal content - appears ever different according as it enters into this or that phenomenal context and, if incorporated in a line or surface qualitatively identical with it, melts indistinguishably into this background, losing its phenomenal separateness and + +independence. + +§ I 0 The wider class of expe riences of fu lfil ment. Intuitions as intentions which req uire fu lfilment + +We may now further characterize the consciousness of fulfilment by seeing in it an experiential form which plays a part in many other fields of mental life. We have only to think of the opposition between wishful intention and wish-fulfilment, between voluntary intention and execution, of the fulfilment of hopes and fears, the resolution of doubts, the confirmation of surmises etc., to be clear that essentially the same opposition is to be found in very different classes of intentional experiences: the opposition between significant intention and fulfilment of meaning is merely a special case of it. We have dealt with this point previously,6 and delimited a class of intentional experience under the more pregnant name of 'intentions': their peculiarity lies in being able to provide the basis for relations of fulfilment. In this class are ranged all the acts which are in a narrower or wider sense 'logical', including the intuitive, whose role it is to fulfil other intuitions in knowledge. When, e.g., a familiar melody begins, it stirs up definite intentions which find their fulfilment in the melody's gradual unfolding. The same is the case even when the melody is unfamiliar. The regularities governing melody as such, determine intentions, which may be lacking in complete objective definiteness, but which nonetheless find or can find their fulfilments. As concrete experiences, these intentions are of course fully definite: the 'indefiniteness' of what they intend is plainly a descriptive peculiarity pertaining to their character. We may say, in fact, with correct paradox (as we did before in a similar case) that 'indefiniteness' (i.e. the peculiarity of demanding an incompletely determined completion, which lies in a 'sphere' circumscribed by a law) is a definite feature of such an intention. Such an intention has not merely a range of possible fulfilment, but imports a common fulfilmentcharacter into each actual fulfilment from this range. The fulfilment of acts which have definite or indefinite intentions is phenomenologically different, and the same holds of fulfilments of intentions whose indefiniteness points + +In our previous example there is also a relation between expectation and fulfilment of expectation. It would, however, be quite wrong to think, conversely, that every relation of an intention to its fulfilment was a relationship involving expectation. Intention is not expectancy, it is not of its essence to be directed to future appearances. If I see an incomplete pattern, e.g. in this carpet partially covered over by furniture, the piece I see seems clothed with intentions pointing to further completions - we feel as if the lines and coloured shapes go on 'in the sense' of what we see - but we expect nothing. It would be possible for us to expect something, if movement promised us further views. But possible expectations, or occasions for poss- + +ible expectations, are not themselves expectations. + +The external perceptions of the senses offer us an indefinite number of relevant examples. The features which enter into perception always point to completing features, which themselves might appear in other possible percepts, and that definitely or more or less indefinitely, according to the degree of our 'empirical acquaintance' with the object. Every percept, and every perceptual context, reveals itself, on closer analysis, as made up of components which are to be understood as ranged under two standpoints of intention and (actual or possible) fulfilment. The same applies to the parallel acts of imagining and picture-thought in general. In the normal case intentions lack the character of expectancy, they lack it in all cases of tranquil perceiving or picturing, and they acquire it only when perception is in flux, when it is spread out into a continuous series of percepts, all belonging to the perceptual manifold of one and the same object. Objectively put: the object then shows itself from a variety of sides. What was pictorially suggested from one side, becomes confirmed in full perception from another; what was merely adumbrated or given indirectly and subsidiarily as background, from one side, at least receives a portrait-sketch from another, it appears perspectivally foreshortened and projected, only to appear 'just as it is' from another side. All perceiving and imagining is, on our view, a web of partial intentions, fused together in the unity of a single total intention. The correlate of this last intention is the thing, while the correlate of its partial intentions are the thing's parts and moments. Only in this way can we understand how consciousness reaches out beyond what it actually experiences. It can so to say + +mean beyond itself, and its meaning can be fulfilled. + +§ II Frustration and conflict. The synthesis + +of disti nction + +In the wider sphere of the acts to which distinctions of intention and fulfilment apply, frustration may be set beside fulfilment, as its incompatible contrary. The negative expression that we normally use in this case, e.g. even the term 'non-fulfilment', has no merely privative meaning: it points to + +a new descriptive fact, a form of synthesis as peculiar as fulfilment. This is so even in the narrower case of significant intentions as they stand to intuitive intentions. The synthesis of recognition, of 'knowing', is the consciousness of a certain agreement. The possibility correlated with agreement is, however, 'disagreement' or 'conflict': intuition may not accord with a significant intention, but may 'quarrel' with it. Conflict 'separates', but the experience of conflict puts things into relation and unity: it is a form of synthesis. If the previously studied synthesis was one of identification, this new synthesis is one of distinction (unfortunately we possess no other positive name). This 'distinction' must not be confused with the other 'distinction' which stands opposed to a positive likening. The oppositions between 'identification and distinction' and between 'likening and distinction' are not the same, though it is clear that a close phenomenological affinity explains our use of the same word. In the 'distinction' which is here in question, the object of the frustrating act appears not the same as, 'distinctfrom the object of the intending act. These distinctions point to wider classes of cases than we have hitherto preferred to deal with. Not only significative, but even intuitive intentions are fulfilled in identifications and frustrated in conflicts. We shall have to explore the whole question of the natural circumscription of the acts to which the terms 'same' and 'other' (we can as well say 'is' and 'is not') have + +application. + +The two syntheses are not, however, completely parallel. Each conflict presupposes something which directs its intention to the object of the conflicting act; only a synthesis of fulfilment can give it this direction. Conflict, we may say, presupposes a certain basis of agreement. If I think A to be red, when it shows itself to be 'in fact' green, an intention to red quarrels with an intention to green in this showing forth, i.e. in this application to intuition. Undeniably, however, this can only be the case because A has been identified in the two acts of signification and intuition. Were this not so, the intention would not relate to the intuition. The total intention points to an A which is red, and intuition reveals an A which is green. It is in the coincidence of meaning and intuition in their direction to an identical A, that the moments intended in union with A in the two cases, come into conflict. The presumed red (i.e. red of A) fails to agree with the intuited green. It is through identity that such non-coincident aspects correspond with each other: instead of being 'combined' by fulfilment, they are 'sundered' by conflict. An intention is referred to an appropriate aspect in intuition from which it + +is also turned away. + +What we have here said with special regard to significant intentions and the frustrations they encounter, applies also to our whole previously sketched class of objectifying intentions. We may generally say: An intention can only be frustrated in conflict in so far as it forms part of a wider intention whose completing part is fulfilled. We can therefore not talk of conflict in the case + +of simple, i.e. isolated, acts. + +§ 12 Total and partial ide ntification and di sti nction as the common phenomenological foundations of pred i cative and determining forms of express ion + +The relation between intention (in particular, meaning-intention) and fulfilment that we have so far considered, was that of total agreement. This was a limitation due to our aim of maximum simplicity: to achieve this, we abstracted from all form, even from the form that announces itself in the little word 'is' . In the relation of an expression to external or internal intuition, we considered only those parts of the expression that fit what we intuit like a garment. But by bringing in conflict as the possibility opposed to the case of total agreement - conflict that could therefore, somewhat misleadingly, be called 'total conflict' - we are made aware of certain new possibilities, the important cases of partial agreement and disagreement between + +an intention and the act which fulfils or frustrates it. + +We shall, from the start, keep the closer treatment of these possibilities so general, that the validity of all essential results will be clear for intentions of the above indicated wider class, and not merely, therefore, for + +meaning-intentions. + +All conflict pointed to the fact that the frustrated intention in question was part of a more comprehensive intention, which partially fulfilled itself (i.e. in the supplementary parts) while the original part was estranged. In every conflict there is, accordingly, in a certain fashion, both partial agreement and partial conflict. Our attention to objective relations should have revealed these possibilities, since wherever we can talk of coincidence, we can talk about the correlated possibilities of exclusion, inclusion and + +intersection. + +If we keep to the case of conflict, the following additional points suggest + +themselves: + +If a 6 is frustrated in a 0 in that e is associated with other intentions 1), I... which are fulfilled, these latter need not be so united with 6, that the whole e (6; 1); I .•• ) deserves to be called an act constituted on its own, one 'in which we live', and to whose unified object we 'pay heed'. In the texture of conscious, intentional experience, there are many possibilities of pointing selection of acts and act-complexes, which remain for the most part unrealized. And only such pointed unities are relevant when we are speaking of individual acts and their syntheses. The case of pure and complete frustration therefore consists in the fact that 6 alone, not e, is emphasized or at least mainly emphasized, and that a pointed consciousness of conflict establishes unity only between 6 and O. Our interest in other words, is specially directed to the objects corresponding to 6 and O. This happens when a green-intention is frustrated by an intuited red, and the green and red are alone attended to. If the clashing intuition of the red is expressed at all, i.e. by a verbal intention fulfilled in it, we should perhaps say: 'This (red) is not + +green'. (Of course this sentence does not have the same meaning as the sentence 'The verbal intention "green" is frustrated by the intuition of red' . For the new expression renders objective the relation of acts which concerns us, and turns new meaning-intentions upon the latter in total fulfilment.) It can also be the case that a e (e; T}; I .•. ) enters synthesis as a whole, and is herewith either associated with a corresponding whole e (0; T}; I •.• ) or specially associated with its isolated part O. In the former case there is in part coincidence among the combined elements, i.e. among T}, I .•. and in part total conflict, (e, 0). The whole synthesis has the character of a total conflict, but of conflict not pure, but mixed. In the other case 0 alone stands out as the corresponding act, for the reason, perhaps, that in mixed conflict the unity of e (0; T}; I ••• ) is resolved. The special synthesis of conflict unites e (0; T}; I ... ) and (0), which is appropriately expressed by 'This (whole object, the red-tiled roof) is not green' . This important relation may be called one of exclusion (Ausscheidung). Its central character is plainly unaffected, when e and 0 are themselves complex, so that we can distinguish between pure and mixed exclusion. Roughly speaking, the latter may be illustrated by the example 'This (red-tiled roof) is no green-tiled roof'. Let us now consider the case of inclusion. An intention can be fulfilled in an act which contains more than its fulfilment needs, in so far as the latter presents an object which contains the intention's object, either as a common-or-garden part, or as a 'moment' explicitly or implicitly thought of as belonging to it. We are of course ignoring the acts in which a more comprehensive objective field is set up as an objective background, acts not delimited as unities nor as preferential carriers of attention: otherwise we should be brought back to the synthesis of total coincidence. Let us suppose that a red-tiled roof is presented to us, and that the meaning-intention behind the word 'red' is fulfilled in it. The verbal meaning is here fulfilled with complete coincidence in the intuited red, but the total intuition of the red-tiled roof, relieved sharply as a single item from the background, through the work of attention, still enters into a peculiar sort of synthetic unity with the meaning-intention Red: '(This) is red'. We speak here of a relation of 'subsumption' (Einordnung), the opposite of the exclusion mentioned above. + +Subsumption can obviously only be pure. + +The act of subsumptive synthesis, as the act which puts together the intending and fulfilling acts in its total unity, has its objective correlate in the relation of partial identity of the corresponding objects. Talk of subsumption points in this direction: it pictures our grasp of the relation as an activity which subsumes the part in the whole. The same objective relationship is, with a change of conceptual standpoint - pointing to unnoticed phenomenological differences casually revealed in our form of expression expressed in the words: 'eg has eg' or 'eg pertains to eg' . The index g makes us aware that it is the intentional objects of the acts in question which enter into these relations; we stress the intentional objects, the objects as they are + +referred to in these acts. The application of these remarks to the case of exclusion, and to the expressions 'has not' or 'does not pertain', is obvious. To the mere 'is' objective identity belongs in all cases, to the 'is not' nonidentity (conflict). That we are specially dealing with a relation of subsumption or exclusion requires other means of expression, e.g. the adjectival form, which marks off what is had or what pertains as such, just as the substantival form expresses its correlative, the thing which has as such, i.e. in its function as 'subject' of an identification. In the attributive, or more generally determining form of expression (even complete identity determines), being is hidden in the inflexion of the adjective, to the extent that it is not explicitly and separately expressed in a relative clause, or, per contra, not wholly suppressed ('this philosopher Socrates'). Whether the always mediate expression of non-identity, whether in cases of predication or attribution, or in substantival forms such as 'non-identity', 'non-agreement', expresses a necessary relation of actual 'negation' to an affirmation which, if not actual, is at least present in modified form, would lead to discussions into which + +we do not now care to enter. + +All normal statements are accordingly statements of identity or nonidentity, and expressions of the same wherever there is a relation to 'corresponding intuition', i.e. where the intention towards identity or non-identity fulffis itself in a completely achieved identification or distinction. 'The tiled roof', as we would say in our previous case provided a mere intention went before, 'is really red'. The predicate-intention fits the subject which is presented and intuited as, e.g., 'this tiled roof'. In the opposite case we say: 'It + +is not really red'; the predicate does not pertain to the subject. + +But if the meaning of 'is' finds a fulffiment based on an actual identification (which often has the character of a fulfilment), it is clear that we are here passing beyond the sphere on which we had hitherto always kept our eye, without being quite clear as to its limits, the sphere namely of expressions that can really be fulfilled through corresponding intuition. Or rather we are made aware that intuition, in the common-or-garden sense of external or internal 'sensibility', which we took as an obvious basis in our treatment, is not the only function that can rightly be styled 'intuitive', and can be regarded as capable of carrying out the work of fulfilment. We leave the closer exploration of this emerging difference to the Second Section of the + +present Investigation. + +We must stress, in conclusion, that the above exposition has not provided a complete analysis of the judgement, but a mere fragment of the same. We have ignored the quality of the synthetic act, the differences between attri- + +bution and predication etc. + +Chapter 2 + +Indirect characterization of objectifying intentions and + +their essential varieties through + +differences in the syntheses of + +fu lfilment + +§ 13 The synthesis of knowi ng (recogn ition) as the characte ristic fo rm of fu lfil ment for objectifyi ng acts. Subsu mption of acts of meaning under the class of + +objectifying acts + +We have, in the above treatment, classed meaning-intentions in the wider class of 'intentions' in the pregnant sense of the word. All intentions have corresponding possibilities of fulfilment (or of opposed frustration): these themselves are peculiar transitional experiences, characterizable as acts, which permit each act to 'reach its goal' in an act specially correlated with it. These latter acts, inasmuch as they fulfil intentions, may be called 'fulfilling acts', but they are called so only on account of the synthetic act of fulfilment, or rather of self-fulfilment. Such transitional experience is not always the same in character. In the case of meaning-intentions, and not less clearly in the case of intuitive intentions, such experiences are unities of knowing, or unities of identification in respect of their objects. This need not be so in the wider class of intentions in general. Everywhere we may speak of coincidences, and everywhere we shall meet with identifications. But the latter often depend on an inwrought act of a sort which permits of a unity of identification and + +also serves as the foundation of one in the contexts in question. + +An example will clarify the matter. The self-fulfilment of a wish is achieved in an act which includes an identification, and includes it as a necessary component. For there is a law which ties the quality of wishing to an underlying presentation, i.e. to an objectifying act, and more precisely to a 'mere presentation', and this leads to a complementary law tying a wish-fulfilment to an underlying act, which incorporates this presentation in its identifying grasp. A wishful intention can only find its fulfilling satisfaction in so far as the underlying mere presentation of the thing wished for becomes transformed into the corresponding percept. What we have, however, is not this mere transformation, the mere fact of imagination dissolved in perception: both enter in unity into the character of an act of identifying coincidence. In this synthetic character, we have it constituted that a thing is really and truly + +so (i.e. as we had previously merely pictured and wished): this of course does not exclude the possibility that such 'really being so' is merely putative, and especially, in most cases, that it is inadequately presented. If a wish is based on a purely signitive presentation, this identification can of course involve the more special coincidence described above, in which meaning is fulfilled by an intuition that fits it. The same could plainly be said of all intentions that, as objectifying acts, are based on presentations, and what applies to + +fulfilment carries over, mutatis mutandis, to the case of frustration. + +It is clear accordingly, to stick to our example, that even if the fulfilment of a wish is founded on an identification, and perhaps on an act of intuitive recognition, this latter act never exhausts the fulfilment of the wish, but merely provides its basis. The self-satisfaction of the specific wish-quality is a peculiar, act-character, different in kind. It is by a mere analogy that we extend talk of satisfaction, and even of fulfilment, beyond the sphere of + +emotional intentionality. + +The peculiar character of an intention accordingly goes with the peculiar character of its fulfilling coincidence. Not only does every nuance of an intention correspond to some nuance of the correlatedfulfilment, and likewise of the self-fulfilling activity in the sense of a synthetic act, but to the essentially diff erent classes of intention there also correspond pervasive class-differences in fulfilment (in the twofold sense mentioned above). And obviously the members which belong to these parallel series belong also to a single class of acts. The syntheses of fulfilment in the case of wish- and will-intentions certainly show close affinities, and differ deeply from those occurring, e.g., in the case of meaning-intentions. On the other hand, the fulfilments of meaning-intentions and of intuitive acts are definitely of the same character, and so in the case of all acts that we classed as 'objectifying' . We may say of this class of acts which alone concerns us here, that in them unity of fulfilment has the character of unity of identification, possibly the narrower character of a unity of knowing, i.e. of an act to which objective identity is the + +corresponding correlate. + +We must here emphasize the following point: As pointed out above, every fulfilment of a 'signitive' by an intuitive act has the character of a synthesis of identification. But it is not the case, conversely, that, in each synthesis of identification, a meaning-intention is fulfilled, and fulfilled by a corresponding intuition. In the widest sense, certainly, we do ordinarily speak of every actual identification as a recognition. But, in a narrower sense, what is clearly felt to be at issue is an approach to a goal of knowledge and, in the narrowest sense of a critique of knowledge, the arrival at that goal. To tum this mere feeling into clear insight, and to define the precise sense of this approach or arrival, will yet be our task. Meanwhile we shall maintain that the unity of identification, and thereby all unity of knowing in the narrower and the narrowest sense, has its place of origin in the sphere of objecti- + +Their peculiar manner of fulfilment will therefore suffice to characterize the unified class of acts to which it essentially belongs. We can accordingly define objectifying acts as those whose syntheses of fulfilment have a character of identification, while their synthesis of frustration has a character of distinction. We can also define them as acts which can function phenomenologically as members of possible syntheses of identification and distinction. Lastly, presuming a law as yet unformulated, we can define them as the intending, fulfilling or frustrating acts which have a possible knowledgefunction. To this class belong also the synthetic acts of identification and distinction themselves: they are themselves either a merely putative grasp of identity or non-identity, or a corresponding real grasp of the one or the other. This putative grasp can be either 'confirmed' or 'refuted' in an act of knowing (in the pregnant sense of the word): identity is really grasped, i.e. 'adequately perceived' , in the former case, as non-identity in the latter. Our analyses have been lightly sketched rather than thoroughly executed, but they lead to the result that both meaning-intentions and acts of meaningfulfilment, acts of 'thought' and acts of intuition, belong to a single class of objectifying acts. We establish thereby that acts of another sort can never exercise any sense-giving function, and that they can be 'expressed' only in so far as the meaning-intentions which attach to words are fulfilled in percepts or imaginations which have as objects the acts requiring expression. While, therefore, where acts function meaningfully, and achieve expression in this sense, a 'signitive' or intuitive relation to objects is constituted in them, in the other cases the acts are mere objects, and objects, of course, for other + +acts which here function as the authentic carriers of meaning. + +Before we discuss this matter more closely, and seek to refute many plausible counter-arguments - see the final Section of this Investigation - we must explore the remarkable facts of fulfilment somewhat more carefully, + +and in the sphere of objectifying acts. + +§ 14 Phenomenological characte rization of the + +distinction between sign itive and intu itive intentions + +through pecu liarities of fu lfil ment + +(a) Sign. image and self-presentation + +In the course of the last discussion we have been led to note how the generic character of an intention closely coheres with that of its synthesis of fulfilment, so that the whole class of objectifying acts can be defined through the identification generically characteristic of their syntheses of fulfilment, whose nature we take to be familiar. This thought leads us on to ask whether the specific differences within this class of objectifications, may not likewise rest upon corresponding differences in the mode of fulfilment. Objectifying intentions are basically divided into significative and intuitive + +intentions: let us try to give an account of the difference between these types + +of act. + +Since the starting point of our treatment lay in expressed acts, we took signitive intentions to be the significations, the meanings of expressions. If we leave aside the question whether the same acts which give sense to expressions can also function outside of the sphere of meaning, these signitive intentions always have intuitive support in the sensuous side of the expression, but not on that account intuitive content. Though in a manner one + +with intuitive acts, they yet differ from them in kind. + +We can readily grasp the distinction between expressed and purely intuit- + +ive intentions if we contrast signs with likenesses or images. + +The sign has in general no community of content with the thing it signifies; it can stand as readily for what is heterogeneous, as for what is homogeneous with itself. The likeness on the other hand is related to the thing by similarity: where there is no similarity, there can be no talk of a likeness, an image. The sign as object is constituted for us in an act of appearing. This act is not significant: it needs, as we held in former analyses, to be tied up with a new intention, a new way of taking things, through which a novel, signified object takes the place of the old, intuitively apparent one. The likeness similarly, e.g. the marble bust, is as much a thing as anything else: the new way of regarding it first makes it a likeness. Not merely a thing of marble appears before us, but we have, based on this appearance, a refer- + +ence to a person through a likeness. + +The intentions attaching to the phenomenal content are, in either case, not externally tied up with it, but essentially based upon it, and in such a way that the character of the intention is determined thereby. It would be a descriptively wrong notion of the matter, to think of the whole difference as lying in the fact that the same intention which, in the one case is tied to the appearance of an object like the object referred to, is in the other case tied to the appearance of an object unlike it. For the sign, too, can be like what it signifies, even entirely like it: the sign-presentation is not thereby made into a presentation by way of a likeness. A photograph of the sign A is immediately taken to be a picture of the sign. But when we use the sign A as a sign of the sign A, as when we write 'A is a letter of the Latin written alphabet', we treat A, despite its representational similarity, as a sign, and not as a likeness. The objective fact of similarity between what appears and what is meant, is accordingly irrelevant: it is not, however, irrelevant where something is presented by way of a likeness. This shows itself in the possibility of fulfilment: it was only the recollection of this possibility which allowed us to bring in 'objective' similarity in this context. The likeness-presentation plainly has the peculiarity that, when it achieves fulfilment, the object which appears before it as likeness gets identified through similarity with the object given in the fulfilling act. Having held this to be the peculiarity of a presentation by way of likeness, we have admitted that fulfilment of like by like + +internally fixes the character of a synthesis of fulfilment as imaginative. But, when, on the other hand, casual likeness between sign and thing signified leads to a knowledge of their mutual resemblance, this knowledge is not at all a case of the peculiar consciousness of identity, when similar is referred to similar and made to coincide with it in the manner of likeness and original thing. It is rather of the very essence of a significative intention, that in it the apparent objects of intending and fulfilling acts (e.g. name and thing named in their fully achieved unity) 'have nothing to do with one another'. It is clear, therefore, that descriptively distinct modes of fulfilment, being rooted in the descriptively distinct character of our intention, can help us to + +detect these latter differences, and to find definitions for them. + +We have so far only considered the difference between signitive and imaginative intentions. If we ignore less weighty distinctions within the wider sphere of imaginative acts - we have preferred to consider representation by way of physical images, instead of stressing those of fantasy - we must still + +consider the case of percepts. + +As opposed to imagination, perception is characterized by the fact that in it, as we are wont to express the matter, the object 'itself' appears, and does not merely appear 'in a likeness' . In this we at once recognize characteristic differences in syntheses of fulfilment. Imagination fulfils itself through the peculiar synthesis of image-resemblance, perception through the synthesis of identical thinghood (sachlichen Identitiit). The thing establishes itself through its very self, in so far as it shows itself from varying sides while remaining + +one and the same. + +(b) The perceptual and imaginative adumbration of + +the object + +We must, however, pay heed to the following distinction. Perception, so far as it claims to give us the object 'itself', really claims thereby to be no mere intention, but an act, which may indeed be capable of offering fulfilment to other acts, but which itself requires no further fulfilment. But generally, and in all cases of 'external' perception, this remains a mere pretension. The object is not actually given, it is not given wholly and entirely as that which it itself is. It is only given 'from the front', only 'perspectivally foreshortened and projected' etc. While many of its properties are illustrated in the nuclear content of the percept, at least in the (perspectival) manner which the last expressions indicate, many others are not present in the percept in such illustrated form: the elements of the invisible rear side, the interior etc., are no doubt subsidiarily intended in more or less definite fashion, symbolically suggested by what is primarily apparent, but are not themselves part of the intuitive, i.e. of the perceptual or imaginative content, of the percept. On this hinges the possibility of indefinitely many percepts of the same object, all differing in content. If percepts were always the actual, genuine + +self-presentations of objects that they pretend to be, there could be only a single percept for each object, since its peculiar essence would be exhausted + +in such self-presentation. + +We must, however, note that the object, as it is in itself- in the only sense relevant and understandable in our context, the sense which the fulfilment of the perceptual intention would carry out - is not wholly different from the object realized, however imperfectly, in the percept. It is part so-to-say of a percept's inherent sense to be the self-appearance of the object. Even if, for phenomenological purposes, ordinary perception is composed of countless intentions, some purely perceptual, some merely imaginative, and some even signitive, it yet, as a total act, grasps the object itself, even if only by way of an adumbration. If we may conceive of a percept put into a relation of fulfilment to the adequate percept that would offer us the object itself, in the ideally strict and most authentic sense, then we may say that a percept so intends its object that this ideal synthesis would have the character of a partial coincidence of the purely perceptual contents of intending and fulfilling acts, and also the character of a complete coincidence of both complete perceptual intentions. The 'purely perceptua1' content in 'externa1' perception is what remains over when we abstract from all purely imaginative and symbolic components: it is the 'sensed' content to which its own, immediate, purely perceptual interpretation is given, which evaluates all its parts and moments as self-projections of corresponding parts and moments of the perceptual object, and so imparts to its total content the character of a 'perceptual picture', a perceptual adumbration of the object. In the ideal, limiting case of adequate perception, this self-presenting sensed content coincides with the perceived object. This common relation to the object 'in itself', i.e. to the ideal of adequation, enters into the sense of all perception, and is also manifest in the phenomenological mutual belongingness of the manifold percepts pertaining to a single object. In one percept the object appears from this side, in another from that side; now it appears close, now at a distance etc. In each percept, despite these differences, one and the same object is 'there', in each it is intended in the complete range of its familiar and of its perceptually present properties. To this corresponds phenomenologically a continuous flux of fulfilment or identification, in the steady serialization of the percepts 'pertaining to the same object'. Each individual percept is a mixture of fulfilled and unfulfilled intentions. To the former corresponds that part of the object which is given in more or less perfect projection in this individual percept, to the latter that part of the object that is not yet given, that new percepts would bring to actual, fulfilling presence. All such syntheses of fulfilment are marked by a common character: they are identifications binding self-manifestations of an object to self-manifestations + +of the same object. + +It is at once clear that similar distinctions apply in the case of imaginative presentation. Here too the same object is pictured, now from this and now + +from that side. Corresponding to the synthesis of manifold perceptions, where the same object always presents itself, we have the parallel synthesis of manifold imaginations, in which the same object appears in a likeness. To the changing perceptual adumbrations of the object there are corresponding imaginative adumbrations, and in the ideal of perfect copying the projection would coincide with the complete likeness. If imaginative acts are at one time fulfilled in imaginative contexts, and at another time through corresponding percepts, the difference lies plainly in the character of their synthesis of fulfilment: the passage from likeness to likeness has a different character + +from the passage from likeness to original thing. + +The above analysis will be of use for the further investigations to be carried on in the next chapter; they also show the mutual affinity of percepts and imaginations, and their common opposition to 'signitive' intentions. In all cases we distinguish between an actually given, appearing content, which is not what we mean, and an object which is what we mean - whether we signify, represent or perceive it - or between a sign-content on the one hand, and the imaginative or perceptual projection of the object on the other. But while sign and thing signified 'have nothing to do with one another', there are inner affinities between a thing's imaginative and perceptual projections and the thing itself, affinities which are part of the very sense of our use of such words. These relationships are phenomenologically documented in differences in their constitutive intentions, and not less in their syntheses of fulfilment. This account does not, of course, affect our interpretation of every fulfilment as being an identification. In all cases an intention comes into coincidence with the act which offers itfulness, i.e. the object which is meant in it is the same as the object meant in the fulfilling act. We were not, however, comparing these objects of meaning-reference, but signs and adumbrations in their relations to such objects, or to what corresponds phenomenologically + +to these relationships. + +Our interest in the preceding paragraphs was primarily directed to peculiarities in syntheses of fulfilment: these enable us to differentiate intuitive and signitive acts in a merely indirect manner. Only in the further course of our investigation - in §26 - shall we be able to give a direct characterization, based on an analysis of the intentions, and without regard to their possible + +fulfilments. + +§ 15 Sign itive intentions beyond the limi ts of the + +meaning-function + +In our last discussion we have pinned down certain components of intuitive acts as signitive intentions. But in the whole of our investigations up to this point, signitive acts were for us acts of meaning, sense-giving factors attached to expressions. The terms 'signification' and 'signitive intention' were for us synonymous. It is now time to ask ourselves whether the same acts, or + +acts essentially similar to those found to function in meaning, may not + +occur quite divorced from this function and from all expressions. + +That this question must be answered affirmatively, is shown by certain cases of wordless recognition, which exhibit the precise character of verbal recognition, although words, in their sensuous-signitive content, are not actually present at all. We recognize an object, e.g. as an ancient Roman milestone, its scratchings as weather-worn inscriptions, although no words are aroused at once, or indeed at all. We recognize a tool as a drill, but its name will not come back to us etc. Genetically expressed, present intuitions stir up an associative disposition directed to the significant expression. But the meaning-component of this last alone is actualized, and this now radiates backwards into the intuition which aroused it, and overflows into the latter with the character of a fulfilled intention. These cases of wordless recognition are none other than fulfilments of meaning-intentions, but phenomenologically divorced from the signitive contents which otherwise pertain to them. Comparable examples are furnished by reflection on the normal interweavings of scientific pondering. We observe here how trains of thought sweep on to a large extent without bondage to appropriate words, set off by a flood of intuitive imagery or by their own associative + +interconnections. + +With this is connected the further fact that expressive speech goes so far beyond the intuitive data necessary for the actual appropriateness of the expression of acquaintance. This has, no doubt, an opposed ground in the extraordinary ease with which verbal images are revived by intuitions, and can themselves then revive symbolic thoughts without corresponding intuitions. But we must also observe, contrariwise, how the reproduction of imaged words often lags quite far behind the trains of thought revived by each present intuition. In both these ways a large number of inadequate expressions arise, which do not apply in a straightforward manner to the primary intuitions actually present, nor to the synthetic formations actually built upon them, but range far beyond what is thus given. Curious mixtures of acts result. Objects are, strictly speaking, only 'known', as they are given in their actual intuitive foundation, but, since the unity of our intention ranges further, objects appear to be known as what they are for this total intention. The character of knowing is accordingly somewhat broadened. Thus we recognize (know) a person as an adjutant of the Kaiser, a handwriting as Goethe's, a mathematical expression as the Cardanian formula, and so on. Here our recognition can of course not apply itself to what is given in perception, at best it permits possible application to intuitive sequences, which need not themselves be actualized at all. In this manner recognitions, and sequences of recognitions, are possible on a basis of partial intuitions, which would on a priori grounds, not at all be possible on a basis of complete actual intuitions, since they combine incompatibles in themselves. There are, and are only too many, false and even absurd recognitions. But 'really' + +they are not recognitions, i.e. not logically worthwhile, complete 'knowings', not recognitions in the strong sense. To say this is to anticipate later discussions. For we have not yet clarified the ordering of the levels of knowledge + +(a matter here touched upon), nor the ideals which limit these. + +So far we had to do with signitive intentions, which exist identically, and just as they are, both within and without the function of meaning. But countless signitive intentions lack either a fixed or a passing tie with expressions, though their essential character puts them in a class with meaningintentions. I here recur to the perceptual or imaginative course of a melody, or of some other familiar type of event, and to the definite or indefinite intentions and fulfilments which arise in such a course. I refer likewise to the empirical arrangement and connection of things in their phenomenal coexistence, in regard to whatever gives the things appearing in this order, and especially the parts in each unified individual thing, the character of a unity involving precisely this order and this form. Representation and recognition through analogy may unite likeness and original (analogon and analogizatum), and may make them seem to belong together, but they cannot unite what is not merely contiguously given together, but what appears as belonging together. And even if, in the realization of representations through contiguity, images anticipating what is signitively represented are confirmed by their fulfilling originals, the unity among such contiguous representatives and what is represented through them can be given by no relation of picturing (since such a relation is not operative among them) but only through the entirely peculiar relation of signitive representation by way + +of contiguity. + +We may therefore rightly see, in inadequate percepts and imaginations, interwoven masses of primitive intentions, among which, in addition to perceptual and imaginative elements, there are also intentions of a signitive kind. We may therefore maintain, in general, that all phenomenological differences in objectifying acts reduce to their constituent elementary intentions and fulfilments, the former bound to the latter through syntheses of fulfilment. On the side of intentions, the only last differences are those between signitive intentions, as intentions by way of contiguity, and imaginative intentions, as intentions by way of analogy, each plain and pure in their own kind. On the side of fulfilment, intentions of either sort again function as components, but on occasion (as in the case of perception) we have components which cannot be called intentions, since they only fulfil but require no fulfilment, self-presentations of the object meant by them in the strictest sense of the word. The character of the elementary acts then determines the characters of the syntheses of fulfilment, which in their turn determine the homogeneous unity of the complex act. The emphatic power of attention helps to transfer the character of this or that elementary act to the unity of the act as a whole: this whole act becomes imagination or signification or pure perception. And where two such unified acts enter into + +relation, relationships of agreement and conflict arise, whose character is determined by the total acts underlying such relations, and ultimately by + +their elements. + +In the next chapter these relationships will be further tracked down, within the limits in which they can be phenomenologically ascertained and epistemologically evaluated. We shall keep strictly to phenomenologically given unities, and to the sense inherent in these and declared in their fulfilment. We shall thus avoid the temptation to embark on hypothetical construction, with whose doubts a clarification of knowledge should in no way be burdened. Chapter 3 + +The phenomenology of the levels + +of knowledge + +§ 16 Simple ide ntificati on and fu lfil ment + +In describing the relation of significant intention to fulfilling intuition we began with the verbal expression of a percept, and said that the intentional essence of the intuitive act fitted in with, or belonged to, the semantic essence of the significative act. This is plainly so in every case of total identification, where acts of like quality, i.e. both assertive or both unassertive, are synthetically unified; where the acts are of unlike quality, the identification is solely based on their materials. This carries over, mutatis mutandis, to cases of partial identification, so that we may hold that the material or matter is the aspect of the character of each act which comes up for synthesis, that is essential + +for identification (and naturally also for distinction). + +In the case of identification, the 'matters' are the special carriers of the synthesis, without themselves being identified. For talk of identification is, in virtue of its sense, concerned with the objects presented by such 'matters' . On the other hand, in the act of identification, the matters themselves achieve coincidence. Every example shows, however, that even where qualities are alike, the acts need not become quite alike: this is due to the fact that an act is not exhausted by its intentional essence. What remains over will reveal its importance in a careful phenomenological investigation of the levels of knowledge, which will be our task. It is clear from the start that, if knowledge admits of degrees of perfection, even when matter is constant, matter cannot be responsible for such differences of perfection, and cannot therefore determine the peculiar essence of knowledge as against any identification whatever. We shall tie our further investigation to a discussion of the previously + +studied difference of mere identification and fulfilment. + +We equatedl fulfilment with knowledge (in the narrower sense of the word) indicating that we were only talking of certain forms of identification which brought us nearer to the goal of knowledge. What this means may be elucidated by saying: In each fulfilment there is more or less complete intuitive illustration (Veranschaulichung). What the intention means, but presents only in more or less inauthentic and inadequate manner, the fulfilment - the act + +attaching itself to an intention, and offering it 'fu1ness' in the synthesis of fulfilment - sets directly before us, or at least more directly than the intention does. In fulfilment our experience is represented by the words: 'This is the thing itself' . This 'itself' must not be understood too strictly, as if there must be some percept bringing the object itself to actual phenomenal presence. It is possible that, in the progress of knowledge, in the gradual ascent from acts of poorer, to acts of ever richer epistemic fu1ness, we must at length always reach fu1filling percepts: this does not mean that each step, each individual identification that we call a fu1filment, need contain a percept as its fulfilling act. The relative manner in which we speak of 'more or less direct' and of 'self', indicates the main point: that the synthesis of fu1filment involves an inequality in worth among its related members. The fulfilling act has a superiority which the mere intention lacks: it imparts to the synthesis the fulness of 'self', at least leads it more directly to the thing itself. The relativity of this 'directness', this 'self', points further to the fact that the relation of fulfilment is of a sort that admits of degrees. A concatenation of such relations seems accordingly possible where the epistemic superiority steadily increases. Each such ascending series points, however, to an ideal limit, or includes it as a final member, a limit setting an unsurpassable goal to all advances: the goal of absolute knowledge, of the adequate self- + +presentation of the object of knowledge. + +We have thereby achieved, at least in preliminary fashion,2 the characteristic differentiating mark of fulfilments within the wider class of identifications. For not every identification represents such an approach to a goal of knowledge: there can well be a purposeless infinity of ever further identifications. There are, e.g., indefinitely many arithmetical expressions having the same numerical value 2, which permit us to add identification to identification in infinitum. Just so there may be infinitely many images of one and the same thing, determining again the possibility of endless chains of identifications tending to no goal of knowledge. The same holds for the endlessly many + +percepts of one and the same thing. + +If we pay heed to the constitutive elementary intentions in these intuitive examples, we shall of course find moments of true fulfilment entering into the total act of identification. This happens when we set image-presentations side by side which are not of completely equal intuitive content, so that the new image brings out many things much more clearly, and perhaps sets something before us 'just as it is', while a former image merely 'projects' it or denotes it symbolically. If we imaginatively envisage an object turning itself to every side, our sequence of images is constantly linked by syntheses of fulfilment in respect of its partial intentions, but each new imagepresentation does not, as a whole, fulfil its predecessor, nor does the whole series progressively approach any goal. Just so in the case of the manifold percepts belonging to the same external thing. Gain and loss are balanced at every step: a new act has richer fulness in regard to certain properties, + +for whose sake it has lost fulness in regard to others. But against this we may hold that the whole synthesis of the series of imaginations or percepts represents an increase in fulness in comparison with an act singled out from the series: the imperfection of the one-sided representation is, relatively speaking, overcome in the all-sided one. We say 'relatively speaking', since the all-sided representation is not achieved in such a synthetic manifold in the single flash which the ideal of adequation requires, as a pure selfpresentation without added analogizing or symbolization: it is achieved piecemeal and always blurred by such additions. Another example of an intuitive fulfilment-series is the transition from a rough drawing to a more exact pencil-sketch, then from the latter to the completed picture, and from this to the living finish of the painting, all of which present the same, visibly + +the same, object. + +Such examples from the sphere of mere imagination show that the character of fulfilment does not require that assertive quality in the intending and fulfilling acts which is part of the logical concept of knowledge. We prefer to speak of 'knowledge' where an opinion, in the normal sense of a + +belief, has been confirmed or attested. + +§ 17 The qu estion of the re lation between fu lfil ment + +and intu itive illustration + +We must now enquire into the part played in knowledge by the various kinds of objectifying acts - signitive and intuitive acts - and, under the latter rubric, acts of perception and imagination. Here intuitive acts plainly seem to be preferred, so much so, in fact, as to incline one to call all fulfilment intuitive illustration (Veranschaulichung) - as we did above in passing - or to describe the work of fulfilment, wherever one deals with intuitive intentions, as a mere increase in intuitive fulness. The relation between intention and fulfilment plainly underlies the formation of the conceptual couple: thought (more narrowly, concept), on the one hand, and corresponding intuition, on the other. But we must not forget that a notion of intuition oriented towards this relation does not at all coincide with that of an intuitive act, although, through the inherent tendency towards intuition which enters into the sense of all fulfilment, it closely depends on the latter and even presupposes it. To make a thought clear to oneself means, primarily, to give epistemic fulness to the content of one's thought. This can, however, be achieved, in a certain fashion, even by a signitive presentation. Of course, if we ask for a clearness which will make matters self-evident, which will make 'the thing itself' clear, render its possibility and its truth knowable, we are referred to intuition in the sense of our intuitive acts. For this reason talk of 'clearness' in epistemological contexts plainly has this narrower sense, it indicates recourse to fulfilling intuition, to the 'originative source' of con- + +Carefully analysed examples are now needed if we are to confirm and develop what has just been suggested. These will help us to clear up the relation between fulfilment and intuitive illustration, and to render quite precise the part played by intuition in every fulfilment. Differences between authentic and inauthentic illustration (or fulfilment) will distinguish themselves clearly, and the difference between mere identification and fulfilment will also therewith reach final clarity. The work of intuition will be shown to be that of contributing to the intended act, when authentically fulfilled, a genuinely novel element, to which the name 'fulness' may be given. We are thereby made aware of a hitherto unstressed side of the phenomenological content of acts, which is fundamental for knowledge. 'Fulness' must take its place as a new 'moment' in an intuitive act alongside of its quality and its matter, a moment specially belonging to the matter which it in some manner completes. + +§ 18 The gradations of mediate fu lfil me nts. + +Mediate presentati ons + +The formation of every mathematical concept which unfolds itself in a chain of definitions reveals the possibility of fulfilment-chains built member upon + +member out of signitive intentions. We clarify the concept (53) + +4 by having + +recourse to the definitory presentation: Number which arises when one forms the product 53 . 53 . 53 . 53. If we wish to clarify this latter concept, we must go back to the sense of 53, i.e. to the formation 5 . 5 . 5. Going back further, we should have to clarify 5 through the definitory chain 5 = 4 + 1, 4 = 3 + 1, 3 = 2 + 1, 2 = 1 + 1. After each step we should have to make a substitution in the preceding complex expression or thought and, were this proceeding indefinitely repeatable - it is certainly so in itself, just as it is certainly not so for us - we should at last come to the completely explicated sum of ones of which we should say: 'This is the number W)4 "itself" '. It is plain that an act of fulfilment not only corresponded to this final result, but to each individual step leading from one expression of this number, to the expression next in order, which clarified it and enriched its content. In this manner each ordinary decimal number points to a possible chain of fulfilments, whose links are one less in number than the number of their component units, so that chains of indefinitely many numbers are possible a priori. We usually talk as if, in the sphere of mathematics, the straightforward meaning of a word were identical with the content of its complex defining expression. In this case there could be no talk of fulfilment-chains: we should be moving among pure identities wholly tautological in character. But if one considers the complexity of the thought-formations which arise through substitution, and compares them, in those very simple cases where such substitution can be fully carried out, with the significative intentions that one at first experienced, one can hardly seriously think that in these last intentions all this complication was present from the start. It is plain that + +there are real differences in intention which, whatever their more precise description, are knit together through relationships of fulfilment which + +identify them as wholes. + +A remarkable property of the cases just discussed, and of the class of significative presentations which they illustrate, lies in the fact that in them the content of the presentations - or, more clearly their 'matter' - dictates a determinate order of fulfilment a priori. The fulfilment which here results mediately, can never also result immediately. To each signitive intention of this class there is a definite, proximate fulfilment or group of fulfilments, which in its turn has a definite, proximate fulfilment, etc. This property is also characteristic of certain intuitive intentions, as when we represent a matter to ourselves through images (pictures) of images (pictures). The matter of the presentation here also prescribes a prime fulfilment, which puts the primary image 'itself' before our eyes, but to this intention a new intention pertains, whose fulfilment leads on to the thing itself. What is common to all mediate presentations, whether intuitive or signitive, may be put by saying that they are presentations which do not present their objects straightforwardly, but by way of presentations built upon other presentations to a higher or lower degree. To put it more pointedly, they are presentations which present their objects as objects of other presentations, or as related to objects so presented. As objects can be presented in relation to any other objects, so they can be presented in relation to presentations. These presentations are presented presentations in the relational presentation: they belong + +among its intentional objects, not among its constituents. + +In connection with the class of cases just mentioned, we speak of mediate (or superordinate) intentions or fulfilments. The rule holds that every mediate intention requires a mediate fulfilment, which naturally, after a finite + +number of steps, ends up in an immediate intuition. + +§ 19 Disti nction between mediate presentati ons and + +presentations of prese ntations + +From these mediate presentations we must, however, distinguish presentations of presentations, i.e. presentations simply directed upon other presentations as their objects. Although such presented presentations are, generally speaking, themselves intentions, and so capable of fulfilment, the nature of the presenting presentations which are in question requires no mediate fulfilment through fulfilment of the presented presentation. The intention of P 1 (P2), a presentation of a presentation, is directed to P2: it is fulfilled, and completely fulfilled, when P2 'itself' is present. It is not enriched when the intention of P2 is fulfilled in its turn, when its object appears in an image or in a richer image, or even in a percept. For Pl refers, not to this object, but only to its presentation P2. Nothing obviously alters if the emboftement becomes more complex, e.g. in the case expressed by the symbol Pl(P2(P3)) etc. + +The thought 'signitive presentation' , for instance, is fulfilled in the intuition of a signitive presentation, e.g. of the presentation 'integral', or of the presentation 'signitive presentation' itself. These examples must not be misunderstood as meaning that the signitive presentation 'integral' itself claimed an intuitive status, as if the concepts of intuition and signitive act (meaningintention) were here confounded. It is not the signitive presentation 'integral' but the inner percept of this presentation that serves as the fulfilling intuition to the thought 'signitive presentation' . This presentation is not the fulfilling intuition, but the object of the fulfilling intuition. As the thought of a colour has its fulfilment in the act of intuiting this colour, so the thought of a thought has its fulfilment in an act of intuiting this thought, and its final intuitive fulfilment in an adequate percept of the same. Here as elsewhere, the mere being of an experience involves neither its intuition, nor, more particularly, its perception. It must be noted that, in our general opposition between thought or intention, and fulfilling intuition, intuition is not to be understood as mere outward intuition, the perceiving or imagining of external physical objects. As our just discussed example shows, and as the nature of presentation makes obvious, 'inner' perception or 'inner' imagination can + +function as a fulfilling intuition. + +§20 Genuine intu itive illustration in eve ry fu lfil ment. + +Authentic and inauthentic intu itive illustration + +Now that we have sufficiently stressed and clarified the distinction between mediate presentations and presentations of presentations, it will be proper to turn to what they have in common. Each mediate presentation includes, on the above analysis, presentations of presentations, inasmuch as it refers to its object as the object of certain presentations, which it itself presents. Thus if we think of 1000 as 103, we think of it as the number characterized as the object of the presentation which would arise were we to carry out the exponentiation in question. From this it is clear that genuinely intuitive illustrations play the essential part in all fulfilment of mediate intentions, and at each step in such fulfilment. The characterization of an object as object of a presented presentation (or as one related in a certain manner to objects so defined) presupposes in its fulfilment the fulfilment of these presentations of presentations, and these 'inwoven' intuitive fulfilments are the first to give the whole identification its character of a fulfilment. Its gradual increase in 'fulness' consists solely in the fact that, one by one, all its presentations of presentations have been fulfilled, whether such presentations were 'inwoven' in it from the beginning, or have emerged in the process of fulfilment through realizing 'construction' of these presented presentations, and through intuition of them when realized, so that in the end the dominant, total intention, with its structure of conjoined and subordinate intentions, appears as identified with an immediate intention. This last identification thereby has + +as a whole the character of a fulfilment. This kind of fulfilment is, however, a case of inauthentic intuitive illustration, since we are only entitled to predicate authentic intuitive illustration if fulness is not added anywhere, but only imparts an increase to the object presented by the presentation as a whole, which accordingly becomes more fully presented. This means no more, ultimately, than that a purely signitive presentation is without any fulness, and that all fulness rather resides in the actual 'making present' + +(Vergegenwiirtigung) of properties that pertain to the object itself. + +We shall presently pursue this last thought. Here we shall add that the difference we called one of 'authentic' and 'inauthentic intuitive illustration' could also be called one of authentic and inauthentic fulfilment, since an intention aims at its object, is as it were desirous of it, and since fulfilment, in the pregnant sense of the word only registers the fact that some part of the fulness of the object is imparted to the intention. We must, however, still hold that inauthentic and authentic fulfilments are alike marked out among syntheses of identification by a common phenomenological character (that of fulfilment in the wider sense), and that there is a peculiar principle to the effect that all inauthentic fulfilment implies authentic fulfilments, and indeed + +borrows its character of fulfilment from these authentic cases. + +To demarcate the difference between authentic and inauthentic intuitive illustrations somewhat more precisely, and at the same time deal with a class of cases where inauthentic intuitive illustrations have every appearance of + +authenticity, we add the following remarks: + +It is not always the case that, when the fulfilment of a signitive intention is consummated on an intuitive basis, the 'matters' of the acts concerned, as presupposed above, are in a relationship of coincidence, so that the object which appears intuitively also comes before us as itself meant in our act of meaning. Only when this happens, however, may one talk of intuitive illustration in the true sense: only then is a thought realized perceptually, or illustrated imaginatively. The case is different when the fulfilling intuition presents an indirectly represented object, as when the use of a geographical name calls up the imaginative presentation of a map, which blends with the meaning-intention of this name, or as when a statement about certain streetconnections, courses of rivers, features of mountains, is confirmed by what stands inscribed on a map before us. Here intuition should not be said to fulfil in the true sense of the word: its own matter does not enter into action. The real basis of fulfilment does not lie in it at all, but in a plainly signitive intention intertwined with it. That the apparent object here functions as indirectly representing the object meant and named, means, phenomenologically speaking, that its constitutive intuition is now the bearer of a novel intention, an intention pointing beyond the apparent object, and thereby characterizing it as a sign. The analogy of what appears and what is meant, which may be present here, does not lead to a straightforward presentation by way of an image, but to a sign-presentation resting upon the latter. The + +outline of England as drawn in the map, may indeed represent the form of the land itself, but the pictorial image of the map which comes up when England is mentioned, does not mean England itself in pictorial fashion, not even mediately, as the country pictured on the map. It means England after the manner of a mere sign, through external relations of association, which have tied all our knowledge of land and people to the map-picture. When, therefore, our naming intention is fulfilled through this mental picture, it is not the object imagined in the latter (the map), which counts as the very thing meant by the name, but the original object which the name represents. + +§2 1 The 'fulness' of a presentation + +It will, however, now be necessary to view the achievement of intuitive intentions more closely. Since the fulfilment of mediate intentions refers back to the fulfilment, the intuitive fulfilment of immediate intentions, and since it has transpired that the final outcome of the whole mediate process is an immediate intention, we now concern ourselves with the question of the intuitive fulfilment of immediate intentions and of the relationships and laws governing their sphere. This question we therefore attack. But we may observe from the start that, in the following investigations, only the 'matter' -side of an act's intentional essence will have relevance for the relationships to be established. The qualities of our intention (whether assertive + +or merely presentative) can be varied indifferently. We begin with the following proposition: + +To every intuitive intention there pertains, in the sense of an ideal possibility, a signitive intention precisely accommodated to its material. This unity of identification necessarily has the character of a unity of fulfilment, in which the intuitive, not the signitive member, has the character of being the fulfiller, and so also, in the most authentic sense, the giver of fulness. We only express the sense of this last statement in a different way if we say that signitive intentions are in themselves 'empty', and that they 'are in need of fulness' . In the transition from a signitive intention to the corresponding intuition, we experience no mere increase, as in the change from a pale image or a mere sketch to a fully alive painting. The signitive intention is rather lacking in every sort of fulness: the intuitive presentation first brings fulness to it, and, through identification, into it. A signitive intention merely points to its object, an intuitive intention gives it 'presence', in the pregnant sense of the word, it imports something of the fulness of the object itself. However far an imaginative presentation may lag behind its object, it has many features in common with it, more than that, it is like this object, depicts it, makes it really present to us. A signitive presentation, however, does not present analogically, it is 'in reality' no 'presentation', in it nothing of the object comes to life. The ideal of complete fulness is, accordingly, the fulness of the object itself, as the sum total of its constitutive properties. The fulness + +of the presentation is, however, the sum total of properties pertaining to the presentation itself, through which it analogically gives presence to its object, or apprehends it as itself given. Fulness is, accordingly, a characteristic moment of presentations alongside of quality and matter, a positive constituent only in the case of intuitive presentations, a privation of the case of signitive. The 'clearer' a presentation is, the higher its pictorial level, the richer it is in fulness. The ideal offulness would, accordingly, be reached in a presentation which would embrace its object, entire and whole, in its phenomenological content. If we include individualizing features in the fulness of the object, such features can be embraced by no imagination, only by a percept. But, if we ignore these features, a definite ideal exists for imagination as well. We must accordingly return to the features of the presented object: The more of these features enter into the analogical representation and, as regards each separate feature, the greater the similarity with which the presentation represents it in its content, the greater is the fulness of the presentation. Somehow, no doubt, every feature of an object is included in the scope of every presentation, and so in that of the pictorial presentation, but not every property is analogically represented, the phenomenological content of the presentation does not contain a peculiar, so-to-say analogizing or depicting moment for each. The sum total of the intimately fused moments which are thought to underlie purely intuitive (in this case imaginative) ways of regarding things, which first gives them the character of being representative of corresponding objective moments, constitutes the fulness of the imaginative presentation. Hence in addition to imaginative representations, there are also perceptual ones, graspings of the thing itself, self-exhibitions of objective moments. If we assemble the sum total of the imaginatively or perceptively functioning moments of the perceptual presentation, we have marked off + +the fulness of the latter. + +§22 Fulness and 'intu itive su bstan ce' (Gehalt) + +Closely regarded, the concept of fulness is still fraught with an ambiguity. The above mentioned moments can be looked at in respect of their own existential content, without regard to the functions of pure imagination or perception, which first confer on them the value of being a picture or a perspectivally slanted self-revelation, and so a value for the function of fulfilment. On the other hand, one can consider these moments in their interpretation, i.e. not these moments alone, but the full pictures or slanted self-revelations in question. Ignoring only intentional qualities, one can deal with purely intuitive acts as wholes, which include these moments in themselves, since they give them an objective significance. These 'purely intuitive' acts we conceive as mere constituents of the intuitions just mentioned, being the element in them which gives to the moments previously mentioned, a relation to corresponding objective properties which are represented through + +them. We ignore therewith (in addition to the qualities) the yet further attached signitive relations to further parts or sides of the object which are + +not, properly speaking (intuitively), represented. + +It is plainly these purely intuitive constituents which impart to total acts the character of percepts or imaginings, i.e. their intuitive character, and which function in the system of serially ordered fulfilments as the element which confers 'fulness', or which enriches or increases the same when already present. To deal with this ambiguity in our talk of 'fulness' we shall + +introduce the following distinguishing terms: + +By intuitively presentative or intuitively representative contents (Inhalten) we understand those contents of intuitive acts which, owing to the purely imaginative or perceptual interpretations that they sustain, point unambiguously to definitely corresponding contents in the object, represent these in imagined or perceived perspectival slantings. The act-aspects which characterize them in this manner, we ignore. Since the character of imagination lies in analogical picturing, in 'representation' in a narrower sense, while the character of perception can be called strictly presentative, the following distinctive names suggest themselves: For the intuitively presentative contents in either case - analogizing or picturing contents, on the one hand, and strictly presentative or self-presentative contents, on the other. The expressions 'imaginatively slanted contents' and 'perceptively slanted contents' are also very apt. The intuitively presentative contents of outer perception define the concept of sensation in the ordinary, narrow sense. The intuitively presentative contents of external fantasy are sensory phantasms or images. The intuitively presentative or intuitively representative contents in and with the interpretation put upon them, we call the intuitive substance (Gehalt) of the act: in this we still ignore the quality of the act (whether assertive or not), as being indifferent to the distinctions in question. On the above, all signitive components of an act are excluded from its intuitive 'substance'. 3 + +§23 Relationships of we ight between the intu itive and sign itive 'su bstan ce' (Gehalt) of one and the same act. Pure intuition and pure sign ification. Perceptual and + +imaginal content, pure perception and pure + +imagination. Gradations of fu lness + +To increase the clearness of the concepts just marked off, and to aid in the marking off of a new set of concepts, rooted in the same soil, we embark on + +the following discussion: + +In an intuitive presentation (Vorstellung) an object is meant in the manner of perception or imagination: in this manner it is more or less perfectly made apparent. To each part and each property of the object, including its reference to a here and a now, there must necessarily be a corresponding part or moment of the conscious act. What we do not mean, is simply not + +there for oui presentation (Vorstellung). We now find in general that it is possible to draw the following phenomenological distinction between + +(1) The purely intuitive 'substance' (Gehalt) of the act, i.e. all that corresponds in the act to the sum total of the object's properties that 'become apparent', (2) The signitive 'substance' of the act, which corresponds to the sum total of the remaining, subsidiarily given properties of the object, which do not + +themselves become apparent. + +We all draw such a distinction, in purely phenomenological fashion, in the intuition involved in the percept or image of a thing, between whatever in the object is truly made apparent, the mere 'side' from which the object is shown to us, and whatever lacks intuitive presentation (Darstellung), is hidden by other phenomenal objects etc. Such talk plainly implies, what phenomenological analysis within certain limits definitely proves, that even what is not presented (Nicht-Dargestelltes) in an intuitive presentation (Vorstellung) is subsidiarily meant, and that an array of signitive components must accordingly be ascribed to the latter, from which we have to abstract, if we wish to keep our intuitive content pure. This last gives the intuitively presenting (darstellende) content its direct relation to corresponding objective moments: other novel and, to that extent, mediate, signitive intentions, + +are attached to these by contiguity. + +If we now define the weight of the intuitive (or signitive) content as the sum total of the intuitively (or signitively) presented (vorgestellte) moments of the object, both 'weights' in each presentation (Vorstellung) will add up to a single total weight, i.e. the sum total of the object's properties. Always therefore the symbolic equation holds: i + s = 1. The weights i and s can plainly vary in many regards: the same, intentionally same, object can be intuitively given with more or less numerous, ever varying properties. The signitive content also alters correspondingly, it is increased or diminished. + +Ideally we now have the possibility of two limiting cases: + +i=O s= 1 i = 1 s = O. + +In the former, the presentation (Vorstellung) would have only signitive content: no property of its intentional object would remain over which was brought to intuitive presentation (Darstellung) in its content. The special case of purely signitive presentations, well-known to us as pure meaning- + +intentions, therefore appears here as a limiting case of intuition. + +In the second case the presentation (Vorstellung) has no signitive content whatever. In it all is fulness: no part, no side, no property of its object fails to be intuitively presented (dargestellt), none is merely indirectly and subsidiarily meant. Not only is everything that is intuitively presented also meant - so much is analytically true - but whatever is meant is also intuitively presented. This new class of presentations may be defined as pure intuitions, the + +term here used with innocuous ambiguity, at times to cover complete acts, at times such acts in abstraction from their quality. We may speak distin- + +guishingly of qualified and unqualified pure intuitions. + +In each presentation (Vorstellung) we can therefore surely abstract from all signitive components, and limit ourselves to what is really represented in its representative content. By so doing we form a reduced presentation, with a reduced object in regard to which it is purely intuitive. We can accordingly say that the intuitive substance (Gehalt) of a presentation comprises all that is pure intuition in it, just as we may also speak of the object's purely intuitive content, of all that is rendered intuitive in this presentation. The like applies to the signitive substance of the presentation: this can be said to be + +all that is pure signification in it. + +Each total act of intuition has either the character of a percept or an imagination: its intuitive substance is then either perceptual or imaginative substance or content. This must not be confused with the perceptually or + +imaginatively presenting content in the sense defined in §22. + +Perceptual content comprises (though not in general exclusively) strictly presentative contents: imaginative contents comprise only analogizing contents. It is not to the point that these latter contents permit of another interpretation (as in the case of physical images), in which they function + +strictly presentatively. + +On account of the mixture of perceptual and imaginative components which the intuitive substance of a percept permits and usually exhibits, we can again consider adopting a division of perceptual content into pure perceptual content, on the one hand, and supplementary image-content, on the other. If then, in each pure intuition we take Pp and Ip to be the weights of its purely perceptual and purely imaginative components, we can write down + +the symbolic equation + +where I symbolizes the weight of the total intuitive content of the pure intuition, and thus the total content of its object. If Ip = 0, i.e. if the pure intuition is free from all imaginal content, it should be called a pure perception: we shall here ignore the qualitatively assertive character usually embraced in the sense of the term 'perception' . But if Pp = 0, the intuition is called pure imagination. The 'purity' of pure perception relates, therefore, not merely to signitive, but also to imaginative supplements. The narrowing of an impure percept which throws out symbolic components yields the pure intuition which is immanent in it: a further reductive step then throws out + +everything imagined, and yields the substance of pure perception. + +Can the intuitively presentative content in the case of pure perception be identified with the object itself? The essence of pure presentation (in the strict sense) surely consists in being a pure self-presentation of the object, + +one which means the intuitively presentative content directly (in the manner of 'self') as its object. This would, however, be a paralogism. The percept, as presentation in the strict sense, so interprets the intuitively presentative content, that the object appears as itself given with and in this content. Presentation (in the strict sense) is pure, when each part of the object is actually and intuitively presented in the content, and none is merely imagined or symbolized. As there is nothing in the object not strictly presented, so there is nothing in the content not strictly presentative. Despite such exact correspondence, self-presentation may still have the character of the mere, even if all-sided perspectivity (of a completed perceptual picture): it need not attain the ideal of adequation, where the intuitively presenting content is also the intuitively presented content. The pure picture-presentation, which completely depicts its object through its freedom from all signitive additions, holds in its intuitively presentative content a complete likeness of the object. This likeness can approach the object more or less closely, to a limit of complete resemblance. The same may be true in the case of pure perception, with the sole difference, that imagination treats the content as a likeness or image, whereas perception looks on it as a self-revelation of the object. Pure perception no less than pure imagination admits, accordingly, of differing degrees of fulness, without thereby altering its intentional object. Regarding the degrees of fulness of intuitive content, to which degrees of fulness of rep- + +resentative content run eo ipso parallel, we may distinguish: + +1. The extent or richness of the fulness, according as the content of the object achieves intuitive presentation with greater or less completeness. 2. The liveliness of this fulness, i.e. the degree of approximation of the primitive resemblances of the intuitive presentation to the corresponding + +moments of content in the object. + +3. The reality-level (Realitiitsgehalt) of the fulness, the greater or less + +number of its strictly presentative contents. + +In all these regards, adequate perception represents an ideal: it has a maximum of extent, liveliness and reality: it is the self-apprehension of the + +whole, full object. + +§24 Graded series of fu lfil me nts + +We framed our talk of 'fulness' with an eye to relationships of 'fulfilment', that peculiar form of the synthesis of identification. But in our last results we not only threw light on the concept of fulness, but also on its differences of greater or lesser completeness, liveliness and reality, as well as on the gradations in pictorialization and perspectival projection, and all by way of relationships among the inner 'moments' of our presentations, or among these and the objective moments that they intend. But it is plain that to these relationships there correspond possible gradients of increase, founded on syn- + +Fulfilment arises out of the first application of fulness as such, in the identifying accommodation of 'corresponding' intuition to a signitive intention. In the context of coincidence the intuitive act 'gives' its fulness to the signitive act. The consciousness of increase is here founded on the partial coincidence of the fulness with correlative parts of the signitive intention, while to the corresponding empty parts of both intentions, which alike enter this identifying coincidence, no part of this sense of increase can be ascribed. A continuous increase in fulfilment is further achieved in the continuity of intuitive acts or serial fulfilments which present the object with ever more + +extended and intense illustrativeness. That B + +2is a 'more perfect' image than + +B l > means that fulfilment obtains in the synthetic context of the pictorial + +presentation in question, and increased fulfilment in the direction of B + +2 • Here + +as elsewhere distances pertain to increases, and transitivity to concatenated + +relationships. If B + +2is at once > B1 + +, and B + +3> B2 + +, then B + +3> Bl and this last + +distance exceeds those which mediate it. This is so at least if we take separate account of the three moments of fulness, i.e. extent, liveliness and reality, + +which were distinguished above. + +These increases and gradients of increase correspond, as analysis shows, to resemblances and gradients of resemblance among the intuitively presentative contents of the fulnesses. Likeness of presentative contents, or concatenations of such likenesses, are not, however, to be taken to be the same as simple or concatenated increases: they are not so when these 'fulnesses' are considered in their own being as contents, in abstraction from their representative function in the relevant acts. Only through this latter function, i.e. through the fact that, in the order of graded fulfilments, and of the increases obtaining among its acts, each later act of fulness appears richer, do the representative contents of the acts achieve their ascending order. They appear one after the other as not only themselves furnishing fulness, but as furnishing it ever more abundantly. To call such components 'fulnesses' is to talk relatively and functionally: it is to express a characteristic accruing to the contents through the acts, and through the part played by these acts in possible syntheses of fulfilment. Our term here resembles the term 'object'. To be an object represents no positive mark, no possible species of content: it refers to the content only as intentionally correlated with a presentation. For the rest, relationships of fulfilment and increase plainly have their foundation in the phenomenological 'substance' (Gehalt) of our acts, considered purely in their specificity. We are concerned throughout only with ideal relationships determined by the ideal Species in question. In the synthesis of intuitive acts there is, however, not always an increase in fulness: partial fulfilment can go hand in hand with partial emptying, as we mentioned above. The distinction between mere identification and fulfilment points back to the fact, we may say, that in the case of the former there may be either no genuine fulfilment, since we have to do only with asserted identities among acts alike lacking in fulness, or because the fulfilment or + +enriched fulfilment which obtains goes together with a simultaneous emptying or surrender of previous fulness, so that no emphatic unmixed consciousness of increase arises. In any case the primitive relations among our elementary intentions are either fulfilments of empty (i.e. purely signitive) intentions, or supplementary fulfilment of intentions already to some extent + +filled, i.e. increase and realization of an imaginative intention. + +§2S Ful ness and intentional matter + +We now wish to discuss the relation between the new concept of presentational content covered by the name 'fulness', with content in the sense of 'matter', which last has played such a large part in our investigation up to this point. 'Matter' was classed as that moment in an objectifying act which makes the act present just this object in just this manner, Le. in just these articulations and forms, and with special relation to just these properties or relationships. Presentations which agree in their matter do not merely present the same object in some general fashion: they mean it in the most complete fashion as the same, as having exactly the same properties. The one presentation confers nothing on the object in its intention which the other presentation does not likewise confer. To each objectifying articulation and form on one side there is a corresponding articulation and form on the other, in such a manner that the agreeing elements of the presentations have an identical objective reference. In this sense we said in our Fifth Investigation, in elucidating the concepts of 'matter' and 'semantic essence': 'Two judgements are in essence the same judgement (Le. judgements with the same 'matter'), if everything that would hold of the state of affairs judged according to one, would likewise hold of it according to the other, and nothing different would hold of it in either case. The truth-value of the judgements is the same'. They mean the same in regard to the object, even if they are otherwise quite different, if the one, e.g., is achieved signitively, + +while the other is more or less illustrated by intuition. + +I was led to form this notion through a consideration of what is identical in the assertive and understanding use of the same expression, where one may 'believe' the content of some statement, while another leaves it undecided, without disturbing this content's identity, in which case it also makes no difference whether expression occurs in connection with correspondent intuition, and whether it can so occur or not. One might therefore be tempted - I myself hesitated long on this point - to define meaning as this very 'matter', which would, however, have the inconvenience that the moment of assertion in, e.g., a predicative statement, would fall outside of that statement's meaning. (One could no doubt limit the concept of meaning in this fashion, and then distinguish between qualified and unqualified meanings.) Our comparison of meaning-intentions with their correlative intuitions, in the static and dynamic unity of identifying coincidence, showed us, however, + +that the very thing that we marked off as the 'matter' of meaning, reappeared once more in the corresponding intuition, and furnished the means for an identification. Our freedom, therefore, to add to or take away intuitive elements, and even all correspondent intuitions, wherever we limited our concern to the abiding meaningfulness of a given expression, was based on the fact that the whole act attaching to the sound of our words had the same 'matters' on the intuitive as on the meaning side, in respect, that is, of such + +elements of meaning as receive intuitive illustration at all. + +It is clear, therefore, that the concept of 'matter' must be defined by way of the unity of total identification as the element in our acts which serves as a basis for identification, and that all differences of fulness which go beyond mere identification, and which variously determine peculiarities of fulfilment and increase of fulfilment, have no relevance in the formation of this conception. However the fulness of a presentation may vary within its possible gradients of fulfilment, its intentional object, intended as it is intended, remains the same: its 'matter' , in other words, stays the same. Matter and fulness are, however, by no means unrelated and, when we range an intuitive act alongside a signitive act to which it brings fulness, the former act does not differ from the latter merely by the joining on of a third distinct moment of fulness to the quality and matter common to the two acts. This at least is not the case where we mean by 'fulness' the intuitive content of intuition. For intuitive content itself already includes a complete 'matter', the matter of an act reduced to a pure intuition. If the intuitive act in question was already purely intuitive, its matter also would be a constituent of its intuitive content. The relations which obtain here will be best set forth by establishing the + +following parallelism between signitive and intuitive acts. + +A purely signitive act would be a mere complex of quality and matter, if indeed it could exist by itself at all, i.e. be a concrete experiential unity 'on its own'. This it cannot be: we always find it clinging to some intuitive basis. This intuition of a sign may have 'nothing at all to do' with the object of the significative act, it may stand to it in no relation of fulfilment, but it realizes its possibility in concreto of being an altogether unfulfilled act. The following proposition therefore seems to hold: An act of signification is only possible in so far as an intuition becomes endued with a new intentional essence, whereby its intuitive object points beyond itself in the manner of a sign (whether as a sign regularly or fleetingly used). More closely considered, this proposition does not, however, seem to express the necessities of connection which obtain here with the needed analytic clearness, and perhaps says more than is justified. For we can, it seems, say that it is not our founding intuition as a whole, but only its representational content, which really assists the signitive act. For what goes beyond this content, what pins down the sign as a natural object, can be varied at will without disturbing the sign's signitive function. Whether the letters of a verbal sign are of wood, iron or printer's ink etc., or seem to be such objectively, makes no difference. Only their + +repeatedly recognizable shape is relevant, not as the objective shape of the thing of wood etc., but as the shape actually present in the intuitively presentative sensuous content of intuition. If there is only a connection between the signitive act and the intuitively presentative content of our intuition, and if the quality and matter of this intuition mean nothing to this signitive function, then we ought not to say that each signitive act requires a founding intuition, but only that it requires a founding content. It would seem that any content can function in this fashion, just as any content can function as + +the intuitively presentative content of an intuition. + +If we now turn our regard to the parallel case of the purely intuitive act, its quality and matter (its intentional essence) are not capable of separate existence on their own: here too a supplement is required. This is furnished by the representative content, i.e. the content - sensuous in the case of a sensuous intuition - which in its present fusion with an intentional essence has acquired the character of being an intuitive representative. If we bear in mind the fact that the same (e.g. sensuous) content can at one time carry a meaning, and at another time an intuition - denoting in one case and picturing in the other - we are led to widen the notion of a representative content, and to distinguish between contents which represent signitively (signitive representatives) and contents which represent intuitively (intuitive representatives). Our division is, however, incomplete. We have so far considered only the purely intuitive or purely signitive acts. If we bring in the mixed acts as well, those we ordinarily class as intuitive, we find them peculiar in the fact that their representative content is pictorial or self-presentative in respect of one part of what it objectively presents, while being merely denotative as to the remaining part. We must accordingly range mixed representatives beside purely signitive and purely intuitive representatives: these represent signitively and intuitively at the same time, and in regard to the same intentional essence. + +We may now say: + +Each concretely complete objectifying act has three components: its quality, its matter and its representative content. To the extent that this content functions as a purely signitive or purely intuitive representative, or as both together, the act is a purely signitive, a purely intuitive or a mixed act. + +§26 Cont inuation. Representation or interpretation (Auffassung). Matte r as the interp retative sense, the interpretative fo rm and the interp reted content. Differentiati ng characte rization of intu itive and + +sign itive interpretation + +We may now ask what this 'functioning' really stands for, since we have it as an a priori possibility that the same content, bound up with the same quality and matter, should function in this threefold manner. It is plain that it can only be the phenomenological peculiarity of the relevant form of unity that + +can give a phenomenologically discoverable content to our distinction. This form specially unites the matter to the representative content, since the representative function is unaffected by change in the quality. Whether, e.g., an imaginative picturing claims to be the calling up of a real object or to be merely imaginative, makes no difference to its pictorially presentative character, that its content bears the function of an image-content. We therefore call the phonomenological union of matter with representative content, in so far as it lends the latter its representative character, the form of representation, and the whole engendered by these two moments the representation pure and simple. This designation expresses the relation between representing and represented content (latter = the object or part of the object represented) by going back to its phenomenological foundation. Leaving aside the object as something not phenomenologically given, and endeavouring merely to express the fact that, when a content functions representatively, we are always differently 'minded', we may speak of a change in interpretation (Auffassung). We may also call the form of representation the interpretative form. Since the matter after a manner fixes the sense in which the representative content is interpreted, we may also speak of the interpretative sense. If we wish to recall the older term, and at the same time indicate an opposition to form, we may also speak of the interpretative matter. In each interpretation we must therefore distinguish phenomenologically between: interpretative matter or sense, interpretative form and interpreted content; this last is to be distinguished from the object of the interpretation. The term 'apperception' is unsuitable despite its historical provenance, on account of its misleading terminological opposition to 'perception'; 'apprehension' would be more usable. Our next question concerns the distinguishing marks of the various modes of representation or interpretation which, as we saw, can be different even when the interpretative matter - the 'as what' of interpretation - is constant. In the previous chapter we characterized differences of representations through differences in forms of fulfilment, in the present context we have regard to an internal characterization limited to the proper descriptive stuff of intentions. If we may make use of the beginnings of an analytical clarification which our previous treatment suggested, as well as of our subsequent advances in the general grasp of 'representation', the following train of ideas + +suggests itself: + +We begin with the observation that signitive representation institutes a contingent, external relation between matter and representative content, whereas intuitive representation institutes one that is essential, internal. The contingency of the former consists in the fact that an identical signification can be thought of as attached to every content whatsoever. Significative matter has a general need for supporting content, but between the specific nature of the former and the specific being of the latter no bond of necessity can be found. Meaning cannot, as it were, hang in the air, but for what it means, + +the sign, whose meaning we call it, is entirely indifferent. + +The case of purely intuitive representation is quite different. Here there is an internal, necessary connection between matter and representing content, fixed by the specific stuff of both. Only those contents can be intuitively representative of an object that resemble it or are like it. Phenomenologically put: we are not wholly free to interpret a content as this or as that (or in this or that interpretative sense) and this has more than an empirical foundation - every interpretation including a significative one is empirically necessary - since the content to be interpreted sets limits to us through a certain sphere of similarity and exact likeness, i.e. through its specific substance. The internality of the relation does not merely forge a link between the interpretative matter as a whole and the whole content: it links their parts on each side piece by piece. This occurs in the presupposed case of pure intuition. In the case of impure intuition the specific union is partial: a part of the matter - the matter of the reduced, and therefore, of course, pure, intuition - provides the intuitive sense in which the content is interpreted, while the remainder of the matter undergoes no representation through similarity or exact likeness, but merely through contiguity, i.e. in mixed intuition the representative content functions as intuitive representative for one part of the matter, but as signitive representative for the remaining part. If one finally asks how one and the same content (in the sense of 'same matter') can at times be 'taken up' in the manner of an intuitive, and at times in the manner of a signitive representative, in what the differing nature of these interpretative forms consists, I can give them no further answer. We + +are facing a difference that cannot be phenomenologically reduced. + +In these discussions we have treated representation independently as a union of matter and representative content. If we go back again to the complete acts, these reveal themselves as combinations of act-quality with either intuitive or signitive representation. The whole acts are called intuitive or signitive, a difference determined by these inwrought representations. The study of relations of fulfilment led us above to the concept of intuitive substance or fulness. If we compare that case of concept-formation with the present one, it sets bounds to the purely intuitive representation (i.e. pure intuition) that belongs to an act of impure intuition. 'Fulness' was a notion specially framed for the comparative treatment of acts in their fulfilling function. The limiting case opposed to pure intuition, pure signification, is + +of course the same as purely signitive representation. + +§27 Represe ntations as the necessary bases of presentation in al l acts. Fi nal clarificat ion of tal k about the diffe rent modes of the re lation of + +consciousness to its object + +Each objectifying act includes a representation in itself. Every act whatever, following the conclusions of the Fifth Investigation (see particularly the + +penultimate chapter, §41) is either itself an objectifying act, or has such an act as its basis. The ultimate bases of all acts are therefore 'presentations' in + +the sense of representations. + +Talk of the differing mode of relation of an act to its objects has been shown, + +in the above discussions, to cover the following essential ambiguities: 1. The quality of acts, the modes of believing, entertaining, wishing, doubt- + +ing etc. + +2. The underlying representation, and + +(a) the interpretative form, i.e. whether the object is presented in purely signitive, or intuitive, or mixed fashion. Here also belong the differences + +between a perceptual and an imaginative presentation etc.; + +(b) the interpretative matter: whether the object is presented in this or that 'sense', e.g. significatively through differing meanings, presenting the same + +object but qualifying it differently; + +(c) the interpreted contents: whether the object is presented by way of this or that sign, or by way of this or that representative content. In the latter case, if we consider the matter more closely, the laws connecting intuitive representatives with matter and form, entail that we are also concerned with + +differences that affect form even where matter remains constant. + +§28 Intentional esse nce and fu lfill ing sense. Epistemic esse nce. Intuitions in specie + +In our First Investigation (§ 14) we opposed 'fulfilling sense' to meaning (or fulfilling meaning to intending meaning) by pointing to the fact that, in fulfilment, the object is 'given' intuitively in the same way in which the mere meaning means it. We then took the ideally conceived element which thus coincides with the meaning, to be the fulfilling sense, and said that, through this coincidence, the merely significant intention (or expression) achieved + +relation to the intuitive object (expressed this and just this object). + +This entails, to employ conceptual formations later introduced, that the fulfilling sense is interpreted as the intentional essence of the completely and + +adequately fulfilling act. + +This conceptual formation is entirely correct and suffices for the purpose of pinning down the entirely general aspects of the situation where a signitive intention achieves relation to its intuitively presented object: it expresses the important insight that the semantic essence of the signitive (or expressive) act reappears identically in corresponding intuitive acts, despite phenomenological differences on either side, and that the living unity of identification realizes this coincidence itself, and so realizes the relation of the expression to what it expresses. On the other hand it is clear, in virtue precisely of this identity, that the 'fulfilling sense' carries no implication of fulness, that it does not accordingly include the total content of the intuitive act, to the extent that this is relevant for the theory of knowledge. It might be + +thought objectionable that we have conceived the intentional essence so narrowly as to exclude such an important constituent of the act; and one so decisive for knowledge. We were guided by the thought that the essence of an objectifying intention must be something which no intention of this sort could lack, or which could not be freely varied in it, without having an ideally necessary effect on its relation to its object. Purely signitive acts are, however, 'empty' acts, acts lacking in the moment of fulness, and so only the unity of quality and matter can count as the essence of an objectifying act. It might now be objected that signitive intentions without sensuous support are impossible, that they also have intuitive fulness in their fashion. But, in the sense of our treatment of signitive representation, and our earlier treatments of authentic and inauthentic illustration, this is really not fulness. Or rather it is fulness, but not fulness of the signitive act, but of the act on which it is founded, the act in which the sign is set up as an intuitive object. This fulness may, we saw, vary without limit, without affecting the signitive intention, and what concerns its object. Taking into account this circumstance, as well as the fact that, even in intuitive acts, fulness may vary, albeit within bounds, while the same object is constantly meant, with the same properties and with the same act-quality, we plainly need a term to stand for + +the mere unity of quality with matter. + +But it is now also useful, on the other hand, to frame a more embracing concept. We accordingly define as the epistemic essence of an objectifying act (in opposition to its merely semantic essence) all the content which has relevance for its knowledge-function. The three components of quality, matter and fulness (or intuitive content) all belong to it. If we wish to avoid the overlap of the last two components, and have wholly exclusive components, we may make it consist of quality, matter and intuitively representative content, the last of which falls away in empty intentions, together with all 'fulness' . All objectifying acts having the same epistemic essence are the 'same' act for the ideal purposes of the theory of knowledge. When we speak of objectifying acts in specie, we have a corresponding idea in mind. The same + +holds of (deliberately) restrictive talk of intuitions in specie etc. + +§29 Complete and defective intuitions. Adeq uate and objective ly complete intu itive illustrat ions. fssentia + +(fssenz) + +In an intuitive presentation a varying amount of intuitive fulness is possible. This talk of a varying amount points, as we argued, to possible gradients of fulfilment: proceeding along these, we come to know the object better and better, by way of a presentative content that resembles it ever more and more closely, and grasps it more and more vividly and fully. We know also that intuition can occur where whole sides and parts of the object meant are not apparent at all, i.e. the presentation has an intuitive content not con- + +taining pictorial representatives of these sides and parts, so that they are only presented 'inauthentically', through inwrought signitive intentions. In connection with these differences, which result in very different modes of presentation for one and the same object, with meaning governed by the same matter, we spoke above of differences in the extent of fulness. Here + +two important possibilities must be distinguished. + +1. The intuitive presentation presents its object adequately, i.e. with an intuitive substance (Gehalt) of such fulness, that to each constituent of the object, as it is meant in this presentation, a representative constituent of + +the intuitive content corresponds. + +2. Or this is not the case. The presentation contains no more than an + +incomplete projection of the object: it presents it inadequately. + +Here we are talking of the adequacy or inadequacy of a presentation to its object. Since, however, we speak more widely of adequacy in contexts of fulfilment, we introduce yet another set of terms. We shall speak of complete and defective intuitions (more particularly of complete and mutilated percepts or imaginations). All pure intuitions are complete. The following considerations will at once show that the converse does not hold, and that our proposed division does not simply coincide with that of pure and impure intuitions. Whether presentations are simple or complex is a matter regarding which nothing is presupposed in the distinction just drawn. Intuitive presentations + +may, however, be complex in two ways: + +(a) The relation to the object may be simple in so far as the act (more specifically, its matter) has no constituent acts (or no separate matters) that independently present the same total object. This does not preclude the possibility that an act should be made up of partial intentions homogeneously fused, which relate to the individual parts or sides of its object. One can scarcely avoid assuming such complexity in the case of 'external' percepts and imaginations, and we have proceeded on this assumption. But, on the + +other hand we have + +(b) the kind of complexity in which the total act is built out of constituent acts, each of which independently is a full intuitive presentation of the same object. This we have in those extremely remarkable continuous syntheses which bind together a multitude of percepts which pertain to the same object, into a single 'many-sided' or 'all-sided' percept, which deals with the object continuously in 'varying positions' . There are the corresponding syntheses of imagination. In the continuity of a prolonged fusion-intosameness not broken up into isolated acts, the same single object appears singly, not as often as individual acts can be distinguished. It appears, however, with altering fulness of content, though the matters, and likewise the qualities remain steadfastly the same, at least when the object is known from all angles, and repeatedly comes to light in its unenriched familiarity. + +The distinction between adequacy and inadequacy relates also to these continuous syntheses. An adequate presentation of, e.g., an external thing is + +possible in synthetic form in respect of its all-sided surface-contours: in the + +form of an objectively simple presentation, it is impossible. + +Of complete intuitions it is plain that objectively simple ones, but by no means always objectively complex ones, are pure intuitions. The pure intuition which corresponds to an empirical thing is denied to us, it lies hidden after a fashion in the complete synthetic intuition itself, but as it were dispersedly, with a perpetual admixture of signitive representation. If we reduce this synthetic intuition to its pure form, we do not have the pure intuition possible in an objectively simple presentation, but a continuum of intuitive contents, in which each aspect of the object quite often achieves intuitive representation, achieves ever varied perspectival projection, and in which only the continuous fusion of identity constitutes the phenomenon of + +objective unity. + +When an intuitive fact serves to give fulness in connection with a signitive intention, perhaps in connection with a meaning-intention expressed in words, similar possibilities arise. The object as it is meant can receive an adequate or an inadequate intuitive illustration. The former possibility covers two + +separable possibilities in the case of complex meanings: + +First, that to all parts (members, moments, forms) of the meaning, which themselves have a meaning-character, fulfilment should accrue through cor- + +responding parts of the fulfilling intuition. + +Secondly, that the fulfilling intuition, to the extent that its object is meant in any articulations and forms which have been drawn into the function of + +fulfilment, is intrinsically adequate to its object. + +The first determines the completeness of the adaptation of signitive acts to corresponding intuitions; the second the completeness of the adaptation of + +signitive acts - through complete intuitions - to the object itself. + +The expression 'a green house' can thus be intuitively illustrated if a house is really present to our intuition as green. This is a case of the first perfection. The second requires an adequate presentation of a green house. We generally only have the former in mind when we speak of an adequate illustration of expressions. To find distinct terms for this double perfection we shall speak of an objectively perfect intuitive illustration of our signitive presentation as opposed to its adequate, but objectively defective, intuitive + +illustration. + +Similar relationships obtain in the case of an intuitive illustration which conflicts with, rather than fulfilling a meaning. When a signitive intention encounters frustration from an intuition, because perhaps it refers to a green A, though the same A, perhaps any A at all, is red, and is now intuited as red, the objective completeness of the intuitive realization of conflict requires that all constituents of the meaning-intention should find an objectively complete intuitive illustration. It is therefore necessary, not merely that the A-intention should receive complete objective fulfilment in the intuition in question, but also that the green-intuition should be fulfilled, though + +naturally in another intuition which cannot be united to the intuition of the red A. It is not then merely the signitive green-intention, but the same intention in its objectively complete fulfilment, which is at odds with the red-intuition: these two intuitive moments are in total 'rivalry', while the correlative intuitive wholes are in partial rivalry. This rivalry especially touches, as one might say, the intuitive or intuitively presentative contents of these + +fulfilling acts. + +If nothing special is prefaced we shall in future speak of 'intuitive illustra- + +tions' only in the case of fulfilments (not frustrations). + +Distinctions of fulness in cases where quality and matter are identical, + +prompt us to frame one further important concept: + +We shall say that two intuitive acts have the same essentia (Essenz), if their pure intuitions have the same matter. A percept, and the whole possibly existent infinity of imaginative presentations, which all present the same object with the same breadth of fulness, have one and the same essentia. All objectively complete intuitions with one and the same matter have the same + +essentia. + +A signitive presentation has no essentia in its own right. But a certain essentia may, in an inauthentic sense, be ascribed to it, if it permits of complete fulfilment through one of the possible manifold of intuitions pertaining + +to this essentia, or, what is the same, if it has a 'fulfilling sense'. + +This probably clarifies the true meaning of the scholastic term essentia, + +which certainly hinges on the possibility of a 'concept' . + +Chapter 4 + +Consistency and inconsistency + +§30 The ideal distinction of meani ngs into the possi ble or real (rea/e) and the impossi ble or + +imagin ary + +It is not possible to fit intuitive acts to every signitive intention in the manner of an 'objectively complete intuitive illustration' .' Meaning-intentions may accordingly be divided into the possible (internally consistent) and the impossible (internally inconsistent, imaginary). This division, and the law underlying it, does not concern acts in isolation - this applies also to all other propositions propounded here - but their epistemic essence in general, and therein their 'matters' taken generally. For it is not possible that a signitive intention with matter M should find a possibility of fulfilment in some intuition, while another signitive intention with the same matter M, should lack this possibility. These possibilities and impossibilities do not refer to intuitions actually found in certain empirical interweavings of consciousness: they are not real (reale), but ideal possibilities, with their sole ground in specific character. In the sphere of the verbally expressed, to which we may without essential loss limit ourselves, the axiom runs: Meanings (i. e. concepts and propositions in specie) divide into the possible and the + +impossible (the real and the imaginary). + +Drawing on our just made notional constructions, we may define the possibility (reality) of a meaning by saying that there is an adequate essentia which corresponds to it in specie in the sphere of objectifying acts, an essentia whose matter is identical with its own, or what is the same, that it has a fulfilling sense, or that there exists in specie a complete intuition whose matter is identical with its own. This 'exists' has here the same ideal sense as in mathematics; to reduce it to the possibility of corresponding particulars is not to reduce it to the possibility of anything different, but merely to employ an equivalent turn of phrase. (This is true, at least, when 'possibility' is given its 'pure', and therefore non-empirical, sense, and is 'real' only in this 'pure' fashion.) The idea of the possibility of a meaning really expresses, to look at the matter more exactly, a generalization of the relation of fulfilment in the case + +of objectively complete intuitive illustration, and the above definitions are to be regarded, not as classifications of words, but as the ideal, necessary and sufficient criteria of possibility. They really state the specific law that where such a relationship obtains between the matter of a meaning and the matter of an essentia, possibility also obtains, and conversely also that in every case + +of possibility such a relationship obtains. + +Further: that such an ideal relationship obtains at all, i.e. that this generalization holds objectively, and is therefore in its own turn 'possible' - this itself amounts to a law which may be simply expressed in the words: There are possible meanings (it must be noted that 'meaning' does not stand for the act of meaning). Not every empirical relationship permits such a generalization. If we find this intuited paper rough, we cannot pronounce generally 'Paper is rough', as we can pronounce generally, on the basis of a certain + +actual act of meaning: 'This meaning is possible (real), + +. Just for this reason + +the proposition 'Every meaning is either possible or impossible', is no mere case of the law of excluded middle, in the familiar sense which excludes contradictory predicates from individual subjects, and can only pronounce such an exclusion for such subjects. The exclusion of contradictory predicates in an ideal sphere (e.g. the sphere of numbers, of meanings etc.) is by no means obvious, but must be demonstrated afresh in each such sphere, or set up as an axiom. We may recall that we cannot, for instance, say that every kind of paper is either rough or not rough, for this would entail that every individual paper of a particular sort was rough, or that every individual paper of that particular sort was not rough: such assertions are obviously not valid for every possible species. There accordingly really lies, behind the division of meanings into possible and impossible, a peculiar general law rich in content, a law that governs phenomenological moments in ideal fashion by binding their species in the manner of general + +propositions. + +To be able to utter such an axiom, one must see its truth, and that we possess self-evidence in our case is certain. If we realize, e.g., the meaning of the expression 'white surface' on an intuitive basis, we experience the reality of the concept; the intuitive appearance really presents something white and a surface, and precisely as a white surface. This implies that the fulfilling intuition does not merely present a white surface, but brings it to intuitive givenness through its content as completely as its meaning-intention + +demands. + +Impossibility is ranged beside possibility as an Idea of equal title, which should not merely be defined as a negation of possibility, but should be realized by way of a peculiar phenomenological fact. This is, moreover, presupposed by the fact that the concept of impossibility can find application, and that it can appear in an axiom: There are impossible meanings. The equivalence of talk about impossibility and inconsistency shows us that this + +phenomenological fact is to be sought in the realm of conflict. + +§3 1 Com pati bil ity or consistency as an ideal re lat ionship in the widest sphere of contents in ge neral. Com pati bil ity of 'concepts' as meanings + +We start with the concept of consistency or compatibility, which governs the widest sphere of contents in general (objects in the widest sense of the word). Two contents, which are parts of any whole, are united in it, and are accordingly compatible, consistent within the unity of the whole. This seems emptily obvious, but the same contents will still be compatible when they chance not to come together. There is good sense in speaking of a compatibility of contents, whose actual union always has been, and always will be, excluded. But if two contents are unified, their union proves not only their own compatibility, but that of an ideal infinity of other cases, namely of all pairs of contents exactly like them and belonging to similar kinds. It is clear what this points to, and that the following axiom is by no means an empty assertion: Compatibility does not pertain to dispersed individual specimens, but to the Species of contents. If, e.g., the moments of redness and roundness have once been found unified, a complex Species is at once reached by ideative abstraction, and can forthwith be given, which embraces both the Species of redness and roundness in its specifically grasped form of combination. It is the ideal 'existence' of this complex Species in which the compatibility of redness and roundness, in each thinkable instance, has its a priori foundation, a compatibility which is an ideally valid relationship whether empirical union occurs anywhere in the world or not. If the valuable sense of talk of compatibility is pinned down as the ideal being of the corresponding complex Species, a yet weightier point must be made: that talk of compatibility always relates to some sort of whole, which is the decisive point for our logical interest. Such talk is applied when we are considering whether or not certain given contents can be fitted together on a pattern set by certain forms, a question decided in the affirmative if we can exhibit a whole of the sort in question. The correlate of this compatibility of contents is the 'possibility' of the complex meanings: this follows from our above criteria of possibility. The appropriate essentia, the complete intuitive illustration of the corresponding complex content, proves the compatibility of its parts, and conversely furnishes an essentia and a corresponding meaning to such incompatibility. The reality of a meaning is therefore equivalent to: the meaning is an objectively complete 'expression' of an intuitive compatibility of content. In the limiting case of a simple content one can define the validity of the simple species as a 'compatibility with self'. Obviously the combination of expression and expressed (meaning and corresponding, i.e. objectively quite adequate, intuition) is itself again a combination of compatibles, whose specific content we determined above. In talk of compatibility as regards meanings ('concepts'), we are not merely concerned with their compatibility in a whole - this would rather be a purely logico-grammatical + +compatibility in the sense of our Fourth Investigation - but are rather concerned with a compatibility of meanings in a 'possible' meaning, i.e. a meaning compatible with corresponding intuition in the unity of objectively adequate knowledge. We have here accordingly a derived, secondary form of speech. The same is true of the term 'possibility'. The original possibility (or reality) is the validity, the ideal existence of a Species: it is at least fully guaranteed by this. Next the intuition of an individual case which corresponds to this possibility, and the intuitable individual itself, are possible. Finally the meaning realized with objective completeness in such an intuition is said to be possible. The difference between talk about compatibility and talk about possibility consists solely in the fact that, while the latter denotes the simple validity of a Species, the former (prior to the widening of the notion to cover the limiting case) connotes the relationship of the component Species in a Species which counts as one, and in connection therewith also the relationship of the partial intuitions in a total intuition, of the partial contents to be intuited within a total content to be intuited as one, of partial meanings to be fulfilled within a total meaning to be fulfilled as one. + +Finally we remark that the concept of essentia, like the concepts of possibility and compatibility, imparts its original sense derivatively to the realm of meaning. The original concept of essentia is expressed in the proposition: + +Every valid species is an essentia. + +§32 In com patibil ity (confli ct) of contents in ge neral Contents are incompatible, to pursue the opposed case down to its general grounds, if they cannot suffer each other in the unity of a whole. Put phenomenologically: no unified intuition must be possible which presents such a whole with complete adequacy. But how shall we know this? In empirical instances we attempt to unite contents, sometimes successfully, sometimes without success - we experience an absolute resistance. But the factual failure does not establish a necessary failure. Possibly greater power could ultimately overcome the resistance. Nonetheless, in our empirical concern with the contents in question, and our attempted removal of their 'rivalry', we experience a peculiar relationship of the contents, again grounded in their specific being, and with an ideality quite independent of the empirical effort, and all the other features of the individual case. It is the relationship + +of conflict. + +This relationship puts quite definite sorts of content into relation, within quite definite associations of contents. Colours conflict with one another, not in general, but only in specific contexts: several moments of colour, of varying specific difference, are incompatible as simultaneous overlays of one and the same bodily extension, while they are quite compatible if set side by side within a single extension. This is universally the case. A content of the sort q is never simply incompatible with a content of the sort p: talk of their + +incompatibility always relates to a definite sort of combination of contents W(a, b ... p) which includes p, and should now include q as well. The word 'should' certainly indicates an intention, a presentative and generally also a voluntary intention, which thinks of the q, given in any intuition I(q) , as brought into the present intuition of W, which presents q signitively in W. This intention we shall, however, ignore, just as, in the case of compatibility, we ignored the intention towards unification, as well as the process of transference and union. We only maintain the presence of a descriptively peculiar relationship between q - the remainder of A is variable at will and plays no further part - and p, within the whole of contents W, and that this whole is independent of the individual element in the case. In other words, it is grounded purely in the Species W, p and q. What is specific in the consciousness of conflict pertains to these Species, i.e. the generalization of the situation is actual, is realizable in an intuitively unified consciousness of universality, it yields a unified, valid ('possible') Species which unites p and + +Q, through conflict, on the basis of W. + +§33 How confli ct can also be a foundation fo r un ity. Rel at ivity of the tal k of com pati bil ity and conflict + +To this last expression and sentence there attach a series of disquieting doubts and questions. Does conflict unify? Is the unity of conflict a unity of possibility? Unity in general certainly underlies possibility, but does not the + +latter absolutely exclude conflict, inconsistency? + +These difficulties are resolved when we remember that not only talk of an incompatibility, but also talk of a compatibility, necessarily relates to a certain whole Wwhich, subjectively speaking, governs our intention. Looking out from the specific make-up of this whole, we call its parts compatible. We should call the same contents p, q ... (which here function as parts) incompatible, if in our symbolic intention towards their unity within such a whole, we experienced intuitive conflict instead of intuitive unity. The correlation of the two possible cases in relation to the two definite sorts of wholes, or combinations of compatible or incompatible contents, is clear. This relation also determines the sense of these terms. We do not call p, q ... simply compatible, merely considering that they are unified and not at all how they are so, but in the light of their union after the manner of W, and that this union of p, q ... excludes the conflict of the same p, q ... in relation to the same W. Contents p, q ... are similarly not said to be simply incompatible, but in the light of the fact that they will not 'suffer' one another within the framework of a unity of the sort W which just happens to interest us. The intention to such a unity brings out a conflict instead of such a unity: the exclusion of unity by correlated conflict once more also plays its part. The consciousness of conflict entails 'disunity', since it excludes the W-type unity which is in question here. With this direction of interest, conflict + +does not itself count as unity, but as separation, not as a combination but a sundering. But if we change the relations, an incompatibility can also function as a unity, e.g. between the character 'conflict' and the contents separated by it. This character is compatible with these contents, and perhaps incompatible with others. If our dominant intention is upon the wholeshaped-by-conflict which is the whole for the parts just mentioned, then, when we find such a whole, when conflict accordingly obtains, there is compatibility among these parts, p, q ... in this context, and in the conflict which separates them. This conflict is not a conflict among the members of the intended conflict, whose absence it in fact indicates, but a conflict attaching to the contents p, q ... united without conflict in one intuition, and the moment of conflict which is made intuitive in another intuition. The paradox of talking of a unification-through-conflict is cleared up by noting the relativity of these concepts. One can no longer object: 'Conflict absolutely excludes unity. In the manner of conflict anything and everything could ultimately be unified. Where unity fails, there conflict obtains, and to allow this conflict once more to count as a unity, is to obliterate the absolute, stark distinction between unity and conflict, and corrupt its true sense'. No, we may now presume to reply, conflict and unity do not 'absolutely' exclude one another, but only in a variously determined correlation which changes from case to case. In this correlation, they exclude each other as stark opposites, and only if we limit our 'absolutely' to some such tacitly presupposed correlation can we be satisfied with our polemical assertion. Not everything, moreover, can be unified in the form of a conflict, but only such things as serve to base a conflict, and none of the things that are or could be unified. For in the meaning of this talk of union-in-the-form-ofconflict it is implied that the form of conflict of a p, q ... thought of as in a certain combination Wo, shall count as a unity, which as a unity re-establishes union and compatibility, and so corresponds to the W we mentioned above. But if unity obtains among p, q ... in respect of the combination Wo, then these p, q ... will not permit themselves to be brought into a relationship of conflict in respect of this combination, since combination as such means + +unity. + +So not everything can really be united in the form of conflict, at least not for the stated reason that failure of unity would be manifest in a conflict, which would therefore restore unity through conflict. We understand the confusion here fallen into, the confounding of underlying relations. The failure of the unity Wo, fixes the character of the conflict attaching to p, q ... within the context determined by the notion Woo This conflict does not, however, yield the unity Wo, but another unity. As regards the former it has the character of a separation, as regards the new unity that of a combination. All this is in order, as an example will make clear. In relation to a peculiar phenomenal context, red and green are called incompatible, red and round compatible. The character of conflict determines incompatibility in + +the first case, it produces separation between red and green. Despite this, in regard to another kind of combination, it helps to establish a unity, i.e. in regard to the type of combination conflict among the sensuous qualities of a phenomenal object. Conflict is now a unity between red and green, a unity in respect of the elements conflict, red, green. As opposed to this 'conflict of red and round' is now disunity in respect of these elements conflict, red, + +round. + +§34 Some axioms + +After this elucidation, very important for our basic analysis, of the sense of relations of compatibility, we can lay down primitive axioms and complete their phenomenological clarification. The first would be the axiom of the convertibility of relations of compatibility (or incompatibility), which our analysis of the underlying phenomenological relationships makes immedi- + +ately clear. + +The next axiom to be set up requires more consideration: that unity and conflict (or compatibility and incompatibility) - each pair related to the same basis of correlation - exclude each other reciprocally (or are incompatible with one another). We need no longer emphasize that incompatibility is not the mere privation of compatibility, not the mere fact that a certain unity does not objectively obtain. Union and conflict are notions with different phenomenological foundations, and we are therefore really uttering a statement with content if we say that if a p conflicts with a q as regards the form of unity W(p, q ... ) - such conflict is a phenomenologically positive character - the union of a p with a q in the sense of the same W is 'impossible'. The phenomenological ground of this fact has been laid bare in the previous discussion: when we try to unite actual conflict between p, q ... with the corresponding unity of p, q ... - actually to impose the form of unity W which has been somewhere really intuited in the case of items m, n ... in the pertinent case of conflict on the same items p, q .. . - a new conflict emerges, which has its roots in the first conflict and the elsewhere intuited form of unity. Analogous things are plain in the converse case, which may for the + +rest be regarded as an application of the first axiom. + +The propositions that there is a conflict, and the proposition that there is no unity among any given p, q ... (the same in both cases), say exactly the + +same thing. Every 'not' expresses a conflict. + +When a conflict attaches to the circumstance that p, q shall be in conflict, that p, q ... shall be one in the form of conflict, p, q ... are one. In other words: If p, q are not in conflict, are not not unified, they are unified (axiom of + +double negation) which entails that: + +Either unity or conflict obtains - one or other is the case - there is no third + +Four possibilities must here be distinguished, expressed in the following + +terms: + +Unity } { obtains Conflict does not obtain. + +Non-unity is, however, another name for conflict, and non-conflict (accord- + +ing to the previous axiom) an equivalent of unity. + +The final elucidation of these axioms, and their relation to purely logical axioms, goes beyond the boundaries of the present Investigation. What we have here adduced is only intended to point to the internal relations that we desire to track down later: they make us aware, very vividly, that we are here already working to lay down the phenomenological foundations of + +pure logic. + +§3 5 In com pati bil ity of concepts as meani ngs + +Incompatibility, like compatibility, appears in thought in connection with signitive intentions directed to certain combinations, in connection, accordingly, with signitive and intuitive identifications. The concept of incompatibility does not relate to intentions, but the identically styled concept which relates to intentions is derivative, is a special case of the original notion, very definite in scope, and with limited openings for relations of frustration. Here we have an analogue of the matters set forth above (§3 1) in regard to compatibility or consistency. Talk of incompatibility in regard to meanings ('concepts') may again be said to express, not any and every ideal incompatibility of the same, not, e.g., a purely grammatical incompatibility. It has to do only with the relationship of the partial meanings within a complex meaning, which does not fulfil itself in an objectively complete illustration, but is, or may be frustrated. Plainly conflict of the intuitively illustrated contents underlies such frustration, although (be it noted) this conflict is not itself meant and expressed. Otherwise conflict would pertain to the fulfilling 'intuition' , and the expression would express adequately, and in an entirely + +'possible' manner, an objective impossibility. + +The connection between the meaning and each of the unified intuitions which cancel each other in the process of intuitive conflict, is likewise one of + +conflict (of course with partial coincidence). + +The ideal laws to be set up for the possibility of meanings are based on the original, more general concepts, and on the axioms set up for such concepts above (which have, however, to be carried further). Here we have such + +propositions as: + +Incompatibility and compatibility among the same meanings, in relation + +Of a pair of contradictory meanings - of meanings such that what the one means as incompatible the other means as compatible - one is possible and + +the other impossible. + +The negative of a negative - i.e. a meaning which presents incompatibility in a given matter M as itself involving incompatibility - is equivalent to the corresponding positive meaning. This positive meaning is defined as the meaning which presents the inner consistency of the same M through the same presentative matter (the matter left over after the negations have been + +cancelled). + +Quite obviously a real theory of meanings according to their logical relations would demand that all such propositions should be enunciated and + +proved in a systematically ordered fashion. + +We break off our fragmentary discussions, leaving their completion to later investigations. We need, in the interests of logic, a much more extensive, completely executed phenomenology and theory of identifications and differentiations, particularly of such as are partial, as well as of their obviously + +close relations to the doctrine of unity and conflict. + +Chapter 5 + +The ideal of adeq u ation. Self-evidence and truth + +§36 Introd uction + +In our discussions up to this point we have said nothing of the qualities of acts, nor presumed anything in regard to them. Possibility and impossibility have indeed no special relation to these qualities. It makes no difference, e.g., to the possibility of a proposition, whether we realize the propositional matter as matter for an act of assertion (not of an act that assents to something in the accepting or recognizing manner of approval, but in the manner of a simple act of belief or taking for true), or whether we use it, in qualitatively modified fashion, as the matter of a pure presentation. A proposition is always 'possible', when the concrete act of propositional meaning permits of a fulfilling identification with an objectively complete intuition of matching material. It is likewise irrelevant if this fulfilling intuition is a percept, or a pure construction of fantasy, etc. Since the summoning up of imaginative pictures is more subject, in varying degrees, to our will, than that of percepts and assertions, we incline to relate possibility specially to the picture-life of fantasy. A thing counts as possible, if it allows itself, objectively speaking, to be realized in the form of an adequate imaginative picture, whether we ourselves, as particular empirical individuals, succeed in thus realizing it or not. But through the ideal linkage between perception and imagination, which assures us a priori that to each percept a possible image corresponds, this proposition is equivalent to our own, and the limitation of the concept + +to imagination not essential. + +What we have now to do, quite briefly, is to discuss the effect of these just indicated differences upon relationships of fulfilment, so that our treatments may at least reach a provisional term, as well as a view over further researches. + +§3 7 The fu lfill ing fu nction of percepti on. The ideal + +of ul timate fu lfil ment + +We have seen that differences in the completeness of 'fulness' have an important bearing on the manner in which objects are made present in + +presentations. Signitive acts constitute the lowest step: they possess no fulness whatever. Intuitive acts have fulness, in graded differences of more and less, and this is already the case within the sphere of imagination. The perfection of an imagination, however great, still leaves it different from a perception: it does not present the object itself, not even in part, it offers only its image, which, as long as it is an image at all, never is the thing itself. The latter we owe to perception. Even this, however, 'gives' us the object in varied gradations of perfection, in differing degrees of 'projection'. The intentional character of perception, as opposed to the mere representation of imagination, is that of direct presentation. This is, as we know, an internal difference of acts, more precisely of their interpretative form. But 'direct' presentation does not in general amount to a true being-present, but only to an appearance of presence, in which objective presence, and with it the perfection of veridicity (Wahr-nehmung, perception) exhibits degrees. This is shown by a glance at the corresponding scale of fulfilment, to which all exemplification of perfection in presentation is here, as elsewhere, referred. We thereby become clear that a difference extends over the fulness of perception that we sought to cover by our talk of perceptual projection, a difference that does not concern fulness in respect of its sensuous stuff, its internal character, but means a graded extension of its character as fulness, i.e. of the interpretative character of the act. From this point of view many elements of fulness count for us - quite apart from anything genetic, for we know full well that these, like all similar differences, have an associative origin - as final presentations of the corresponding objective elements. They offer themselves as identical with these last, not as their mere representatives: they are the thing itself in an absolute sense. Other cases again count as mere adumbrations of colour, perspectival foreshortenings etc., in which case it is clear that to such locutions something corresponds in the phenomenological content of the act prior to all reflection. We have already dealt with these 'projective' differences, and found them, pictorially transferred, in the case of imagination. Every projection is representative in character, and represents by way of similarity, but the manner of this representation by similarity differs according as the representation takes the projected content as picture or self-presentation (self-projection) of the object.! The ideal limit, which an increase of fulness of projection permits, is, in the case of perception, the absolute self of the thing (as in imagination it is its absolutely resembling image), and that for + +every side and for every presented element of the object. + +The discussion of possible relationships of fulfilment therefore points to a goal in which increase of fulfilment terminates, in which the complete and entire intention has reached its fulfilment, and that not intermediately and partially, but ultimately and finally. The intuitive substance of this last fulfilment is the absolute sum of possible fulness; the intuitive representative is the object itself, as it is in itself. Where a presentative intention has achieved its last fulfilment, the genuine adaequatio rei et intellectus has been brought + +about. The object is actually 'present' or 'given', and present as just what we have intended it; no partial intention remains implicit and still lacking + +fulfilment. + +And so also, eo ipso, the ideal of every fulfilment, and therefore of a significative fulfilment, is sketched for us; the intellectus is in this case the thought-intention, the intention of meaning. And the adaequatio is realized when the object meant is in the strict sense given in our intuition, and given as just what we think and call it. No thought-intention could fail of its fulfilment, of its last fulfilment, in fact, in so far as the fulfilling medium of + +intuition has itself lost all implication of unsatisfied intentions. + +One sees that the perfection of the adequation of thought to thing is twofold: on the one hand there is a perfect adaptation to intuition, since the thought means nothing that the fulfilling intuition does not completely present as belonging to the thought. In this the two previously (§29) distinguished 'perfections' are plainly comprehended: they yield what we called the 'objective completeness' of the fulfilment. On the other hand the complete intuition itself involves a perfection. The intuition fulfils the intention which terminates in it as not itself again being an intention which has need of further fulfilment, but as offering us the last fulfilment of our intention. We must therefore draw a distinction between the perfection of the adaptation to intuition, which is 'adequation' in the natural, wider sense, and the perfection of final fulfilment which presupposes this fulfilment, and which is an adequation with the 'thing itself'. Each faithful, unalloyed description of an intuitive object or event provides an example of the former perfection. If the object is something in interior experience, and is grasped as it is in reflex perception, then the second perfection may be added, as when, for instance, looking back on a categorical judgement just made, we speak of the subjectpresentation in this judgement. The first perfection is, however, lacking, when we call the tree standing before us a 'cultivated' variety of apple-tree, or when we speak of the 'vibratory frequency' of the note just dying away, or, in general, when we speak of such properties of perceptual objects as, however much they may be marginally meant in our perceiving intention, are not even more or less projectively present in what actually appears. The following observation is also in place. Since an ultimate fulfilment may contain absolutely no unfulfilled intentions, it must issue out of a pure percept. An objectively complete percept, but one achieved by the continu- + +ous synthesis of impure percepts, will not fill the bill. + +Against our mode of treatment, which places the final fulfilment of all intentions in perception, it may be objected that the realized consciousness of the universal, the consciousness which gives fulness to conceptually general presentations, and which sets the 'universal object itself' before our eyes, rests on a ground of mere imagination, or is at least indifferent to the difference between perception and imagination. The same is obviously true, as a consequence of what has just been said, of all self-evident general + +assertions, which make themselves plain to us, in axiomatic fashion, 'from + +our very notions alone'. + +This objection points to a gap in our investigation that has already been touched on from time to time. We first took perception, with immediate obviousness, as being the same as sense-perception, intuition as being the same as sensuous intuition. Tacitly, without any clear consciousness, we have frequently gone beyond the bounds of these notions, e.g. in connection with our discussions of compatibility. We regularly did this, when, e.g., we spoke of intuiting a conflict or a union, or some other synthesis as such. In our next chapter, which deals generally with categorial forms we shall show the need to widen the concepts of perception and other sorts of intuition. To remove our objection, we shall now only say that the imagination, which serves as basis for generalizing abstraction, does not therefore exercise an actual, authentic function of fulfilment, and so does not play the part of a 'corresponding' intuition. What is individually singular in phenomena, is not itself, as we have several times stressed, the universal, nor does it contain the + +universal as a real (reel!) 'piece' of itself. + +§38 Positi ng acts in the fu nction of fu lfil me nt. Self-evidence in the loose and strict sense + +Under the rubric of 'intentions', positing and non-positing acts have so far been indiscriminately ranged. Nonetheless, though the general character of fulfilment essentially depends on the 'matter' of acts, which alone is relevant to an array of most important relationships, the quality of acts shares in the determination of others, and to such a degree that talk of intention, of directed aiming, really only seems to suit assertive acts. Our thought (Meinung) aims at a thing, and it hits its mark, or does not hit it, according as it agrees or does not agree in a certain way with perception (which is here an assertive act). Positing then agrees with positing: the intending and fulfilling act are alike in this quality. Mere presentation, however, is passive: it leaves matters 'in suspense'. Where by chance an adequate percept accompanies a mere presentation, a fulfilling coincidence certainly issues from the mutually fitting 'matters' of the acts: in the transition, however, the presentation acquires an assertive note, and the unity of coincidence itself certainly has this note quite homogeneously. Each actual identification or differentiation is an assertive act, whether itself founded on assertions or not. This last briefly-worded proposition adds an all-important characterization to the results of our last chapter, a characterization determining all relationships of compatibility: the theory of identifications and differentiations thereby reveals itself, with more clearness than before, as a chapter in the theory of judgement. For according as positing or non-positing acts function in our intentions or their fulfilments, they illuminate distinctions like that between illustration, perhaps exemplification, on the one hand, and verification or + +confirmation and its opposite refutation, on the other. The concept of veri fication relates exclusively to positing acts in relation to their positing fulfilment, + +and ultimately to their fulfilment through percepts. + +To this last pre-eminent case we now give closer consideration. It is a case in which the ideal of adequation yields us self-evidence (Evidenz). We speak somewhat loosely of self-evidence wherever a positing intention (a statement in particular) finds verification in a corresponding, fully accommodated percept, even if this be no more than a well-fitting synthesis of coherent single percepts. To speak of degrees and levels of self-evidence then has a good sense. Here are relevant all approximations of percepts to the objective completeness of their presentation of their object, all further steps towards the final ideal of perfection, the ideal of adequate perception, of the complete self-manifestation of the object, however it was referred to in the intention to be fulfilled. But the epistemologically pregnant sense of self-evidence is exclusively concerned with this last unsurpassable goal, the act of this most perfect synthesis of fulfilment, which gives to an intention, e.g. the intention of judgement, the absolute fulness of content, the fulness of the object itself. The object is not merely meant, but in the strictest sense given, and given as it is meant, and made one with our meaning-reference. It does not matter, for the rest, whether one is dealing with an individual or a universal object, with an object in the narrower sense or with a state of affairs, the correlate + +of an identifying or distinguishing synthesis. + +Self-evidence itself, we said, is the act of this most perfect synthesis of coincidence. Like every identification, it is an objectifying act, its objective correlate being called being in the sense of truth, or simply truth - if one does not prefer to award this term to another concept of the many that are rooted in the said phenomenological situation. Here, however, a closer dis- + +cussion is needed. + +§39 Self-evidence and truth + +1. If we at first keep to the notion of truth just suggested, truth as the correlate of an identifying act is a state of affairs (Sachverhalt), as the correlate of a coincident identity it is an identity: the full agreement of what is meant with what is given as such. This agreement we experience in selfevidence, in so far as self-evidence means the actual carrying out of an adequate identification. The proposition that self-evidence is the 'experience' of truth cannot, however, be simply interpreted as telling us that the self-evidence is the perception (in a sufficiently wide sense) of truth and, in the case of strict self-evidence, the adequate perception of truth. For, to recur to a previously voiced doubt (see the addendum to §8 and chapter 7), we must allow that the carrying out of an identifying coincidence is not as yet an actual perception of objective agreement, but becomes so only through its own act of objectifying interpretation, its own looking towards present + +truth. Truth is indeed 'present'. Here we have always the a priori possibility of looking towards this agreement, and of laying it before our intentional + +consciousness in an adequate percept. + +2. A second concept of truth concerns the ideal relationship which obtains in the unity of coincidence which we defined as self-evidence, among the epistemic essences of the coinciding acts. While truth in sense I was the objective item corresponding to the act of self-evidence, truth in this sense is the Idea which belongs to the act-form: the epistemic essence interpreted as the ideal essence of the empirically contingent act of self-evidence, the Idea of + +absolute adequation as such. + +3. We also experience in self-evidence, from the side of the act which furnishes 'fulness', the object given in the manner of the object meant: so given, the object is fulness itself. This object can also be called being, truth, the 'truth' in so far as it is here not experienced as in the merely adequate percept, but as the ideal fulness for an intention, as that which makes an intention true (or as the ideal fulness for the intention's specific epistemic + +essence). + +4. Lastly, considered from the standpoint of the intention, the notion of the relationship of self-evidence yields us truth as the rightness of our intention (and especially that of our judgement), its adequacy to its true object, or the rightness of the intention 's epistemic essence in specie. We have, in the latter regard, the rightness, e.g., of the judgement in the logical sense of the proposition: the proposition 'directs' itself to the thing itself, it says that it is so, and it really is so. In this we have the expression of the ideal, and therefore general, possibility that a proposition of such and such a 'matter' + +admits of fulfilment in the sense of the most rigorous adequation. + +We must further particularly note that the 'being' here in question in our first objective sense of truth, is not to be confused with the 'being' covered by the copula in the affirmative categorical judgement. Self-evidence is a matter of total coincidence, whereas the 'being' of the copula corresponds generally, if not invariably to partial identifications (i.e. judgements of quality). + +But even where total identification is predicated, the two 'beings' will not coincide. For we must observe that in the case of a self-evident judgement, i.e. of a self-evident predicative assertion, being in the sense of truth is experienced but not expressed, and so never coincides with the being meant and experienced in the 'is' of the assertion. This second 'being' is the synthetic moment in what is in the sense of is true - how could it express the fact that the latter is true ? There are in fact several agreements which are here brought to synthesis: one of these, the partial, predicative one, is meant assertively and perceived adequately, and so self-presented. (What this means will become clearer in the next chapter by way of the more general doctrine of categorial objectification.) This is the agreement of subject with predicate, the suiting of predicate to subject. We have, in the second place, the agreement which constitutes the synthetic form of the act of self-evidence, and therefore + +of the total coincidence of the meaning-intention of our assertion with the percept of the state of affairs itself, a coincidence naturally achieved in stages, which do not here concern us further. This agreement is plainly not asserted, it is not objective like the first agreement, which belongs to the state of affairs judged. No doubt it can always be asserted and asserted with self-evidence. It then becomes the verifying state of affairs for a new selfevidence, of which the like is true, and so on. At each step, however, one must distinguish the verifying state of affairs from the state of affairs constitutive of the self-evidence itself, we must distinguish the objectified from + +the not-objectified state of affairs. + +The distinctions just drawn lead to the following general discussion. In our exposition of the relationships of the concepts of self-evidence and truth, we have not drawn a distinction which touches the objective side of the acts which, whether functioning as intentions or fulfilments, find their absolute adequation in self-evidence: we have not, that is, distinguished between states of affairs, on the one hand, and other objects, on the other. We have paid no heed, correspondingly, to the phenomenological difference between acts which relate, on the one hand - acts of agreement and disagreement, predicative acts - and acts which do not relate, on the other. We have paid no need, therefore, to the difference between relational and nonrelational meanings, or to the relational-non-relational distinction among ideally apprehended essences in general. Strict adequation can bring nonrelating as much as relating intentions into union with their complete fulfilments. If we now particularly consider the field of expressions, we need not concern ourselves with judgements as assertive intentions or assertive fulfilments; acts of naming can also achieve their adequation. The concepts of truth, rightness, the true, are generally interpreted more narrowly than we have done: they are connected with judgements and propositions, or with the states of affairs which are their objective correlates. 'Being' is meanwhile mainly spoken of in relation to absolute objects (not states of affairs), though no definite lines are drawn. Our right to our more general interpretation of these concepts is unassailable. The very nature of the case demands that the concepts of truth and falsehood, should, in the first instance at least, be fixed so widely as to span the whole sphere of objectifying acts. It seems therefore most suitable that the concepts of truth and being should be so distinguished, that our concepts of truth - a certain range of equivocation remaining inevitable but hardly dangerous once our concepts are clarified - are applied from the side of the acts themselves and their ideally graspable moments, whereas the concepts of being (genuine being) are applied to the corresponding objective correlates. Truth would then have to be defined in the manner of (2) and (4) as the Idea of adequation, or as the rightness of objectifying assertion and meaning. Being would then have to be pinned down according to (1) and (3) as the identity of the object at once meant and given in adequation, or (in conformity with the natural sense of + +words) as the adequately perceivable thing as such, in an indefinite relation + +to an intention that it is to make true or fulfil adequately. + +After our concepts have been thus widely fixed and assured phenomenologically, we may pass on, having regard to the distinction between relational and non-relational acts (predications versus absolute assertions) to define narrower concepts of truth and being. The narrower concept of truth would be limited to the ideal adequation of a relational act to the corresponding adequate percept of a state of affairs: just so the narrower concept of being would concern the being of absolute objects, and would + +separate this off from the 'subsistence' of the state of affairs. + +The following is accordingly clear: if one defines a judgement as an assertive act in general, then the sphere of judgement, subjectively speaking, coincides with the joint spheres of the concepts true and false in the widest sense of these words. But if one defines it by way of the statement and its possible fulfilment, and ranges under judgements only the sphere of relational assertions, then the same coincidence obtains again, provided that the + +narrower concepts of truth and falsehood are again used as a basis. + +In one-sided fashion we have hitherto favoured the case of self-evidence, the act described as one of total coincidence. But, turning to the correlated case of conflict, we encounter absurdity, the experience of the total conflict between intention and quasi-fulfilment. To the concepts of truth and being the correlated concepts of falsehood and non-being then correspond. The phenomenological clarification of these concepts can be carried out without particular difficulty, once all foundations have been prepared. The negative ideal of an ultimate frustration would first have to be exactly circumscribed. When self-evidence is conceived strictly, in the manner made basic here, it is plain that such doubts as have from time to time been expressed in modern times are absurd, doubts as to whether the experience of selfevidence might not be associated with the matter A for one man, while absurdity is associated with it for another. Such doubts are only possible as long as self-evidence and absurdity are interpreted as peculiar (positive or negative) feelings which, contingently attaching to the act of judgement, impart to the latter the specific features which we assess logically as truth and falsehood. If someone experiences the self-evidence of A, it is selfevident that no second person can experience the absurdity of this same A, for, that A is self-evident, means that A is not merely meant, but also genuinely given, and given as precisely what it is thought to be. In the strict sense it is itself present. But how could a second person refer in thought to this same thing A, while the thought that it is A is genuinely excluded by a genuinely given non-A? One is, it is plain, dealing with a matter of essence, the same matter, in fact, that the law of contradiction (into whose ambiguities the correlations discussed in §39, p. 264 naturally enter) successfully expresses. It is reliably clear, as a result of our analyses, that being and non-being are not concepts which in their origin express opposition among the qualities + +of our judgements. Following our interpretation of the phenomenological relationships involved, every judgement is assertive: this assertion does not characterize the 'is' of which the 'is not' is the qualitative contrary. The qualitative contrary of a judgement is a mere presentation having the same 'matter' . Differences between 'is' and 'is not' are differences in intentional 'matter'. Just as an 'is' expresses predicative agreement after the manner of + +a meaning-intention, so an 'is not' expresses a predicative conflict. + +Second Section + +Sense and understand ing + +Chapter 6 + +Sensuous and categorial intu itions + +§40 The problem of the fu lfil ment of catego rial meaning-forms, with a thought leading towards + +its solution + +In our discussions up to this point we have repeatedly and strongly felt a large gap. It had to do with the categorial objective forms, or with the synthetic functions in the sphere of objectifying acts through which these objective forms come to be constituted, through which they may come to 'intuition' and thereby also to 'knowledge'. We shall now attempt to some extent to fill in this gap, taking our point of departure from the investigation of our first chapter; this was concerned with one limited aim of epistemological clarification: the relation of a meaning-intention as the thing to be expressed, with an expressed sensuous intuition. We shall for the time being again build on the simplest cases of perceptual and other intuitive statements, and shall use them to shed light on the theme of our next treatments, + +in the following manner: + +In the case of a perceptual statement, not only the inwrought nominal presentations are fulfilled: the whole sense of the statement finds fulfilment through our underlying percept. We say likewise that the whole statement gives utterance to our percept: we do not merely say 'I see this paper, an inkpot, several books', and so on, but also 'I see that the paper has been written on, that there is a bronze inkpot standing here, that several books are lying open', and so on. If a man thinks the fulfilment of nominal meanings clear enough, we shall ask him how we are to understand the fulfilment of total statements, especially as regards that side of them that stretches beyond their 'matter', in this case beyond their nominal terms. What may and can furnish fulfilment for those aspects of meaning which make up propositional form as such, the aspects of 'categorial form' to which, e.g., + +the copula belongs? + +Looked at more narrowly, this question also applies to nominal meanings, in so far as these are not totally formless like the meanings for individuals. The name, like the statement, even in its grammatical appearance, possesses + +both 'matter' and 'form' . If it comprises words, the form lies partly in the way these words are strung together, partly in its own form-words, partly in the mode of construction of the individual words, which allows us to draw a distinction between its moments of 'matter' and its moments of 'form' . Such grammatical distinctions refer us back to distinctions of meaning. There is at least a rough expression of the articulations and forms which are rooted in our meaning's essence and the articulations and forms of grammar. In our meanings, therefore, parts of very different kinds are to be found, and among these we may here pay special attention to those expressed by formal words such as 'the', 'a', 'some', 'many', 'few', 'two', 'is', 'not', 'which', 'and', 'or' etc., and further expressed by the substantival and adjectival, singular + +and plural inflection of our words etc. + +How does all this stand as regards fulfilment? Can the ideal of completely adequate fulfilment formulated by us in our third chapter still be maintained? Are there parts and forms of perception corresponding to all parts and forms of meaning? In that case we should have the parallelism between meaningful reference and fulfilling intuition that talk of 'expression' suggests. The expression would be an image-like counterpart of the percept (i.e. in all its parts and forms to be expressed) but reconstituted in a new stuff - an + +ex-pression in the stuff of meaning. + +The prototype for interpreting the relation between meaning and intuiting would then be the relation of the 'proper' individual meaning to corresponding percepts. The man who knows Cologne itself, and therefore possesses the genuine 'proper meaning' of the word 'Cologne', has in his contemporary actual experience something exactly corresponding to the future confirming percept. It is not, properly speaking, a representation of the percept, as, e.g., the corresponding imagination would be. But just as the city is thought to be itself present to us in the percept, so the proper name 'Cologne', in its 'proper meaning', refers, as previously argued, to the same city 'directly' : it means that city itself, and as it is. The straightforward percept here renders the object apparent without the help of further, superordinate acts, the object which the meaning-intention means, and just as the latter means it. The meaning-intention therefore finds in the mere percept + +the act which fulfils it with complete adequacy. + +If instead of considering directly naming, unstructured expressions, we rather consider structured, articulated expressions, the matter seems quite the same. I see white paper and say 'white paper', thereby expressing, with precise adequacy, only what I see. The same holds of complete judgements. I see that this paper is white, and express just this by saying: 'This paper is + +white'. + +We are not to let ourselves be led astray by such ways of speaking; they are in a certain manner correct, yet are readily misunderstood. One might try to use them to show that meaning here has its seat in perception, which, as we have shown, is not so. The word 'white' certainly means something + +attaching to the white paper itself; this 'meaning' therefore coincides, in the state of fulfilment, with the partial percept which relates to the 'whiteaspect' of the object. But the assumption of a mere coincidence with this part-percept is not enough: we are wont to say here that the white thus apparent is known as white and is called so. In our normal talk of 'knowledge', we are, however, more inclined to call the object which is our (logical) subject the thing 'known' . In such knowledge another act plainly is present, which perhaps includes the former one, but is nonetheless different from it: the paper is known as white, or rather as a white thing, whenever we express our percept in the words 'white paper'. The intention of the word 'white' only partially coincides with the colour-aspect of the apparent object; a surplus of meaning remains over, a form which finds nothing in the appearance itself to confirm it. White paper is paper which is white. Is this form not also repeated, even if it remains hidden, in the case of the noun 'paper'? Only the quality-meanings contained in its 'concept' terminate in perception. Here also the whole object is known as paper, and here also a supplementary form is known which includes being, though not as its sole form, in itself. The fulfilment effected by a straight percept obviously does not extend + +to such forms. + +We have but to ask, further, what corresponds in perception to the difference between the two expressions 'this white paper' and 'this paper is white', which are both realized on the same perceptual basis, we have but to ask what side of perception is really brought out by this difference - the difference, that is, of the attributive and the predicative mode of statement - and what, in the case of adequate adaptation, this difference brings out with peculiar exactness, and we experience the same difficulty. Briefly we see that the case of structured meanings is not so simple as the case of a 'proper' individual meaning, with its straightforward relation of coincidence with perception. Certainly one can tell one's auditors, intelligibly and unambiguously that 'I see that this paper is white', but the thought behind such talk need not be that the meaning of this spoken sentence expresses a mere act of seeing. It may also be the case that the epistemic essence of our seeing, in which the apparent object announces itself as self-given, serves to base certain connective or relational or otherwise formative acts, and that it is to these that our expression in its changing forms is adjusted, and that it is in such acts, performed on a basis of actual perception, that our expression, in respect of such changing forms, finds fulfilment. If we now combine these founded acts or rather act-forms with the acts which serve as their foundation, and give the comprehensive name 'founded act' to the whole actcomplexes that result from such formal 'founding', we may say: Granted the possibility just sketched, our parallelism may be re-established, but it is no longer a parallelism between the meaning-intentions of expressions and the mere percepts which correspond to them: it is a parallelism between meaning-intentions and the above mentioned perceptually founded acts. + +§4 1 Cont inuation. Extension of our sphere + +of exam ples + +If we suppose our range of examples widened so as to cover the whole field of predicative thinking, we shall encounter similar difficulties and similar possibilities of resolving them. Judgements in particular will come up which have no definite relation to anything individual which ought to be given through any intuition: they will give general expression to relations among ideal unities. The general meanings embodied in such judgements can also be realized on a basis of corresponding intuition, since they have their origin, mediately or immediately, in intuition. The intuited individual is not, however, what we mean here; it serves at best only as an individual case, an example, or only as the rough analogue of an example, for the universal which alone interests us. So, for instance, when we speak generically of 'colour' or specifically of 'red', the appearance of a single red thing may + +furnish us with a documenting intuition. + +It also at times happens, that one calls such a general statement an expression of intuition. We say, e.g., that an arithmetical axiom expresses what we find in intuition, or we raise objection to a geometrician that he merely expresses what he sees in his figure without deducing it formally, that he borrows from his drawing and omits steps in his proof. Such talk has its good sense (as when the objection scores no mean hit against the formal validity of Euclidean geometry) but 'expression' here means something different from the previous cases. Even in their case expression was not a mere counterpart of intuition: this is even less the case here, where our thought's intention is not aimed at intuitively given phenomena nor at their intuitive properties or relationships, and can in our case not be aimed at them. For a figure understood geometrically is known to be an ideal limit incapable in principle of intuitive exhibition in the concrete. Even in our case, nonetheless, and in the generic field as such, intuition has an essential relation to expression and to its meaning: these, therefore, constitute an experience of general knowledge related to intuition, no mere togetherness of them all, but a unity of felt belongingness among them. Even in our case, concept and proposition are oriented towards intuition, through which alone, after corresponding adjustment, self-evidence, the crown of knowledge, emerges. It requires little reflection, on the other hand, to see that the meaning of the expressions in question is not found in intuition at all, that such intuition only gives them a filling of clarity and in the favourable case of self-evidence. We in fact know only too well that the overwhelming majority of general statements, and in particular those of science, behave meaningfully without any elucidation from intuition, and that only a vanishing section, even of the true and the proven, are and remain open to complete intuitive illumination. + +Even in the general realm, as in the realm of individuals, our natural talk has a relation to intuitively founded acts of thought. Should intuition fall + +wholly away, our judgement would cease to know anything. It means, in all cases, in cogitative style, just what could be known by the aid of intuition, if such judgement is indeed true at all. Knowledge always has the character of a fulfilment and an identification: this may be observed in every case where we confirm a general judgement through subsequent intuition, as in every + +other case of knowledge. + +Our difficulty then is how identification can arise where the form of the general proposition, and in particular its form of universality, would vainly seek sympathetic elements in individual intuition. To remove this difficulty, as in the previous case, the possibility of 'founded acts' suggests itself. This possibility, carried out more fully, would run more or less as follows: + +Where general thoughts find fulfilment in intuition, certain new acts are built on our percepts and other appearances of like order, acts related quite differently to our appearing object from the intuitions which constitute it. This difference in mode of relation is expressed by the perspicuous turn of phrase employed above: that the intuited object is not here itself the thing meant, but serves only as an elucidatory example of our true general meaning. But if expressive acts conform to these differences, their significative intention will not move towards what is to be intuitively presented, but towards what is universal, what is merely documented in intuition. Where this new intention is adequately fulfilled by an underlying intuition, it reveals its own objective possibility (or the possibility or 'reality' of the universal). + +§42 The disti nction between sensuous stuff and categorial fo rm throughout the whole real m of + +objectifyi ng acts + +After these provisional treatments have shown us our difficulty, and have provided us with a thought leading to its possible removal, we shall embark + +upon our actual discussion. + +We started by assuming that, in the case of structured expressions, the notion of a more or less mirror-like mode of expression was quite unavailing in describing the relation which obtains between meanings to be expressed, on the one hand, and expressed intuitions, on the other. This is doubtless correct and need now only be made more precise. We need only earnestly ponder what things can be possible matter for perception, and what things possible matter for meaning, to become aware that, in the mere form of a judgement, only certain antecedently specifiable parts of our statement can have something which corresponds to them in intuition, while to other parts of + +the statement nothing intuitive possibly can correspond. Let us consider this situation a little more closely. + +Perceptual statements are, completely and normally expressed, articulate utterances of varying pattern. We have no difficulty in distinguishing such types as 'A is P' (where 'A' serves as index for a proper name), 'An Sis P', + +'This Sis P, 'All S are P' etc. Many complications arise through the modifying influence of negation, through the introduction of distinctions between absolute and relative predicates (attributes), through conjunctive, disjunctive and determinative connectives etc. In the diversity of these types certain sharp distinctions of meaning make themselves clear. To the various letters (variables) and words in these types correspond sometimes members, sometimes connective forms, in the meanings of the actual statements which belong to these types. Now it is easy to see that only at the places indicated by letters (variables) in such 'forms of judgement', can meanings be put that are themselves fulfilled in perception, whereas it is hopeless, even quite misguided, to look directly in perception for what could give fulfilment to our supplementary formal meanings. The letters (variables) on account of their merely functional meaning, can doubtless take complex thoughts as their values: statements of high complexity can be seen from the standpoint of very simple judgement-types. The same difference between 'matter' and 'form' therefore repeats itself in what is looked upon, in unified fashion, as a 'term'. But eventually, in the case of each perceptual statement, and likewise, of course, in the case of every other statement that in a certain primary sense, gives expression to intuition, we shall come down to certain final elements of our terms - we may call them elements of stuff - which find direct fulfilment in intuition (perception, imagination etc.), while the supplementary forms, which as forms of meaning likewise crave fulfilment, can find nothing that ever could fit them in perception or acts of like order. This fundamental difference we call, in a natural extension of its application over the whole sphere of objectifying presentation, the categorial and absolute distinction between the form and matter of presentation, and at the same time separate it off from the relative or functional difference which is closely bound up with it, and which has just been subsidiarily touched on above. We have just spoken of a natural extension of our distinction over the whole sphere of objectifying presentation. We take the constituents of thefulfilment which correspond to the material or formal constituents of our meaning-intentions as being material or formal constituents respectively, so making clear what is to count as 'material' or 'formal' in the general sphere + +of objectifying acts. + +Of matter (stuff) and form we often talk in many other senses. We must expressly point out that our present talk of 'matter', which has its contrast in categorial form, has nothing whatever to do with the 'matter' which contrasts with the quality of acts, as when, e.g., we distinguish the 'matter' in our meanings from their assertive or merely presentative quality, this 'matter' being what tells us as what, or as now determined and interpreted, an object is meant in our meanings. To make the distinction easier, we shall not speak of 'matter' in our categorial contrast, but of 'stuff', while wherever 'matter' is meant in our previous sense, we shall talk pointedly + +§43 The objective correlates of categorial forms are + +not 'real' (reolen) moments + +It is now time to illuminate the distinction to which we have just given a name. We shall link on, for this purpose, to our previous examples. + +The form-giving flexion Being, whether in its attributive or predicative function, is not fulfilled, as we said, in any percept. We here remember Kant's dictum: Being is no real predicate. This dictum refers to being qua existence, or to what Herbart called the being of 'absolute position', but it can be taken to be no less applicable to predicative and attributive being. In any case it precisely refers to what we are here trying to make clear. I can see colour, but not being-coloured. I can feel smoothness, but not beingsmooth. I can hear a sound, but not that something is sounding. Being is nothing in the object, no part of it, no moment tenanting it, no quality or intensity of it, no figure of it or no internal form whatsoever, no constitutive feature of it however conceived. But being is also nothing attaching to an object: as it is no real (reales) internal feature, so also it is no real external feature, and therefore not, in the real sense, a 'feature' at all. For it has nothing to do with the real forms of unity which bind objects into more comprehensive objects, tones into harmonies, things into more comprehensive things or arrangements of things (gardens, streets, the phenomenal external world). On these real forms of unity the external features of objects, the right and the left, the high and the low, the loud and the soft etc., are founded. + +Among these anything like an 'is' is naturally not to be found. + +We have just been speaking of objects, their constitutive features, their factual connection with other objects, through which more comprehensive objects are created, and also, at the same time, external features in the partial objects. We said that something corresponding to being was not to be sought among them. For all these are perceptible, and they exhaust the range of possible percepts, so that we are at once saying and maintaining + +that being is absolutely imperceptible. + +Here, however a clarifying supplement is necessary. Perception and object are concepts that cohere most intimately together, which mutually assign sense to one another, and which widen or narrow this sense conjointly. But we must emphasize that we have here made use of a certain naturally delimited, natural, but also very narrow concept of perception (or of object). It is well-known that one also speaks of 'perceiving' , and in particular of 'seeing', in a greatly widened sense, which covers the grasping of whole states of affairs, and even ultimately the a priori self-evidence of laws (in the case of 'insight'). In the narrower sense of perception (to talk roughly and popularly) we perceive everything objective that we see with our eyes, hear with our ears or can grasp with any 'outer' or even 'inner sense'. In ordinary speech, no doubt, only external things and connective forms of things (together with their immediate qualities) can count as 'perceived by the senses' . + +But once talk of an 'inner sense' had been introduced, one should in consistency have widened the notion of sense-perception suitably, so as to include 'inner perception' , and so as to include under the name 'sense-object' the correlated sphere of 'inner objects', the ego and its internal experiences. In the sphere of sense-perception thus understood, and in the sphere, likewise, of sensuous intuition in general - we adhere to our much widened talk of the 'sensuous' - a meaning like that of the word 'being' can find no possible objective correlate, and so no possible fulfilment in the acts of such perception. What holds of 'being' is plainly true of the remaining categorial forms in our statements, whether these bind the constituents of terms together, or bind terms themselves together in the unity of the proposition. The 'a' and the 'the', the 'and' and the 'or', the 'if' and the 'then', the 'all' and the 'none', the 'something' and the 'nothing', the forms of quantity and the determinations of number etc. - all these are meaningful propositional elements, but we should look in vain for their objective correlates (if such may be ascribed to them at all) in the sphere of real objects, which is in fact + +no other than the sphere of objects of possible sense-perception. + +§44 The origin of the con cept of Being and of the remai ning categories does not lie in the real m of + +inner perception + +This holds - we stress it expressly - both of the sphere of outer sense, and of that of 'inner sense'. It is a natural but quite misguided doctrine, universally put about since the time of Locke, that the meanings in question (or the corresponding substantivally hypostatized meanings) - the logical categories such as being and non-being, unity, plurality, totality, number, ground, consequence etc. - arise through reflection upon certain mental acts, and so fall in the sphere of'inner sense', of'inner perception'. In this manner, indeed, concepts like Perception, Judgement, Affirmation, Denial, Collecting, Counting, Presupposing and Inferring arise, which are all, therefore, 'sensuous' concepts, belonging, that is, to the sphere of 'inner sense'. The previous series of concepts do not arise in this manner, since they cannot at all be regarded as concepts of mental acts, or of their real constituents. The thought of a Judgement fulfils itself in the inner intuition of an actual judgement, but the thought of an 'is' does not fulfil itself in this manner. Being is not a judgement nor a constituent of a judgement. Being is as little a real constituent of some inner object as it is of some outer object, and so not of a judgement. In a judgement, a predicative statement, 'is' functions as a side of our meaning, just as perhaps, although otherwise placed and functioning, 'gold' and, 'yellow' do. The is itself does not enter into the judgement, it is merely meant, signitively referred to, by the little word 'is'. It is, however, self-given, or at least putatively given, in the fulfilment which at times invests the judgement, the becoming aware of the state of affairs supposed. Not only + +what is meant in the partial meaning gold, nor only what is meant in the partial meaning yellow, itself appears before us, but also gold-being-yellow thus appears. Judgement and judgemental intuition are therefore at one in the self-evident judgement, and pre-eminently so if the judgement is self- + +evident in the ideally limiting sense. + +If one now understands by 'judging' , not merely meaning-intentions connected with actual assertions, but the fulfilments that in the end fit them completely, it is indeed correct that being can only be apprehended through judging, but this does not at all mean that the concept of being must be arrived at 'through reflection' on certain judgements, or that it can ever be arrived at in this fashion. 'Reflection' is in other respects a fairly vague word. In epistemology it has at least the relatively fixed sense that Locke gave it, that of internal perception: we can only adhere to this sense in interpreting a doctrine which imagines it can find the origin of the concept of Being through reflecting on judgements. The relational being expressed in predication, e.g. through 'is', 'are' etc., lacks independence: if we round it out to something fully concrete, we get the state of affairs in question, the objective correlate of the complete judgement. We can then say: As the sensible object stands to sense-perception so the state of affairs stands to the 'becoming aware' in which it is (more or less adequately) given - we should like to say simply: so the state of affairs stands to the perception of it. As the concept Sensuous Object (Real Object) cannot arise through reflection upon perception, since this could only yield us the concept Perception (or a concept of certain real constituents of Perception), so the concept of State of Affairs cannot arise out of reflection on judgements, since this could only yield us concepts of judgements or of real constituents of judgements. + +That percepts in the one case, and judgements (judgemental intuitions, percepts of states of affairs) in the other, must be experienced, in order that each such act of abstraction should get started, goes without saying, but to be experienced is not to he made objective. 'Reflection', however, implies that what we reflect upon, the phenomenological experience, is rendered objective to us (is inwardly perceived by us), and that the properties to be + +generalized are really given in this objective content. + +Not in reflection upon judgements, nor even upon fulfilments of judgements, but in the fulfilments of judgements themselves lies the true source of the concepts State of Affairs and Being (in the copulative sense). Not in these acts as objects, but in the objects of these acts, do we have the abstractive basis which enables us to realize the concepts in question. And naturally the + +appropriate modifications of these acts yield just as good a basis. + +It is in fact obvious from the start that, just as any other concept (or Idea, Specific Unity) can only 'arise', i.e. become self-given to us, if based on an act which at least sets some individual instance of it imaginatively before our eyes, so the concept of Being can arise only when some being, actual or imaginary, is set before our yes. If 'being' is taken to mean predicative being, + +some state of affairs must be given to us, and this by way of an act which + +gives it, an analogue of common sensuous intuition. + +The like holds of all categorial forms (or of all categories). An aggregate, e.g., is given, and can only be given, in an actual act of assembly, in an act, that is, expressed in the conjunctive form of connection A and B and C ... But the concept of Aggregate does not arise through reflection on this act: instead of paying heed to the act which presents an aggregate, we have rather to pay heed to what it presents, to the aggregate it renders apparent in concreto, and then to lift the universal form of our aggregate to conceptually + +universal consciousness. + +§45 Wi dening of the concept of intuit ion, and in particu lar of the concepts perception and imaginati on. Sensible and catego rial intuition + +If we now ask: 'Where do the categorial forms of our meanings find their fulfilment, if not in the "perception" or "intuition which we tried provisionally to delimit in talking of "sensibility" " our answer is plainly prefigured in + +the discussions just completed. + +We have taken it for granted that forms, too, can be genuinely fulfilled, or that the same applies to variously structured total meanings, and not merely to the 'material' elements of such meanings, and our assumption is put beyond doubt by looking at each case of faithful perceptual assertion. This will explain also why we call the whole perceptual assertion an expression of perception and, in a derivative sense, of whatever is intuited or itself presented in perception. But if the 'categorial forms' of the expression, present together with its material aspects, have no terminus in perception, if by the latter we understand merely sense-perception, then talk of expressing a percept must here rest on a different meaning: there must at least be an act which renders identical services to the categorial elements of meaning that merely sensuous perception renders to the material elements. The essential homogeneity of the function of fulfilment, as of all the ideal relationships necessarily bound up with it, obliges us to give the name 'perception' to each fulfilling act of confirmatory self-presentation, to each fulfilling act whatever the name of an 'intuition', and to its intentional correlate the name of 'object' . If we are asked what it means to say that categorially structured meanings find fulfilment, confirm themselves in perception, we can but reply: it means only that they relate to the object itself in its categorial structure. The object with these categorial forms is not merely referred to, as in the case where meanings function purely symbolically, but it is set before our very eyes in just these forms. In other words: it is not merely thought of, but intuited or perceived. When we wish, accordingly, to set forth what this talk of 'fulfilment' is getting at, what structured meanings and their structural elements express, what unitary or unifying factor corresponds to + +them objectively, we unavoidably come on 'intuition' (or on 'perception' and 'object'). We cannot manage without these words, whose widened sense is of course evident. What shall we call the correlate of a non-sensuous subject-presentation, one involving non-sensuous structure, if the word 'object' is not available to us? How shall we speak of its actual givenness, or apparent givenness, when the word 'perception' is denied us? In common parlance, therefore, aggregates, indefinite pluralities, totalities, numbers, disjunctions, predicates (right-ness), states of affairs, all count as 'objects', while the acts through which they seem to be given count as 'percepts' . Plainly the connection between the wider and narrower, the supersensuous (i.e. raised above sense, or categorial) and sensuous concept of perception, is no external or contingent matter, but one rooted in the whole business on hand. It falls within the great class of acts whose peculiarity it is that in them something appears as 'actual', as 'self-given'. Plainly this appearance of actuality and self-givenness (which may very well be delusive) is throughout characterized by its difference from essentially related acts through which alone it achieves full clarity - its difference from an imaginative 'making present', or from a merely significative 'thinking of', which both exclude 'presence' (so to say appearance 'in person'), though not excluding the belief in being. As regards the latter, imaginal or symbolic representation is possible in two manners: in an assertive manner, asserting something's being in imaginal or symbolic fashion, and in a non-assertive manner, as 'mere' imagination or thinking without taking something to be. We need not enter more closely into the discussion of these differences after the analyses of the previous section, which permit of a sufficiently general interpretation. It is clear, in any case, that the concept of imagination must be widened in correspondence with the concept of perception. We could not speak of something super-sensuously or categorially perceived, if we could not imagine this thing 'in the same manner' (i.e. not merely sensuously). We must therefore draw a quite general distinction between sensuous and categorial intuition (or show + +the possibility of such a distinction). + +Our extended concept of Perception permits, further, of a narrower and a wider interpretation. In the widest sense even universal states of affairs can be said to be perceived ('seen', 'beheld with evidence'). In the narrower sense, perception terminates upon individual, and so upon temporal being. + +§46 Phenomenological analysis of the distinction between sensuous and categorial perception + +In our next treatments we shall first only discuss individual percepts, then widen our treatment to take in individual intuitions of the same order. The division between 'sensuous' and 'supersensuous' percepts was only very superficially indicated and quite roughly characterized above. Antiquated talk of external and internal senses, plainly stemming from the naive + +metaphysic and anthropology of daily life, may be useful in pointing out the sphere to be excluded, but a true determination and circumscription of the sensory sphere is not thereby reached, so depriving the concept of categorial perception of its descriptive underpinning. To ascertain and clarify the said distinction is all the more important, since such fundamental distinctions as that between categorial form and sensuously founded matter, and the similar distinction between categories and all other concepts, depends wholly on it. Our concern is therefore to seek more profound descriptive characterizations, which will give us some insight into the essentially different constitution of sensuous and categorial percepts (or intuitions in general). For our immediate purposes it is, however, unnecessary to carry out an exhaustive analysis of the phenomena involved. That would be a task that would require extraordinarily comprehensive treatments. Here it is sufficient to concentrate on some weightier points, which may help to mark off both + +sorts of acts in their mutual relation. + +It is said of every percept that it grasps its object directly, or grasps this object itself. But this direct grasping has a different sense and character according as we are concerned with a percept in the narrower or the wider sense, or according as the directly grasped object is sensuous or categorial. Or otherwise put, according as it is a real or an ideal object. Sensuous or real objects can in fact be characterized as objects of the lowest level of possible intuition, categorial or ideal objects as objects of higher levels. + +In the sense of the narrower, 'sensuous' perception, an object is directly apprehended or is itself present, if it is set up in an act of perception in a straightforward (schlichter) manner. What this means is this: that the object is also an immediately given object in the sense that, as this object perceived with this definite objective content, it is not constituted in relational, connective, or otherwise articulated acts, acts founded on other acts which bring other objects to perception. Sensuous objects are present in perception at a single act-level: they do not need to be constituted in many-rayed fashion in acts of higher level, whose objects are set up for them by way of other + +objects, already constituted in other acts. + +Each straightforward act of perception, by itself or together with other acts, can serve as basic act for new acts which at times include it, at times merely presuppose it, acts which in their new mode of consciousness likewise bring to maturity a new awareness of objects which essentially presupposes the old. When the new acts of conjunction, of disjunction, of definite and indefinite individual apprehension (that - something), of generalization, of straightforward, relational and connective knowledge, arise, we do not then have any sort of subjective experiences, nor just acts connected with the original ones. What we have are acts which, as we said, set up new objects, acts in which something appears as actual and self-given, which was not given, and could not have been given, as what it now appears to be, in these foundational acts alone. On the other hand, the new objects are based on the + +older ones, they are related to what appears in the basic acts. Their manner of appearance is essentially determined by this relation. We are here dealing with a sphere of objects, which can only show themselves 'in person ' in such founded acts. In such founded acts we have the categorial element in intuition and knowledge, in them assertive thought, functioning expressively, finds fulfilment; the possibility of complete accord with such acts determines the truth, the rightness, of an assertion. So far we have of course only considered the sphere of perception, and only its most elementary cases. But one sees at once that the distinction of straightforward and founded acts can be extended from percepts to all intuitions. We clearly envisage the possibility of complex acts which in mixed fashion have a part-basis in straightforward percepts and a part-basis in straightforward imaginations, and the further possibility of setting up new foundations on intuitions which themselves have foundations, and so building up whole series of foundings upon foundings. We further see that signitive intentions have structures patterned on such foundings whether of lower or higher order, and that again mixtures of signitive and intuitive acts emerge out of such 'founding', founded acts, in short, that are built on acts of one or the other sort. Our first task, however, is to deal with the elementary cases and elucidate them + +completely. + +§47 Co nti n uati on. Characte rization of + +sense-percepti on as 'straightfo rward ' percepti on + +We shall now scrutinize the acts in which sensuous concreta and their sensuous constituents are presented as given; as opposed to these we shall later consider the quite different acts in which concretely determinate States of Affairs, Collections and Disjunctions are given as complex thought-objects, or as objects of higher order, which include their foundational objects as real parts (reell) in themselves. We shall then deal with acts of the type of generalizing or indefinitely individual apprehension, whose objects certainly are of higher level, but which do not include their foundational objects in themselves. In sense-perception, the 'external' thing appears 'in one blow' , as soon as our glance falls upon it. The manner in which it makes the thing appear present is straightforward: it requires no apparatus of founding or founded acts. To what complex mental processes it may trace back its origin, and in + +what manner, is of course irrelevant here. + +We are not ignoring the obvious complexity that can be shown to exist in the phenomenological content of the straightforward perceptual act, and + +particularly in its unitary intention. + +Many constitutive properties certainly pertain to the thing when it appears with a given content, some of them themselves 'falling under perception', others merely intended. But we certainly do not live through all the articulated acts of perception which would arise were we to attend to all the details + +of the thing, or, more precisely, to the properties of the 'side turned to us', were we to make them objects in their own right. No doubt ideas of such supplementary properties, not given in perception, are 'dispositionally excited', no doubt intentions which relate to them contribute to perception, and determine its total character. But, just as the thing does not appear before us as the mere sum of its countless individual features, which a later preoccupation with detail may distinguish, and as even the latter does not dirempt the thing into such details, but takes note of them only in the ever complete, unified thing, so the act of perception also is always a homogeneous unity, which gives the object 'presence' in a simple, immediate way. The unity of perception does not therefore arise through our own synthetic activity, as if only a form of synthesis, operating by way of founded acts, could give unity of objective reference to part-intentions. It requires no articulation and hence no actual linkage. The unity of perception comes into being as a straightforward unity, as an immediate fusion of part-intentions, + +without the addition of new art-intentions. + +We may also be unsatisfied with a single glance, we may handle the thing from all sides in a continuous perceptual series, feeling it over as it were with our senses. But each single percept in this series is already a percept of the thing. Whether I look at this book from above or below, from inside or outside, I always see this book. It is always one and the same thing, and that not merely in some purely physical sense, but in the view of our percepts themselves. If individual properties dominate variably at each step, the thing itself, as a perceived unity, is not in essence set up by some overreaching act, + +founded upon these separate percepts. + +Considering things more closely, we should not present the matter as if the one sensible object could be presented in a founded act (in a continuously developing act of perceiving), while it merely does not need to be presented in such an act. Closer analysis shows that even a continuous perceptual flux involves a fusion of part-acts in one act, rather than a peculiar + +act founded upon such part-acts. + +To prove this we embark on the following discussion. + +The individual percepts of our series have a continuous unity. Such continuity does not amount to the mere fact of temporal adjunction: the series of individual acts rather has the character of a phenomenological unity, in which the individual acts are fused. In this unity, our manifold acts are not merely fused into a phenomenological whole, but into one act, more precisely, into one concept. In the continuous running on of individual percepts we continuously perceive the single, selfsame object. Can we now call this continuous percept, since it is built out of individual percepts, a percept founded upon them? It is of course founded upon them in the sense in which a whole is founded on its parts, not however in the sense here relevant, according to which a founded act manifests a new act-character, grounded in the act-characters that underlie it and unthinkable apart from these. In + +the case before us perception is merely, as it were, extended: it allows parts to be broken off from itself which can function as complete, independent percepts. But the unification of these percepts into a continuous percept is not the performance of some peculiar act, through which a new consciousness of something objective is set up. We find, instead, that absolutely nothing new is objectively meant in the extended act, but that the same object is continuously meant in it, the very object that the part-percepts, taken singly, + +were already meaning. + +One might lay stress on this sameness, and say that our unity is plainly a unity of identification, that the intention of the serially arranged acts coincides continuously, and that so the unity arises. This is certainly right. But unity of identification is unavoidably distinct, does not say the same as the unity of an act of identification. An act means something, an act of identification means identity, presents it. In our case an identification is performed, but no identity is meant. The object meant in the differing acts of the continuous perceptual series is indeed always the same, and the acts are one through coincidence, but what is perceived in the series, what is rendered objective in it, is solely the sensible object, never its identity with self. Only when we use the perceptual series to found a novel act, only when we articulate our individual percepts, and relate their objects to each other, does the unity of continuity holding among these individual percepts - the unity of fusion through their coinciding intentions - provide a point d'appui for a consciousness of identity. Identity itself is now made objective, the moment of coincidence linking our act-characters with one another, serves as representative content for a new percept, founded upon our articulated individual percepts. This brings to intentional awareness that what we now see and what we saw before are one and the same. Naturally we have then to do with a regular act of our second group. Our act of identification is in sober fact a new awareness of objectivity, which causes a new 'object' to appear to us, an object that can only be apprehended or given in its very + +selfhood in a founded act of this sort. + +Before we penetrate further into our new class of acts and objects, we must, however, first round off our treatment of straightforward percepts. If we may presume to have cleared up the sense of the concept of a straightforward percept, or, what we take for the same, of sense-perception, then we have also cleared up the concept of a sensible or real object (in the most basic sense of 'real'). We define a real object as the possible object of a straightforward percept. There is a necessary parallelism between perception and imagination, which guarantees that a possible imagination (or more precisely a whole series of imaginations) having the same essence, corresponds to each possible percept, a straightforward imagination is correlated with each straightforward percept, thereby giving certainty to the wider concept of sensible intuition. We can then define sensible objects as the possible objects of sensible imagination and sensible intuition in general: this of + +course involves no essential generalization of our previous definition. The + +parallelism just stressed makes both definitions equivalent. + +Through the concept of a real object, the concept of a real part, or more particularly, the concepts of a real piece, and a real moment (real feature), and a real form, are determined. Each part of a real object is a real part. In straightforward perception we say that the whole object is explicitly given, while each of its parts (in the widest sense of 'parts') is implicitly given. The sum total of objects that can be explicitly or implicitly given in straightforward percepts constitutes the most widely conceived sphere of + +sensible objects. + +Each concrete sensible object is perceptible in explicit fashion, and so also every piece of such an object. How does the matter stand in regard to abstract moments? Their nature makes them incapable of separate being: their representative content, even where there is merely representation by way of analogy, cannot be experienced alone, but only in a more comprehensive concrete setting. But this does not mean that their intuition need be a founded act. It would be one, if the apprehension of an abstract moment was necessarily preceded by the apprehension of the concrete whole or of its complementary moments, such an apprehension being an act of intuitive turning towards its object. This I do not find obvious. It is clear, per contra, that the apprehension of a moment and of a part generally as a part of the whole in question and, in particular, the apprehension of a sensuous feature as a feature, or of a sensuous form as a form, point to acts which are all founded: these acts are in our case of a relational kind. This means that the sphere of 'sensibility' has been left and that of 'understanding' entered. We shall now subject the just mentioned group of founded acts to a closer + +consideration. + +§48 Characterization of catego rial acts as + +fo unded acts + +A sensible object can be apprehended by us in a variety of ways. It can, first of all, of course, be apprehended in 'straightforward' fashion. It is this possibility, which like all the other possibilities here in question must be throughout interpreted as 'ideal', which characterizes the sensible object as a sensible object. Understood in this manner, it stands as it were simply before us: the parts which constitute it are indeed in it, but are not made our explicit objects in the straightforward act. The same object can, however, be grasped by us in explicating fashion: acts of articulation can put its parts 'into relief', relational acts bring the relieved parts into relation, whether to one another or to the whole. Only through such new modes of interpretation will the connected and related members assume the character of 'parts' (or of 'wholes'). The articulating acts and, taken in retrospect, the act we call 'straightforward', are not merely experienced one after the other: + +overreaching unities of act are rather always present, in which, as new objects, + +the relationships of the parts become constituted. + +Let us first look at the relationships of parts and wholes: limiting ourselves to the simplest cases, let us consider the relationships A is or has a and a is in A. To point to the founded acts in which these typical states of affairs become constituted as data, and to clear up the just employed forms of categorical statement (to lead them back to their intuitive origin and adequate fulfilment) are one and the same. We are not, however, here concerned with the qualities of acts, but only with the constitution of their interpretative forms: to that extent our analysis, if regarded as an analysis of + +judgement, will be defective. + +An act of perception grasps A as a whole, at one 'blow' and in straightforward fashion. A second act of perception is trained upon a, the part or dependent moment, that belongs constitutively to A. These two acts are not merely performed together, or after one another, in the manner of disjoined experiences; rather are they bound together in a single act in whose synthesis A is first given as containing 0 in itself. Just so, a can, with a reversal of the direction of relational perception, achieve self-givenness as pertaining to A. + +Let us now try to penetrate a little deeper. + +The total intuitive reference to our object implicitly contains an intention to o. For perception purports to grasp the object itself: its 'grasping' must therefore reach to all its constituents in and with the whole object. (Naturally we are here only concerned with what constitutes the object as it appears in perception, and as what it appears in perception, and not with such constituents as may pertain to it in 'objective reality', and which only later + +experience, knowledge and science will bring out.) + +In the narrowing down of our total percept to one specific percept, the part-intention to a will not be torn out of the total appearance of A, so as to break up the latter's unity, but an independent act will have a as its own perceptual object. At the same time one's continuously operative total percept will coincide with this specific percept in respect of one implicit partintention. The 'content' which represents a, will be functioning as the same content in a twofold fashion and, in so far as it does this, it will effect a coincidence, a peculiar unity of the two representative functions; we shall, in other words, have two coincident interpretations, both sustained by the representative content in question. But this unity of these two representative functions will now itself take on a representative role. It will not itself count in its own right as an experienced bond among acts: it will not set itself up as our object, but will help to set up another object. It will act representatively, and to such effect, that A will now appear to contain a in itself (or, + +with a reversed direction, a will appear as contained in A). + +According, therefore, to our 'interpretative standpoint', or to the 'sense of our passage' from part to whole or contrariwise - which are both novel phenomenological characters making their contribution to the total intentional + +matter of the relating act - there will be two possibilities, marked off in a priori fashion, in which the 'same relation' can achieve actual givenness. To these correspond two a priori possibilities of relation, objectively different, yet tied together by an ideal law, possibilities which can only be directly constituted in founded acts of the sort in question, which can achieve 'self- + +givenness to perception' only in acts built up in this manner. + +Our exposition obviously applies to all specific forms of the relation between a whole and its parts. All such relationships are of categorial, ideal nature. It would be a mistake to try to locate them in the straightforwardly given whole, to discover them in this whole by analysis. The part certainly lies hidden in the whole before all division into members, and is subsidiarily apprehended in our perceptual grasp of this whole. But this fact, that it thus lies hidden in the whole, is at first merely the ideal possibility of bringing the part, and the fact that it is a part, to perception in correspondingly articu- + +lated and founded acts. + +The matter is plainly similar in the case of external relations, from which predications such as 'A is to the right of B', 'A is larger, brighter, louder than B etc.', take their rise. Wherever sensible objects - directly and independently perceptible - are brought together, despite their mutual exclusion, into more or less intimate unities, into what fundamentally are more comprehensive objects, then a possibility of such external relations arises. They all fall under the general type of the relation of part to parts within a whole. Founded acts are once more the media in which the primary appearance of the states of affairs in question, of such external relationships, is achieved. It is clear, in fact, that neither the straightforward percept of the complex whole, nor the specific percepts pertaining to its members, are in themselves the relational percepts which alone are possible in such a complex. Only when one member is picked out as principal member, and is dwelt on while the other members are still kept in mind, does a determination of members by members make its appearance, a determination which varies with the kind of unity that is present and plainly also with the particular members set in relief. In such cases also the choice of a principal member, or of a direction of relational apprehension, leads to phenomenologically distinct forms of relationship, correlatively characterized, which forms are not genuinely present in the unarticulated percept of the connection as a straightforward phenomenon, but which are in it only as ideal possibilities, the possibilities, + +that is, of fulfilling relevant founded acts. + +A real (reel/e) location of these relations of parts in the whole would be a confusion of distinct things: of sensuous or real (realen) forms of combination, with categorial or ideal ones. Sensible combinations are aspects of the real (realen) object, its actual moments, present in it, if only implicitly, and capable of being 'lifted out of it' by an abstractive percept. As against this, forms of categorial combination go with the manner in which acts are synthesized: they are constituted as objects in the synthetic acts built upon our + +sensibility. In the formation of external relations sensuous forms may serve as foundations for the categorial forms which correspond to them, as when, in the face of the sensuously intuited contact of the contents A and B within a comprehensive whole W, we, observe, and perhaps verbally express our observation, in the synthetic forms 'A is in contact with B', or 'B is in contact with A'. But, in constituting the latter forms, we bring new objects into being, objects belonging to the class of 'states of affairs', which includes none but 'objects of higher order'. In the sensible whole, the parts A and B are made one by the sensuously combinatory form of contact. The abstraction of these parts and moments, the formation of intuitions of A, B and contact, will not yet yield the presentation A in contact with B. This demands a novel act which, taking charge of such presentations, shapes and combines + +them suitably. + +§49 Added note on nomi nal fo rmations + +We shall now make an important addition to our analysis up to this point: this concerns the shaping which synthetically combined presentations, each on their own account, may undergo. We have already studied this important point in a special class of cases: we observed, in our Fifth Investigation that an assertion can never be made, in unmodified form, the basis of a synthetic act built upon it, the subject- or object-member of a new assertion. An assertion, we said, must first of all take on nominal form, whereby its state of affairs becomes objective in a new, nominal fashion (Inv. v, §§35, 36). In this fact the intuitive distinction we have in view is brought out, a distinction which does not merely hold of the relata of the hitherto discussed syntheses of lowest grade, immediately based on sensibility, but of all presentations presided over by 'many-rayed' syntheses of whatever kind or level. We may at first then hazard the general statement: Objectifying acts which exist purely 'on their own ', and 'the same' objectifying acts serving to constitute the terms of some relation or other, are not really the same acts: they differ phenomenologically, and diff er in respect of what we have called their intentional matter. Their interpretative sense has changed, and hence the changed meaning of their adequate expression. It is not as if something had merely been shoved in between unchanged presentations, a bond which combined them in merely external fashion. The working of synthetic thought, of intellection, has done something to them, has shaped them anew, although, being a categorial function, it has done this in categorial fashion, so that the sensuous content of the apparent object has not been altered. The object does not appear before us with new real (realen) properties; it stands before us as this same object, but in a new manner. Its fitting into its categorial context gives it a definite place and role in this context, the role of a relatum, and in particular of a subject- or object-member. These are differences that + +It is no doubt easier to pay heed to changes of meaning in our expressive symbols than to modifications of our direct presentations themselves: the situation, e.g., in the field of straightforward intuitions, when we compare such intuitions within and without some relational function, is far from clear, and I have not therefore touched on it in my last Investigation. There isolated sense-percepts were put on a level with nominally functioning acts (see Inv. v, §33). Just as the object in a straightforward percept directly confronts us, so too does the state of affairs in the act which names it, and so too does any categorially formed object. The gradual constitution of the object has been completed, as a finished object it becomes a term in a relation: it keeps, it seems, its constitutive sense quite unaltered. One can certainly say that the phenomenological change in sense made by entry into a relational act is at first masked by the very fact that the new form includes the whole previous interpretative sense in itself, to which it only imparts the new sense of a 'role'. Perception remains perception, the object is given as it was before given, 'only' it is 'put into relation'. Such shapings due to our synthetic function do not alter the object itself, we count them only as pertaining to our subjective activity, and we therefore overlook them in phenomenological reflections aiming at a clarification of knowledge. We should in consistency therefore say: A state of affairs also is the same state of affairs when it functions as logical subject (or generally when it functions nominally), and it has its ultimate constitution in the same act of originative intuition as when it functioned in isolation. When, however, it functions as a relatum in an act of higher level, it is constituted with a new form (and with, so to say, the characterizing costume of its role) of which the nominal form is the adequate expression. Further researches will however be necessary for + +a last clearing-up of the phenomenological situation just tackled. + +§50 Sensuous fo rms catego rially grasped but not + +fu nct ioning nomi nally + +We have so far only spoken of the re-shapings of terms put into such relations as that of whole and part. External relations, however, show us how sensuous forms enter into the unity of a relation (in its predicate) without undergoing nominal reification, e.g. 'A brighter than B', 'A to the right of B' etc. There are undeniable phenomenological differences - differences in interpretative sense - between cases where we, so to say, pay direct attention to the form of brightness, and make this our nominal object, as when we say 'This relation of brightness (between A and B) is more readily noticeable than that one (between M and N)" and the quite different cases, where this form of brightness is meant as in the above expression 'A is brighter than B'. In the latter class of cases we once more have a categorial form pointing to a peculiar function in the total relational situation. Concepts such as Terms of Relations, Form of Relation, Subject, Object etc., concepts not + +always clearly expressed and certainly insufficiently clarified, plainly lead back to differences in such categorial forms with which in this and previous + +paragraphs we have become familiar. + +§5 1 Coll ectiva and disjunctiva + +We have so far discussed, as instances of categorial and synthetic objectforms, only certain very simple forms of states of affairs, those of total and partial relations of identity, and of simple external relations. We now turn our regard to two further examples, to synthetic forms, i.e. which, though not themselves states of affairs, nevertheless play a large part in connection with states of affairs: Collectiva and Disjunctiva. The acts in which these are constituted as data are those which furnish a fulfilling intuition for the + +meanings of the conjunctions 'and' and 'or' . + +What intuitively corresponds to the words 'and' and 'or', to 'both' or 'either', is not anything, as we rather roughly put it above, that can be grasped with one's hands, or apprehended with some sense, as it can also not really be represented in an image, e.g. in a painting. I can paint A and I can paint B, and I can paint them both on the same canvas: I cannot, however, paint the both, nor paint the A and the B. Here we have only the one possibility which is always open to us: to perform a new act of conjunction or collection on the basis of our two single acts of intuition, and so mean the aggregate of the objects A and B. In the situation just viewed as an example this act is constituted as an imaginative presentation of A and B, while this aggregate is only given as 'itself ', in the manner of perception, and can only be so given, in just such an act, an act merely modified in a conformable manner, and which is founded on the percepts of A and B. That we speak of an act which unites these percepts, and not of any connection or mere coexistence of these percepts in consciousness, depends on the fact that a unitary intentional relation is here given, and a unitary object which corresponds to it; this object can only be constituted in such a connection of acts, just as a State of Affairs can only be constituted in a relational act-connection. We at once see the essential mistake made by those eminent modern logicians who have tried to explain the conjunctive association of names or statements through a mere conscious coexistence of nominal or propositional acts, and have so surrendered and as an objective + +form in Logic. + +1 + +We must also guard against confusing the straightforward percepts of sensuously unified manifolds, series, swarms etc., with the conjunctive percepts in which alone the consciousness of plurality is itself properly constituted. I have tried to show in my Philosophy of Arithmetic how the sensuously unifying characters - I there called them 'figural' or 'quasi-qualitative' moments of sensuous intuitions - serve as signs of plurality. This means that they serve as sensuous points d'appui for the signitively mediated cognition + +of plurality as such, and of plurality of the kind in question - which cognition now has no need of an articulated grasp and knowledge of individual items, but does not therefore as yet possess the character of a genuine intui- + +tion of the collection as such.2 + +§52 Un ive rsal objects constituti ng themselves in + +un iversal intuitions + +The simple synthetic acts with which we have so far concerned ourselves were so founded upon straightforward percepts that the synthetic intention was subsidiarily directed to the objects of these founding percepts, inasmuch as it held them together in ideal 'contents' or brought them to a relational unity. This is a universal character of synthetic acts as such. We now turn to examples from another set of categorial acts, in which the objects of the founding acts do not enter into the intention of the founded one, and would only reveal their close relation to it in relational acts. Here we have the field of the universal intuition - an expression which no doubt will not seem better + +to many than 'wooden iron' . + +Abstraction gets to work on a basis of primary intuitions, and with it a new categorial act-character emerges, in which a new style of objectivity becomes apparent, an objectivity which can only become apparent - whether given as 'real' or as 'merely imagined' - in just such a founded act. Naturally I do not here mean 'abstraction' merely in the sense of a setting-in-relief of some non-independent moment in a sensible object, but Ideational Abstraction, where no such non-independent moment, but its Idea, its Universal, is brought to consciousness, and achieves actual givenness. We must presuppose such an act in order that the Very Sort, to which the manifold single moments 'of one and the same sort' stand opposed, may itself come before us, and may come before us as one and the same. For we become aware of the identity of the universal through the repeated performance of such acts upon a basis of several individual intuitions, and we plainly do so in an overreaching act of identification which brings all such single acts of abstraction into one synthesis. Through such acts of abstraction, woven into new act-forms, there arise, further, acts of universal determination, acts, that is, which determine objects generally as subsumed under certain species A, or + +acts in which unspecified objects of a sort A become present to us. + +In an act of abstraction, which need not necessarily involve the use of an abstract name, the universal itself is given to us; we do not think of it merely in significative fashion as when we merely understand general names, but we apprehend it, behold it. Talk of an intuition and, more precisely, of a percep- + +tion of the universal is in this case, therefore, well-justified. + +Difficulties arise, however, from another quarter. Talk of 'perception' presupposes the possibility of correspondent imagination: a distinction between them, we held, is part of the natural sense of our ordinary talk about + +'intuition' . But it is just this distinction that we cannot here draw. This seems to stem from the fact that abstractive acts do not differ in consonance with the character of the straightforward intuitions which underlie them; they are quite unaffected by the assertive or non-assertive character of such underlying acts, or by their perceptual or imaginative character. The Red, the Triangle exemplified in mere phantasy is specifically the same as the Red, the Triangle exemplified in our percepts. Our consciousness of the universal has as satisfactory a basis in perception as it has in parallel imagination, and, wherever it arises, the Idea Red, the Idea Triangle, is itself apprehended, is intuited in the one unique way which permits no distinction between image + +and original. + +We must, however, note that the examples adduced were all cases of the adequate perception of the universal. The universal was here truly grasped and given on the basis of truly correspondent instances. Where this is the case, there seems in fact to be no parallel imagination having the same intuitive content, and this is so in every case of adequate perception. For how, we may ask, even in the realm of individuals, could a content pattern itself on itself, since, taken as itself, it cannot also be meant as its own analogon? And how can the note of assertion be wanting, where the meant content is the one experienced and given? It is quite different in, e.g. , the case where mathematical analysis has given us an indirectly conceived Idea of a certain class of curves of the third order, though we have never seen any curve of this sort. In such a case an intuitive figure, e.g. of a familiar thirdorder curve, perhaps actually drawn, perhaps merely pictured, may very well serve as an intuitive image, an analogon, of the universal we are intending: our consciousness of the universal is here intuitive, but analogically intuitive, in its use of an individual intuition. And does not an ordinary rough drawing function analogically in comparison with an ideal figure, thereby helping to condition the imaginative character of the universal presentation? This is how we contemplate the Idea of a steam-engine, basing ourselves on a model of a steam-engine, in which case there can naturally be no talk of an adequate abstraction or conception. In such cases we are not concerned with significations, but with universal representations by way of analogy, with universal imaginations, in short. If, however, the consciousness of mere analogy lapses, as may happen, e.g. , in the intuition of a model, we have a case of the perception of the universal, even if it is one + +of inadequate perception. + +In the same way we may now discover the previously missing differences between an assertive, and a merely contemplative, consciousness of the universal. Where we contemplate a universal object in a merely analogizing, imaginative fashion, we may also mean it assertively, and this act, like any assertive reference, may be confirmed or refuted by adequate future perception. The former happens wherever the universal meaning is fulfilled by an adequate percept, i.e. by a new consciousness of the universal which constitutes itself + +on the basis of a 'true' abstraction from the corresponding individual percept. The universal object is then not merely presented and posited, but is itself given to us. Again we can have an analogizing presentation of the universal, without actually positing it. We conceive it, but leave it in suspense. The intention to the universal which here rests on an intuitive basis makes no decision regarding 'being' or 'non-being', only one regarding the possibility or impossibility of the universal, and of its presentation through + +adequate abstraction. + +Chapter 7 + +A study in categorial + +representation + +§53 Backward reference to the researc hes of our + +fi rst section + +The founded acts analysed by us in select examples were considered by us to be intuitions, and intuitions of the new types of object that they brought to light, objects which can only be given in founded acts of a sort and form which corresponds to each of them. The explanatory value of this extended use of the concept Intuition can only lie in the fact that we are not here dealing with some inessential, merely disjunctive widening of a concept, which permits us to extend the sphere of that concept over the spheres of any heterogeneous concepts whatsoever, ! but with an authentic generalization, which rests on a community of essential features. We call the new acts 'intuitions' in that, with a mere surrender of a 'straightforward' relation to their object - the peculiar sort of immediacy defined by us as 'straightforwardness' - they yet have all the essential peculiarities of intuitions: we find in their case the same essential divisions, and they show themselves capable of achieving the same fully performedJulfilments. This last mentioned capacity is particularly important for our purposes, for it was with a view to such performances that this whole investigation has been conducted. Knowledge as the unity of fulfilment is not achieved on a mere basis of straightforward acts, but in general, on a basis of categorial acts: when, accordingly, we oppose intuition to thought (as meaning), we cannot mean by 'intuition' merely + +sensuous intuition. + +The conception of categorial acts as intuitions, first brings true perspicuity into the relation of thought to intuition - a relation that no previous critique of knowledge has made tolerably clear: it is the first to render knowledge itself intelligible, in its essence and its achievement. Through such a conceptual extension the theses of our first section first gain adequate confirmation. To all intuitions, in our present widest sense, however near or far they may stand from sensibility, expressive meanings correspond - as their possible ideal counterparts. The divisions drawn by us within 'epistemic essence', and the concepts framed in close connection therewith, retain their + +validity in this wider sphere, though marked off by us in relation to a nar- + +rower one. + +Each categorial act of intuition has therefore: + +1. its quality; + +2. its (intentional) material, or interpretative sense; + +3. its representing contents. + +These distinctions do not reduce to distinctions amongfounding acts. The quality of a total act may differ from that of a basic act, just as basic acts, when many, may be differently qualified, as, e.g., in an idea of a relation + +between a fictitious object and one taken to be real. + +Not only has each of the founding acts its own material, but the founded act imports its own material: it is true to say that this novel material, or, where this includes the materials of basic acts, the newly added part of it, is + +founded on the materials of the basic act. + +Finally, also, the new act has representing contents in regard to which there are serious difficulties. Must new representing contents be assumed for + +this new material, and what can these be? + +§54 The qu estion of the rep rese nti ng contents of + +catego rial fo rms + +When one begins to analyse categorial acts, one is struck by the apparently irrefutable observation, that all differences of categorial acts reduce to corresponding differences of the acts on which they are founded, i.e. that the new element imported by the categorial function represents an increase of content that cannot be further differentiated. How else could an imaginative presentation of a collection differ from the percept of the same collection, than in respect of the intentional manner in which its members are given? As regards the form of connection, one would say, no further intelligible distinction can be drawn in the two cases. Or should one say that the form of a collection - what we express by the word 'and' - is specifically different according as it is perceptually or imaginatively apparent? In that case we ought to think that the appearances of phantasy might be bound together by the collective form of perception, while perceptual phenomena might be bound together by the collective form of phantasy, and each differently. But + +this is plainly unthinkable, nay, unintelligible. + +Nothing, it might be objected, is easier than just what has been said. Why should we not assemble certain perceptual objects in thought in order to refer imaginatively to some other aggregate? And why should we not assemble imaginative phenomena in thought in order to refer only to this imaginative aggregate, and so to perceive the latter? We may certainly do exactly this. But the perceptual objects will then be functioning as images, and the act of collection will not be directly founded on percepts, but on the + +imaginations built upon them. Just so, in the other case, we shall not be collecting the objects of our fancyings, but those fancyings themselves, i.e. the act of collection will not be directly founded on fancyings, but upon 'inner percepts' directed upon these latter. This establishes no difference between 'real' collections on a basis of perceived objects, and 'imaginary' collections on a basis of imagined objects: such a difference does not exist, except as a + +difference in underlying acts. + +The same seems to hold for all other modifications that the collective consciousness can show us. The universality or specificity, definiteness or indefiniteness, or whatever other categorial forms may come into play for our underlying objects, will also determine the character of our collective presentation, but not so that we shall be able to find phenomenological differences in the connective character itself: it is always the same and. According as our underlying presentations differ in type, we have a collection of universal objects before us (e.g. Species of colour, Red and Blue and Yellow), or a collection of individual objects (Aristotle and Plato), a collection of definite objects (as in the previous example) or of indefinite ones (a person and another person, a colour and a tone). One cannot conceive how differences in acts of collection should be possible except in respect of differ- + +ences in the acts which underlie them. + +The same also seems immediately clear in regard to relational intuitions. Relating always displays an identity of form, all variation depending on the + +underlying acts. + +In this situation can we still hope for ascertainable differences between representing contents and interpretative sense in respect to the newly added part of a founded act, the form of connection in the case of synthetic acts? In the case of straightforward intuitions, interpretative sense (material) and representing content were intimately united: they were mutually related, and far from independent in their variations. Nonetheless they underwent abundant shifts as against one another. The representing sensum could stay the same while the interpretative sense altered, and could vary while the latter remained constant. An imaginative presentation, e.g., can remain identical in respect, not only of material, but also of extent of fulness, and can nonetheless notably change in respect of vivacity. In the sphere of sense, the distinction between material and representing content can be readily pointed out and unhesitatingly acknowledged. How is it, however, in the case of categorial acts, where, if we ignore their act-foundation, variability seems entirely absent? Are we to say that they lack the distinction in question as regards their form, that they have no representing contents which extend beyond the representing contents of their underlying acts? When these underlying acts are themselves categorial, e.g. acts of ideation, these too will lack representation, which will be found only in their ultimate foundation of + +§55 Arguments fo r the assumption of pecul iar + +categorial representing contents + +In default of an attitude to this question we must emphatically observe that, in the previous exposition, the complete absence of differentiation among forms, as against the multifarious changes in the total act and its foundation, has perhaps been exaggerated, even misinterpreted. For when the whole act is a perceptual presentation, its form, qua form of a perceptual presentation, certainly differs in character from that of an imaginative presentation. If the form is what is really new and essential in the categorial presentation, it must share in the import of each essential character that penetrates the whole and that belongs to it as a whole. If reflection fails to show us differences of interpretative sense in the form, or at least in the form of the synthetic act - the matter has already been treated sufficiently as regards the abstractive act in the discussions of §52 - this can be explained by the fact that we involuntarily abstract from these interpretative characters, since they do not distinguish and mark off the moment of synthesis, but rather pervade the complete, founded act equally. Instead we attend exclusively to the common element that confronts us in, e.g. , all forms of collective synthesis. But just this common element could be the representing content that we are looking for. As, in straightforward sense-perception, the homogeneous unity of the perceptual sense pervades the total representation, having definite relations to each separate part of the representing content, without seeming to inner reflection to be made up of separate partial conceptions, so, in the case of categorial intuitions, the interpretative sense pervades the total act and its representing content, without being clearly divided to match the representing contents that can be distinguished by reflection. The above exposition contains, if we allow the interpretation, the important truth that in all change of founding acts and interpretative forms, there is a unique representing content for each sort of founded act. The abundant multiplicity of sense-qualities, of sensible forms etc., is at the disposal of straightforward sensuous intuition for purposes of representation. In the sphere of collective intuitions or intuitions of identity etc., we were always limited to one sort: the form of and is everywhere the same, and so is the is-form etc. These forms were here to be understood as analogues of the sense-kernel, of what is sensuous in sensuous intuition: there was to be abstraction from quality + +and from interpretative sense. + +One might here suspect that the wish was being father to the thought, and might direct attention to a fact issuing from our former treatment: that representing contents are by no means essential constituents of acts. For it is the peculiarity of all signitive acts that they lack representing contents, i.e. authentic representing contents which themselves relate to the internal being of the object. For signitive acts, too, have their non-authentic representing contents, which do not stand for the object meant in the act, but for some + +other object, the object of an underlying act. If non-authentic representing contents suffice, then we of course have no more difficulty, for such contents are present in our case, since underlying acts always provide them. The authentic representing contents of these underlying acts can be seen as nonauthentically representative in relation to the acts founded on them. + +But the comparison with merely signitive acts makes us vividly aware that founded acts cannot do without authentic representation, and representation as regards categorial form. We are made mindful of relations of possible fulfilment, of the 'fulness' which intuitive acts confer on signitive ones, of the ascending scales formed among intuitive acts by variable fulness, of final adequation as an ideal limit. Representing contents constitute the difference between 'empty' signification and 'full' intuition; they are responsible for 'fulness', as is shown by the fact that they determine one sense of 'fulness' (see §22). Only intuitive acts render their object apparent, seeable, for the reason, namely, that a representing content is there, which the interpretative form sees as a likeness, or as the very self, of the object. This is a fact rooted in the universal essence of the relation of fulfilment, and must therefore be demonstrable in our present sphere too. In this present sphere, too, we find 'signitively' opposed to 'intuitively': the opposition between objectifying acts which mean a categorial object signitively, and the parallel acts which present the same object through the same interpretative sense intuitively, whether 'in likeness' or 'in very self'. Since the intentional material is the same in both cases, we can again only treat the new element in our categorial intuition as being representative, as setting the object before us in its content, as treating experienced contents as representing an object meant. Such representation cannot, however, be exclusively carried out in underlying acts, for it is not solely their objects that are presented, but the whole + +state of affairs, the whole aggregate etc. + +§56 Conti nuation. The me ntal linkage of combined acts and the categorial un ity of co rrespond ing objects One might for a moment suppose that, in the case, e.g., of a relation, only the relata were presented, and that the new element consisted in a mere mental character connecting the two appearances. A connection of acts is not, however, pro tanto, a connection of objects. At best it can help to make such a connection apparent: it is not itself the connection that appears in it. A mental bond can be established among acts, and can cause an objective relation to appear before us, while this relation, though it unites truly existent objects, has no being at all. If we judge significatively, without intuitive representation of the state of affairs judged - as is the case in ordinary arithmetical judgements - the relational unity of the act is articulated, and has a mental form of connection entirely analogous to that of the corresponding intuition. But the state of affairs is not, in the strong sense of the + +word, 'apparent': it is merely meant. If we contrast with this a case of intuitive representation, as when we identify the colour of two perceived surfaces, or of two surfaces recalled in memory, or a person represented in two imaginative presentations, then identity is likewise meant, but is meant in a perceptual manner, in a manner that gives us the object, or, in the case of imagination, that gives us a likeness of it. What makes such differences possible? Ought we to locate the whole difference in the founding acts? Against this we must object that, e.g., in the signitive identification, the identity of the meant objects is not experientially lived through but is merely thought of, whereas, in the case of intuited objects, the identity is indeed perceived or imagined, but is only given and lived through where adequation is full and strict. The mental bond, which establishes the synthesis, is therefore a bond of thought or meaning (Meinung) and is as such more or less fulfilled. It is merely a nonindependent constituent of the total meaning, a significative constituent of a significative meaning, and an intuitive constituent of an intuitive meaning, but at all events a constituent which itself shares the character of this meaning, and with this its differences of fulness. We are therefore not unjustified in interpreting the situation as involving that this constituent also exercises a representative function. As we compare different cases in the light of the possibility just raised, we believe that we may reduce the mental bond experienced in actual identification, collection etc. (,actual' = authentic, intuitive) to a universal common feature, to be thought of separately from quality and interpretative sense, and yielding in such reduction the representative con- + +tent that pertains specially to the moment of categorial form. + +§5 7 The representi ng contents of the founding intuitions are not im med iately connected by the + +represe nti ng content of the synthetic fo rm + +Certain not unimportant observations must here suggest themselves as natural + +additions. + +Objectively considered, a synthesis, e.g. one of identity, of attribution etc., belongs to the founding objects: identity is, e.g., identity of the person, attribution the relation between the subject tree and the predicate fruit-bearing. The connected objects appear before us by way of their representing contents, and it might be thought that the synthetic bond, in which (or by way of which, perhaps in the manner of a representing content) the connection comes before us as a form, is also the simple and direct phenomenological + +bond between the representing contents of the underlying objects. + +As against this we affirm that the moment of synthesis establishes no direct connection between the representing contents of the basic acts, but that, e.g., the phenomenological form of identification has its essential basis in the underlying acts as such, i.e. it has its basis in what these acts are and contain, + +in addition to their representing contents. + +If the lived-through moment of identity, its mental character, were an immediate bond between the representing sense-contents - we may confine ourselves to the simplest case where the founding acts and objects are sensuous - the unity established by this moment would also be a sensuous unity, like, e.g., the spatial or qualitative patterns or other forms of unity which likewise have their foundation in the sense-contents in question. All sensuous (real) unity, as our Third Investigation has set forth, is unity founded in the various kinds of sense-content. The concrete contents are many-sided, they sustain various abstract moments in themselves, they underlie manifold possibilities of alteration and connection. We accordingly refer many kinds of connection to this or that moment in such contents. If particular unions are not always founded in the generic characters of complex wholes, taken in their complete specific content, they are nonetheless founded in the primitive generic characters which correspond to the moments of the whole in question. The real lack of relation between categorial act-forms and the sense-contents of their bases, shows itself in the limitless variability of the generic characters of these contents; in other words, no genus of content lacks an a priori possibility of functioning in the foundation of categorial acts of every sort. What is categorial is not bound up with representing sensuous contents, but only and necessarily with their objects, and yet not with them in their sensuous (real) content. This means that the mental character in which the categorial form is constituted is bound up phenomenologically with the acts in which the objects are constituted. In these acts, sense-contents are representatively present, and so certainly contribute to such acts. They do not, however, make up the characteristic essence of these acts, and they can also exist without the interpretation which first renders them representative: in the latter case, they are there, but nothing thereby appears, and nothing is consequently there to be connected, or to be treated as subject or predicate etc., in categorial fashion. The categorial moment of the synthetically founded act does not bind these unessential elements of the founding acts together, but binds what is essential to them both: it connects, in all circumstances, their intentional materials, and is in a real sense founded upon these last. This is what was said above quite generally: in all categorial acts, we maintained, the material of the founded acts was founded in the materials of the founding acts. Identity, e.g., is no immediate form of unity among sensuous contents, but is a 'unity of consciousness' based upon one or another (repeated or inwardly different) consciousness of the same object. This holds in all cases. It is true, no doubt, that intuitions of all sorts, whether straightforward or categorial, by their nature submit to the same categorial formations, but this only means that categorial formation rests phenomenologically on what is universal in an objectifying act, or is a function essentially bound up with the generic element in objectifying acts. Only experiences of this class permit categorial syntheses, and such synthesis + +Particularly in the case of adequate synthetic intuitions, immediately based on individual intuitions, must we guard against the tempting delusion of an immediate phenomenological connection, present at least on this lowest level of categorial synthesis, between the representing sense-contents of the one underlying act and those of the other. In virtue of the functional dependence of the adequation (evidence) of the total act on the adequation of its founding intuitions, the situation would seem to have the following pattern: since the founding acts are adequate, the representing contents coincide with the object represented. If on such a basis the intuition of a relation arises, a relation, e.g., between part and whole, the relational act too is evident in character: the relation itself is truly given with the truly given contents. The mental bond of relating, conceived as a relation among sensuous contents and objects, + +here binds these experienced sense-contents as with a direct bond. + +Binds them with nothing, one might object. Not the sense-contents, but the adequate intuitions of such contents, serve to base the unity of the act of relating. Here as elsewhere we must look to the objects, to the sensuous contents at once representing and represented, in order to perform the act of relating, to relate this content as whole to that content as part. Relations can only be given on a basis of given objects: objects are, however, not given in mere lived experience, in itself blind, but only and solely in percepts, and in our case in the perception of lived through contents which no longer + +represent something beyond themselves. + +All this confirms our original introduction of categorial acts as founded acts. It is essential to these acts, in which all that is intellectual is constituted, that they should be achieved in stages. Objectivations arise on a basis of objectivations, and constitute objects which, as objects of higher order, objects in a wider, intellectual sense, can only come to light in such founded acts. This excludes from synthetic acts that immediate unity of representation which unites all representative contents of straightforward intuitions. The complete synthetic intuition therefore arises (if we are right in our above attempted interpretation which requires a most careful pondering) in so far as the mental content which binds the underlying acts itself sustains interpretation as the objective unity of the founded objects, as their relation + +of identity, of part to whole etc. + +§58 The re lation of our two distinctions: outer and + +inner sense, also sense for categories + +I t i s now extremely important to bring to complete clearness the relation between the two distinctions introduced by us at the very beginning of this Investigation, the distinction between outer and inner sensibility, on the one hand, and between straightforward and categorial acts, on the other. + +A presentation as a mental experience, whether it be straightforward or founded, sensuous or categorial, belongs to the sphere of 'inner sense' . Is + +there no contradiction in this? Is an inner percept, which reflects on an act, and a founded act to boot, e.g. on an actual insight into the equation 2+ I =1 + 2, not eo ipso a founded percept, and therefore a non-sensuous one? In this act of perception the founded act is given together with the acts that underlie it, and is given in the strongest sense of the word. It belongs to and is part of the real make-up of the (inner) percept. In so far as the latter directs itself to the former act, it is itself related to it, and is therefore itself + +a founded percept. + +We shall here obviously have to reply: to perceive an act, or an actmoment, or an act-complex of any sort, is to perceive sensuously, since it is to perceive straightforwardly. This cannot be doubted, since the relation of an act which perceives to an act which is perceived is no relation of foundation, even if we take a founded act to be the act perceived. The foundedness of an act does not mean that it is built on other acts in any manner whatsoever, but that a founded act, by its very nature or kind, is only possible as built upon acts of the sort which underlie it, and that, as a result, the objective correlate of the founded act has a universal element of form which can only be intuitively displayed by an object in a founded act of this kind. The intuitive consciousness of the universal cannot, e.g., exist without underlying individual intuition, nor an identification without underlying + +acts which relate to the identified objects etc. + +The perception, however, which we direct to a founded act could as readily be directed to a non-founded act and to any objects of outer sense, e.g. horses, colours etc. In each case perception consists in a straightforward looking at our object. The material of perception (its interpretative sense) stands in no necessary relation to the material of the perceived act. The whole phenomenological content of this act has rather the sheer character of a representative content, it is objectively interpreted in accordance with the interpretative form of perception, as being this very act of perception itself. For this reason also, every abstraction based on inner sense, e.g. the abstraction which looks to a founded act, is a sensuous abstraction. As opposed to this, an abstraction which is itself built upon a founded act, is, to the extent that this founded act has the character of an intuition, even that of a categorial intuition, a categorial abstraction. If we look at an intuitive act of identification, i.e. an intuition of identity, and if we abstract from it the moment of identification, we have performed a sensuous abstraction. But if, while living through an identification, we turn our regard to objective identity, and make this the basis of our abstraction, we have performed a categorial abstraction (cf. the closer discussion in §60). The objective moment of identity is no act, and no form of an act: it is an objective categorial form. As against this, on the other hand, the moment of identification, that unites the founded acts phenomenologically, is a sensuous and categorial act-form. The same difference essentially divides those concepts framed on a ground of reflection on any intuitive acts, from the quite different concepts + +framed on the ground of these intuitive acts themselves. I perceive a house and, reflecting on my percept, frame the concept of perception. But if I look simply at the house, I use my percept itself, rather than the percept of this percept, as the founding act for an abstraction, and the concept of house arises. There is accordingly nothing remarkable in saying: The same mental moments which are sensuously given in inner perception (and which therefore function in it as sensuous representing contents) may, in a founded act of the character of a categorial perception or imagination set up a categorial form, + +and so sustain a totally different categorial representation. + +The non-independence of categorial forms as forms, is mirrored in the department of inner sense in the fact that the moments in which a categorial form can be constituted - moments2 narrowly restricted for each form, so that each type of form corresponds to a single type of moment - themselves represent non-independent mental contents, moments founded on characters of acts. Since, however, all characters of acts have their ultimate foundation in the contents of outer sense,3 we note that there is an essential + +phenomenological gulf in the field of sense. We have principally to distinguish between: + +1. the contents of reflection, those contents which are themselves charac- + +ters of acts or founded upon such characters; + +2. the primary contents, those contents in which all contents of reflection + +are either immediately or mediately founded. + +These latter would be the contents of 'externar sensibility, which is here plainly not defined in terms of some metaphysical distinction of outward and inward, but through the nature of its representing contents, as being ultimately foundational, phenomenologically lived-through contents. The primary contents form a unique highest genus, which divides into many species. The manner in which the contents of reflection have their foundation in primary contents is the loosest conceivable: it is such that reflective contents are never bound to a narrower class than the whole class of these + +primary contents. + +Corresponding to the difference between purely sensuous and purely categorial objects of intuition, there is a distinction of representing contents: only reflective contents can serve as purely categorial representing contents. One might now try to pin down the concept of a category by saying that it comprises all objective forms arising out of the forms, and not out of the matters, of conceptual interpretation. The following misgiving no doubt might arise. Ought we not also to attribute to sensuous intuition the character of a categorial act, in so far as through it the form of objectivity is constituted? For what we perceive does not merely exist in perception, but is given in it as an object. The concept of an object is, however, framed as the correlate of the concept of perception, and so presupposes, not merely an act of abstraction, but also acts of relation. It therefore also qualifies as a categorial + +Chapter 8 + +The a priori laws of authentic and + +inauthentic thinking + +§59 The complication into ever new fo rms. The pure theory of the forms of possible + +intuitions + +The varied forms of founded acts where, instead of straightforward, sensuously-intuitive objects, categorially formed and synthetically connected objects are constituted, permit manifold complications into new forms: in consequence of certain a priori categorial laws, categorial unities may again and again become the objects of new connecting, relating or ideating acts. Universal objects, e.g., can be collectively connected, the collections thus formed can in their tum be collectively connected with other collections of similar or different type, and so on in infinitum. The possibility of unlimited complication is here self-evident and a priori. Just so, within certain lawbound limits, one can unify states of affairs in new states of affairs, pursue an indefinitely extended search for internal and external relations among all such possible unities, use the results of such discovery as terms for novel relations etc. Obviously such complication is achieved in founded acts of ever higher level. The governing legality in this field is the intuitive counterpart of the grammatical legality of pure logic. In this case, also, we are not concerned with laws which seek to assess the real being of the objects presented at different levels. These laws at all events say nothing directly about the ideal conditions of possibilities of adequate fulfilment. To the pure theory of the forms of meanings we here have a corresponding pure theory of the forms of intuitions, in which the possibility of the primitive types of simple and complex intuitions must be established by intuitive generalization, and the laws of their successive complication into ever new and more complex intuitions must be laid down. To the extent that adequate intuition itself represents a type of intuition, the pure theory of intuitive forms embraces all the laws which concern the forms of adequate intuition: these have a peculiar relevance to the laws of the adequate fulfilment of significative intentions, or + +of intentions already intuitive. + +§60 The re lative or fu nctional di fference between matte r and fo rm. Pure acts of understanding and those mixed with sense. Sensuous concepts and + +catego ries + +The relative, merely functional difference of matter and form hangs together with the possibility of making categorial intuitions the foundations for new categorial intuitions, and thereupon of expressing them in corresponding expressions and meanings. This difference was indicated above in passing (§42). In an absolute sense, a founding sensibility provides the matter for, all acts of categorial form which are built upon it. In a relative sense, the objects of founding acts furnish this matter, relatively, that is, to the newly emergent forms of the founded acts. If we relate two objects already categorial, e.g. two states of affairs, these states of affairs are our matter relatively to the relation which brings them together. To this definite use of the concepts of matter and form the traditional distinction between the matter and form of statements corresponds exactly. The terms of a statement express the founding acts of the whole 'relational presentation', or, what is the same, they are names for its founding objects, and therefore represent the place in which alone contributions of sense may be sought. But founding objects may themselves be categorial in type. Plainly fulfilment is carried out in a chain of acts which take us down a whole ladder of foundations'. Indirect presentations here play an essential part, whose exact investigation is an important + +task in a clarification of the complex forms of cognitive thought. + +Acts of straightforward intuitions we called 'sensuous'; founded acts, whether leading back immediately or mediately to sense, we called 'categorial' . But it is worth our while to draw a distinction, within the sphere of categorial acts, between those acts that are purely categorial, acts of 'pure understanding', and mixed acts of understanding that are blended with sense. It lies in the nature of the case that everything categorial ultimately rests upon sensuous intuition, that a 'categorial intuition', an intellectual insight, a case of thought in the highest sense, without any foundation of sense, is a piece of nonsense. The idea of a pure intellect, interpreted as a faculty of pure thinking (= categorial action), quite cut ofJfrom a 'faculty of sensibility', could only be conceived before there had been an elementary analysis of knowledge in the irrefragable evidence of its being. Nonetheless, the distinctions just indicated, and with them the concept of a purely categorial act and, if one likes, the further concept of a pure understanding, all have a good sense. If we ponder on the peculiarity of eidetic abstraction, that it necessarily rests on individual intuition, but does not for that reason mean what is individual in such intuition, if we pay heed to the fact that it is really a new way of conceiving, constitutive of generality instead of individuality - then the possibility of universal intuitions arises, intuitions which not merely exclude all individuality, but also all sensibility from their intentional purview. In other + +words, we distinguish between sensuous abstraction, which yields sensuous concepts - purely sensuous or mixed with categorial forms - and purely categorial abstraction, which yields purely categorial concepts. Colour, house, judgement, wish are purely sensuous concepts; colouredness, virtue, the axiom of parallels etc., have a categorial admixture, while unity, plurality, relation, concept are purely categorial. Where we speak absolutely of categorial concepts, purely categorial ones are always meant. Sensuous concepts find their immediate basis in the data of sensuous intuition, categorial concepts in the data of categorial intuition, purely with regard to the categorial form of the whole categorially formed object. If, e.g., the intuition of a relation underlies an abstraction, the abstractive consciousness may direct itself to the relational form in specie, so that everything sensuous in what underlies the relation is discounted. So arise categories, which rubric, understood pointedly, merely covers the primitive concepts in our present context. We have just identified concept and Species: this was implicit in the whole sense of our completed discussion. But, if one understands by 'concepts' universal presentations instead of universal objects, whether these be universal intuitions or the universal meanings which correspond to them, our distinction carries over simply to these. It carries over similarly to presentations of the form an A, having regard to the fact that the Species A may include or exclude what is sensible. All logical forms and formulae such as All S are P, No S is P etc., are purely categorial. Here the letters 'S', 'P' etc., merely point indirectly to 'certain', indefinite concepts, variable 'at will'; in the total formula a complex thought, made up of purely categorial elements, corresponds to them. Like all pure logic, so all pure arithmetic, the pure theory of manifolds, pure mathematics, in short, in the widest sense, are pure in the sense that they contain no sensuous concept in their whole theoretical fabric. + +§6 1 Catego rial fo rm ing invo lves no real + +reshaping of the object + +Our talk of categorial form, as has been clear from our last set of discussions, is naturally and harmlessly ambiguous, since we have drawn a thoroughgoing distinction between act and object. We mean by categorial form, on the one hand, the characters of founded acts, which give form to acts of straightforward or of already founded intuition, and transform them into new presentations of objects. These latter presentations, as opposed to the acts on which they are founded, set up for us a peculiarly modified objectivity: the original objects are now seen in certain interpretative and connective forms which are our categorial forms in the second, objective sense. The conjunctive connection A and B, which as a unified act means a categorial unity of objects (the aggregate of them both), will serve as an example. The expression 'A and B' illustrates, particularly in relation to the meaning of 'and', a further sense of our talk of categorial form, according to which + +significative forms, forms which find possible fulfilment in founded types of act, are called categorial forms, or, more cautiously, categorial forms in a + +loose sense of the word. + +This being premised, we now wish to bring to explicit clearness, for the sake of its importance, a proposition that we have already enunciated and which is really obvious in the light of our whole exposition. This is the proposition that categorial functions, in 'forming' sensible objects, leave their real essence untouched. The object is intellectually grasped by the intelligence, and especially by 'knowledge' (itself a categorial function), but it is not thereby falsified. To clarify this, let us remember the difference mentioned in passing between categorial unities in the objective sense, and real unities such as the unity of the parts of a thing, or of trees in an avenue etc. The unity of the real elements in a mental experience, or the unity of all experiences which coexist in a single individual consciousness, likewise count among such real unities. All such unities, treated as wholes, resemble their parts in being objects in the straightforward, primary sense: they can be intuited in possible straightforward intuitions. They are not merely categorially unified, constituted through a being-considered-together, through collection, disjunction, relation etc. They are intrinsically unified: they have a form of union, perceivable in the whole as a real property, a real moment of unity, and perceivable in the same sense in which any of their connected + +members and their intrinsic properties are perceivable. + +It is quite different in the case of categorial forms. The new objects they create are not objects in the primary, original sense. Categorial forms do not glue, tie or put parts together, so that a real, sensuously perceivable whole emerges. They do not form in the sense in which the potter forms. Otherwise the original datum of sense-perception would be modified in its own objectivity: relational and connective thought and knowledge would not be of what is, but would be a falsifying transformation into something else. Categorial forms leave primary objects untouched: they can do nothing to them, cannot change them in their own being, since the result would otherwise be a new object in the primary, real sense. Evidently the outcome of a categorial act, e.g. one of collection or relation, consists in an objective 'view' (Fassung) of what is primarily intuited, a 'view' that can only be given in such a founded act, so that the thought of a straightforward percept of the founded object, or of its presentation through some other straightforward intuition, is a + +piece of nonsense. + +§62 Our freedom in the categorial forming of given + +material and its lim its. Purely categorial laws + +(laws of 'auth entic' th inking) + +Real, sensuous forms of unity, whether external or internal, are determined by a law governing the essential nature of the parts to be connected; if the + +individuation of these parts is taken in its full extent, they are absolutely determined. All unity points to governing legality, as real unity points to real governing legality. What is really one, must also really be made one. Where we speak of our freedom to unite or not to unite, we are not speaking of contents in their full reality, which includes their spatio-temporal properties. While in this field the consciousness, and especially the direct intuition, of real contents, is eo ipso the consciousness of their real connections and forms, the position is quite different in regard to categorial forms. With real contents none of the categorial forms which fit them is necessarily given: there is abundant freedom to connect and relate, to generalize and subsume etc. There are many arbitrary ways to divide up a sensuously unified group into part-groups: we may at will arrange these diversely divisible part-groups, and effect same-level connections among them, we can also build collections of the second, third ... order upon one another. Many possibilities of categorial shaping therefore arise on the foundation of the same sensuous stuff. Just so, we can compare any item from one and the same sense-complex with any other of its members, or distinguish it from them. We can make either of them the subject-term, or, by arbitrary conversion, the object-term of some relation in question. We can put these relations into relation with one + +another, connect them collectively, classify them etc. + +Great, however, as this freedom of categorial union and formation may be, it still has its law-governed limits. The very fact that categorial forms constitute themselves in founded characters of acts, and in these alone, involves a certain necessity of connection. For how else could we speak of categorial perception and intuition, if any conceivable matter could be put into any conceivable form, and the underlying straightforward intuitions therefore permitted themselves to be arbitrarily combined with categorial characters? Where, e.g., we carry out a whole-part relationship intuitively, we can normally convert it, but not in such a manner that the part, with unchanged real content, can be looked on as the whole, and the whole as the part. It is also not open to us to treat this relation as one of total identity or of total exclusion etc. We can no doubt 'think' any relation between any set of terms, and any form whatever on the basis of any matter - think them, that is, in the sense of merely meaning them. But we cannot really carry out 'foundings' on every foundation: we cannot see sensuous stuff in any categorial form we like, let alone perceive it thus, and above all not perceive + +it adequately. + +In framing our widened concept of perception, we found, eo ipso, a certain tied character in it. This does not mean that the character of perception is really (reell) bound up with sensuous content. This is never the case, for this would mean that nothing existed unperceived, or could exist unperceived. Certainly, however, nothing exists that cannot be perceived. This means that the actual performance of actual acts on the ground of just these straightforward intuitions is in the ideal sense possible. And these + +possibilities, like ideal possibilities in general, are limited by law to the extent that certain impossibilities, ideal incompatibilities, are by law ranged + +alongside of them. + +The ideal laws governing the connection of such possibilities and impossibilities, belong among categorial forms in specie, i.e. among categories in the objective sense of the word. They determine what variations in any given categorial forms there can be in relation to the same definite, but arbitrarily chosen, matter. They circumscribe the ideally closed manifold of the rearrangements and transformations of categorial forms on the basis of constant, selfsame matter. This matter is here only relevant in so far as it must be kept intentionally identical. But, to the extent that the species of this matter are quite freely variable, and are only subject to the obvious ideal condition of capacity to sustain the forementioned forms, the laws in question are of an entirely pure and analytic character, and quite independent of the particularity of their matter. Their general expression, therefore, contains no reference to material species, but makes exclusive use of algebraical symbols as bearers of indeterminately general presentations of certain matters, variable in all + +but the identity they must keep with themselves. + +To gain insight into these laws, does not therefore require an actual carrying out of a categorial intuition, which makes its matters truly intuitive: any categorial intuition suffices, which puts the possibility of the categorial formation in question before one's eyes. In the generalizing abstraction of this comprehensive possibility the unitary, intuitive 'insight' into the law is achieved: this insight has, in the sense used in our doctrine, the character of an adequate general percept. The general object, which is itself present in it, is the categorial law. We may assert: The ideal conditions of categorial intuition in general are, correlatively regarded, the conditions of the possibility of the objects of categorial intuition, and of the possibility of categorial objects simpliciter. That an object thus and thus categorially formed is possible, is essentially related to the fact that a categorial intuition - a mere imagination - can set such an object completely before one's eyes, to the fact, in other words, that the requisite categorial syntheses and other categorial acts can be really performed on the basis of the founding intuitions concerned (even if the + +latter are imaginary). + +What categorial formations are in fact permitted by given materials of perception or imagination, what categorial acts can be really carried out on the basis of their constitutive sensuous intuitions: on this point our analytic laws, which are here our ideal conditions, say nothing. That boundless arbitrariness does not here obtain, that 'actual' performability has not here the character of empirical actuality, but of ideal possibility, is shown by our above examples. These also make plain that it is the particularity of the matter which, from case to case, circumscribes possibility, so that we can, e.g., say that W is really a whole as regards w, or that g is really a property of G etc. In such cases, of course, the categorial form (unlike its + +real counterpart) is not limited to the kinds of content covered by W, w, G, g, so as to have no bearing on contents of other kinds. Contrariwise it is evident that contents of all kinds can be formed by all categories. For categorial forms are not founded on material contents, as we have already explained above (cf. §57). These pure laws can therefore not prescribe what forms a given matter can assume, but can only tell us that, when it, and any matter in general, assumes a certain form, or is capable of assuming it, a definitely limited circle of further forms remains open to the same matter. There is, i.e., an ideally closed circle of possible transformation of a functioning form, into ever new forms. The ideal possibility of these new forms in relation to the same matter, has its a priori guarantee in the before mentioned analytic + +laws which embody the presuppositions in question. + +These are the pure laws of authentic thinking, the laws, that is, of categorial intuitions in virtue of their purely categorial forms. For categorial intuitions function in the thought of theory as actual or possible fulfilments (or frustrations) of meanings, and impart to statements (according to their mode of functioning) the logical values of truth and falsehood. On the laws here considered the normative regulation of purely signitive, or admixedly signitive, + +thought depends. + +To expound this matter more precisely, and to clear up the special sense implied in talk of the laws of authentic thinking, we must take a closer look + +into the sphere of meanings and of meaning-fulfilments. + +§63 The new laws of the val id ity of sign itive and ad mixed ly sign itive acts (laws of inauthentic + +thinking) + +In our discussions up to this point we have thought of categorial acts as free from all significative side-structures, as carried out, but not as founding acts of knowing or naming. Every unprejudiced analyst will concede that we can, e.g., intuit aggregates, or many primitive states of affairs, without expressing them nominally or propositionally. We now oppose the case of mere signification to the case of mere intuition: we note that to all acts of categorial intuition, with their categorially formed objects, purely significative acts may correspond. This is an obvious a priori possibility. There is no act-form relevant here, to which there is not a corresponding possible form of meaning, and each meaning can be thought of as carried out without a correlated intuition. The ideal of a logically adequate language is that of a language which can give unambiguous expression to all possible matters and all possible categorial forms. To its words certain significative intentions unambiguously pertain, which can come alive even in the absence of 'corresponding', i.e. of fulfilling, intuition. There is therefore, running parallel to all possible primary and founded intuitions, a system of primary and + +The realm of meaning is, however, much wider than that of intuition, i.e. than the total realm of possible fulfilment. For, on the meaning-side, an endless host of complex meanings arises, which lack 'reality' or 'possibility'. They are patterns of meanings assembled together into unitary meanings, to which, however, no possible unitary correlate of fulfilment can correspond. For this reason there is no complete parallelism between categorial types, i.e. types of categorial intuition, and types of meaning. To each categorial type of lower or higher level a meaning-type corresponds, but to every type formed by free significative welding to complex types, there is not a corresponding type of categorial objectivity. We recall types of analytic contradiction such as 'an A which is not an A', 'All A's are B's and some A's are not B's' etc. Only in connection with primitive types can and must such parallelism obtain, since all primitive meanings 'originate' in the fulness of correlated intuition, or, to put the matter more plainly, since talk of compatibility and incompatibility applies only in the sphere of what is put together, or is to be put together, simple meanings, as expressions of what is simple, can never be 'imaginary'. This applies also to every simple form of meaning. While 'Something that is at once A and not-A' is impossible, 'an A and a B' is possible, since the and-form, being simple, has a 'real' sense. If we transfer the term 'categorial' to the realm of meaning, a peculiar significative form (and a peculiar meaning-form in specie) will correspond to each authentic categorial form, whether to one authentic in the objective sense, or to the corresponding categorial form of intuition (in which what is categorially objective is perceptually or imaginatively constituted). In this form of signification we achieve significative reference to a collection or a disjunction, an identity or a non-identity etc. Whenever one opposes presentation in the authentic, to presentation in an inauthentic sense, one normally has the intuitive-significative antithesis in mind (though occasionally, no doubt, one is thinking of the other antithesis of adequate-inadequate). Our present cases would accordingly be cases of collection, disjunction, identifica- + +tion, abstraction etc., in an inauthentic sense. + +If one includes under the rubric of 'acts of thinking' , all the categorial acts through which judgements, as predicative significations, gain fulness and their whole value for knowledge, we must distinguish between authentic acts of thinking and inauthentic ones. The inauthentic acts of thinking would be the significant intentions behind statements and, by a natural extension, all significative acts which could possibly function as parts of such predicative intentions: all significative acts can plainly function in this fashion. The authentic acts of thinking would lie in the corresponding fulfilments, i.e. the intuitions of states of affairs, and all intuitions which function as possible parts of such intuitions. All intuitions can function in this manner: there is, in particular, no categorial form that could not be a constituent of the form of a state of affairs. The general doctrine of the form of symbolic judgements (the meanings of statements) includes that of the forms of meaning in general + +(the pure logico-grammatical forms). Just so the general doctrine of the pure forms of the intuitions of states of affairs (and of the pure forms of states of affairs) includes that of the categorial forms of intuitions (and of objective + +categorial forms) in general. + +If, as often happens, thinking is identified with judging, we should have to distinguish between authentic and inauthentic judging. The concept of judging would then be pinned down by the element common to statementintention and statement-fulfilment, i.e. by the intentional essence compounded of quality and intentional material. As acts of thinking in the widest sense, not only acts of judging, but also all possible part-acts in judgements, would have to count: we should be brought back to a definition equivalent to our + +previous definition of the concept Act of Thinking. + +In the sphere of inauthentic thinking, of pure signification, we are beyond all bounds of categorial laws. Here anything and everything can be brought together in unity. We spoke of this in our Fourth Investigation: we pointed to the purely logico-grammatical laws which, as laws of complication and modification, distinguish the spheres of sense and nonsense. In inauthentic categorial formation and transformation, we are free as long as our meanings are not nonsensically conglomerated. But if we wish to avoid formal and real nonsense, the widest sphere of inauthentic thought, of the significatively combinable, is very much narrowed. We are now concerned with the objective possibility of complex meanings, with the possibility of their application to an intuition which fulfils them totally and singly. The pure laws of the validity of meanings, of the ideal possibility of their adequate intuitive illustration, obviously runs parallel to the pure laws governing the combination and + +transformation of authentic categorial forms. + +In the pure laws of the validity of meanings, we are again not dealing with laws from which the validity of any given meaning can be read off, but with the possibilities, determined in purely categorial fashion, of the combination and transformation of meanings, that can be undertaken, salva veritate, in each possible given case, i.e. without prejudicing the possibility of a fulfilment of meaning, to the extent that this previously existed. If, e.g., the statement 'w is a part of W' is valid, then a statement of the form 'W is a whole relatively to w' is also valid. If it is true that there is an A which is B, then it is also true that a certain A is B, or that not all A's are not B's etc. In such propositions, what is material is boundlessly variable; hence all material meanings are replaced by algebraical signs of indirect and wholly unfixed significance. For this reason such propositions are characterized as analytic. In this situation, it is again irrelevant whether the matter is constituted in percepts or in imaginations. The possibilities and impossibilities concern the setting up of acts giving adequate intuitive illustration to the form of a meaning whatever its material substratum: we are concerned, in short, with the pure conditions of the possibility of completely adequate signification in general, which, in their tum, depend on the pure conditions of the possibility + +of categorial intuition in general. These laws of the validity of meanings are not, of course, themselves identical with the authentic categorial laws, but they follow the latter faithfully, in virtue of the law which regulates the + +connection of significant intentions with fulfilments of meaning. + +The whole treatment that we have just completed requires a natural, obvious extension. We have simplified the matter to the extent of confining our discussion to two extremes only: we opposed completely intuitive, i.e. actually executed categorial act-forms, on the one hand, to purely signitive, i.e. not authentically executed act-forms, on the other, forms only to be realized in processes of possible fulfilment. The ordinary cases are, however, mixtures: thought proceeds intuitively in many stretches, in many stretches signitively, here a categorial synthesis, a predication, a generalization is really carried out, there a merely signitive intention directed to such a categorial synthesis attaches to the intuitively, or to the only verbally presented members. The complex acts arising in this manner have, taken as a whole, the character of inauthentic categorial intuitions: their total objective correlate is not actually, only inauthentically, presented. Its 'possibility', i.e. the objective possibility of its correlate, is not guaranteed. The sphere of inauthentic thinking must accordingly be made wide enough for it to take in these mixed act-forms also. Everything we have said then holds, mutatis mutandis, for such an extension. Instead of talking of the laws of the validity of mere meanings, merely symbolic judgements etc., we shall also have to speak of the laws of the validity of signitively admixed presentations or judgements. Where there is talk of merely symbolic thinking, it is generally + +these mixed cases that one has in mind. + +§64 The pure logico-gram matical laws are laws for any understanding whatever, and not merely fo r any hu man understandi ng. Their psyc hol ogical meaning and normative fu nction in re lation to inad equate + +thought + +Both sorts of laws are, of course, of an ideal nature. That a piece of sensory stuff can only be apprehended in certain forms, and bound together according to certain forms, that the possible transformation of these forms is subject to pure laws, in which the material element varies freely, that the meanings to be expressed are likewise limited to certain forms, which they can change only in prescribed manners, if they are not to lose their true expressibility - all this does not depend on the empirical contingencies of the course of consciousness, not even on the contingencies of our intellectual or common-human organization. It depends on the specific nature of the acts in question, on their intentional and epistemic essence; it belongs not to the nature of just our (individual or common-human) sensibility, nor just our understanding, but rather to the Ideas of Sensibility and Understanding in + +general. An understanding governed by other than the purely logical laws would be an understanding without understanding. If we define understanding, as opposed to sensibility, as the capacity for categorial acts, also, perhaps, as a capacity for expression and meaning directed upon such acts, and made 'right' by them, then the general laws rooted in the specific nature of these acts belong to the definitory essence of understanding. Other beings may gaze upon other 'worlds', they may also be endowed with 'faculties' other than ours, but, if they are minded creatures at all, possessing some sort of intentional experiences, with the relevant differences between perception and imagination, straightforward and categorial intuition, meaning and intuition, adequate and inadequate knowledge - then such creatures have both sensibility and understanding, and are 'subject' to the pertinent laws. The laws of authentic thinking naturally, therefore, belong also to the nature of human consciousness, to our common human 'psychic organization'. But they are not characteristic of this organization in respect of its peculiar character. The laws are rooted, we said, in the purely specific character of certain acts: this means that they concern these acts not just in so far as they occur together in a human organization. They pertain rather to all possible organizations which can be made up of acts of this sort. The differentiating peculiarities of each type of mental organization, all that distinguishes, e.g. , the human consciousness as such, in the manner of a natural historical species, is not at all affected by such pure laws as are the laws of thought. A relation to 'our' mental organization, or to 'consciousness in general' (understood as the aspects of consciousness common to men in general), does not define the pure and genuine, but a grossly distorted a priori. The notion of a common mental organization, like that of a physical organization, clearly has a merely 'empirical' meaning, the meaning of a mere 'matter of fact' . But pure laws are precisely pure of matter of fact, they tell us not what is generally wont to be in this or that province of the real, but what absolutely goes beyond all wont and all divisions into spheres of reality, and that for the reason that what is in question belongs to the essential make-up of what is. The true logical a priori, therefore concerns all that pertains to the ideal essence of understanding as such, to the essence of its act-species and act-forms, to that, accordingly, which cannot be eliminated, as long as the understanding, and the acts definitory of it, are what they are, i.e. thus and + +thus natured, maintaining their selfsame conceptual essence. + +The extent, accordingly, to which the logical laws and, in the first instance, the ideal laws of authentic thinking, also claim a psychological meaning, and the extent to which they govern the course of actual mental happenings, is at once clear. Each genuine 'pure' law, expressing a compatibility or an incompatibility grounded in the nature of a given species, will, in relation to species of mentally realizable contents, limit the empirical possibilities of psychological (phenomenological) coexistence and succession. What is seen to be incompatible in specie, cannot be brought together, be + +rendered compatible, in empirical instances. In so far as the logical thought of experience is, to an incomparably major extent, conducted inadequately and signitively, we can think, believe, many things which in truth, in the manner of authentic thought, the actual carrying out of merely intended syntheses, cannot be brought together at all. Just for this reason the a priori laws of authentic thinking and authentic expression become norms for merely opinion-forming, inauthentic thought and expression. Put somewhat differently: on the laws of authentic thinking other laws are founded, formulable too as practical norms, which express in a manner suited to the sphere of signitive or admixedly signitive presentation, the ideal conditions of a possible truth (or rightness in general), the ideal conditions, that is, of 'logica1' compatibility (logical, since related to possible adequation) within this sphere of admixedly signitive thinking. The laws of inauthentic thinking do not hold psychologically like empirical laws governing the origin and change of such thought, but as the possibilities or impossibilities of adequation founded in their ideal purity in the variously formed acts of inauthentic thinking in + +relation to corresponding acts of authentic thinking. + +§65 The sensel ess problem of the real meaning of + +the logical + +We now also completely understand why the notion of a course of the world violating the laws of logic - the analytic laws of authentic thinking and the consequent norms of inauthentic thinking - or of the need or possibility of first grounding these laws in experience, the 'matter of fact' of sense, and fixing for them their limits of validity - is a piece of pure nonsense. We ignore the fact that even a probabilistic grounding on facts is a grounding which, as such, obeys ideal principles, principles which by anticipation we see to rest upon 'authentic' experiences of probability, both as regards their specific content and their status as laws. Here we must rather stress that the so-to-say facticity of a fact belongs to sensibility, and that to call in sensibility to help provide a basis for purely categorial laws - laws whose very meaning excludes all sensibility and facticity, which make pure assertions of essence about categorialforms, as forms of possible correctness and truth as such - represents a most obvious IJETaj300"lS Eis &]..]..0 yevos. Laws which refer to no fact cannot be confirmed or refuted by a fact. The problem, earnestly and profoundly treated by great philosophers, as to the 'real or formal meaning of the logical', is therefore a nonsensical problem. One requires no metaphysical or other theories to explain the agreement of the course of nature and the 'native' regularities of the understanding. Instead of an explanation, one needs only a phenomenological clarification of meaning, thinking and knowing, and of the ideas and laws which spring from these. The world constitutes itself as a sensuous unity: its very meaning is to be the unity of actual and possible straightforward percepts. Its true being, + +however, precludes its being adequately given, or given without qualification, in any closed process of perception. It is for us always a quite inadequately meant unity for theoretical research, in part intended through straightforward and categorial intuition, in part through signification. The further our knowledge progresses, the better and more richly will the idea of the world be determined, the more, too, will inconsistencies be excluded from it. To doubt whether the world really is as it appears to us to be, or as it is thought of in contemporary theoretical science, and as it counts for the well-grounded belief of the latter, has a good sense, since inductive science can never construct an adequate world-picture, however far it may carry us. But it is also nonsensical to doubt whether the true course of the world, the true structure of the world in itself, could conflict with the forms of thinking. For this would mean that a definite, hypothetically assumed sensibility, which would bring the world to adequate representation in an ideally complete set of unending perceptual processes, would be capable of assuming categorial forms, while forcing syntheses upon them that are generically ruled out by the universal nature of such forms. That they are thus ruled out, and that the laws of the categories hold as pure laws in abstraction from all sensuous stuff, and are accordingly unaffected by limitless variation of such stuff, this we do not merely think, but we see it to be true. It is given to us in fullest adequacy. This insight is of course achieved subjectively on the basis of any casual empirical intuition, but it is a generic insight relating purely to form. The basis of abstraction contains in this case, as in others, nothing presupposed by the ideal possibility and validity of the Idea + +abstracted from it. + +It would further be possible to demonstrate ad nauseam the absurdity involved in considering the possibility of an illogical course of the world in signitive thought, thereby making this possibility hold, and destroying in one breath, so to say, the laws which make this or any other possibility hold at all. We could also point out that a correlation with perceivability, intuitability, meanability and knowability, is inseparable from the sense of being in general, and that the ideal laws, therefore, which pertain to these possibilities in specie, can never be set aside by the contingent content of what itself happens to be at the moment. But enough of such argumentations, which merely ring the changes on one and the same position, and have + +already given us guidance in the Prolegomena. + +§66 Distinction between the most important differences mixed up in the cu rrent opposition of + +'i ntuiti ng' and 'th inking' + +The above investigations should have imported a satisfactory, general clearness into the much used, but little clarified, relation between thinking and intuiting. We here list the following oppositions, whose confusion has vexed + +epistemological research so inordinately, and whose distinctness has become + +quite clear to ourselves. + +1. The opposition between intuition and signification. Intuition as perception or imagination - it is irrelevant whether categorial or sensuous, adequate or inadequate - is opposed to mere thinking, as merely significative reference. Our parenthetically noted differences are, of course, generally ignored. We consider them very important, and now specially stress them. 2. The opposition between sensuous and categorial intuition. We therefore oppose sensuous intuition in the ordinary, straightforward sense, to categorial intuition, or intuition in the extended sense. The founded acts, characteristic of the latter, now count as the thought which 'intellectualizes' sensuous + +intuition. + +3. The opposition between inadequate and adequate intuition, or, more generally, between adequate and inadequate presentation (since we are classing intuitive and significative presentation together). In an inadequate representation we merely think that something is so (appears so), in adequate presentation we look at the matter itself, and are for the first time made + +acquainted with its full selfhood. + +4. The opposition between individual intuition (usually conceived, with what is plainly baseless narrowness, as sensuous intuition) and universal intuition. A new concept of intuition is fixed by means of this opposition. It is opposed to generalization, and so, further, to the categorial acts implying generalization, and also, in unclear admixture, to the significative counterparts of such acts. 'Intuition', we now say, merely presents the individual, while 'thought' points to the universal, is carried out by way of 'concepts'. One generally speaks in this context of the opposition between 'intuition and + +concept'. + +How strongly we tend to let these oppositions shade into one another would be shown by a criticism of Kant's theory of knowledge, which throughout bears the impress of the failure to draw any clear distinction among these oppositions. In Kant's thought categorial (logical) functions play a great role, but he fails to achieve our fundamental extension of the concepts of perception and intuition over the categorial realm, and this because he fails to appreciate the deep difference between intuition and signification, their possible separation and their usual commixture. And so he does not complete his analysis of the difference between the inadequate and adequate adaptation of meaning to intuition. He therefore also fails to distinguish between concepts, as the universal meanings of words, and concepts as species of authentic universal presentation, and between both, and concepts as universal objects, as the intentional correlates of universal presentations. Kant drops from the outset into the channel of a metaphysical epistemology in that he attempts a critical 'saving' of mathematics, natural science and metaphysics, before he has subjected knowledge as such, the whole sphere of acts in which pre-logical objectivation and logical thought are performed, + +to a clarifying critique and analysis of essence, and before he has traced back the primitive logical concepts and laws to their phenomenological sources. It was ominous that Kant (to whom we nonetheless feel ourselves quite close) should have thought he had done justice to the domain of pure logic in the narrowest sense, by saying that it fell under the principle of contradiction. Not only did he never see how little the laws of logic are all analytic propositions in the sense laid down by his own definition, but he failed to see how little his dragging in of an evident principle for analytic propositions really helped to clear up the achievements of analytic thinking. + +Addi tional note to the second edition + +All the main obscurities of the Kantian critique of reason depend ultimately on the fact that Kant never made clear to himself the peculiar character of pure Ideation, the adequate survey of conceptual essences, and of the laws of universal validity rooted in those essences. He accordingly lacked the phenomenologically correct concept of the a priori. For this reason he could never rise to adopting the only possible aim of a strictly scientific critique of reason: the investigation of the pure, essential laws which govern acts as intentional experiences, in all their modes of sense-giving objectivation, and their fulfilling constitution of 'true being'. Only a perspicuous knowledge of these laws of essence could provide us with an absolutely adequate answer to all the questions regarding our understanding, questions which can be + +meaningfully raised in regard to the 'possibility of knowledge'. + +Third Section + +Clarification of our + +introd uctory problem + +Chapter 9 + +Non-objectifying acts as apparent + +fu lfilments of meaning + +§67 That not eve ry act of meaning incl udes an act + +of knowing + +Having gone far enough in our investigation of the relation between meaning and corresponding intuition in regard to much more general problems, and having thus done enough to lay bare the essence of authentic and inauthentic expression, we have reached clearness on the difficult issues which troubled us at the beginning of this Investigation, and which first + +prompted us to undertake it. + +We have, above all, rid ourselves of the temptation to conceive of the meaning-function of expressions as in some sense a case of knowing, and in fact a case of classification, a temptation which springs from a line of thought touched on above (§ 1), and which always crops up in important epistemological contexts. One says: An expression must surely give expression to some act of the speaker, but in order that this act should find its appropriate speech-form, it must be suitably apperceived and known, a presentation as a presentation, an attribution as an attribution, a negation as a negation etc. Our reply is that talk of knowledge refers to a relationship between acts of thought and fulfilling intuitions. Acts of thought are not, however, brought to expression in statements and parts of statements, e.g. names, in such a manner that they in their turn are thought of and known. Otherwise these last acts would be the carriers of meaning, it would be they primarily that were expressed, they would accordingly be in need of other new acts of thought, and so on in infinitum. If I call this intuited object a 'watch', I complete, in naming it, an act of thought and knowledge, but I know the watch, and not my knowledge. This is naturally so in the case of all acts that confer meaning. Should I utter the word 'or' in a context of expressive speech, I carry out a disjunction, but my thought (of which the disjoining is a part) is not trained upon the disjoining but upon the (objective) disjunctivum, in so far as this last enters into the unitary state of affairs. This disjunctivum is known and objectively denominated. The word 'or' is accordingly no name, and likewise no non-independent appellation of disjoining; it merely gives + +voice to this act. Naturally this applies also to complete judgements. If I assert something, I think of things, that things stand in this or that manner: this is what I express, and perhaps also know. But I do not think and know my act of judging, as if I were also making it into my object, and were classifying it as a judgement and naming it through this form of expression. But does not the grammatical adaptation of expression to expressed act point to an act of knowing in which such adaptation is performed? In a certain manner or in certain cases it does, in all those cases, that is, where the sense of 'expression' dealt with by us at the beginning of the present Investigation is relevant. This is not the case where we are dealing with expression as a mere 'voice-giving', in which case all meaning-conferring counts as expressed by our words (as verbal noises), and again not where 'expression' means the same as 'meaning', and what is expressed is one and the same meaning. In the two latter senses, every statement, whether merely significative or intuitively fulfilled, expresses something: it expresses the judgement (our conviction), or that 'judgement's content' (the selfsame propositional meaning). But in the former sense only the intuitively fulfilled statement (or the statement which is to be intuitively fulfilled) expresses something, in which case not the verbal noise, but the already sense-enlivened locution represents the 'expression' of the corresponding intuition. It is the function that lends meaning to our words which is primarily and universally responsible for the unitary interweaving of the signitive intentions attaching to those words. The latter merely make up a signitive judgement, in which they lack all fulfilling intuition: the synthesis of agreement or disagreement, which our total signitive intention expresses (or claims to express) is here not authentically carried out, only signitively meant. But if, contrariwise, the indicated synthesis is authentically carried out, the authentic synthesis will coincide with the non-authentic one (the synthesis in signification). Both are one and the same intentional essence, representing one and the same meaning, the simple, selfsame judgement, whether carried out intuitively or merely signitively. Similar things plainly hold for cases where only some of our verbalized intentions enjoy intuitive 'fulness' . The signitive acts involve the same meaning as the intuitive, though without the latter's fulness; they merely 'express' this meaning. The suggestions of this word are the more fitting, since signitive acts likewise preserve the sense of an intuition after the latter has disappeared, like an empty shell without the intuitive kernel. The unity of coincidence is, in the case of the intuitive judgement, a true unity of knowledge (if not a unity of relational cognition): we know, however, that, in the unity of knowledge, it is not the fulfilling act (here the authentic synthesis of judgement) that we know, but the fact which is its objective correlate. In intuiting things we carry out a judging synthesis, an intuitive thus it is or thus it is not. Because our expressive intention, with its associated word-sounds (the grammatical expression) applies itself to this act of fact-envisagement, we achieve knowledge of the intuited fact in question. + +§68 The controve rsy regard ing the interpretation of the pecul iar gram mati cal forms which express + +non-objectifying acts + +We now turn to a final discussion of the seemingly trivial, but, correctly regarded, most important and difficult point at issue (see above, §l ff.) whether the familiar grammatical forms used in our speech for wishes, questions, voluntary intentions - acts, generally speaking, we do not class as 'objectifying' - are to be regarded as judgements concerning our acts, or whether these acts themselves, and not merely such as are 'objectifying', can function as 'expressed', whether in a sense-giving or sense-fulfilling fashion. We are dealing with sentences like 'Is IT a transcendental number?' 'May heaven + +help us!' etc. + +The teasing character of the question is shown by the fact that pre-eminent logicians since Aristotle have been unable to agree on its answer. Statements express the fact that something is, or that something is not, they assert, they judge about something. In their case alone can one talk of true and false. A wish or a question asserts nothing. We cannot object to one who utters them: 'What you say is untrue'. He would not even understand our objection. Bolzano thought this argument invalid. He said: 'A question like "What is the relation of the diameter of a circle to its circumference?" asserts nothing about what it enquires into, but it asserts something nonetheless: our desire, in fact, to be informed concerning the object asked about. It is indeed capable of truth and falsehood, and is false when our desire is + +mis-stated by it' (Bolzano, Wissenschaftslehre 1, §22, p. 88). + +We may doubt, however, whether Bolzano has not here confused two things: the adequacy or inadequacy of an expression - here a word-sound to our thought, and the truth or falsehood which relates it to the content of that thought, and its adequacy to the thing. Regarding the adequacy of an expression (as word-sound) to our thought, we can speak in two senses, one which relates to unsuitability - as when a speaker chooses to express the thoughts which fill his mind in words whose customary meaning conflicts with the latter - and one relating to untruthfulness, i.e. to deliberately deceptive, lying speech - as when the speaker does not wish to express the thoughts actually filling his mind, but others at variance with these, and merely imagined by him: he wishes to express these thoughts as if they were filling his mind. A suitable, sincerely employed expression can still state both what is true and what is false, according as through its sense it expresses what is or is not, or, what is the same, according as its sense can be adequately fulfilled + +or frustrated by a possible adequate percept. + +One might now counter Bolzano as follows. One can talk of sincerity and insincerity, of suitability and unsuitability, in the case of every expression, but one can only talk of truth and falsehood in the case of statements. A speaker can, accordingly, be objected to in different ways. 'What you say is + +false': this is the factual objection. And 'You are not speaking sincerely' or 'You are expressing yourself unsuitably' : this is the objection of insincerity or inadequacy of speech. Objections of the latter sort are the only ones that can be made to a questioner. He is perhaps pretending, or is using his words incorrectly, and saying something different from what he intends to say. But one can raise no factual objection to him, since he is making no factual claim. If one treats the objection concerned with unsuitability of expression as showing that a question expresses a judgement, one, i.e., that would be completely expressed in the form 'I am asking whether .. .', one would have in consistency to treat each expression in the same manner, and so to treat the true sense of each statement whatever as being what we adequately express in the word-form 'I am asserting that .. .'. But the same would have to hold of these restatements, which would accordingly land us in an infinite regress. In all this it is easily seen that this abundance of ever new statements is no mere abundance of words, but yields new statements by no means equivalent to the original ones, let alone identical in meaning. Does such nonsensical consistency not compel us to acknowledge an essential difference between one order of sentence-forms and another? (How this difference really must be interpreted is explained in our next section: cf. the final paragraph.) Here two positions can be taken up. Either one can say: The question of sincerity affects every utterance: a judgement accordingly pertains to each utterance as such, a judgement relating to the experience of the speaker which is to be intimated. A man who speaks, intimates something, and to this the intimating judgement corresponds. But what is intimated or expressed differs from case to case: the interrogative sentence intimates a question, the imperative sentence a command, the indicative sentence a judgement. Each indicative sentence therefore implies a double judgement, a judgement, namely, about this or that fact, and a second judgement, passed by the + +speaker as such, upon this first judgement as his own experience. + +This appears to be Sigwart's position. We read (Logik, 1, 2nd Edn., 17 f + +Note): + +The imperative undoubtedly includes an assertion, to the effect, namely, that the speaker wills the action he is demanding, the optative that he wishes what he utters. This assertion is involved in the fact of speech, not in the content of what he utters; every statement of the form A is B accordingly involves the assertion, based on the mere fact of speech, that the thinker thinks and believes what he says. These assertions regarding the subjective state of the speaker, involved in the fact that he speaks, and valid on the assumption of his sincerity, accompany all speech in the same fashion, and can accordingly not serve as a basis for + +differentiating our various sentence-forms. + +Another way of conceiving the matter would be to reject the 'intimating judgement', and to regard the consequent duplication of judgement in the + +case of indicative sentences as a contingent complication, only exceptionally present, and first brought into the picture, moreover, by descriptive reflection. Against this one might hold that, in each case of adequate, not contextually elliptical speech what was expressed was essentially one, in the interrogative sentence a question, in the optative sentence a wish, in the indicative sentence a judgement. Before I had completed these Investigations, I myself thought this position unavoidable, hard as it was to reconcile with the phenomenological facts. I thought myself compelled by the following argu- + +ments, that I now accompany with suitable criticism. + +§69 Argume nts for and against the Ari stote lian + +con ception + +According to the doctrine which is opposed to that of Aristotle, a man who, e.g., utters a question will be communicating to another his wish to be informed regarding the state of affairs in question. This communication regarding the speaker's actual experience is, it is held, a statement like any communication. In the form of the question itself there is no express saying that one is asking whether ... ; this form only marks off the question as a question. Our speech, therefore, is a case of contextual ellipticity. The circumstances of utterance make it obvious that it is the speaker himself who asks the question. The complete meaning of the sentence does not, accordingly lie in what its mere word-sounds suggest, but is determined by the occasion, the context, the relation to the person speaking at the moment. In favour of the Aristotelian conception, many replies could now be given. (a) The argument ought to apply equally to indicative sentences, so that we have to interpret the sentence 'S is P' as a contextual ellipsis for the new + +expression 'I judge that S is P', and so on in infinitum. + +(b) The argument is based on the view that the expressed sense of the interrogative sentence differs from its real sense. For, undeniably, in the interrogative or wish-sentence, the relation of the wish to the wisher does not need to be brought out, as little as, in the case of the indicative sentence, the relation of the judgement to the judging person. If this relation is not part of the explicit sense of the sentence, but only of its contextually variable part, this concession gives one all that one could want. The explicit meaning can be altered in certain circumstances, but there will surely also be circumstances where it will be just what we mean. In such cases the mere question (and similarly the mere request or command etc.) will receive wholly ad- + +equate expression. + +(c) More careful comparison with the indicative sentences of ordinary speech favours the Aristotelian conception. In verbal communication such a sentence intimates that one is judging, and it is the grammatical form of the indicative sentence which brings out the judgement as such. On the utterance of such grammatically framed speech, the effect forthwith attends, that + +the person addressed takes the speaker to be judging. This effect cannot, however, constitute the meaning of the expression, which surely means the same in soliloquy as in communicative speech. The meaning lies rather in + +the act of judging as the identical judgement-content. + +The same could be the case in regard to interrogative sentences. The meaning of an interrogative sentence is unchanged whether we deal with an internal question or an overt one. The relation of speaker to person addressed belongs here, as in the case compared, to the merely communicative function. And just as in that case the 'content of judgement', i.e. a certain specific character of judgement, determined in this or that manner as regards content, constituted the meaning of the indicative sentence, so here the content of the question constitutes the meaning of the interrogative sentence. In both cases the ordinary meaning can undergo circumstantial modifications. We may utter an indicative sentence with the primary intention, not of communicating the relevant state of affairs, but the fact that we have the conviction in question, and mean to put it forward. This intention, buttressed, perhaps, by non-grammatical aids (stress, gesture), may be understood. Here what underlies our words is a judgement relating to our explicit judgement. Just so, in the case of an interrogative or wish-sentence, our primary intention may lie, not in our mere wish, but in the fact that we wish to express the wish to a hearer. Naturally this interpretation could not hold in all cases. It could not hold, e.g., where a burning wish bursts spontaneously from the heart. The expression then is intimately one with + +the wish, it clings to it immediately and directly. + +Criticism. Regarded more closely, this argument only proves that a thought relating to the communicative function cannot be part of the sense of every sentence. The opposing argument is refuted: it rests on the false assumption that all expression is communicative, and that communication is always a judgement regarding the internal (intimated) experiences of the speaker. But its thesis is unrefuted, at least when suitably modified. For we cannot exclude the possibility that the controversial wish-, request-, and commandsentences etc., are still judgements about the relevant experienced acts of wishing, asking and willing, and that it is only as being so, that they can give these experiences adequate expression. If there is no place for judgements here in the narrower sense of predications - Aristotle certainly had this conception of the controversial sentences - perhaps there is place for them + +in a wider sense of assertive objectivations in general. + +I. As regards (a) we note, further, that the case of statements is not the same as, e.g., that of questions. If we transform the sentence 'S is P' into the sentence 'I judge that S is P', or into any related sentence, which expresses a relation to the judging person, however indefinitely, we obtain not merely altered meanings, but such as are not equivalent to the original ones: for the straightforward sentence may be true, the subjectivized sentence false, and conversely. The situation is wholly different in the case compared. Even if + +one refuses to speak of true and false in this case, one can surely always find a statement that 'in essence says the same' as the original question or wishform, e.g. 'Is S P?' = 'I should like to know .. .' or 'One would like to know whether S is P' etc. May such sentence-forms not imply a relation to the speaker, even if only indefinitely and subsidiarily? Does the preservation of 'essential meaning' in the transformed indicative forms not point to the fact that the meaning-giving acts are at least of the same general sort as judgements? These considerations also deal with (b): not the mere experience of wishing or willing, but the inner intuition of these experiences (and the signification adapted to this intuition) will be relevant to our meaning. This + +conception is, however, affected by the following argument: + +2. There is another way in which one might try to interpret the expressed forms in question as judgements. If we utter a wish, even in soliloquy, we put it, and the wished-for content, into words, we accordingly have a presentation of it, and of what constitutes it. The wish is, however, not any merely presented wish, but the living wish that we have just taken note of. And it is this wish, and this wish as such, that we want to intimate. It is not, accordingly, our mere presentation, but our inner percept, i.e. really a judgement, that achieves expression. It is not, indeed, a judgement of the same sort as our ordinary assertions, that predicate something of something. In the expression of a wish, it is only our concern to grasp the internally noted experience conceptually (significatively) in straightforward affirmation, and to express its simple existence. It is not our concern to make a relational predication about such an experience, connecting it with the experiencing + +subject. + +Against this conception it may be objected that the situation is exactly the same for expressed judgements as for all other expressed experiences. If we state something, we judge, and our words cover not only the presentation underlying our judgement, but also our judgement itself (i.e. in the form of an assertion). We should, therefore, also conclude here that the judgement is internally perceived, and that the meaning of our statement lies in the straightforwardly affirmative judgement about what we perceive, i.e. about our judgement. If no one finds such a conception acceptable in the case of a statement, it cannot be seriously entertained in the case of other independent sentences. We recall what was said in our last section. The expressions which fit themselves to the expressed experiences, are not related to them in the way that names are, nor in any analogous manner. Our experiences are not first objectively presented, and then brought under concepts, as if, together with each new word, a subsumption or predication had taken place. A person who judges gold to be yellow, does not judge that the presentation which accompanies his use of the word 'gold' is yellow: he does not judge that the manner of judging he carries out when he utters the word 'is' falls under the concept 'is' etc. The word 'is' does not in fact symbolize judgement, but the being which is found in a state of affairs. 'Gold', likewise, + +does not name a presentative experience: it names a metal. Expressions name experiences only when such experiences have been made objects of presentation or judgement in reflection. The same holds for all words, even syncategorematic ones, in their relation to what is objective: they mean this + +in their fashion even when they do not name it. + +Expressions are not therefore associated as names with the acts which fill our minds at each moment, acts in which we live without judging about them reflectively: such expressions belong rather to the concrete being of the acts themselves. To judge expressly is to judge, to wish expressly is to wish. To name a judgement or wish is not to judge or wish, but merely to name. A judgement named need never be judged by the man who names it, a wish named never wished by him. And, even when this is not so, the naming expresses no judgement or no wish, but a presentation related to one or the + +other. + +Criticism. This objection also exposes the weakness of our at first attractive preliminary argument. It is clear from it, as from our previous discussions, that not every expression (qua the expression it is) presupposes a judgement or other act, which makes the intimated experience its object. This again does not dispose of the thesis: we have not shown, just in the case of the sentence-forms under discussion, that they are not judgements about momentary wishing, questioning or requesting experiences, or that they do not express their straightforward existence in the speaker. True, to name a wish is not therefore to wish, but is experiencing a wish and naming it in the same breath, not also a case of wishing? So that, even if expressed wishing is necessarily a wishing which involves naming and stating, the proposition still + +holds, that expressed wishing is wishing and not mere naming. + +3. The controversial expressions have the form of sentences, and at times the form of categorical sentences with subjects and predicates. From this it follows that they can also be treated as having predication in their content, and not merely as predications in relation to one, same, unmentioned subject '1'. E.g. 'May God protect the Kaiser', 'The coachman should harness the horses'. A 'may' or a 'should' is uttered: the subject in question is + +apprehended as standing under a requisition or an obligation. + +One could here rejoin: Where a 'should' counts as an objective predicate and is actually attributed as such, the should-sentence has not merely the force of a wish or a command, or not this alone. An objective obligation can be said to hold, though the man stating it need experience no act of the kind which constitutes an actual consciousness of obligation. If I know that someone's will is bound by a relationship of service or by custom or morality, I can judge that he should and must do something. But this expresses no living wish, desire or obligation. Statements of obligation may indeed serve in appropriate contexts to express acts of this sort, e.g. 'John must harness the horses!' But it is clear that here no mere objective obligation is expressed, but my own will, and this not in my words, but rather in my tone + +and in the circumstances. In such circumstances the predicative form doubtless does duty for an imperative or optative form, i.e. the thought-predication implied by the words is either not carried out at all, or is merely subsidiary. It is undeniable, lastly, that the predicative interpretation only is plausible in certain cases, and not in the case in question. B. Erdmann, who otherwise leans towards it, does not favour it in this case. (See B. Erdmann, Logic, 11, + +§45, pp. 27 1 ff) + +Criticism. It may be questioned whether this refutation suffices. That a should-predicate has an objective sense and value cannot be doubted. But that, where this is not true, nothing is predicated or at least judged, is by no means proved. One might maintain: When we issue a command to someone, e.g. a command to the coachman John to harness the horses, he counts for us as someone subordinate to our will: he is apprehended as such by us and accordingly addressed in this form of expression. We say: 'John, harness the horses!' That he is one who should harness horses is here predicated of him, naturally in the expectation of corresponding practical results, and not merely to attest that he counts as such for me. The expression of the command is relative. We can think of no one commanded, without at the same time thinking, definitely or indefinitely, of someone who commands him. This being wholly obvious requires no explicit expression. Instead of the cumbrous form 'I command etc.', we employ the brief imperative, whose form points to a communicative relation. The speech-forms 'should' and 'must' were not originally used by a commander in face of the commanded to express his actual voluntary intent, but only when a more objective expression of his own or someone else's voluntary intent was needed, e.g. when there was a third person relaying someone else's command or when a legislating will found expression in a law. When communication between commander and commanded lapses, the imperative, which fits the conscious situation of the former, loses application. This conception can be applied generally. One can say: In the optative, what we wish is presented as wished, and stated to be such. Just so, in a requesting form, what we request is presented as requested, in a question what we ask presented as asked etc. These acts are related in our presentation to their intentional objects, and are so themselves made objective as reflexive predicates attaching to the + +latter. + +In the communicative situation, many others of the expressions in question have, like commands, the role of telling the hearer (like essentially occasional expressions) that the speaker is performing certain intimated acts (of request, congratulation, condolence etc.) with an intentional regard to his auditor. To the extent that expressions of all sorts may in full consciousness be informed by the wish to communicate with others, and to acquaint others with one's own convictions, doubts, hopes etc., they are perhaps all accompanied by reflex acts directed upon such inner experiences and, more precisely, by acts which intuitively relate the latter to the speaker and to the + +person addressed. This accordingly holds of communicative statements as well. These acts of reflection and reference do not on that account form part of the meaning of a statement and of all other expressions, but this may very well be said of expressions of our controversial class, in virtue of which they + +are in all cases directed to inner experiences of the speaker. + +In solitary mental life - if we disregard exceptional cases of talking to oneself, asking oneself questions, desiring or commanding oneself - relation to an auditor falls away, and the subjective expressions in question, which are still applicable, express the simple being of inner experiences in more or less definite relation to the subject. In a monologue a question is either of the form 'I ask myself whether .. .', or relation to the subject vanishes entirely: the interrogative expression becomes a mere name, or not really even that. For the normal use of a name is in a context of predicative or attributive relation, of which there is here no question. Since the expression becomes one with the intuited inner experience as a knowing of the latter, an interweaving of factors arises having the character of a self-enclosed phenomenon. To the extent that, in such interweaving, we live principally in an interrogative act, with which our expression merely fits in, and to which it gives articulate voice, the whole interweaving is called a question. Knowledge is not here a theoretical function - this is the case only in predication, while here nothing is predicated. The question is known and expressed, without being 'subjectivized', in the sense of being made either the subject or the object of predicative acts. Plainly this directly expressive sense of the interrogative sentence helps to constitute the predicative interrogation - I ask myself whether etc. - or the meaning which corresponds to such altered + +circumstances. + +§70 Decision + +If by a 'judgement' one means a predicative act, then our discussions have shown that our disputed sentences do not invariably express judgements. Even in these cases, however, an unbridgeable gulf separates us from the logicians who side with Aristotle. On their view, names, statements, optative sentences, interrogations, commands etc., are coordinated expressive forms, and coordinated in the following manner: names express presentations, statements express judgements, optative sentences express wishes etc. Presentations, judgements, questions etc., in short, acts of all sorts, can serve to confer meaning in exactly the same fashion, for to 'express acts' means the same in all cases, i.e. to have one's meaning in such acts. We, on the other hand, see a fundamental difference between names and statements, on the one hand, and the expressions of our controversial group, on the other. The acts of presentation or judging expressed by names or statements may confer or fulfil meaning, but are not therefore meant; they do not become objects of naming and predication, but are constitutive of such objects. On + +the other hand we find, in flat contrast, that the acts 'expressed' by our controversial expressions, though seeming to confer meanings, are made into objects. This may happen, as we saw, through inner intuition reflectively directed upon such acts, and generally also through relational acts based on such intuitions. It may also happen by way of certain acts of signification, perhaps only partially uttered, which attach as cognitions to these inner intuitions and acts of relating, thereby making their objects, the acts, namely, of asking, wishing, commanding etc., into objects named and otherwise talked of, and perhaps into components of predicated states of affairs. In these acts of objectification lie the true meanings of our controversial expressions. We are not in their case concerned with acts which confer meaning in some fundamentally new manner, but only with contingent specifications of the one, unique class of meaning-intentions. And, just so, the acts which fulfil meaning do not fall into different classes, but belong to the one, unique class of intuitions. It is not the wishes, commands etc., themselves that are expressed by these grammatical patterns and their significations; it is rather the intuitions of these acts that serve as fulfilments. When we compare indicative with optative sentences, we must not coordinate judgements with + +wishes, but states of affairs with wishes. What results accordingly is the fact that: + +The ostensible expressions of non-objectifying acts are really contingent specifications of statements and other expressions of objectifying acts which + +have an immense practical and communicative importance. + +The contentious issue here dealt with is of fundamental importance, since on its solution depends, on the one hand, whether we accept a doctrine which makes all meaning, whether in intention or fulfilment, of a single kind - the genus of objectifying acts, with their fundamental division into the significative and the intuitive - or whether, on the other hand, we decide to pennit acts of all sorts to confer or fulfil meaning. The issue is, of course, not less important because it is the first to call our attention to the fundamental triplicity of the ambiguity of talk about 'expressed acts', on whose analysis our present Investigation first embarked (cf. §2 above). There it was + +said that we may mean by 'expressed acts': + +1. The significative acts which give expressions meaning, and which have, + +in their significative fashion, a certain objectivity of reference. + +2. The intuitive acts, which frequently fulfil the significant intent of an expression, and so represent the significantly meant objects intuitively, and + +in a parallel intuitive 'sense'. + +3. The acts which are the objects of signification, and likewise of intuition, in all cases where an expression (in sense 2) expresses the speaker's own experiences of the moment. If these are not objectifying acts, their nature will + +not pennit them to function under the rubrics 1 and 2. + +The root of all our difficulties lies in the fact that, in the direct application of expressions (or acts to be expressed) to intuitively grasped inner experiences, + +our significative acts are completely fulfilled by the inner intuition which attaches to them, so that both are most intimately blended, while these same intuitions, being internal, exhaust themselves in the straightforward pres- + +entation of the acts that they mean. + +Finally we must observe that the distinction made above as against Bolzano - between cases where only the subjective objection can be raised - the objection to the expression's sincerity or adequacy - and cases where the factual objection can be raised - the objection related to objective truth and falsity - that this distinction has, on a closer survey, no true connection with our controversial question. For it has a quite general concern with the difference between expressions relating to intuitively envisaged act-experiences, and experiences not so relating. In the first class there are many quite uncontroversial predications, e.g. all statements of the form 'I ask whether .. .', 'I command, wish that .. .' etc. And, be it noted, there can be no factual objections to subjective judgements thus formulated: they are true or false, but truth here coincides with sincerity. In the case of other statements which aim at what is 'objective' (i.e. not at the self-expressing subject and his experiences) the factual question concerns our meaning. The question of sincerity depends on the possibility of seeming assertions, from which the genuine, normal act of meaning is absent. Really there is no judgement; the meaning of a statement is presented in the context of an intent to deceive. + +External and internal perception: physical and psychical phenomena + +The concepts of external perception and perception of self, of sensuous and internal perception, have for the naive man the following content. External perception is the perception of external things, their qualities and relationships, their changes and interactions. Perception of selfis the perception that each can have of his own ego and its properties, its states and activities. Asked who this perceived ego may be, the naive man would reply by pointing to his bodily appearance, or would recount his past and present experiences. To the further question whether all this is included in his percept of self, he would naturally reply that, just as the perceived external thing has many properties, and has had many in the course of its changes, which are not for the moment 'open to perception', so a corresponding fact holds for his perceived ego. In the changing acts of self-perception appear, on occasion, such and such presentations, feelings, wishes and bodily activities of the ego, just as the exterior or the interior of a house, or such and such sides and parts of it, enter from time to time into outer perception. Naturally, however, the ego remains the perceived object in the one case, as the house + +is in the other. + +For the naive man our second pair of notions, that of sensuous and internal perception, does not altogether coincide with the pair just discussed, that of outward perception and perception of self. We perceive sensuously what we perceive by the eye and the ear, by smell and taste, in brief, through the organs of sense. In this field everyone locates, not only external things, but his own body and bodily activities, such as walking, eating, seeing, hearing etc. What we call 'inner perception', on the other hand, concerns mainly such 'spiritual' experiences as thinking, feeling and willing, but also everything that we locate, like these, in the interior of our bodies, do not connect + +with our outward organs. + +In philosophical diction, both pairs of terms - we usually prefer the pair of 'internal and external perception' - express only one pair of concepts. After Descartes had sharply separated mens and corpus, Locke, using the + +terms 'sensation' and 'reflection', introduced the two corresponding classes of perception into modem philosophy. This division has remained in force till today. External perception was regarded, following Locke, as our perception of bodies, while inner perception was the perception that our 'spirits' or 'souls' have of their own activities (their cogitationes in the Cartesian sense). A division of perceptions is accordingly mediated by a division among the objects of perception, though a difference in origin is likewise set beside it. In one case perception arises from the effects of physical things operating through the senses on our spirits, in the other case out of a reflection on the activities carried out by the mind on the basis of 'ideas' won through sensation. + +2 + +In quite recent times men have been much concerned to achieve an adequate overhaul and a deepening of Locke's obviously vague and rough positions. General epistemological interests were, on the one hand, responsible for this move. We recall the traditional estimate of the relative value for knowledge of the two forms of perception: external perception is deceptive, inner perception evident. In this evidence lies one of the basic pillars of knowledge, which scepticism cannot shake. Inner perception is also the only case of perception where the object truly corresponds to the act of perception, is, in fact, immanent in it. It is also, to speak pointedly, the one type of perception that deserves the name. In the interest of perceptual theory, we must therefore enter more exactly into the essence of inner, as opposed to outer perception. Psychological interests were, on the other hand, involved. Men were concerned with the much-debated fixing of the domain of empirical psychology and, particularly, with establishing for it its own justification as against the natural sciences, by marking out for it a peculiar territory of phenomena. Even the prime place in epistemology readily accorded to psychology as basic philosophical discipline, required that its objects be defined with as few epistemological commitments as possible; it should not, therefore, concern itself with transcendent realities of so controversial a type as soul and body as if they were obvious data. Locke's classification of perceptions had just such a presupposition: it was therefore at once unsuited, and not in fact designed, to serve as a basis for a definition of psychology, and to do justice to the interests mentioned. It is clear, further, that if a distinction of perceptions is set up on the basis of an anticipated distinction between bodily and spiritual matters, then the former distinction cannot be used as a basis of distinction between the science of bodily and the science of spiritual phenomena. The matter would be different if one could succeed in finding purely descriptive marks for a division of percepts, marks which left our classes unaltered in extent, and which, while lacking all epistemological presuppositions, would serve to demarcate the corresponding bodily phenomena + +A possible path seemed here to be opened by the Cartesian approach through doubt, with its emphasis on the epistemological position of inner perception. We have already touched on this above. The line of thought, + +which develops here, runs as follows: + +However widely I may extend my critical doubts regarding knowledge, I cannot doubt that I exist and am doubting, or again, while I experience them, that I am having presentations, am judging, feeling or however else I may designate such inwardly perceived appearances: to doubt in such a case would evidently be irrational. We accordingly have absolute 'evidence' regarding the existence of the objects of inner perception, we have that clearest cognition, that unassailable certainty which distinguishes knowledge in the strictest sense. It is quite different in the case of outer perception. It lacks 'evidence', and the frequent conflicts in statements relying upon it point, in fact, to its capacity to deceive. We have therefore no right to assume from the outset that the objects of outer perception really and truly exist as they seem to us to be. We have, in fact, many reasons to think that they do not really exist at all, but can at best lay claim to a phenomenal or 'intentional' existence. If one makes the reality of a perceived object part of the notion of perception, then outer perception is not, in this strict sense, perception at all. This evident character will in any case give us a descriptive mark, free from presuppositions regarding metaphysical realities, which will enable us to sort out our various classes of perceptions. It is a character given with, or absent from, the perceptual experience itself, and this alone + +determines our division. + +If we now consider the phenomena presented by these various classes of perceptions, they unmistakably constitute essentially distinct classes. This is not to assert that the objects in themselves, i.e. the souls and bodies, that we rightly or wrongly range under them, differ essentially: a purely descriptive treatment that avoids all transcendence establishes an unbridgeable gulf between these phenomena. On the one side we have the sensory qualities, which in themselves form a descriptively closed class, whether there are such things as senses and sense-organs or not. They form a Kind in the strict Aristotelian sense of the word. To these are added features necessarily attaching, either to sense-qualities in general, or to single ranges of such qualities (again strict Aristotelian species), or, conversely, features themselves necessarily presupposing qualities, and only able to achieve concrete being in association with them. Here well-known propositions come up for treatment, e.g. no intuited spatiality without qUality. Many would say that the converse obtained also: No quality without something spatial. Others would here only approve particular cases: No colour, no tactile quality without something spatial. Further propositions of the same class would be: No tone-quality without intensity, no timbre without tone-qualities etc. l + +On the other side we have phenomena such as having presentations, judgements, surmises, wishes, hopes etc. We here enter, as it were, another world. + +These phenomena have relation to what is sensible, but are not themselves to be compared with the latter: they do not belong to one and the same (genuine) kind. When we have first clearly seen the descriptive unity of this class through examples, one finds, with a little attention, a positive mark + +which characterizes them all: the mark of 'intentional inexistence'. + +One can of course use the above descriptive distinction of inner and outer perception to arrive at just such a distinction of the two classes of phenomena. It becomes now a good definition to say: Psychic phenomena are the phenomena of inner perception, physical phenomena those of outer perception.2 In this manner a closer treatment of the two sorts of perceptions leads, not merely to a descriptive, epistemologically important characterization of these perceptions themselves, but also to a fundamental, descriptive division of phenomena into two classes, the physical and the psychical. And we seem to have achieved, for psychological and scientific purposes, a metaphysically uncommitted definition, not oriented towards supposed data in some tran- + +scendent world, but to what is truly given phenomenally. + +Physical phenomena are no longer defined as the phenomena which arise out of the operation of bodies on our minds through our sense-organs, psychic phenomena as the phenomena discovered by us in perceiving the activities of our minds. In both cases the descriptive character of the phenomena, as experienced by us, alone furnishes our criterion. Psychology can now be defined as the science of psychic phenomena, as natural science is of + +physical phenomena. + +These definitions require certain limitations in order to correspond truly to our actual sciences, limitations which point to explanatory metaphysical hypotheses, whereas the phenomena, as descriptively differentiated, remain the true starting-points of our treatments, and the objects to be explained. + +The definition of natural science is particularly in need of limiting conditions, for it is not concerned with all physical phenomena, not with the phenomena of imagination, but only with those which come before senseperception. And, even in their case, it only sets up laws to the extent that these depend on the physical stimulation of the sense-organs. One might express the scientific task of natural science, by saying that natural science is the science which seeks to explain the sequence of the physical phenomena of normal, pure sensations - sensations uninfluenced by peculiar psychical conditions and events - by assuming the action on our senseorgans of a world extended in three space-like dimensions, and taking place in one time-like dimension. Without settling the absolute character of this world, it is satisfied to attribute to it powers provocative of our sensations and influencing each other in their operation, and to set up laws of coexistence and succession for such powers. In stating these, it indirectly states the laws of sequence of the physical phenomena of our sensations, laws conceived in their purity, in scientific abstraction from + +3 + +concomitant mental conditions, as things taking place for an invariant sensibility. The expression 'science of physical phenomena' must be interpreted in this rather complicated way, if it is to be equated with the + +meaning of 'natural science'. + +(Brentano, Psychologie, 1, pp. 127-128) + +In regard to the conceptual demarcation of psychology, it might appear that the concept of the psychic phenomenon should be widened rather than narrowed, since the physical phenomena of imagination fall as entirely in its field of reference as do psychic phenomena in the previously defined sense, and since even the physical phenomena appearing in sensation cannot be disregarded in the doctrine of sensation. But it is plain that such physical phenomena only enter into descriptions of the peculiarities of psychic phenomena as the content of the latter. The same holds of all psychic phenomena which exist only phenomenally. The true subject-matter of psychology can be regarded as consisting solely of psychic phenomena in the sense of actual states. It is exclusively in regard to the latter that we call psychology the science of psychic + +phenomena. + +(Ibid. pp. 129 f) + +The interesting line of thought that I have just expounded represents, as my longer quotations have made plain, the standpoint of Brentano,3 and also that of a whole succession of thinkers who are theoretically close to him. There are further respects, as is well known, in which 'inner perception' plays an important role in Brentano's psychology. I am here only concerned with his doctrine of inner consciousness. Every psychic phenomenon is not merely a consciousness, but itself the content of a consciousness; we are conscious of it in the narrower sense of perceiving it. The flux of inner experience is therefore also a continuous flux of inner percepts, which are most intimately united with the psychic experiences in question. For inner perception is no second, independent act supervening upon a relevant psychic phenomenon; the latter rather involves, in addition to its relation to a primary object, e.g. an externally perceived content, 'itself in all its completeness as presented and known' (ibid. p. 182). In so far as the act directly intends its primary object, it is also subsidiarily directed upon itself. In this way one avoids the endless complication seemingly threatened by the consciousness which accompanies all psychic phenomena (since their multiple division into three 'ground-classes' itself involves an inner perception). The 'evidence' and infallibility of inner perception will also be rendered possible in this manner (ibid. II, ch. 3, pp. 182 ff). Brentano is here, in one of his main views, i.e. in his interpretation of consciousness as a continuous stream + +of internal perception, in harmony with the great thinkers of the past. Even Locke, a true student of experience, defines consciousness as the perception + +of what goes on in a man's own mind.4 + +Brentano's theories have aroused much opposition. This has not only been directed to the doctrines of inner perception just mentioned, whose subtly constructed complexity still certainly requires a phenomenological foundation, but also against his distinction between perceptions and phenomena and, in particular, against the laying down of the tasks of psychology and natural science which is based upon this.5 The relevant questions have repeatedly been made the theme of serious discussion in the past decade, and it is sad that, despite its fundamental importance for psychology and + +epistemology, agreement has not been reached. + +Criticism, it would appear, has not penetrated far enough, to hit upon the decisive points, and to separate what is indubitably significant in Brentano's thought-motivation from what is erroneous in its elaboration. This is due to the fact that the fundamental psychological and epistemological questions which cause controversy in these dimensions of enquiry, have not been sufficiently clarified, a natural consequence of defective phenomenological analysis. On both sides the conception with which men operated remained ambiguous, on both sides there was a consequent falling into delusive confusions. This will be clear from the following criticism of the illuminating + +views of Brentano. + +4 + +According to Brentano inner perception distinguishes itself from outer + +perception: + +1. by its evidence and its incorrigibility, and + +2. by essential differences in phenomena. In inner perception we experience exclusively psychic phenomena, in outer perception physical phenomena. This exact parallelism makes it possible for the first-named distinction to serve as a characteristic distinguishing mark of the perceivable phenomena + +as well. + +As opposed to this, inner and outer perception seem to me, if the terms are naturally interpreted, to be of an entirely similar epistemological character. More explicitly: there is a well-justified distinction between evident and nonevident, or between infallible and fallible perception. But, if one understands by outer perception (as one naturally does, and as Brentano also does) the perception of physical things, properties, events etc., and classes all other perceptions as inner perceptions, then such a division will not coincide at all with the division previously given. For not every perception of the ego, nor every perception of a psychic state referred to the ego, is certainly evident, if by the 'ego' we mean what we all mean by it, and what we all think we perceive in perceiving ourselves, i.e. our own empirical personality. It is + +clear, too, that most perceptions of psychic states cannot be evident, since these are perceived with a bodily location. That anxiety tightens my throat, that pain bores into my tooth, that grief gnaws at my heart: I perceive these things as I perceive that the wind shakes the trees, or that this box is square and brown in colour, etc. Here, indeed, outer perceptions go with inner perceptions, but this does not affect the fact that the psychic phenomena perceived are, as they are perceived, non-existent. Surely it is clear that psychic phenomena, also, can be perceived transcendently? Exactly regarded, all psychic phenomena seen in natural or empirical-scientific attitudes are perceived transcendently. The pure presentedness of experience presupposes a purely phenomenological attitude which will inhibit all transcendent + +assertions. + +I know what will here be objected: that we have forgotten the difference between perception and apperception. Inner perception means the directlyconscious living-through of mental acts, they are here taken as what they are, and not as what they are apprehended or apperceived as. One must, however, reflect that what is true for the case of inner perception must be true also for the case of outer perception. If the essence of perception does not lie in apperception, then all talk of perception in regard to external things, mountains, woods, houses etc., is misguided, and this, the normal sense of the word 'perception', surely illustrated in these cases above all others, must be abandoned. Outer perception is apperception, and the unity of the concept demands that inner perception should be so too. It is of the essence of perception that something should appear in it: apperception, however, constitutes what we call appearance, whether veridical or not, and whether it remains faithfully and adequately in the frame of the immediately given, or anticipates future perception in going beyond it. The house appears to me - in no other manner than that I apperceive actually experienced sense-contents in a certain fashion. I hear a barrel organ - the tones sensed are interpreted as those of a barrel organ. In the same way I apperceivingly perceive my own psychic phenomena, the blessedness quivering through 'me', the grief in my heart etc. They are called 'appearances', or rather + +apparent contents, being contents of apperception. + +5 + +The term 'appearance' is, of course, beset with ambiguities, whose extreme dangers are seen precisely in this case. It will not be useless at this point to list these equivocations explicitly: we have already touched on them in passing in the text of these Investigations. Talk of 'appearance' has a preferred application to acts of intuitive presentation, to acts of perception, on the one hand, and to acts of representation, on the other, e.g. acts of remembering, imagining, or pictorially representing (in the ordinary sense), on a basis + +1. The concrete intuitive experience (the intuitive presentedness or representedness of a given object for us); the concrete experience, e.g., when we perceive the lamp standing before us. Since the qualitative character of the act, whether the object is regarded as real or not, is irrelevant, it can also be ignored entirely, and 'appearance' then coincides with what we defined as + +'representation' in the last Investigation (cf. VI, §26, p. 740). + +2. The intuited (appearing) object, taken as it appears here and now, e.g. + +this lamp as it counts for some percept we have just performed. + +3. In misleading fashion we also call the real (reel/en) constituents of appearances in sense I, i.e. those of the concrete acts of appearing or intuiting, 'appearances'. Such appearances are, above all, the presentative sensations, the experienced moments of colour, form etc., which we fail to distinguish from apparent properties of the (coloured, formed) objects corresponding to them, and apparent in the act which 'interprets' them. That it is important to distinguish between them, that it does not do to confuse a coloursensation with an apparent bodily colouring, the sensation of form with bodily form etc., we have often stressed. Uncritical theories certainly ignore the distinction. But even those who would refuse to say with Schopenhauer that 'the world is my idea', are accustomed to speak as if apparent things were compounded out of sense-contents. One could certainly say that apparent things as such, the mere things of sense, are composed of a stuff analogous to that which as sensation is counted a content of consciousness. This does not affect the fact that the thing's apparent properties are not themselves sensations, but only appear as analogues of sensations. For they are not present, as sensations are, in consciousness, but are merely represented in it, as properties which appear in it, which are transcendently referred to. For this reason perceived external things, likewise, are not complexes of sensations: they are rather objects of appearances, objects appearing as complexes of properties, whose types stand in a peculiar analogy to types found among sensations. We could put what we have just said somewhat differently. Under the rubric of 'sensations', we range certain sorts of experiences of this or that actual kind belonging to a unity of consciousness. If it now happens that, in a unity of consciousness, real properties of analogous kinds appear as external to, and transcending such sensations, we may then call them after these sensational classes, but they are no longer sensations. We emphasize the word 'external', which must of course not be understood spatially. However we may decide the question of the existence or nonexistence of phenomenal external things, we cannot doubt that the reality of each such perceived thing cannot be understood as the reality of a perceived complex of sensations in a perceiving consciousness. For it is plain, and confirmable by phenomenological analysis in each instance, that the thing of perception, this so-called sensational complex, differs in every circumstance, both as a whole and in every + +distinct moment of property, from the sensational complex actually lived through in the percept in question, whose objective apperception first constitutes the perceptual sense, and thereby the apparent thing, in intentional + +fashion. + +It may indeed be said that the original concept of appearance was the one given in our second place above: the concept of what appears, or of what could appear, of the intuitive as such. Having regard to the fact that all sorts of experiences (including the experiences. of outer intuition, whose objects are therefore called outer appearances) can be made objects of reflective, inner intuition, we call all experiences in an ego's experiential unity 'phenomena' . Phenomenology is accordingly the theory of experiences in general, inclusive of all matters, whether real (reel/en) or intentional, given in experiences, and evidently discoverable in them. Pure phenomenology is accordingly the theory of the essences of 'pure phenomena' , the phenomena of a 'pure consciousness' or of a 'pure ego': it does not build on the ground, given by transcendent apperception, of physical and animal, and so of psycho-physical nature, it makes no empirical assertions, it propounds no judgements which relate to objects transcending consciousness: it establishes no truths concerning natural realities, whether physical or psychic - no psychological truths, therefore, in the historical sense - and borrows no such truths as assumed premisses. It rather takes all apperceptions and judgemental assertions which point beyond what is given in adequate, purely immanent intuition, which point beyond the pure stream of consciousness, and treats them purely as the experiences they are in themselves: it subjects them to a purely immanent, purely descriptive examination into essence. This examination of essence is also pure in a second sense, in the sense of Ideation; it is an a priori examination in the true sense. So understood, all the Investigations of the present work have been purely phenomenological, in so far, that is, as they did not have ontological themes, and did not, as in the Third and Sixth Investigation, seek to make a priori assertions regarding the objects of possible consciousness. They did not speak of psychological facts and laws in an 'objective' nature, only of pure possibilities and necessities, which belong to any form of the pure 'cogito': they spoke of these as regards their real (reel/en) and their intentional contents, or as regards their apriori possibilities of connection with other such patterns in an ideally + +possible conscious context. + +As the term 'appearance' is ambiguous, so also, and consequently, is the term 'perception' , and so are all further terms used in connection with perception. These ambiguities fill theories of perception with confused errors. The 'perceived' is, e.g., what appears in perception, i.e. its object (the house) and, further, the sense-content experienced in it, i.e. the sum of the presenting contents, which in their interconnection are 'interpreted' as the house, + +Sa + +6 + +Excerpt from the First Edition which was replaced by the first two para- + +graphs of the third note in the preceding §5 in Edition II. + +3. If we are only clear that we have to draw a distinction in our intuition between sensations as lived experiences, which are accordingly components of the subject, and phenomenal determinations, as components of the intentional object, and that both only coincide in the ideal case of adequate intuition (which does not come into question for us), then we readily see that our inwoven sensations cannot themselves count as appearances, whether in the sense of acts or of apparent objects. Not in the former, since under the rubric of sensations we sum up certain non-acts, which perhaps receive an objectifying interpretation in acts; not in the latter, since acts would have to be part of the phenomenal objectivity of sensations, acts which would have to direct their intention to them. Such acts are indeed possible, but that they are part of the stock-in-trade of every percept, and this in relation to the percept's presentative sensations, cannot be shown to be necessary either by descriptive analysis or on genetic grounds. All this goes without saying for imaginative intuitions as well, in relation to their imaginatively rep- + +resentative contents. + +If one has once got to the point of regarding all components of appearances in sense 1 as themselves appearances, then it is a further, almost unconscious step to regard everything psychic, all lived experi- + +ences in the experiential unity of the ego, as phenomena. + +How misleading such ambiguities show themselves to be appears in Brentano's theory, with its division into inner and outer perception according to evidential character and separate phenomenal class. We are told that: Outer perception is not evident, and is even delusive. This is undoubtedly the case if we mean by the 'physical phenomena' what such perception perceives, physical things, their properties and changes etc. But when Brentano exchanges this authentic, and alone permissible sense of the word 'perceive', for an improper sense which relates, not to external objects, but to presenting contents, contents, i.e., present as real parts (reell angehOrigen) in perception, and when he consequently gives the name of 'physical phenomena', not merely to outer objects, but also to these contents, these latter seem infected with the fallibility of outer perception. I believe that stricter divisions are necessary here. If an external object (a house) is perceived, presenting sensations are experienced in this perception, but they are not perceived. When we are deluded regarding the existence of the house, we are not deluded regarding the existence of our experienced sense-contents, + +since we do not pass judgement on them at all, do not perceive them in this perception. If we afterwards take note of these contents - our ability to do this is, within certain limits, undeniable - and if we abstract from all that we recently or usually meant by way of them, and take them simply as they are, then we certainly perceive them, but perceive no external object through them. This new perception has plainly the same claim to inerrancy and evidence as any 'inner' perception. To doubt what is immanent (in consciousness), and is meant precisely as it is, would be quite evidently irrational. I may doubt whether an outer object exists, and so whether a percept relating to such objects is correct, but I cannot doubt the now experienced sensuous content of my experience, whenever, that is, I reflect on the latter, and simply intuit it as being what it is. There are, therefore, evident percepts of 'physical' + +contents, as well as of 'psychical'. + +If it were now objected that sensuous contents are invariably and necessarily interpreted objectively, that they are always bearers of outer intuitions, and can only be attended to as contents of such intuitions, the point need not be disputed: it would make no difference to the situation. The evidence of the existence of these contents would be as indisputable as before, and would also not be our evidence for 'psychic phenomena' in the sense of acts. The evidence for the being of the whole psychic phenomenon implies that for each of its parts, but the perception of the part is a new perception with a new evidence, which is by no means that of the whole phenomenon. An analogous ambiguity to that which affects the notion of a physical phenomenon, will also be found, if our conception is consistent, in the case of the notion of the psychic phenomenon. This is not the case for Brentano. He understands by a psychic phenomenon only an actually present actexperience, and by an inner perception a perception which simply apprehends such an experience, just as it is there. Brentano ignores the fact that he has only done justice to one class of percepts of psychic phenomena under the name of 'inner perception', and that it is not possible to divide all percepts into the two groups of outer and inner. He also ignores the fact that the whole evidential prerogative accorded to his 'inner perception' hangs upon the fact that he has employed an essentially distorted concept of perception in the case of inner perception, and that it does not depend on the peculiarity of inwardly perceived 'phenomena'. Had he treated as genuine percepts of physical phenomena only such objective interpretations and apprehensions as survey their objects adequately, he could have attributed evidence to that perception of sense-experiences which was by him assigned to outer perception, and he could not have said of inner perception (in his sense) that it is 'really the only sort of perception in the true sense of the + +word' (ibid. p. 11 9). + +It is absolutely clear that the conceptual pairs of inner and outer, and of evident and non-evident perception, need not coincide at all. The first pair is determined by the concepts of physical and psychical, however these may + +be demarcated; the second expresses the epistemologically fundamental antithesis studied in our Sixth Investigation, the opposition between adequate perception (or intuition in the narrowest sense, whose perceptual intention is exclusively directed to a content truly present to it) and the merely supposing, inadequate perception, whose intention does not find fulfilment in present content, but rather goes through this to constitute the lively, but always one-sided and presumptive, presentedness of what is transcendent. In the first case the experienced content is also the object of perception, in the second, content and object fall asunder. The content represents what it does not itself have, what is, however, made manifest in it, and what is, in a certain sense, its analogue (if we confine ourselves to what is immediately + +intuited), as body-colour is an analogue of sense-colour. + +In this separation we have the essence of the epistemological difference that men look for between inner and outer perception. It is the operative factor in the Cartesian treatment of doubt. I can doubt the truth of an inadequate, merely projective perception: the intended, or, if one likes, intentional, object is not immanent in the act of appearing. The intention is there, but the object itself, that is destined finally to fulfil it, is not one with it. How could its existence be evident to me? But I cannot doubt an adequate, purely immanent perception, since there are no residual intentions in it that must yet achieve fulfilment. The whole intention, or the intention in all its aspects, is fulfilled. Or, as we also expressed it: the object is not in our percept merely believed to exist, but is also itself truly given, and as what it is believed to be. It is of the essence of adequate perception that the intuited object itself really and truly dwells in it, which is merely another way of saying that only the perception of one's own actual experiences is indubitable and evident. Not every such percept is evident. In the percept of toothache, e.g., a real experience is perceived, and yet our perception often deceives: the pain appears to bore a sound tooth. The possibility of our error is plain. The perceived object is not the pain as experienced, but the pain in a transcendent reference as connected with the tooth. Adequate perception involves, however, that in it the perceived is experienced as it is perceived (as the perception thinks or conceives it). In this sense we obviously only have an adequate percept of our own experiences, and of these only to the extent that we apprehend them purely, without going apperceptively + +beyond them. + +7 + +It might now be objected: An experience is surely the same as a psychic phenomenon. What, then, is the dispute all about? I answer: If one means by 'psychic phenomena' the real (realen) constituents of our consciousness, the experiences themselves that are there, and if one further means by inner percepts, or percepts of psychic phenomena, adequate percepts, whose + +intention finds immanent fulfilment in the experiences in question, then the scope of inner perception will of course coincide with that of adequate + +perception. It is important, however, to note: + +1. That psychic phenomena in this sense are not the same as psychic phenomena in Brentano's sense, nor as Descartes's cogitationes, nor as Locke's acts or operations of mind, since in the sphere of experiences as such + +all sense-contents, all sensations, also belong. + +2. That the non-inner perceptions (the remainder class) will not then coincide with outer perceptions in the ordinary sense of the word, but with the much wider class of transcendent, inadequate perceptions. If a sense-content, or sense-complex or sequence of sense-contents is apprehended as a thing out there, as a multitude, an articulated connection of several things, or as a change in things, an external happening etc., we have an outer percept in the ordinary sense. But a non-sensuous content can also belong to the representative stuff of a transcendent percept, particularly in association with sense-contents. Our perceived object can then as readily be an external object with perceived mental properties (this happens in differing fashion in the apprehension of one's own and other men's bodily being as 'persons') or, as in psycho-physical apperception, an inner object, a subjective experience, + +perceived with physical properties attaching to it. + +3. When in psychology, as the objective science of animal mentality, we mean by perceptions of psychic phenomena the perceptions that a man has of his own experiences, which the perceiver apprehends as belonging to himself, this particular person, all inner perceptions are no less cases of transcendent apperception than are outer perceptions. Among these there are some which (with some abstraction) count as adequate, in so far as they seize the man's own (relevant) experiences in their very selves. But in so far as even such 'adequate' inner perceptions apperceive the experiences they apprehend as those of a percipient, psycho-physical, personal ego, and so as belonging to the presented objective world, they are in this respect infected with an essential inadequacy. There are, further, cases of inner perception, as there are cases of outer perception, where the perceived object, in the sense given to it in our percept, has no existence. The distinction, fundamental even for psychology, between adequate and inadequate perception psychological adequateness being understood as the abstraction we mentioned - intersects the distinction between inner and outer perception, and therefore + +pervades the sphere of the former. + +8 + +The ambiguities of the word 'phenomenon' allow us first to call apparent objects and their properties 'phenomena', then to apply the term to the experiences which constitute their act of appearing (particularly to the experienced contents in the sense of sensations) and, lastly, to all experiences + +whatever. These ambiguities explain why we tend to confuse two essentially + +different types of psychological division of 'phenomena'. + +1. Divisions of experiences, e.g. the division of experiences into acts and non-acts. Such divisions naturally fall into the sphere of psychology, which accordingly has to deal with all experiences, which it of course apperceives + +in transcendent fashion as experiences of animal beings in nature. + +2. The division of phenomenal objects into, e.g. , such as seem to belong to the consciousness of an ego and such as do not seem to do so, i.e. the division into psychical and physical objects (contents, properties, relations etc.). In Brentano these two divisions are confused. He simply opposes physical to psychical phenomena, and defines them unmistakably as a division of experiences into acts and non-acts. But he at once mixes up, under the rubric of physical phenomena the contents of sense,6 and apparent external objects (or their phenomenal properties), so that the division now becomes a division of phenomenal objects into physical and psychical (in an ordinary or near-ordinary sense), in which the latter division furnishes the names. Closely connected with this confusion is the erroneous criterion, also used by Brentano, to divide the two classes of phenomena: that physical phenomena only exist 'phenomenally and intentionally, while psychical phenomena also 'have an actual existence as well as an intentional one'.? If we understand by 'physical phenomena' phenomenal things, it is at least sure that they do not need to exist. The forms of productive fancy, most of the objects of artistic representation in paintings, statues, poems etc., hallucinatory and illusory objects, exist only in a phenomenal and intentional manner, i.e. they do not exist in the authentic sense at all; only the relevant acts of appearing exist with their real (reellen) and intentional contents. The matter is quite different in the case of physical phenomena interpreted as sensed contents. The sensed (experienced) colour-contents, shape-contents etc., which we enjoy when we look at Bocklin's picture of the Elysian Fields, and which, informed by an imaginative act-character, are made into the consciousness of the pictured objects, are real (reelle) constituents of this experience. And they do not exist in merely phenomenal, intentional fashion (as apparent, merely intended contents) but in actuality. One must not forget, of course, that 'actual' does not here mean the same as 'external to consciousness', but + +the same as 'not merely putative'. + +Investigation III: On the theory of wholes and parts + +In troduction + +As regards these 'formal objective categories' and the formal ontological truths of essence pertaining to them, see the statements of the last chapter of the Pro- + +legomena, (I §§67 I). + +The diffe rence betwe en in dependent and non-ind ependent + +objects + +The two Husserlian terms, real and reell, here occur in the same sentence, the former connoting what is actually there in the space-time world, and not abstract or ideal, the latter what is actually immanent in an experience, and not merely + +'meant' by it. [Translator's note] + +2 In the present discussion, there is no danger of confusion between 'presented content', in the sense of any presented object (in the psychological sphere: any psychological datum), and 'presented content' in the sense of 'what' the presenta- + +tion signifies. + +3 Principles, Introduction, §1O. + +4 Almost exactly as formulated by C. Stumpf in Uber den psychologischen Ursprung + +der Raumvorstellung (1 873), p. 109. + +5 Stumpf previously used the expression 'partial content', but now prefers to speak + +of an 'attributive moment'. + +6 In the following expositions I employed my essay, 'On Abstract and Concrete Contents', (Number I of the 'Psychological Studies in the Elements of Logic', + +Phi/os. Monatshefte, 1894, Vol. xxx). + +7 Loc. cit. p. 11 2. 8 Loc. cit. p. 11 3. + +9 Cf. Ehrenfels, 'Uber Gestaltqualitiiten', Vierteljahrsschrift fur wiss. Phi/osophie (1 890); my Phi/osophie der Arithmetik (1891), particularly the whole of ch. XI, Meinong, 'Beitriige Zur Theorie der psychischen Analyse', Zeitschriftf Psychologie + +u. Physiologie d Sinnesorgane, VI (1 893). + +10 Cf. the words italicized by us. + +11 The ontological transformation of the notion of self-evidence into one of pure essential lawfulness - a transformation which starts at this point and which decisively influences the content of the rest of the Investigation - has already + +been clearly carried out in my 'Bericht tiber deutsche Schriften zur Logik', (1 894) + +Archiv fiir Syst. Philos. III, p. 225, n. 1. + +12 See my Philosophie der Arithmetik (1891), ch. XI, p. 228 (an 'avenue' of trees, a + +'flock' of birds, a 'flight' of duck, etc.). + +13 From my 'Psychologische Studien zur elementaren Logik' , Philos. Monatshefte, + +(1 894), xxx, p. 162. + +14 Stumpf as is well known at first defines 'fusion' in a narrower sense, as a relation of simultaneous sense-qualities, as a result of which they appear as parts of a sensational whole. He does not however fail to point to the wider concept that + +we here find pivotal. Cf. Tonpsychologie, 11 §17, pp. 64jJ. + +15 See Investigation II, §4l, where we spoke figuratively of a mere 'being emphasized' of dependent moments in the consciousness of ideating abstraction, against those + +cases where they themselves are the intended, noticed objects. + +16 The moment which is presentative of the spatial extension of the apparent col- + +oured figure in space. + +17 'Position' and 'magnitude' here naturally stand for phenomena in the sensational sphere, presentative moment for the intentional (apparent) position and magni- + +tude in the straightforward sense. + +2 Thou g hts towards a theory of the pure fo rms of wholes + +and parts + +1 In the sense namely of the abbreviated mode of speech defined in the last section, + +which must everywhere be remembered here. + +2 More precisely: in the unity of a visual intuitum as such. + +3 From Prop. 4 in §14, above. + +4 See Bolzano's, Wissenschaftslehre, 1, §58, p. 25 1, and Twardowski, loco cit. §9, + +pp. 49 / + +5 A new expression of Prop. 3 in §14, above. + +6 [Husserl here has 'volumness' which I take to be an unsuccessful venture into + +English, Trans.] + +7 See my Philosophie der Arithmetik (1891), p. 232. + +8 One must certainly distinguish the sensuous moment of likeness from likeness as a categorial unity: the former is related to the latter as the sensuous characters of plurality, which serve us as direct indications of multiplicity and diversity, stand to multiplicity and diversity themselves. See my Phil. der Arithmetik, p. 233. This first work of mine (an elaboration of my Habilitationsschrift, never published and only partially printed, at the University of Halle, 1887) should be compared with all assertions of the present work on aggregates, moments of unity, combinations, wholes and objects of higher order. I am sorry that in many recent treatments of the doctrine of 'form-qualities', this work has mostly been ignored, though quite a lot of the thought-content of later treatments by Cornelius, Meinong etc., of questions of analysis, apprehension of plurality and combination, is already to be found, differently expressed, in my Philos. der Arithm. I think it would still be of use today to consult this work on the phenomenological and ontological issues in question, especially since it is the first work which attached importance to acts and objects of higher order and investigated them + +thoroughly. 9 See §1 1, above. + +10 See Prolegomena, Vol. 1 (§§67-72) on the role of formalization for constituting the idea of a pure logic as mathesis universalis. We must emphasize again that where we speak simply of 'abstraction', as we have done so far, we mean the + +emphasis on a non-independent 'moment' of content, or the corresponding idea- + +tion under the title of 'ideating abstraction', but not formalization. + +11 See §19, above. 12 Prop. 3, in §19, above. + +Investigation IV: The di stinction between ind ependent and non-ind ependent meani ngs and the idea of pure grammar + +I ntrod uction + +We could equally say: 'of presentations' . For plainly an answer to the more specialized question also answers the more general question relating to presenta- + +tions or objectifying acts as such. + +2 Twardowski (op. cit. above p. 94) removes the whole basis for making such a distinction when he objects, as against Bolzano (whom we here follow) that there are no simple objects. Cf. Twardowski's own question where he speaks expressly of presented objects. We are here dealing with objects of reference as such. + +3 Twardowski, op. cit. p. 98. + +4B. Bolzano, Wissenschaftslehre (Sulzbach, 1837), I, §57. 'Presentation' means for Bolzano 'presentations-in-themselves', which corresponds to our concept of + +meaning. + +5 A. Marty, 'Uber subjektlose Slitze', Vierteljahrschrift fur wis. Phi/os., vmth year, + +p. 293, note. + +6 Marty, 'Uber das Verhliltnis von Grammatik und Logik', Symbolae Pragenses + +(1 893), p. 121, n. 2. + +7 In his last-mentioned article Marty defines a categorematic sign as one which independently arouses a complete presentation, through which an object is named. But the definition of the syncategorematic sign which follows (see above) does not clearly bring out that the grammatical division rests on an essential division + +in the field of meaning, as Marty certainly thought. + +8 The word 'presentation', carefully regarded, does not here mean 'act of presentation', but merely what is presented as such, together with the articulations and forms with which it is present in consciousness. The 'presentational form' is therefore the form of what is presented as such; we must keep this in rind in + +what follows. + +9 A. Marty recently wrote, in his 'Untersuchungen zur Grundlegung der allgemeinen Grammatik und Sprachphilosophie' (Halle, 1908) of 'autosemantic' and 'syn- + +semantic' signs (pp. 205 ff). + +10 The mode of speech need not be taken as literally as Marty has done in his Untersuchungen, pp. 21 1/, as meaning that we build total meanings out of 'bricks' of partial meaning that could also exist separately. That this is a wrong conception is precisely the theme of my further argued doctrine of non-independent meanings. I cannot see how the exposition above can bear such an interpretation, and that it is in any way touched by Marty's objections. See the further discussions + +below regarding the understanding of isolated syncategorematica. + +11 In so far as these and the rest have not lost their articulate meanings in the + +evolution of speech. + +12 We dealt with an analogous, closely related question in §2. + +13 In our whole exposition 'fulfilment' must of course be taken to cover the opposed state of 'frustration' , the phenomenologically peculiar situation in which absurdly combined meanings in a meaningful whole make their incompatibility + +plain in intuitive clarification and in 'bringing to insight': the intended unity is + +'frustrated' in intuitive disunity. + +14 §15. + +15 The genuine contribution traditional logic makes to pure logic including the whole logic of the syllogism, is part of the logic of propositional meanings (or + +'apophantic' logic). + +16 I gladly accept A. Marty's objections (which I do not think otherwise fit the main features of the present Investigation or the other Investigations of this work) that I went too far, in the First Edition when I said that 'all censure of the old doctrine of grammaire generale et raisonnee only affects the uncleanness of its historical expressions and their mixture of the a priori and the empirical'. Nonetheless, the sharpest words of censure were directed against it for trying to make + +a rational, logical element count in speech. + +Investigation V: On intentional experi en ces and + +the ir 'contents' + +I Consciousn ess as the phenomenolog ical subsistence of the + +e g o and consciousne ss as inner percepti on + +1 See my Ideas towards a Pure Phenomenology, etc., in the lahrbuch fur Phi/os. u. phiinom. Forschung, 1 (1913), Section 2. [fhe present paragraph is an insertion in + +the Second Edition.] + +2 Which is only in question qua phenomenal, since we exclude all questions regarding its existence or non-existence, and that of the empirical ego which appears in it, if we wish our treatments to have, not a descriptive-psychological, but a purely phenomenological value. One should note how, up to this point and for the future, each analysis can be first conducted as mere psychology, but there really permits of that 'purification' which gives it value as 'pure' phenomenology. + +[Second Edition comment.] + +3 Or what we also call its 'appearance' in the sense given above, which will also be employed in future, the sense in which a (phenomenologically understood) + +experience is itself styled an 'appearance'. + +4 In the First Edition the name 'phenomenological ego' was given to the stream of + +consciousness as such. + +5 The opposition to the doctrine of a 'pure' ego, already expressed in this paragraph, is one that the author no longer approves of, as is plain from his Ideas cited + +above (see ibid. , §57, p. 107; §80, p. 159). + +6 The text as here set forth is taken over without essential change from the First Edition. It fails to do justice to the fact that the empirical ego is as much a case of transcendence as the physical thing. If the elimination of such transcendence, and the reduction to pure phenomenological data, leaves us with no residual pure ego, there can be no real (adequate) self-evidence attaching to the 'I am' . But if there is really such an adequate self-evidence - who indeed could deny it? - how can we avoid assuming a pure ego? It is precisely the ego apprehended in carrying out a self-evident cogito, and the pure carrying out eo epso grasps it in phenomenological purity, and necessarily grasps it as the subject of a pure + +experience of the type cogito. + +7 Cf. the whole of §4 in Natorp's Einleitung in die Psychologie nach kritischer + +8 I have since managed to find it, i.e. have learnt not to be led astray from a pure grasp of the given through corrupt forms of ego-metaphysic cf. note to §6. + +2 Conscious ness as in tentional expe rience + +My deviations from Brentano are not on the same lines as the qualifications that he found necessary to add to the inadequate simplifications of which he was clearly conscious (See Psychologie, I, pp. 127 If). This will be plain from the + +discussions in App. 2 at the end of this volume. + +2 We could not say 'experiencing contents', since the concept of 'experience' has its prime source in the field of 'psychic acts'. Even if this concept has been widened to include non-acts, these for us stand connected with, ranged beside and attached to acts, in a unity of consciousness so essential that, were it to fall away, + +talk of 'experiencing' would lose its point. 3 See further the Appendix referred to above. + +4Psycho logie, I, 11 5. + +5 We are not therefore troubled by such vexed questions as to whether all mental phenomena, e.g. the phenomena of feeling, have the peculiarity in question. We must ask instead whether the phenomena in question are mental phenomena. The oddness of the question springs from the unsuitability of its wording. More + +about this later. + +6 Within the framework of psychological apperception, the purely phenomenological concept of experience fuses with that of mental reality, or rather, it turns into the concept of the mental state of an animal being (either in actual nature or in an ideally possible nature with ideally possible animals, i.e. without existential implications). Later on the pure phenomenological generic Idea intentional experience transforms itself into the parallel, nearly related psychological generic concept. According as psychological apperception is kept out or kept in, the same sort of + +analysis has phenomenological or psychological import. + +7 Psychologie, p. 111 (end of §3). + +8 Psychologie, p. 104. + +9 Cf. Brentano, Psychologie, pp. 266-7, 295 and passim. + +lO No reference to selective attention or notice is included in the sense of the 'refer- + +ence' involved in our 'intention' . See also §l3. + +11 We may here ignore the various possible assertive traits involved in the believed being of what is presented. One should again recall that it is possible to leave out all presupposing of natural reality, persons and other conscious animals included therein in our completed studies, so that they are understood as discussions of ideal possibilities. One finally sees them in the light of methodological exclusions, which cut out whatever is matter of transcendent apperception and assertion, so as to bring out what is really part of an experience and of its essence. Experience has then become the pure experience of phenomenology, from which psychological + +apperception has likewise dropped away. + +12 As regards the seemingly obvious distinction between immanent and transcendent objects, modelled on the traditional schema of inner conscious image v. extraconscious being-in-itself, cf. the Appendix at the end of this chapter. l3 Cf. the additional note to ch. I, above, pp. 93-4, and my Ideen zu einer reinen + +Phiinomenologie, l.c. + +14 Cf. §19. + +15 We are in complete agreement with Natorp (Einleitung in die Psychologie, 1st edn, p. 21) when he objects to fully serious talk about 'mental activities', or 'activities of consciousness', or 'activities of the ego', by saying that 'consciousness only + +appears as a doing, and its subject as a doer, because it is often or always accompanied by conation'. We too reject the 'mythology of activities': we define + +'acts' as intentional experiences, not as mental activities. 16 P. Natorp, Einlei/tung in die Psychologie, 1st edn, p. 18. + +17 Last three sentences added in Edition II. + +18 Cf. my 'Psychological Studies .. .', Phi/os. Monatshelte, xxx, (1 894), p. 182. 19 The much discussed dispute as to the relation between perceptual and imaginative presentation can have no satisfactory outcome in default of a properly prepared phenomenological foundation and consequent clarity in concepts and questions. The like holds of enquiries as to the relation of simple perception to representational or sign-consciousness. It can be readily shown, I think, that actcharacters differ in such cases in pictorial representation, e.g. an essentially new + +mode of intention, is experienced. + +20Psychologie, I, pp. 11 6If 21 [Paragraph added in Edition II.] + +22 Here as elsewhere I identify the pain-sensation with its 'content', since I do not recognize peculiar sensing acts. Naturally I reject Brentano's doctrine that presentative acts, in the term of acts of feeling-sensation, underlie acts of feeling. 23 I point here, for purposes of comparison, and perhaps completion, to H. Schwarz's Psychologie des Willens (Leipzig, 1900) which in §12 deals with similar questions. 24 In the First Edition I wrote 'real or phenomenological' for 'real'. The word 'phenomenological' like the word 'descriptive' was used in the First Edition only in connection with real (reelle) elements of experience, and in the present edition it has so far been used predominately in this sense. This corresponds to one's natural starting with the psychological point of view. It became plainer and plainer, however, as I reviewed the completed Investigations and pondered on their themes more deeply - particularly from this point onwards - that the description of intentional objectivity as such, as we are conscious of it in the concrete actexperience, represents a distinct descriptive dimension where purely intuitive description may be adequately practised, a dimension opposed to that of real (reellen) act-constituents, but which also deserves to be called 'phenomenological'. These methodological extensions lead to important extensions of the field of problems now opening before us and considerable improvements due to a fully conscious separation of descriptive levels. Cf. my Ideen zu einer reinen Phiinomenologie, Book I, and particularly what is said of Noesis and Noema in Section III. + +25 Paragraph added in the Second Edition. + +26 Real would sound much better alongside 'intentional' but it definitely keeps the notion of thinglike transcendence which the reduction to real (reell) immanence in experience is meant to exclude. It is well to maintain a conscious association of + +the real with the thinglike. + +27 We have here a case of 'foundation' in the strict sense of our Third Investigation. + +We only use the term in this strict sense. + +28 Investigation I, §§9, 10. + +29 Cf. §1O. + +30 We encountered this fact in criticizing the prevailing theory of abstraction. See + +Inv. II, §22. + +31 Cf. the Appendix to this chapter. + +32 Confusion results from unavoidable ambiguities in talk of the definite and the indefinite. One speaks, e.g., of the indefiniteness of perceptual judgements, which consists in the fact that the rear side of a perceived object is subsidiarily meant, but indefinitely, whereas the clearly seen front side seems definite. Or one speaks of the indefiniteness of 'particular' assertions, e.g. An A is B, Some A's are B's, as opposed to the definiteness of the singular assertion 'This A is B' . Such definite- + +nesses and indefinitenesses differ in sense from those in the text: they belong among the particularities of possible 'matters', as will be plainer in what follows. 33 One constantly notices that all the empirical psychological aspects of the examples fall out and become irrelevant with the ideational grasp of the + +phenomenological difference of essence. + +34 Cf. §§ 17, 30. + +35 For the moment we permit ourselves this improper mode of expression, which in + +its proper interpretation assorts ill with the image-theory. + +36 Which does not mean, we must repeat, that the object is noticed, or that we are thematically occupied with it, though such things are included in our ordinary + +talk about 'referring'. + +3 The matter of the act and its underlyin g presentation I At the time, of course, of the appearance of this work's First Edition. + +2 'Mere' presentations, we iterate, as opposed to acts of belief How the sense of Brentano's proposition stands up to changes in our concept of presentation will + +be thoroughly investigated in the next two chapters. + +3 See Inv. III, §§4 jJ. + +4 I have here ignored the disputed sub-species of Affirmative and Negative Judgement. If anyone accepts them he can everywhere substitute 'Affirmative Judgement' for 'Judgement' in the present discussion, while those who reject them, may take our words as they stand. It makes no essential difference to our + +argument. + +5 Cf. my Ideas, Book I, Section 3, §109. A deeper knowledge of the peculiarity of 'qualitative modification' ('neutrality-modification') requires extensions of the doctrine of act-quality. These leave the essential content of our discussions in this chapter untouched, but involve a partial reinterpretation of their outcome. + +4 Study of fo undin g presentations with special re gard to the + +theory of jud gement + +Conjunctive or disjunctive plurality on the subject side, as illustrated by 'A and B are P', 'A or B is P' are therefore excluded. We may also say: the subject-function is as such singular, while predication is not plural in a wider sense of the word. 2 Here we have, in a pure logico-grammatical context, a certain sort of significant + +modification grounded in the pure essence of Meaning (cf. Inv. IV). + +3 See Inv. IV, §1 l, and the additional note to §13. + +5 Further contri butions to the theory of jud gement. + +'Presen tati on' as a qual itatively unitary genus of nomi nal and + +propositional acts I Cf. the examples in §34. + +2 It must be noted that this mode of expression is a circumlocution. 3 [§38, from this point onwards, is mainly a Second Edition supplement.] 4 All this must of course not be understood in an empirical-psychological manner. We are concerned here (as everywhere in this investigation) with a priori possibilities rooted in pure essence, which are as such grasped by us with apodictic + +5 Cf. however the interpretation of a 'community of kind' as a peculiar relation of 'essence and counter-essence' in my Ideas, p. 233. The further pursuit of the + +4 Consistency and inconsistency + +Understanding of the analytical clarifications attempted in this chapter and the next, and assessment of their possible achievements, depends entirely on keeping the strict concepts hitherto elaborated firmly in mind, and not letting the vague + +ideas of popular speech take their place. + +5 The ideal of ad equati on. Se lf-evidence and truth + +1 Cf. §23 . + +Second section: Sense and understan ding + +6 Sensuous and cate gorial in tuitions + +Thus we read in Sigwart (Logic, I (ed. 2), p. 206): 'The verbal conjoining of sentences through "and" ... expresses only the subjective fact of their coexistence in one conciousness, and it therefore has no objective meaning.' Cf. also + +p. 278. + +2 It was precisely this question: how estimates of plurality and number are possible at a glance, and may therefore be achieved in straightforward, and not in founded intuition, while true collection and counting presuppose articulated acts of higher order - it was this question that independently led me to take note of those intuitively unifying characters which v. Ehrenfels called 'Gestalt-qualities', and which he dealt with in a penetrating manner in a work which appeared before mine, and which was dominated by quite different points of view. ('Uber GestaltqualiHiten', Viertelj. f wiss. Philosoph ie, 1890. Cf. my Philosophie der Arithmetik, + +ch. XI.) + +7 A Study in categorial rep resentation + +If a represents the constitutive features in a concept and f3 those of any other concept whatever, one can always construct the form: Something that is either a or f3. This external sort of conceptual extension which I call 'disjunctive', can at times prove very useful. It plays, e.g., an important role in the development of artificial mathematical techniques not sufficiently appreciated by logicians. The logic of mathematics is in fact in its infancy: few logicians have even seen that here is a field of great problems, fundamental for the understanding of mathematics and of mathematicizing natural science, and admitting of strict solution + +despite all their difficulty. + +2 See §55. + +3 Naturally not in particular kinds of such contents but in the total genus of such + +contents as such. + +Appendix: External and in ternal perception: physical and + +psych ical phenomena + +It is remarkable that no one has tried to found a positive determination of 'physical phenomena' on these intuitive interconnections. In pointing to them, I depart from my role as a reporter. To employ them seriously, one must, of course, have due regard to the ambiguity of talk about 'physical phenomena', an + +2Brentano (Psychologie, I, pp. 11 8 f) says it is a distinguishing mark of all psychic phenomena 'that they are only perceived in an inner consciousness, whereas outer perception alone is possible in the case of physical phenomena' . It is emphatically said on p. 11 9 that this determination characterizes psychic phenomena adequately. 'Inner consciousness' is here merely another expression for inner + +perception. + +3 Up to the positive mark of physical phenomena given in 2 above. I hope, further, to have achieved accuracy in restating the main points of view which have been + +governing factors in the doctrines of the thinkers I value so highly. + +4 Locke's Essay, II. i. 19. Locke is not perfectly consistent in so far as he expressly makes 'perception' an apprehension of ideas, and yet makes the apprehension of the ideas of mental activities depend on special acts of reflection, that only at times supervene on these activities. This is obviously due to the wretched dual concept 'idea' which promiscuously covers the presentations of contents that may be experienced, and also the experienced contents themselves. See our Inv. II, §1O. 5 Criticism, as it strikes me, generally stops at the first provisional theses of Brentano - psychology as a science of psychic phenomena, natural science of physical phenomena - without thinking of the 'tacit limitations' which Brentano himself expounded with characteristic clarity and acuteness. I have been all the more + +happy, therefore, to recall them by the full citations given above. + +6 Brentano understands by 'sensations' acts of sensing, and opposes them to sensed contents. In our mode of speech, as expounded above, no such distinction obtains. We call 'sensations' the mere fact that a sense-content and, further, that a non-act in general, is present in the experiential complex. In relation to appearing, talk of 'sensing' only serves to point to the apperceptive function of such contents (that they function as bearers of an interpretation, in which the appearance + +in question is carried out perceptually or imaginatively). + +7 Cf. Brentano, loco cit. §7, p. 120. In detailed examples he says: 'Knowledge, joy, desire, exist actually, colour, tone, warmth only phenomenally and intentionally.' On p. 104 he lists as examples of physical phenomena: 'A figure, landscape that I + +see . . . warmth, cold, smell that I sense.' + +In dex + +a priori 9, 11 , 39-41, 70-1, 122, 126, 129, 154, 172, 186, 203, 229, 277, 288, 311, 343; analytic/synthetic laws 19, 21; existence 22-3; laws 17, 49, 61-4, 66, 69, 71-4; proof 25; truth 55; whole/part relationship 27 abbreviated expressions 56-8 abstract 10, 17, 29, 40, 41, 88, 137, + +298 + +abstraction 39, 292, 306-7 absurdity 67-8, 71-4, 76, 223, 266 + +acceptance 140-3 + +act-character 80, 96, 102, 103, 105, 11 9-22, 134-5, 137, 164, 201, 202, + +284, 285 + +act-quality 122, 129, 144, 145, 146, 149, + +151, 169-70, 184 + +acts 59, 80, 90, 93, 96-7, 100-12, 114-19, 137, 140, 146-9, 151, 167, 183, 222-3, 285-9, 306, 309, 323, + +332, 344, 348 + +adequate, adequation 246-9, 261, 263-6, 272, 292-3, 294, 302, 310, 313-16, 318, 325-7, 346-7 adjectival presentation 69 aesthetic intention 96 affirmation 167 aggregate 39 + +agreement 213, 225, 324 + +ambiguity 158, 17 1-4, 197, 343, 344, + +345, 347-8 + +analytic: laws 19-21, 72; propositions + +21 + +apodictic 12, 62, 67, 136 apophantic logic 72 + +appearance 83-4, 341-3 apperception 103, 105, 243 Aristotle 76, 325, 327, 328 arithmetic 65, 154, 307 articulated objects 5 assent 140-3 + +assertion 68, 139, 147-9, 155-7, 158, 160, 226, 262-3, 293, 334 + +association 18, 32-4 attention 103, 11 6-19 attribution 153, 273 + +authentic 186, 312-14, 316, 324; contents 298-9; illustration 23 1-3; presentation 60-1; thinking 308-1 1 + +being 265-6, 278-80, 294 being-in-consciousness 91-3 belief 130, 164, 166 Berkeley, G. 5-6 Bocklin, A. 348 Bolzano, B. 54, 325 boundaries 16, 45, 73 + +Brentano, F. 28, 54, 87, 94-8, 102, 107, 11 0, 129-30, 160, 169, 339-40, 344, + +345, 348 bundle theory 101 + +categorematic expressions 54, 58 categorial, acts 185-6, 286-9, 295-6, 299-300, 306; content 298-9; form 37, 60, 12 1-2, 185, 271-6, 280-1, 29 1, 296-7, 307-8, 310, 31 1, 317; ideas 69; intuition 280-1, 310; laws 308-1 1; meaning 312; objective correlates 277-8; objects 304; + +perception 28 1-3; predicate 37, 11 5-16; structures 70-1; unity 38-9 categories 19, 70, 278-80, 304, 306-7; formal-logical 21; semantic 62-3 + +causation 19, 45, 108-9 class-concept 205 classification 20 1-2, 205 coincidence 199, 208, 22 1, 232 + +collectiva 29 1-2 communication 327-32 + +compatibility 67-8, 252-6, 31 2, 315 + +completeness 246-9, 261 + +complexity 11 5-19, 130-1 , 168-9, 229; defined 4; of expressions 53-5; of + +meaning 50-5 + +concatenation of association 33-4 concept 69, 76, 172, 173, 175, 184, 279, + +290-2, 306-7 + +concrete 10, 16-17, 24, 83, 88; acts 59, 172; complex 51-3; experience 145; + +temporal 43; whole 286 concretum, proximate/absolute 29 conflict 21 1-12, 213, 225, 253-7 + +connection 296, 301 + +consciousness 80, 87-9, 98, 100-1 , 103-4, 105-6, 126, 129, 138, 146, 158, 174, 206-8, 244-5, 30 1, 303, 309, 315, 339-40, 343; experience 82-4, 85-6; inner 86-7; stream of 22-3; varied ambiguity of term 81-2 content 5-7, 22, 80, 81, 85-6, 93, 103-4, 106, 132-3, 13 5, 145, 175-6, 209, 235, 246, 297, 304, 311, 344-5; by itself 10-1 1, 16; of consciousness 11 9; incompatible 253-4; inseparable 6-7; intuitively emphatic/blended 13-15; nature of 9-10; plurality + +37-8 + +defective expressions 56-8 Descartes, R. 90, 335, 337 description 15, 17, 112-13 determination 10-1 3, 197 discontinuity 14, 15-16 disjunctiva 29 1-2, 323 + +ego 82-6, 88-9, 91-3, 98, 100-1 , 125, + +164, 340, 343 + +Ehrenfels, C. von 8, 176 + +emotion 96 empiricism 43 + +epistemology 91, 136, 295 + +equivalence 154 + +essence 9, 43, 64-7, 74, 76, 96, 122-5, 129, 130-1 , 154, 158, 183-4, 246, + +250; exact/inexact 15 + +essentia 253 ethics 136 events 82 exclusion 214 + +existence 21, 22-4, 36, 37, 68, 11 3, 164 + +expectation 21 1 + +experience 6, 52, 82-4, 93, 101-6, 136-7, 145, 147, 201, 279, 329-30, 333, 342, 346; consciousness/content relation 85-6; phenomenological/ + +popular concept 84-5 + +expression 50, 55-8, 11 7, 19 1-5, 223, 272, 274, 312, 316, 323-4, 325-6, 330, 333-4; acts 192-5; complex 53-5; modification of meanings 64-7; + +percept 195-6; unity 206-8 + +extension 7-8, 18, 30 + +external: perception 95, 335-9, 340-1, 342, 345; relations 288-9, 290 + +facts 155, 343 + +falsehood 266, 329, 334 feeling 107-9; sensations/acts distinction 109-12 + +form 5, 8, 22, 36, 68-71, 272, 296-7, + +305-8 formal laws 72 formality 21, 39-41, 49 + +foundation 34-5, 36-9, 40, 44; concept 25-7; mediate/immediate 28; reciprocal/one-sided 27-8 + +founded: acts 11 5-16, 286-9, 295, 303; contents 58-60; object 308 fragmentation 40, 42, 44 + +frustration 21 1-12, 21 3-14, 217, 266 fulfilment 60-1, 79, 184, 195, 198, 210-1 1, 215, 216-18, 22 1, 226-9, 245-6, 259-63, 27 1-3, 278-80, 295, 306, 312, 324; graded 238-40; mediate 229-30; unity 209-10 + +fulness 233-5, 240-2, 259, 299, 324; + +gradations 234-8 + +fusion 15-17 + +generality of words 202-6 + +genus 12 + +grammar 49, 54-5, 64, 66, 325-7; of + +pure logic 71-4, 75 grounded judgement 194 + +hetero-grammatical modes of + +expression 65 Hobbes, T. 90 Humboldt, W. von 76 Hume, D. 126, 174 + +hypothetical predication 11 5-16 + +Idea (ideation) 15, 97, 103, 106, 112, 136, 154, 279, 317; categorial 69; independent/non-independent 13; + +universal 43 ideal 79, 11 2, 264 + +identity 104, 123, 206-8, 215, 218, + +226-8, 285, 30 1, 303 + +illusion 137-8 image 125-7, 218-20 + +imagination 165-7, 172-4, 202, 220-2, 224, 234-8, 259, 280-1, 297 immanence 125-7, 164, 343; characters + +104; objectivity 98-100 immediate 28, 30, 32 impossibility 25 1 inclusion 214 + +incompatibility 67-8, 253-4, 257-8 independent: contents 13-15; ideas 13; meaning 55-7; relative 22-4 inner: experience 136; perception 86-7, 89, 95, 135-6, 23 1, 335-7, 339-41, + +345, 347; sense 278, 302-3 inseparability 6-7; examples 7-9; objective determination 9-10 + +insight 70, 82 + +intention 11 6, 122-5, 158, 167, 184, 210-1 1, 21 3-14, 224, 226, 233, 257 intentional: characters 104, 129; content 11 2-15; essence 122-5, 130-1, 158, 183-4; experience 93, 101-3, 147; feelings 107-12; inexistence 175; + +objects 95-100, 101-2, 11 3-15, + +118-19 intentionality 107 + +interpretation 6, 52, 103, 105, 20 1, 242-4, 272, 287, 298, 302, 343 intuition 90, 106, 11 6-17, 136, 172, 184-5, 199-200, 20 1-2, 210-1 1, 21 8-19, 226, 228-9, 233, 234-8, 242-4, 245-9, 25 1, 261, 272, 274-5, 279, 280-1 , 295, 297, 303-4, 308, 309, 313, 31 7-19, 323, 324, 333, 344; complete/mutilated 246-9; genuine + +23 1-3; universal 292-4 intuitive separation 13-15 isolability 9; mutual 28 + +judgements 54, 76, 89, 96, 114, 11 7, 123, 125, 130, 13 1-2, 135, 139-40, 141-3, 146-57, 158, 160, 166-7, 192, 193, 194, 256-7, 267, 274, 278-80, 312-13, 324, 326-7, 328-9, 332-4, + +345 + +Kant, I. 21, 126, 318-19 knowing 204, 205, 216-18, 323 knowledge 226-8, 246, 273, 275, 308, + +31 9, 332 + +language 54-5, 64 + +laws 12, 43, 59, 72, 313-16, 343; categorial 308-1 1; compounding of meanings 68-71; governing combinations of meanings 61-4; material/formal dist.inction 19-20; multiplicity 17-18; nonsense/ absurdity 71-4; of thought 308-14 + +likeness 21 9-20, 222, 299 + +Locke, J. 90, 174, 278, 335-6, 340 logic 49, 75-6, 174, 316-17 logico-grammatical, compatibility 252-3; forms 68-71; laws 162, 313, + +314-16 + +manifolds 106, 29 1, 307 many-rayed acts 161 + +material, acts 159-62; forms 63; + +moments 60 mathematics 307 + +matter 119-22, 128-9, 133-4, 137-9, 140-1, 158-9, 164, 166, 171, 175, 184, 226, 250, 272, 276; fulness/ intentional 240-2; interpretative 242-4; isolated 144-5; as presentation 129-3 1 meaning-fulfilment 184, 19 1-2 meaning-intention 61, 79, 174, 184, 19 1-2, 207, 214, 217, 250, 273, + +276 + +meaning(s) 49, 132, 184, 196-201, 208, 222-5, 272-3, 312, 313-14, 315, 323, 334; combinations 61-4, 67-8; complex 50-5; compounding 68-71; implied 51-3; incompatible 257-8; independent/non-independent 55-7; modifications 64-7; simple 50 mediate 28, 30, 32, 229-3 1 + +Meinong, A. 8 memory 104, 172 + +mental: acts 80, 81, 94; character 30 1; + +phenomena 95-7, 315 metaphysics 90, 106 Mill, J. S. 160 + +modification 71, 159-60, 162; imaginative 165-7; qualitative + +162-7 + +moment(s) 4, 12, 20, 28-9, 30, 31-2, 55, 137, 145, 277-8, 286, 333; nonindependent 36, 40-1 ; piecing of wholes 41-5; qualitative 7-8; of unity 8-9, 14, 35-8; variable 7 + +mutilated intuitions 246-9 + +names 67, 147-9, 152-3, 155-7, 192, 332; positing/non-positing 149-52, + +154, 162 + +Natorp, P. 91-2, 93, 106 natural science 89-91, 103, 338 + +nature 42, 43 near 32-4 necessity 12 + +nominal: acts 152-4, 159, 161, 169-70, 171; formations 289-9 1; meanings + +66-7; presentation 69 + +non-acts 106-12 + +non-independence 36; contents 13-15; experience 145; ideas 13; laws + +governing 17-18, 19-20; meanings 55-6, 57, 58-60; moments 40-1, 44, 55, 59; objects 12-1 3; relative 22-4 non-objectifying acts 325-7, 333 nonsense 67-8, 76, 316, 326; laws + +71-4 + +objectifying acts 158-65, 167, 169-70, 171, 216-18, 245, 250, + +275-6 objectivity 49 + +objects 125-7, 132, 201-2, 208, 277, 299-300, 332-3; complexity 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F7514 The foundations of arithmetic : a 1960 togico-mathematical enquiry into the + +concept of number / Gottlob Frege ; Translated by J» L« Austin. 2nd rev. + +ed. New York : Harper, 1960. xxiii, 119 p. ; 21 cm. (Harper torchbooks ) Translation of: Grundlagen der Arithmet ik. + +Includes bibiographical references. + +#10129 Gift \$ . . + +1. Number concept. 2. Mathematics- Philosophy. 3. Logic, Symbolic and mathematical. I. Title + +10 SEP 91 1864616 NEWCxc A62-1847 + +The + +FOUNDATIONS + +of + +ARITHMETIC + +DUE DATE + +The + +FOUNDATIONS + +of + +ARITHMETIC + +A logico-mathematical enquiry into the concept of number + +GOTTLOB FREGE + +Translated by J. L. Austin + +Second Revised Edition + +i + +HARPER TORCHBOOKS /The Scicnce Library + +HARPER if BROTHERS, NEW YORK + +THE FOUNDATIONS OF ARITHMETIC Printed in the United States of America + +This volume was first published in 1950 by Basil Blackwell & Mott, Ltd. The revised edition of 1953 is here reprinted by arrangement. + +V First Harper Torchbook edition published 1960 + +Translator's Note + +Words and footnotes in square brackets are insertions by the translator. The pagination of the German text is the same as in the original German edition, except that in the original the "Analysis of Contents" pages were + +not numbered. + +Some of Frege's references and quotations, which are not always accurate, + +have been corrected in the translated version. + +Translator''s Preface to the Second Edition Though users of the first edition of this version will perhaps not be anywhere seriously misled in doctrine, a large number of passages in it have called, and some even howled, for improvements in fidelity or lucidity. The translator's thanks are due to several readers, and in particular to Mr. P. T. Geach, for their trouble in contributing emendations and suggestions: nothing could be more + +welcome than more of the same. + +There isjustice in the general criticism that the version is too long. Here and there it has been possible to do something to correct this, but itis too late and too difficult now to strike a fresh compromise throughout between the claims of brevity and those of naturalness and clarity. Frege is an unusually, even at times an unduly, succinct writer, and the German text must be allowed to remain the + +final testimony to his style. + +The translations originally chosen for Frege's principal terms remain unchanged, except that Begrijfsrvort has now become "concept word" instead of "general term" and rvirklicb "actual" instead of "existent." Critics of some others of these translations have perhaps not sufficiently realized that Frege's inherited philosophical vocabulary (at least as he was using it at this period) is a dated one. It is that which was Englished by his contemporaries, the "British Idealists":' and they certainly used, for example, "idea" for Vorstellung and "proposition" for Sat':^ though not unnaturally they attached to those words meanings different from (and doubtless less clear than) those fashionable half a century later. Frege's thought cannot be reproduced accurately, nor can his terms be translated consistently, unless we are prepared to accept, even in him, + +something short of complete (or contemporary) sophistication. + +Analysis of Contents. + +j I + +. Recent work in mathematics has shown atendency towards rigour + +ofproofand sharp definition of concepts + +§ 2. This critical examination must ultimately extend to the concept + +of Number itself. The aim of proof + +§ 3. Philosophical motives for such an enquiry: the controversies as to whether the laws of number are analytic or synthetic, a priori or + +a posteriori. Sense of these expressions .... § 4. Task of the present work + +I. Views of certain writers on the nature of arithmetical propositions. + +Are numericalformulae provable? + +§ 5- Kant denies this, which Hankel justly calls a paradox + +§ 6. Leibniz's proof that 2 + 2 = 4 contains a gap. Grassmann's + +definition of <7 + i is faulty + +§ 7. Mill's view that the definitions of the individual numbers assert observed facts, from which the calculations follow, is without foundation ...... § 8. These definitions do not require, for their legitimacy, the obser- vation of his facts + +§ 24. Wide range of applicability of number. Mill. Locke. Leibniz's immaterial metaphysical figure. If number were something sensible, it could not be ascribed to anything non-sensible , . 30 + +§ 25. Mill's physical difference between 2 and j. Number according + +to Berkeley not really existent in things but created by the mind. 52 + +Is number something subjective? § 26. Lipschitz's description of the construction of numbers will not do, and cannot take the place of a definition of the concept. Number not an object for psychology, but something objective 33 + +§ 27. Number is not, as Schloemilch claims, the idea of the position + +of an item in a series ........ 36 + +The set theory of Number. 28. Thomae's name-giving . . . . . . .58 + +> III. Views on unity and one. Does the number word "one" express a property of objects? + +§ 29. Ambiguity of the terms "iLova^" and "unit". E. Schroder's definition of the unit as an object to be numbered isapparently pointless. The adjective "one" does not add anything to a + +description, cannot serve as a predicate . . . . -39 + +§ 30. Attempts to define unity by Leibniz and Baumann seem to blur + +the concept completely . . . . . . .41 + +§ 31. Baumann's criteria, being undivided and being isolated. The + +notion of unity not suggested to us by every object (as Locke) . 41 + +§ 32. Still, language does indicate some connexion with being un- + +divided and isolated, with a shift of meaning however . . 42 § 33. Indivisibility (G. Kopp) as a criterion of the unit is untenable . 43 + +Are units identical with one another} § 34. Identity as the reason for the name "unit". E. Schroder. Hobbes. Hume. Thomae. To abstract from the differences between things does not give us the concept of their Number, nor does it make the things identical with one another . . 44 + +§ 35. Indeed diversity is actually necessary, if we arc to speak of + +plurality. Descartes. E. Schroder. W. S.Jevons ... 46 + +§ 56. The view that units are different also comes up against difficulties. + +Different distinct ones in W. S.Jevons 46 + +§ 37. Definitions of number in terms of the xmit or one by Locke, + +Leibniz and Hesse ........ 48 + +§ 38. "One" isa proper name, "unit" a concept word. Number + +cannot be defined as units. Distinction between "and" and + . 48 + +§ 39. The difficulty of reconciling identity of units with distinguish- + +ability is concealed by the ambiguity of "unit" . ... 50 + +§ 40- + +§ 41- § 42- + +§ 43. § 44. + +Attempts to overcome the difficulty. Space and time as means of distinguishing between units. Hobbes. Thomae. Against them: Leibniz, Baumann, W. S. + +Jevons . . . . . • • • • -5^ The purpose not achieved -55 + +Position in a series as a means of distinguishing between units. Hankel's putting 54 Schroder's copying of objects by the symbol i . . '54 + +Jevons' abstraction from the character of the differences while retaining the fact of their existence, o and i are numbers like the rest. The difficulty still remains J 5 + +Solution of the difficulty. + +% 45. Recapitulation .... + +§ 46. A statement of number contains an assertion about a concept Objection that the number varies while the concept does not § 47. That statements of number are statements of fact explained by + +the objectivity of concepts . § 48. Removal of certain difficulties § 49. Qjrroboration found in Spinoza . § 50. E. Schroder's account quoted § 51. Correction of the same + +§ J 2. Corroboration found in a German idiom + +§ 53. Distinction between component characteristics of a concept and + +its properties. Existence and number + +§ 54. Unit the name given to the subject of a statement of number, How indivisible and isolated. How identical and distinguish + +able + +58 + +64 + +65 + +IV. The concept of Number. + +Etie/y individual number is a self-subsistent object. + +§ 5 J + +. Attempt to complete the definitions of the individual numbers + +as given by Leibniz ........ 67 + +§ 56. The attempted definitions are unusable, because what they + +define is a predicate in which the number is only an element . 67 + +§ 57. A statement of number should be regarded as an identity + +between numbers ........ 68 + +§ J 8. Objection that we can form no idea of number as a self-subsistent + +object. In principle number cannot be imagined ... 69 + +§ 59. Because we cannot imagine an object, we are not to be debarred + +from investigating it ........ 70 + +\$ 60. Even concrete things are not always imaginable. In seeking the meaning of a word, we must consider it in the context of a + +proposition. ......... 71 + +§ 61. Objection that numbers are not spatial. Not every objective + +object is spatial 72 + +To obtain the concept of Number, we must fix the sense of a numerical identity. + +§ 62. We need a criterion for numerical identity .... 73 + +§ 63. Possible criterion in one-one correlation. Doubt as to the logic + +of defining identity specially for the case of numbers . . 73 + +S 64. Examples of similar procedures: direction of a line, orientation + +of a plane, shape of a triangle ...... 74 + +% 6;. Attempt at a definition. A second doubt: are the laws of identity + +satisfied? 76 + +S + +66. Third doubt: the criterion of identity fails to cover all cases . 77 § 67. We cannot supplement it by taking as a defining characteristic + +of a concept the way in which an object is introduced . . 78 S 68. Number as the extension of a concept ..... 79 § 69. Elucidation ......... 80 + +Our definition completed and its worth proved. § 70. The relation-concept . . . . . . . .81 § 71. Correlation by means of a relation 83 § 72. One-one relations. The concept of Number .... 84 + +§ 94. That a concept is free from contradiction is no guarantee that + +anything falls under it, and itself requires to be proved . .105 + +§ 95. We cannot regard {c—b) without more ado as a symbol which + +solves the problem of subtraction + +§ 96. Not even the mathematician can create things at will § 97. Concepts are to be distinguished from objects + +§ 98. Hankel's definition of addition .... § 99. The formalist theory defective .... § loo. Attempt to produce an interpretation of complex numbers by + +extending the meaning of multiplication in some special way .1 10 + +§ loi. The cogency of proofs is affected, unless it is possible to produce + +such an interpretation . . . . . . . .111 + +§ 102. The mere postulate that it shall be possible to carry out some + +operation is not the same as its own fulfilment. . . . 11 + +§ 103. Kossack's definition of complex numbers is only a guide towards a definition, and fails to avoid the importation of foreign elements. Geometrical representation of complex numbers . 112 + +§ 104. What is needed is to fix the sense of a recognition-judgment for + +the case of the new numbers + +. . . . . .114 + +§105. The charm of arithmetic lies in its rationality . . . • "5 § 106-109. Recapitulation . . . . . . .115-119 + +INTRODUCTION + +When we ask someone what the number one is, or what the symbol i means,\* we get as a rule the answer "Why, a thing". And if we go on to point out that the proposition "the number one is a thing" is not a definition, because it has the definite article on one side and the indefinite on the other, or that it only assigns the number one to the class of things, without stating which thing it is, then we shall very likely be invited to select something for ourselves—anything we please—to call one. Yet if everyone had the right to understand by this name whatever he pleased, then the same proposition about one would mean different things for different people,—such propositions would have no common content. Some, perhaps, will decline to answer the question, pointing out that it is impossible to state, either, what is meant by the letter a, as it is used in arithmetic; and that if we were to say "<2 means a number," this would be open to the same objection as the definition "one is a thing." Now in the case of a it is quite right to decline to answer: a does not mean some one definite number which can be specified, but serves to express the generality of general propositions. If, in ^ + ^ — a = a, we put for a + +\* [I have tried throughout to translate Bedeutung and its cognates by "meaning" and Sinn and its cognates by "sense", in view of the importance Frege later attached to the distinction. But it is quite evident that he attached no + +special significance to the words at this period.] + +XIV some number, any we please but the same throughout, we get always a true identity.\* This is the sense in which the letter a is used. With one, however, the position is essentially dif ferent. Can we, in the identity 1 + 1 = 2, put for i in both places some one and the same object, say the Moon? On the contrary, it looks as though, whatever we put for the first i, we must put something different for the second. Why is it that we have to do here precisely what would have been wrong in the other case? Again, arithmetic cannot get along with a alone, but has to use further letters besides (^, c and so on), in order to express in general form relations between different numbers. It would therefore be natural to suppose that the symbol i too, if it served in some similar way to confer generality on propositions, could not be enough by itself. Yet surely the number one looks like a definite particular object, with properties that can be specified, for example that of remaining unchanged when multiplied by itself? In this sense, a has no properties that can be specified, since whatever can be asserted of tf is a common property of all numbers, whereas i^ = i asserts nothing of the Moon, nothing of the Sun, nothing of the Sahara, nothing of the Peak of Teneriffe; for what could be + +the sense of any such assertion? + +Questions like these catch even mathematicians for that matter, or most of them, unprepared with any satisfactory answer. Yet is it not a scandal that our science should be so unclear about the first and foremost among itsobjects, and one which is apparently so simple? Small hope, then, that we shall be able to say what number is.If a concept fundamental to a mighty science gives rise to difficulties, then it is surely an imperative task to investigate it more closely until those difficulties are overcome; especially as we shall hardly succeed in finally clearing up negative numbers, or fractional or complex numbers, so long as our insight into the foundation + +of the whole structure of arithmetic is still defective. + +\* [Gleichung. This also means, and would often be more naturally translated, "equation". But I have generally retained "identity", because this is sometimes essential and because Frege does understand equations as identities. For similar reasons I have translated gleich "identical", though it can mean + +"equal" or even merely "similar". Cp. §§ 34, 65.] + +XV Many people will be sure to think this not worth the trouble. Naturally, they suppose, this concept is adequately dealt with in the elementary textbooks, where the subject is settled once and for all. Who can believe that he has anything still to learn on so simple a matter? So free from all difficulty is the concept of positive whole number held to be, that an account of it fit for children can be both scientific and exhaustive; and that every schoolboy, without any further reflexion or acquaintance with what others have thought, knows all there is to know about it. The first prerequisite for learning anything is thus utterly lacking—I mean, the knowledge that we do not know. The result is that we still rest content with the crudest of views, even though since Herbart's^ day a better doctrine has been available. It is sad and discouraging to observe how discoveries once made are always threatening to be lost again in this way, and how much work promises to have been done in vain, because we fancy ourselves so well off that we need not bother to assimilate its results. My work too, as I am well aware, is exposed to this risk. A typical crudity confronts me, when I find calculation described as "aggregative mechanical thought".^ I doubt whether there exists any thought whatsoever answering to this description. An aggregative imagination, even, might sooner be let pass; but that has no relevance to calculation. Thought is in essentials the same everywhere: it is not true that there are different kinds of laws of thought to suit the different kinds of objects thought about. Such differences as there are consist only in this, that the thought is more pure or less pure, less dependent or more upon psychological influences and on external aids such as words or numerals, and further to some 1 Collected Works, ed. Hartenstein, Vol. X, part i, Umriss pddagopscber Vorlesungen, § 252, n. 2: "Two does not mean two things, but doubling" etc. 2 K. Fischer, System der 'Logik und Metaphjsik oder Wissenschaftslehre, 2nd edn., + +§94- + +XVI extent too in the finer or coarser structure of the concepts involved; but it is precisely in this respect that mathematics + +aspires to surpass all other sciences, even philosophy. + +The present work will make it clear that even an inference like that from n to n -\- i, which on the face of it is peculiar to mathematics, is based on the general laws of logic, and that there is no need of special laws for aggregative thought. It is possible, of course, to operate with figures mechanically, just as it is possible to speak like a parrot: but that hardly deserves the name of thought. It only becomes possible at all after the mathematical notation has, as a result of genuine thought, been so developed that it does the thinking for us, so to speak. This does not prove that numbers are formed in some peculiarly mechanical way, as sand, say, is formed out of quartz granules. In their own interests mathematicians should, I consider, combat any view of this kind, since it is calculated to lead to the disparagement of a principal object of their study, and of their science itself along with it. Yet even in the works of mathematicians are to be found expressions of exactly the same sort. The truth is quite the other way: the concept of number, as we shall be forced to recognize, has a finer structure than most of the concepts of the other sciences, even although it is still one of the simplest in arith- + +metic. + +In order, then, to dispel this illusion that the positive whole numbers really present no difficulties at all, but that universal concord reigns about them, I have adopted the plan of criticiz ing some of the views put forward by mathematicians and philosophers on the questions involved. It will be seen how small is the extent of their agreement—so small, that we find one dictum precisely contradicting another. For example, some hold that "units are identical with one another," others that they are different, and each side supports its assertion with arguments that cannot be rejected out of hand. My object in this is + +XVll to awaken a desire for a stricter enquiry. At the same time this preliminary examination of the views others have put forward should clear the ground for my own account, by convincing my readers in advance that these other paths do not lead to the goal, and that my opinion is not just one among many all equally tenable; and in this way I hope to + +settle the question finally, at least in essentials. + +I realize that, as a result, I have been led to pursue arguments more philosophical than many mathematicians may approve; but any thorough investigation of the concept of number is bound always to turn out rather philosophical. It is a task + +which iscommon to mathematics and philosophy. + +It may well be that the co-operation between these two sciences, in spite of many demarches from both sides, is not so flourishing as could be wished and would, for that matter, be possible. And if so, this is due in my opinion to the pre dominance in philosophy of psychological methods of argument, which have penetrated even into the field of logic. With this tendency mathematics is completely out of sympathy, and this easily accounts for the aversion to philosophical arguments felt by many mathematicians. When Stricker,^ for instance, calls our ideas\* of numbers motor phenomena and makes them dependent on muscular sensations, no mathematician can recognize his numbers in such stuff" or knows where to begin to tackle such a proposition. An arithmetic founded on muscular sensations would certainly turn out sensational enough, but also every bit as vague as its foundation. No, sensations are absolutely no concern of arithmetic. No more are mental pictures, formed from the amalgamated traces of earlier sense-impressions. All these phases of consciousness are characteristically fluctuating and indefinite, in strong contrast to the definiteness and fixity of the concepts and objects of + +^ Studien iiber Association der Vorstellungen, Vienna i88;. + +\* [Vorste/Iungen. I have translated this word consistently by "idea", and cognate words by "imagine", "imagination", etc. For Frege it is a psychological + +term, cp. p. xe below.] + +XVUl mathematics. It may, of course, serve some purpose to investi gate the ideas and changes of ideas which occur during the course of mathematical thinking; but psychology should not imagine that it can contribute anything whatever to the foundation of arithmetic. To the mathematician as such these mental pictures, with their origins and their transformations, are immaterial. Stricker himself states that the only idea he associates with the word "hundred" isthe symbol loo. Others may have the idea of the letter C or something else; does it not follow, therefore, that these mental pictures are, so far as concerns us and the essentials of our problem, completely immaterial and incidental—as incidental as chalk and blackboard, and indeed that they do not deserve to be called ideas of the number a hundred at all? Never, then, let us suppose that the essence of the matter lies in such ideas. Never let us take a description of the origin of an idea for a definition, or an account of the mental and physical conditions on which we become conscious of a proposition for a proof of it. A proposition may be thought, and again it may be true; let us never confuse these two things. We must remind ourselves, it seems, that a proposition no more ceases to be true when I cease to think of it than the sun ceases to exist when I shut my eyes. Otherwise, in proving Pythagoras' theorem we should be reduced to allowing for the phosphorous content of the human brain; and astronomers would hesitate to draw any conclusions about the distant past, for fear of being charged with anachronism,—with reckoning twice two as four regardless of the fact that our idea of number isa product of evolution and has a history behind it. It might be doubted whether by that time it had progressed so far. How could they profess to know that the proposition 2x2=4 was already in existence in that remote epoch? Might not the creatures then extant have held the pro- + +position 2x2 = 5,from which the proposition 2x2=4 + +was only evolved later through a process of natural selection + +XIX in the struggle for existence? Why, it might even be that 2X2=4 itself is destined in the same way to develop into 2 X 2 = 3! Esf modus in rebusy sunt certi denique fines\ The historical approach, with its aim of detecting how things begin and of arriving from these origins at a knowledge of their nature, is certainly perfecdy legitimate; but it has also its limitations. If everything were in continual flux, and nothing maintained itself fixed for all time, there would no longer be any possibility of getting to know anything about the world and everything would be plunged in confusion. We suppose, it would seem, that concepts sprout in the individual mind like leaves on a tree, and we think to discover their nature by studying their birth: we seek to define them psychologically, in terms of the nature of the human mind. But this account makes everything subjective, and if we follow it through to the end, does away with truth. What is known as the history of concepts is really a history either of our knowledge of concepts or of the meanings of words. Often it is only after immense intellectual effort, which may have continued over centuries, that humanity at last succeeds in achieving knowledge of a concept in its pure form, in stripping off the irrelevant accretions which veil it from the eyes of the mind. What, then, are we to say of those who, instead of advancing this work where it is not yet completed, despise it, and betake themselves to the nursery, or bury themselves in the remotest conceivable periods of human evolution, there to discover, like John Stuart Mill, some gingerbread or pebble arithmetic! It remains only to ascribe to the flavour of the bread some special meaning for the concept of number. A procedure like this is surely the very reverse of rational, and as unmathematical, at any rate, as it could well be. No wonder the mathematicians turn their backs on it.Do the concepts, as we approach their supposed sources, reveal themselves in peculiar purity? Not at all; + +we see everything as through a fog, blurred and undifferentiated. It is as though everyone who wished to know about America were to try to put himself back in the position of Columbus, at the time when he caught the first dubious glimpse of his supposed India. Ofcourse, a comparison like this proves nothing; but it should, I hope, make my point clear. It may well be that in many cases the history of earlier discoveries is a useful study, as a preparation for further researches; but it + +should not set up to usurp their place. + +So far as mathematicians are concerned, an attack on such views would indeed scarcely have been necessary; but my treatment was designed to bring each dispute to an issue for the philosophers as well, as far as possible, so that I found myself forced to enter a little into psychology, if only to repel + +its invasion of mathematics. + +Besides, even mathematical textbooks do at times lapse into psychology. When the author feels himself obliged to give a definition, yet cannot, then he tends to give at least a description of the way in which we arrive at the object or concept concerned. These cases can easily be recognized by the fact that such explanations are never referred to again in the course of the subsequent exposition. For teaching purposes, introductory devices are certainly quite legitimate; only they should always be clearly distinguished from definitions. A delightful example of the way in which even mathematicians can confuse the grounds of proof with the mental or physical conditions to be satisfied if the proof is to be given is to be found in E. Schroder.! Under the heading "Special Axiom" he produces the following: "The principle I have in mind might well be called the Axiom of Symbolic Stability. It guarantees us that throughout all our arguments and deductions the symbols + +^ Lehrbucb der Arithmttlk und Algebra, [Leipzig 1873]. + +XXI remain constant in our memory—or preferably on paper," + +and so on. + +No less essential for mathematics than the refusal of all assistance from the direction of psychology, is the recognition of its close connexion with logic. I go so far as to agree with those who hold that it is impossible to effect any sharp separation of the two. This much everyone would allow, that any enquiry into the cogency of a proof or the justification of a definition must be a matter of logic. But such enquiries simply cannot be eliminated from mathematics, for it is only through answering them that we can attain to the necessary + +certainty. + +In this direction too I go, certainly, further than is usual. Most mathematicians rest content, in enquiries of this kind, when they have satisfied their immediate needs. If a definition shows itself tractable when used in proofs, if no contradictions are anywhere encountered, and if connexions are revealed between matters apparently remote from one another, this leading to an advance in order and regularity, it is usual to regard the definition as sufficiently established, and few questions are asked as to its logical justification. This procedure has at least the advantage that it makes itdifficult to miss the mark altogether. Even I agree that definitions must show their worth by their fruitfulness: it must be possible to use them for constructing proofs. Yet it must still be borne in mind that the rigour of the proof remains an illusion, even though no link be missing in the chain of our deductions, so long as the definitions are justified only as an afterthought, by our failing to come across any contradiction. By these methods we shall, at bottom, never have achieved more than an empirical certainty, and we must really face the possibility that we may still in the end encounter a contradiction which brings the whole edifice down in ruins. For this reason I have felt bound to go back rather further into the general logical foundations of our science than perhaps most mathematicians + +will consider necessary. + +XXll In the enquiry that follows, I have kept to three funda- + +mental principles: + +always to separate sharply the psychological from the + +logical, the subjective from the objective; + +never to ask for the meaning of a word in isolation, but + +only in the context of a proposition; + +never to lose sight of the distinction between concept + +and object. + +In compliance with the first principle, I have used the word "idea" always in the psychological sense, and have distinguished ideas from concepts and from objects. If the second principle is not observed, one is almost forced to take as the meanings of words mental pictures or acts of the individual mind, and so to offend against the first principle as well. As to the third point, it is a mere illusion to suppose that a concept can be made an object without altering it. From this it follows that a widely-held formalist theory of fractional, negative, etc., numbers is untenable. How I propose to improve upon it can be no more than indicated in the present work. With numbers of all these types, as with the positive whole numbers, it is a + +matter of fixing the sense of an identity. + +My results will, I think, at least in essentials, win the adherence of those mathematicians who take the trouble to attend to my arguments. They seem to me to be in the air, and it may be that every one of them singly, or at least something very like it, has been already put forward; though perhaps, presented as they are here in connexion with each other, they may still be novel. I have often been astonished at the way in which writers who on one point approach my + +view so closely, on others depart from it so violently. + +Their reception by philosophers will be varied, depending + +on each philosopher's own position; but presumably those + +XXlll empiricists who recognize induction as the sole original process of inference (and even that as a process not actually of inference but of habituation) will like them least. Some one or another, perhaps, will take this opportunity to examine afresh the principles of his theory of knowledge. To those who feel inclined to criticize my definitions as unnatural, I would suggest that the point here is not whether they are natural, but whether they go to the root of the matter and are + +logically beyond cridcism. + +I permit myself the hope that even the philosophers, if they examine what Ihave written without prejudice, will find + +in it something of use to them. + +§ I. After deserting for a time the old Euclidean standards of rigour, mathematics is now returning to them, and even making efforts to go beyond them. In arithmetic, if only because many of its methods and concepts originated in India, it has been the tradition to reason less strictly than in geometry, which was in the main developed by the Greeks. The discovery of higher analysis only served to confirm this tendency; for considerable, almost insuperable, difficulties stood in the way of any rigorous treatment of these subjects, while at the same time small reward seemed likely for the efforts expended in overcoming them. Later developments, however, have shown more and more clearly that in mathematics a mere moral conviction, supported by a mass of successful applications, is not good enough. Proof is now demanded of many things that formerly passed as self-evident. Again and again the limits to the validity of a proposition have been in this way established for the first time. The concepts of function, of continuity, of limit and of infinity have been shown to stand in need of sharper definition. Negative and irrational numbers, which had long since been admitted into science, have had to submit to a closer scrutiny of their + +credentials. + +In all directions these same ideals can be seen at work rigour of proof, precise delimitation of extent of validity, and + +as a means to this, sharp definition of concepts. + +§ z. Proceeding along these lines, we are bound eventually to come to the concept of Number\* and to the simplest propositions holding of positive whole numbers, which form the foundation of the whole of arithmetic. Ofcourse, numerical formulae like 7+5 = 12 and laws like the Associative Law of Addition are so amply established by the countless applications made of them every day, that it may seem almost ridiculous to try to bring them into dispute by demanding a proof of them. But it is in the nature of mathematics always to prefer proof, where proof is possible, to any confirmation by induction. Euclid gives proofs of many things which any one would concede him without question. And it was when men refused to be satisfied even with Euclid's standards of rigour that they were led to the enquiries set in train by the + +Axiom of Parallels. + +Thus our movement in favour of all possible rigour has already outstripped in many directions the demand originally raised, while the demand has itself continually grown in scope + +and urgency. + +The aim of proof is, in fact, not merely to place the truth of a proposition beyond all doubt, but also to afford us insight into the dependence of truths upon one another. After we have convinced ourselves that a boulder is immovable, by trying unsuccessfully to move it, there remains the further question, what isit that supports it so securely? The further we pursue these enquiries, the fewer become the primitive truths to which we reduce everything; and this simplification is in itself a goal worth pursuing. But there may even be justification for a further hope: if, by examining the simplest cases, we can bring to light what mankind has there done by instinct, and can extract from such procedures what isuniversally valid in them, may we not thus arrive at general methods for forming concepts and establishing principles which will be applicable + +also in more complicated cases? + +\* [Aftzab/, i.e. cardinal number, q). § 4 n. I have always used "Number" to translate this, and "number" for the more usual and general Zah/. Throughout most of the present work the distinction is not important, and Frege uses + +the two words almost indifferendy.] + +3 § 3- Philosophical motives too have prompted me to enquiries of this kind. The answers to the questions raised about the nature of arithmetical truths—are they a priori or a posteriori? synthetic or analytic?—must lie in this same direction. For even though the concepts concerned may themselves belong to philosophy, yet, as I believe, no decision on these questions can be reached without assistance from mathematics—though this depends of course on the sense + +in which we understand them. + +It not uncommonly happens that we first discover the content of a proposition, and only later give the rigorous proof of it, on other and more difficult lines; and often this same proof also reveals more precisely the conditions restrict ing the validity of the original proposition. In general, therefore, the question of how we arrive at the content of a judgement should be kept distinct from the other question. Whence do we derive the justification for its assertion? + +Now these distinctions between a priori and a posteriori, synthetic and analytic, concern, as I see it,^ not the content of the judgement but the justification for making the judgement. Where there is no such justification, the possibility of drawing the distinctions vanishes. An a priori error is thus as complete a nonsense as, say, a blue concept. When aproposition is called a posteriori or analytic in my sense, this is not a judgement about the conditions, psychological, physiological and physical, which have made it possible to form the content of the proposition in our consciousness; nor is it a judgement about the way in which some other man has come, perhaps erroneously, to believe it true; rather, it is a judgement about the ultimate ground upon which rests the justification for hold- + +ing it to be true. + +This means that the question is removed from the sphere of psychology, and assigned, if the truth concerned is a \* By this I do not, of course, mean to assign a new sense to these terms, but only to state accurately what earlier writers, Kant in particular, have meant + +by them. + +4 mathematical one, to the sphere of mathematics. The problem becomes, in fact, that of finding the proof of the proposition, and of following it up right back to the primitive truths. If, in carrying out this process, we come only on general logical laws and on definitions, then the truth is an analytic one, bearing in mind that we must take account also of all propositions upon which the admissibiUty of any of the definitions depends. If, however, it is impossible to give the proof without making use of truths which are not of a general logical nature, but belong to the sphere of some special science, then the proposition is a synthetic one. For a truth to be a posteriori, it must be impossible to construct a proof of it without including an appeal to facts, i.e., to truths which cannot be proved and are not general, since they contain assertions about particular objects. But if, on the contrary, its proof can be derived exclusively from general laws, which themselves neither need + +nor admit of proof, then the truth is a priori.^ + +§ 4. Starting from these philosophical questions, we are led to formulate the same demand as that which had arisen independently in the sphere of mathematics, namely that the fundamental propositions of arithmetic should be proved, if in any way possible, with the utmost rigour; for only if every gap in the chain of deductions is eliminated with the greatest care can we say with certainty upon what primitive truths the proof depends; and only when these are known shall + +we be able to answer our original questions. + +^ If we recognize the existence of general truths at all, we must also admit the existence of such primitive laws, since from mere individual facts nothing follows, unless it be on the strength of a law. Induction itself depends on the general proposition that the inductive method can establish the truth of a law, or at least some probability for it. If we deny this, induction becomes nothing more than a psychological phenomenon, a procedure which induces men to believe in the truth of a proposition, without affording the slightest justification + +for so believing. + +If we now try to meet this demand, we very soon come to propositions which cannot be proved so long as we do not succeed in analysing concepts which occur in them into simpler concepts or in reducing them to something of greater generality. Now here it is above all Number which has to be either defined or recognized as indefinable. This is the point which the present work is meant to settle. ^ On the outcome of this task will depend the decision as to the nature of the laws + +of arithmetic. + +To my attack on these questions themselves I shall preface something which may give a pointer towards their answers. For suppose there should prove to be grounds from other points of view for believing that the fundamental principles of arithmetic are analytic, then these would tell also in favour of their being provable and the concept of Number definable; while any grounds for believing the same truths to be a posteriori would tell in the opposite direction. The rival theories here, therefore, may well be submitted first to a + +passing scrutiny. + +I. Views of certain writers on the nature of arithmetical propositions. + +Are numericalformulae provable? + +§ 5. We must distinguish numerical formulae, such as 24-3 = 5, which deal with particular numbers, from general + +laws, which hold good for all whole numbers. + +The former are held by some philosophers^ to be un provable and immediately self-evident like axioms. Kant^ 1 In what follows, therefore, unless special notice is given, the only "numbers" under discussion are the positive whole numbers, which give the answer to the + +question "How many?". + +2 Hobbes, Locke, Newton. Cf. Baumann, Die Lebren von Zeit, Kaum md + +Mathemattk, [Berlin 1868, Vol. I], pp. 241-42, 365 ff., 475-76. [Hobbes, Examinatio et Emendatio Mathematicae Hodiernae, Amsterdam 1668, Diall. I-III, esp. I, p. 19 and III, pp. 62-63; Locke, Essay, Bk. IV, esp. Cap. iv, § 6 and cap. vii, §§ 6 and 10; Newton, Aritbmetica Universalis, Vol. I, cap. i-iii, esp. iii, n. 24.] 3 Critique of Pure Reason; Collected Works, ed. Hartenstein, Vol. Ill, p. 157 + +[Original edns. A 164/B205]. + +declares them to be unprovable and synthetic, but hesitates to call them axioms because they are not general and because the number of them isinfinite. Hankel^ justifiably calls this conception of infinitely numerous unprovable primitive truths incongruous and paradoxical. The fact is that it conflicts with one of the requirements of reason, which must be able to embrace all first principles in a survey. Besides, is it + +really self-evident that + +155664+ 57863 = 175527? + +It is not; and Kant actually urges this as an argument for holding these propositions to be synthetic. Yet it tells rather against their being improvable; for how, if not by means of a proof, are they to be seen to be true, seeing that they are not immediately self-evident? Kant thinks he can call on our intuition of fingers or points for support, thus running the risk of making these propositions appear to be empirical, contrary to his own expressed opinion; for whatever our intuition of 57863 fingers may be, it is at least certainly not pure. Moreover, the term "intuition" seems hardly appropriate, since even 10 fingers can, in different arrangements, give rise to very different intuitions. And have we, in fact, an intuition of 155664 fingers or points at all? If we had, and if we had another of 57865 fingers and a third of 175527 fingers, then the correctness of our formula, if it were unprovable, would have to be evident right away, at least as + +applying to fingers; but it is not. + +Kant, obviously, was thinking only of small numbers. So that for large numbers the formulae would be provable, though for small numbers they are immediately self-evident through intuition. Yet itis awkward to make a fundamental distinction between small and large numbers, especially as it would scarcely be possible to draw any sharp boundary between them. If the numerical formulae were provable + +^ Vorlesungen iiber die complexen Zahlen und ihren Functionen, p. 53. + +7 from, say, lo on, we should ask with justice "Why not from + +5 on? or from 2 on? or from i on?" + +§ 6. Other philosophers again, and mathematicians, have asserted that numerical formulae are actually provable. + +Leibniz^ says: + +"It is not an immediate truth that 2 and 2 are 4; provided it be granted that 4 signifies 3 and i. It can be proved, as + +follows: + +Definitions: (i) 2 is i and i + +(2) 3 is 2 and i (3) 4 is 3 and i Axiom: If equals be substituted for equals, the equality + +remains.\* + +Proof: 2 + 2 = 2+1 + 1 (by Def. i) = 3 + i (by + +Def. 2) = 4 (by Def. 3). + +.'. 2+2=4 (by the Axiom)." This proof seems at first sight to be constructed entirely from definitions and the axiom cited. And the axiom too could be transformed into a definition, as Leibniz himself does transform it in another passage. ^ It seems as though we need to know no more of i, 2, 3 and 4 than is contained in the definitions. If we look more closely, however, we can dis cover a gap in the proof, which is concealed owing to the omission of the brackets. To be strictly accurate, that is, we + +should have to write: + +2 + 2 = 2 + (i + i) (2 + i) + I = 3 + I = 4- + +What is missing here is the proposition + +2 + (i + i) = (2 + i) + I, + +which is a special case of + +a + {b + c) =^ {a + b) ^- c. If we assume this law, it is easy to see that a similar proof can + +1 Nouveaux Essais, IV, § 10 (Erdmann edn., p. 36}). + +\* Non inelegans specimen demonstrandi in abstractis (Erdmann edn., p. 94). + +\* \Mettant des choses igales d la place, Vigaliti demeure.\ + +8 be given for every formula of addition. Every number, that means, is to be defined in terms of its predecessor. And actually I do not see how a number Uke 437986 could be given to us more aptly than in the way Leibniz does it. Even without having any idea of it, we get it by this means at our disposal none the less. Through such definitions we reduce the whole infinite set of numbers to the number one and increase by one, and every one of the infinitely many numerical formulae can be proved from a few general propositions. + +This opinion is shared by H. Grassmann and H. Hankel. + +Grassmann attempts to obtain the law + +^ + (^ + I) = (^ + ^) + I + +by means of a definition, as follows^: + +"If a and h are any arbitrary members of the basic series, then by the sum a -\- ^ is to be understood that member of the + +basic series for which the formula + +a-\-{h-\-e) = a^h^e + +is valid." + +e here is to be taken to mean positive unity. This definition can be criticized in two different ways. First, sum is defined in terms of itself. If we do not yet understand the meaning of a -\- h, we do not understand the expression a -\- {b -^ e) either. This criticism, however, can perhaps be evaded if we say (admittedly going against the text) that what he is intending to define is not sum but addition. In that case, the criticism could still be brought that ^ + ^ would be an empty symbol if there were either no member or several members of the basic series which satisfied the prescribed condition. That this does not in fact ever happen, Grassmann simply assumes without proof, so that the rigour of his procedure is only + +apparent. + +^ luhrbucb der Mathematik fur bohert Ijehranstalten, Part i Arithmetik, p. 4. + +Stettin i860 [= ges. Math. u. Pbys. Wtrht, ed. Engel, II, i, p. 301]. + +would be synthetic or analytic, a posteriori or a priori, according as the general laws on which their proofs depend are so. John Stuart Mill, however, is of the opposite opinion. At first, indeed, he seems to mean to base the science, like Leibniz, on definitions,^ since he defines the individual numbers in the same way as Leibniz; but this spark of sound sense is no sooner lit than extinguished, thanks to his pre conception that all knowledge is empirical. He informs us, in fact,2 that these definitions are not definitions in the logical sense; not only do they fix the meaning of a term, but they also assert along with it an observed matter of fact. But what in the world can be the observed fact, or the physical fact (to use another of Mill's expressions), which is asserted in the definition of the number 777864? Of all the whole wealth of physical facts in his apocalypse. Mill names for us only a solitary one, the one which he holds is asserted in the defini tion of the number 3 . It consists, according to him, in this, that collections of objects exist, which while they impress the senses thus, °q°, may be separated into two parts, thus, 000. What amercy, then, that not everything in the world isnailed down; for if it were, we should not be able to bring off this separation, and 2+1 would not be 3 ! What apity that Mill did not also illustrate the physical facts underlying the numbers + +o and 1 + +"This proposition being granted," Mill goes on, "we + +term all such parcels Threes." From this we can see that it is really incorrect to speak of three strokes when the clock strikes three, or to call sweet, sour and bitter three sensations + +^ System of "Logic, Bk. Ill, cap. xxiv, § 5 (German translation by J. Schiel). + +2 Op. cit., Bk. II, cap. vi, § 2. + +lO of taste; and equally unwarrantable is the expression "three methods of solving an equation," For none of these is a parcel + +which ever impresses the senses thus, °^°. + +Now according to Mill "the calculations do not follow from the definition itself but from the observed matter of fact." But at what point then, in the proof given above of the proposition 2 + 2=4, ought Leibniz to have appealed to the fact in question? Mill omits to point out the gap in the proof, although he gives himself a precisely analogous proof of the proposition 5 + 2 = 7.^ Actually, there is a gap, consisting in the omission of the brackets; but Mill overlooks + +this just as Leibniz does. + +If the definition of each individual number did really assert a special physical fact, then we should never be able sufficiently to admire, for his knowledge of nature, a man who calculates with nine-figure numbers. Meantime, perhaps Mill does not mean to go so far as to maintain that all these facts would have to be observed severally, but thinks it would be enough if we had derived through induction a general law in which they were all included together. But try to formulate this law, and it will be found impossible. It is not enough to say: "There exist large collections of things which can be split up." For this does not state that there exist collections of such a size and of such a sort as are required for, say, the number 1,000,000, nor is the manner in which they are to be divided up specified any more precisely. Mill's theory must necessarily lead to the demand that a fact should be observed specially for each number, for in a general law precisely what is peculiar to the number 1,000,000, which necessarily belongs to its definition, would be lost. On Mill's view we could actually not put 1,000,000 = 999,999 -f- i unless + +\* Op. cit., Bk. Ill, cap. xxiv, § 5. + +II we had observed a collection of things split up in precisely this peculiar way, different from that characteristic of any and + +every other number whatsoever. + +§ 8. Mill seems to hold that we ought not to form the definitions 2 = 1 + 1, 3=2+1, 4 = 3 + 1, and so on, unless and until the facts he refers to have been observed. It is quite true that we ought not to define 3 as (2 + i), if we attach no sense at all to (2 + 1). But the question is whether, for this, it is necessary to observe his collection and its separation. If it were, the number o would be a pu22le; for up to now no one, I take it, has ever seen or touched o pebbles. Mill, of course, would explain o as something that has no sense, a mere manner of speaking; calculations with o would be a mere game, played with empty symbols, and the only wonder would be that anything rational could come of it. If, however, these calculations have a serious meaning, then the symbol o cannot be entirely without sense either. And the possibility suggests itself that 2 + i, in the same way as o, might have a sense even without Mill's matter of fact being observed. Who is actually prepared to assert that the fact which, according to Mill, is contained in the definition of an eighteen-figure number has ever been observed, and who is prepared to deny that the symbol for such a number has, none + +the less, a sense? + +Perhaps it is supposed that the physical facts would be used only for the smaller numbers, say up to 10, while the remaining numbers could be constructed out of these. But if we can form 11 from 10 and i simply by definition, without having seen the corresponding collection, then there is no reason why we should not also be able in this way to construct 2 out of I and i . If calculations with the number 1 1do not follow from any matter of fact uniquely characteristic of that number, how does it happen that calculations with the number + +12 2 must depend on the observation of a particular collection, + +separated in its own peculiar way? + +It may, perhaps, be asked how arithmetic could exist, if we could distinguish nothing whatever by means of our senses, or only three things at most. Now for our knowledge, certainly, of arithmetical propositions and of their applications, such a state of affairs would be somewhat awkward—but would itaffect the truth of those propositions? If we call a proposition empirical on the ground that we must have made observations in order to have become conscious of its content, then we are not using the word "empirical" in the sense in which it is opposed to "a priori". We are making a psychological statement, which concerns solely the content of the proposition; the question of its truth is not touched. In this sense, all Miinchhausen's tales are empirical too; for certainly all sorts of observations must have been made before they could be + +invented. + +A.re the laws of arithmetic inductive truths? § 9. The considerations adduced thus far make it probable that numerical formulae can be derived from the definitions of the individual numbers alone by means of a few general laws, and that these definitions neither assert observed facts nor presuppose them for their legitimacy. Our next task, therefore, must be to ascertain the nature of the laws involved, MiLL^ proposes to make use, for his proof (referred to above) of the formula 5 + 2 = 7, of the principle that "Whatever is made up of parts, is made up of parts of those parts." This he holds to be an expression in more characteristic language of the principle familiar elsewhere in the form "The sums of equals are equals." He calls it an inductive truth, and a law of nature of the highest order. It is typical of the inaccuracy of + +^ Op. cit., Bk. in, cap. xxiv, § 5. + +13 his exposition, that when he comes to the point in the proof at which, on his own view, this principle should be indispensable, he does not invoke it at all; however, it appears that his inductive truth is meant to do the work of Leibniz's axiom that "If equals be substituted for equals, the equality remains." But in order to be able to call arithmetical truths laws of nature. Mill attributes to them a sense which they do not bear. For example,^ he holds that the identity i == i could be false, on the ground that one pound weight does not always weigh precisely the same as another. But the proposition i = i is + +not intended in the least to state that it does. + +Mill understands the symbol + in such a way that it will serve to express the relation between the parts of a physical body or of a heap and the whole body or heap; but such is not the sense of that symbol. That if we pour 2 unit volumes of liquid into 5 unit volumes of liquid we shall have 7 unit volumes of liquid, is not the meaning of the proposition 5 + 2 = 7, but an application of it, which only holds good provided that no alteration of the volume occurs as a result, say, of some chemical reaction. Mill always confuses the applications that can be made of an arithmetical proposition, which often are physical and do presuppose observed facts, with the pure mathematical proposition itself. The plus symbol can certainly look, in many applications, as though it corres ponded to a process of heaping up; but that is not its meaning; for in other applications there can be no question of heaps or aggregates, or of the relationship between a physical body and its parts, as for example when we calculate about numbers of events. No doubt we can speak even here of "parts"; but then we are using the word not in the physical or geometrical sense, but in its logical sense, as we do when we speak of tyrannicides + +^ Op. cit., Bk. II, cap. vi, § 3. + +14 as a part of murder as a whole. This is a matter of logical subordination. And in the same way addition too does not in general correspond to any physical relationship. It follows that the general laws of addition cannot, for their part, be laws + +of nature. + +§ lo. But might they not still be inductive truths nevertheless? I do not see how that is conceivable. From what particular facts are we to take our start here, in order to advance to the general? The only available candidates for the part are the numerical formulae. Assign them to it, and of course we lose once again the advantage gained by giving our definitions of the individual numbers; we should have to cast around for some other means of establishing the numerical formulae. Even if we manage to rise superior to this misgiving too, which is not exactly easy, we shall still find the ground unfavourable for induction; for here there is none of that uniformity, which in other fields can give the method a high degree of reliability. Leibniz^ recognized this already: + +for to his Philalethe, who had asserted that + +"the several modes of number are not capable of any other difference but more or less; which is why they are simple + +modes, like those of space,"\* + +he returns the answer: + +"That can be said of time and of the straight line, but certainly not of the figures and still less of the numbers, which are not merely different in magnitude, but also dissimilar. An even number can be divided into two equal parts, an odd number cannot; three and six are triangular numbers, four and nine are squares, eight is a cube, and so on. And this is even more the case with the numbers than with the figures; for two unequal figures can be perfectly similar to each other, + +but never two numbers." + +We have no doubt grown used to treating the numbers + +^ Baumann, op. cit.. Vol. II, p. 39 (Erdmann edn., p. 243). + +\* [Derived from Locke, Essay, Bk. 11, cap. xvi, § 5.] + +in many contexts as all of the same sort, but that is only because we know a set of general propositions which hold for all numbers. For the present purpose, however, we must put ourselves in the position that none of these has yet been discovered. The fact is that it would be diflficult to find an example of an inductive inference to parallel our present case. In ordinary inductions we often make good use of the proposition that every position in space and every moment in time is as good in itself as every other. Our results must hold good for any other place and any other time, provided only that the conditions are the same. But in the case of the numbers this does not apply, since they are not in space or time. Position in the number series is not a matter of indifference like position + +in space. + +The numbers, moreover, are related to one another quite differently from the way in which the individual specimens of, say, a species of animal are. It is in their nature to be arranged in a fixed, definite order of precedence; and each one is formed in its own special way and has its own unique peculiarities, which are specially prominent in the cases of o, i and 2. Elsewhere when we establish by induction a proposition about a species, we are ordinarily in possession already, merely from the definition of the concept of the species, of a whole series of its common properties. But with the numbers we have diffi culty in finding even a single common property which has not + +actually to be first proved common. + +The following is perhaps the case with which our putative induction might most easily be compared. Suppose we have noticed that in a borehole the temperature increases regularly with the depth; and suppose we have so far encountered a wide variety of differing rock strata. Here itis obvious that we cannot, simply on the strength of the observations made at this borehole, infer anything whatever as to the nature of the strata at deeper levels, and that any answer to the question, whether the regular distribution of temperature would continue to hold good lower down, would be premature. There is, it is true, a concept, that of "whatever you come to by going on boring," under which fall both the strata so far observed and those at lower levels alike; but that is of little assistance + +i6 to us here. And equally, it will be no help to us to learn in the case of the numbers that these all fall together under the concept of "whatever you get by going on increasing by one." It is possible to draw a distinction between the two cases, on the ground that the strata are things we simply encounter, whereas the numbers are literally created, and determined in their whole natures, by the process of continually increasing by one. Now this can only mean that from the way in which a number, say 8, is generated through increasing by one all its properties can be deduced. But this is in principle to grant that the properties of numbers follow from their definitions, and to open up the possibility that we might prove the general laws of numbers from the method of generation which is common to them all, while deducing the special properties of the individual numbers from the special way in which, through the process of continually increasing by one, each one is formed. In the same way in the geological case too, we can deduce everything that is determined simply and solely by the depth at which a stratum is encountered, namely its spatial position relative to anything else, from the depth itself, without having any need of induction; but whatever is not so + +determined, cannot be learned by induction either. + +The procedure of induction, we may surmise, can itself + +be justified only by means of general propositions of arithmetic —unless we understand by induction a mere process of habitua- + +tion, in which case it has of course absolutely no power whatever of leading to the discovery of truth. The procedure of the sciences, with its objective standards, will at times find a high probability established by a single confirmatory instance, while at others it will dismiss a thousand as almost worthless; whereas our habits are determined by the number and strength of the impressions we receive and by subjective circumstances, which have no sort of right at all to influence our judgement. Induction [then, properly understood,] must base itself on the theory of probability, since it can never render a proposition more than probable. But how probability + +I? theory could possibly be developed without presupposing + +arithmetical laws is beyond comprehension. + +§ II. Leibniz^ holds the opposite view, that the necessary truths, such as are found in arithmetic, must have principles whose proof does not depend on examples and therefore not on the evidence of the senses, though doubtless without the senses it would have occurred to no one to think of them. "The whole of arithmetic is innate and is in virtual fashion in us." What he means by the term "innate" is explained by another passage, where he denies "that Everything we learn is not innate. The truths of number are in us and yet we still learn them, whether itbe by drawing them forth from their source when learning them by demonstration (which + +shows them to be innate), or whether it be . . .". + +Are the laws of arithmetic synthetic a priori or analytic? + +§ 12. If we now bring in the other antithesis between analytic and synthetic, there result four possible combinations, + +of which however one, vi2. + +analytic a posteriori can be eliminated. Those who have decided with Mill in favour of a posteriori have therefore no second choice, so that there remain only two possibilities for us still to examine, viz. synthetic a priori + +and + +analytic. Kant declares for the former. In that case, there is no ^ Baumann, op. cit.. Vol. II, pp. 13-14 (Erdmann edn., pp. 195, 208-9). + +\* Baumann, op. cit.. Vol. II, p. 38 (Erdmann edn., p. 212). + +i8 alternative but to invoke a pure intuition as the ultimate ground of our knowledge of such judgements, hard though it is to say of this whether it is spatial or temporal, or whatever else it may be. Baumann^ agrees with Kant, although for rather different reasons. Lipschitz,^ too, holds that certain propositions, namely that which asserts that Number is independent of the method of numbering and also the Commutative and Associative Laws of Addition, are derived from inner intuition. Hankel^ bases the theory of real numbers on three fundamental propositions, to which he ascribes the character of "common notions" (noftones communes): "Once expounded they are perfectly self-evident; they are valid for magnitudes in every field, as vouched for by our pure intuition of magnitude; and they can without losing their character be transformed into definitions, simply by defining the addition of magnitudes as an operation which satisfies them." In the last statement here there is an obscurity. The definition can perhaps be constructed, but it will not do as a substitute for the original propositions; for in seeking to apply it the question would always arise: Are Numbers magnitudes, and is what we ordinarily call addition of Numbers addition in the sense of this definition? And to answer it, we should need to know already his original propositions about Numbers. Moreover, the expression "pure intuition of magnitude" gives us pause. If we consider all the different things that are called magnitudes: Numbers, lengths, areas, volumes, angles, curvatures, masses, velocities, forces, illuminations, electric currents, and so forth, we can quite well understand how they can all be brought under the single concept of magnitude; but the term "intuition of magnitude," and still worse "pure intuition of + +\* Op. cit., Vol. II, p. 669. + +\* I^hrbuih der Analysis, Vol. I, p. 1 [Bonn 1877]. + +» Op. cit., pp. 54-J5. + +19 magnitude", cannot be admitted as appropriate. I cannot even allow an intuition of 100,000, far less of number in general, not to mention magnitude in general. We are all too ready to invoke inner intuition, whenever we cannot produce any other ground of knowledge. But we have no business, in doing so, to lose sight altogether of the sense of the word + +"intuition". + +Kant in his LA)gic (ed. Hartenstein, vol. VIII, p. 88) + +defines it as follows: + +"An intuition is an individual idea (repr.esentatio siNGULARis), a concept is a general idea (repr.esentatio per NOTAS communes) or an idea of reflexion (REPRyESENTATio + +discursiva)." + +Here there is absolutely no mention of any connexion with sensibility, which is, however, included in the notion of intuition in the Transcendental Aesthetic^ and without which intuition cannot serve as the principle of our knowledge of synthetic a priori judgements. In the Critique of 'Pure Keason + +(ed. Hartenstein, vol. Ill, p. 55)\* we read: + +"It is therefore through the medium of sensibility that objects 2itc given to us and italone provides us with intuitions." It follows that the sense of the word "intuition" is wider in the L.ogic than in the Transcendental Aesthetic. In the sense of the l^ogic, we might perhaps be able to call 100,000 an intuition; for it is not a general concept anyhow. But an intuition in this sense cannot serve as the ground of our knowledge of + +the laws of arithmetic. + +§ 13. We shall do well in general not to overestimate the extent to which arithmetic is akin to geometry. I have already quoted a warning to this effect from Leibniz. One geometrical point, considered by itself, cannot be distinguished in any way from any other; the same appUes to lines and planes. Only when several points, or lines or planes, are included together in a single intuition, do we distinguish them. In geometry, therefore, it is quite intelligible that general pro- + +\* [Original edns., A19/B33] + +20 positions should be derived from intuition; the points or lines or planes which we intuite are not really particular at all, which iswhat enables them to stand as representatives of the whole of their kind. But with the numbers it is different; each number has its own peculiarities. To what extent a given particular number can represent all the others, and at what point its own special character comes into play, cannot be + +laid down generally in advance. + +§ 14. If, again, we compare the various kinds of truths in respect of the domains that they govern, the comparison tells once more against the supposed empirical and synthetic + +character of arithmetical laws. + +Empirical propositions hold good of what is physically or psychologically actual, the truths of geometry govern all that is spatially intuitable, whether actual or product of our fancy. The wildest visions of delirium, the boldest inventions of legend and poetry, where animals speak and stars stand still, where men are turned to stone and trees turn into men, where the drowning haul themselves up out of swamps by their own topknots—all these remain, so long as they remain intuitable, still subject to the axioms of geometry. Conceptual thought alone can after a fashion shake off this yoke, when it assumes, say, a space of four dimensions or positive curvature. To study such conceptions is not useless by any means; but it is to leave the ground of intuition entirely behind. If we do make use of intuition even here, as an aid, it is still the same old intuition of Euclidean space, the only space of which we have any picture. Only then the intuition is not taken at its face value, but as symbolic of something else; for example, we call straight or plane what we actually intuite as curved. For purposes of conceptual thought we can always assume the contrary of some one or other of the geometrical axioms, without involving ourselves in any self contradictions when we proceed to our deductions, despite + +21 the conflict between our assumptions and our intuition. The fact that this is possible shows that the axioms of geometry are independent of one another and of the primitive laws of logic, and consequently are synthetic. Can the same be said of the fundamental propositions of the science of number? Here, we have only to try denying any one of them, and complete confusion ensues. Even to think at all seems no longer possible. The basis of arithmetic lies deeper, it seems, than that of any of the empirical sciences, and even than that of geometry. The truths of arithmetic govern all that is numerable. This is the widest domain of all; for to it belongs not only the actual, not only the intuitable, but everything thinkable. Should not the laws of number, then, be connected + +very intimately with the laws of thought? + +§ 15. Statements in Leibniz can only be taken to mean that the laws of number are analytic, as was to be expected, since for him the a priori coincides with the analytic. Thus he declares^ that the benefits of algebra are due to its borrowings from a far superior science, that of the true logic. In another passage^ he compares necessary and contingent truths to commensurable and incommensurable magnitudes, and maintains that in the case of necessary truths a proof or reduction to identities\* is possible. However, these declarations lose some of their force in view of Leibniz's' inclination to regard all truths as provable: "Every truth", he says, "has its proof a priori derived from the concept of the terms, notwithstanding it does not always lie in our power to achieve this analysis." Though of course the comparison to commensurable and incommensurable magnitudes erects a fresh + +^ Baumann, op. cit.. Vol. II, p. 56 (Erdmann edn., p. 424). \* Baumann, op. cit.. Vol. II, p. 57 (Erdmann edn., p. 83). + +\* Baumann, op. cit.. Vol. II, p. 57 (Pertz edn.. Vol. II, p. 5 j [=Gerhardt edn., + +pbil. Scbr., Vol. U, p. 62]). + +\* \Identitdten\ + +22 barrier between necessary and contingent truths, which for us + +at least is insuperable. + +A very emphatic declaration in favour of the analytic nature of the laws of number is that of W. S.Jevons^: "I hold that algebra is a highly developed logic, and number but + +logical discrimination." + +§ 1 6. But this view, too, has its difficulties. Can the great + +tree of the science of number as we know it, towering, spreading, and still continually growing, have its roots in bare identities\*? And how do the empty forms of logic come to + +disgorge so rich a content? + +To quote Mill:^ "The doctrine that we can discover facts, detect the hidden processes of nature, by an artful manipulation of language, is so contrary to common sense, that a person must have made some advances in philosophy to + +believe it." + +Very true—if it be supposed that during the artful manipulation we do not think at all. Mill is here criticizing a kind of formalism that scarcely anyone would wish to defend. Everyone who uses words or mathematical symbols makes the claim that they mean something, and no one will expect any sense to emerge from empty symbols. But it is possible for a mathematician to perform quite lengthy calcula tions without understanding by his symbols anything intuit able, or with which we could be sensibly acquainted. And that does not mean that the symbols have no sense; we still distinguish between the symbols themselves and their content, even though itmay be that the content can only be grasped by their aid. We realize perfectly that other symbols might have been arranged to stand for the same things. All we need to know is how to handle logically the content as made sensible in the symbols and, if we wish to apply our calculus to physics, how to effect the transition to the phenomena. + +\* The Principles of Science, London 1879, p. 156 [1874 edn., p. 174]- + +\* Op. cit., Bk. II, cap. vi, § 2. + +\* [Identitdten] + +23 It is, however, a mistake to see in such applications the real sense of the propositions; in any application a large part of their generality is always lost, and a particular element enters in, which in other applications is replaced by other particular + +elements. + +§ 17. However much we may disparage deduction, it cannot be denied that the laws established by induction are not enough. New propositions must be derived from them which are not contained in any one of them by itself. No doubt these propositions are in a way contained covertly in the whole set taken together, but this does not absolve us from the labour of actually extracting them and setting them out in their own right. This seen, we can see also the following possibility. Instead of linking our chain of deductions direct to any matter of fact, we can leave the fact where it is, while adopting its content in the form of a condition. By substituting in this way conditions for facts throughout the whole of a train of reasoning, we shall finally reduce it to a form in which a certain result is made dependent on a certain series of conditions. This truth would be established by thought alone or, to use Mill's expression, by an artful manipulation of language. It is not impossible that the laws of number are of this type. This would make them analytic judgements, despite the fact that they would not normally be discovered by thought alone; for we are concerned here not with the way in which they are discovered but with the kind of ground on which their proof rests; or in Leibniz's^ words, "the question here is not one of the history of our discoveries, which is different in different men, but of the connexion and natural order of truths, which is always the same." It would then rest with observation finally to decide whether the conditions included in the laws thus' established are actually fulfilled. Thus we should in the end arrive at the same position as we should have reached by linking our chain + +^ Nouveatoc Essais, IV, § 9 (Erdmann edn., p. 562). + +24 of deductions direct to observed matters of fact. But the type of procedure here indicated is in many cases to be preferred, because it leads to a general proposition, which need not be applicable only to the facts immediately under consideration. The truths of arithmetic would then be related to those of logic in much the same way as the theorems of geometry to the axioms. Each one would contain concentrated within it a whole series of deductions for future use, and the use of it would be that we need no longer make the deductions one by one, but can express simultaneously the result of the whole series,^ If this be so, then indeed the prodigious development of arithmetical studies, with their multitudinous applications, will suffice to put an end to the widespread contempt for analytic judgements and to the legend of the sterility of pure + +logic. + +This is not the first time that such a view has been put forward. If it could be worked out in detail, so rigorously that not the smallest doubt remained, that, it seems to me, + +would be a result not entirely without importance. + +n. Views of certain writers on the concept of Number. + +§ 1 8. On turning now to consider the primary objects of arithmetic, we must distinguish between the individual numbers 3, 4 and so on, and the general concept of Number. + +^ It is remarkable that Mill too (op. cit., Bk. II, cap. vi, § 4) seems to express this view. His sound sense, in fact, from time to time breaks through his prejudice in favour of the empirical. But this same prejudice as often brings everything back into a muddle, by making him confuse the physical applications of arithmetic with arithmetic itself. He seems to be unaware that a hypothetical + +judgement can be true even when the antecedent is not true. + +25 Now we have already decided in favour of the view that the individual numbers are best derived, in the way proposed by Leibniz, Mill, H. Grassmann and others, from the number one together with increase by one, but that these definitions remain incomplete so long as the number one and increase by one are themselves undefined. And we have seen that we have need of general propositions if we are to derive the numerical formulae from these definitions. Such laws cannot, just because of their generality, follow from the definitions of the individual numbers, but only from the general concept of Number. It is this concept that we shall now submit to a closer examination; in the course of this we may expect to have also to discuss the number one and increase by one, as a result of which in turn we shall expect to complete the definitions of + +the individual numbers. + +§ 19. At this point I should like straight away to oppose the attempt to think of number geometrically, as a ratio between lengths or surfaces. Obviously, the thought behind this was to facilitate the numerous applications of arithmetic to geometry by putting the rudiments of both in the closest + +connexion from the outset. + +Newton^ proposes to understand by number not so much a set of units as the relation in the abstract between any given magnitude\* and another magnitude of the same kind which is taken as unity. It may be granted that this is an apt description of number in the wider sense, in which it includes [besides the integers] also fractions and irrational numbers; but it presupposes the concepts of magnitude and of relation in respect of magnitude. This should presumably mean that a definition of number in the narrower sense, or cardinal Number, will still be needed; for Euclid\*\*, in order to define the identity of two ratios between lengths, makes use of the concept of equimultiples, and equimultiples bring us back once again ^ Baiimann, op. cit.. Vol. I, p. 475 [Arithmetica Universalis, Vol. I, cap. ii, 3.] + +\* [quantitas] + +\*\* [Elements, Bk. V., Dcf. 5.] + +26 to numerical identity. However, let it be, as it may be, the case that identity of ratios between lengths can in fact be defined without any reference to the concept of number. Even so, we should still remain in doubt as to how the number defined geometrically in this way is related to the number of ordinary life, which would then be entirely cut off from science. Yet surely we are entitled to demand of arithmetic that its numbers should be adapted for use in every application made of number, even although that application is not itself the business of arithmetic. Even in our everyday sums, we must be able to rely on the science of arithmetic to provide the basis for the methods we use. And moreover, the question arises whether arithmetic itself can make do with a geometrical concept of number, when we think of some of the notions that occur in it, such as the Number of roots of an equation or of numbers prime to and smaller than a given number. On the other hand, the number which gives the answer to the question Hojp many^ can answer among other things how many units are contained in a length. And operations with negative, fractional and irrational numbers can all be reduced to operations with the natural numbers. Perhaps what Newton wished to understand by magnitudes, in defining number as a relation between magnitudes, was not geometrical magnitudes only, but also sets. In that case, however, his definition is useless for our purposes, since the expression "relation between a set and the unit of the set" tells us no more than the expres- + +sion "number by which a set is determined." + +§ 20. The first question to be faced, then, is whether number is definable. Hankel^ declares that it is not, in these words: "What we mean by thinking or putting a thing once, twice, three times, and so on, cannot be defined, because of the simplicity in principle of the concept of putting." But the point is surely not so much the putting as the once, twice and three times. If this could be defined, the indefinability + +\* Op. cit., p. I. + +27 of putting would scarcely worry us. Leibniz is inclined to regard number as an adequate idea, meaning one which isso clear that every element contained in it is also clear, or at least + +as an almost adequate one. + +If the general inclination is, on the whole, to hold that Number is indefinable, that is more because attempts to define it have failed than because anything has been discovered in + +the nature of the case to show that it must be so. + +Is Number a property of external things? + +§ 21. Let us try at least to assign to Number its proper place among our concepts. In language, numbers most commonly appear in adjectival form and attributive construction in the same sort of way as the words hard or heavy or red, which have for their meanings properties of external things. It is natural to ask whether we must think of the individual numbers too as such properties, and whether, accordingly, the concept of Number can be classed along with that, + +say, of colour. + +That it can, seems to be the view of M. Cantor,^ when + +he calls mathematics an empirical science in so far as it begins with the consideration of things in the external world. On his view, number originates only by abstraction from objects. For E. Schroder^ number is modelled on actuality, derived from it by a process of copying the actual units with ones, which he calls the abstraction of number. In this copying, the units are only represented in point of their frequency, all + +^ Grund:;^uge einer Elementarmathematik, p. 2, § 4. Similarly Lipschitz, op. cit., + +p. I. + +\* Op. cit., pp. 6, lo-ii. + +28 other properties of the things concerned, such as their colour or shape, being disregarded. Here frequency is only another name for Number. It follows, therefore, that Schroder puts frequency or Number on a level with colour and shape, and + +treats it as a property of things. + +§ 22. Baumann^ rejects the view that numbers are concepts extracted from external things: "The reason being that external things do not present us with any strict units; they present us with isolated groups or sensible points, but we are at liberty to treat each one of these itself again as a many." And it is quite true that, while I am not in a position, simply by thinking of it differently, to alter the colour or hardness of a thing in the slightest, I am able to think of the Iliad either as one poem, or as 24 Books, or as some large Number of verses. Is it not in totally different senses that we speak of a tree as having 1000 leaves and again as having green leaves? The green colour we ascribe to each single leaf, but not the number 1000. If we call all the leaves of a tree taken together its foliage, then the foliage too is green, but it is not 1000. To what then does the property 1000 really belong? It almost looks as though itbelongs neither to any single one of the leaves nor to the totality of them all; is it possible that it does not really belong to things in the external world at all? If I give someone a stone with the words: Find the weight of this, I have given him precisely the object he is to investigate. But if I place a pile of playing cards in his hands with the words: Find the Number of these, this does not tell him whether I wish to know the number of cards, or of complete packs of cards, or even say of honour cards at skat. To have given him the pile in his hands is not yet to have given him completely the object he is to investigate; I must add some + +1 Op. cit.. Vol. II, p. 669. + +29 further word—cards, or packs, or honours. Nor can we say that in this case the different numbers exist in the same thing side by side, aB different colours do. I can point to the patch of each individual colour without saying a word, but I cannot in the same way point to the individual numbers. If I can call the same object red and green with equal right, it is a sure sign that the object named is not what really has the green colour; for that we must first get a surface which is green only. Similarly, an object to which I can ascribe different numbers + +with equal right is not what really has a number. + +It marks, therefore, an important difference between colour and Number, that a colour such as blue belongs to a surface independently of any choice of ours. The blue colour is a power of reflecting light of certain wavelengths and of absorbing to varying extents light of other wavelengths; to this, our way of regarding it cannot make the slightest differ ence. The Number i, on the other hand, or loo or any other Number, cannot be said to belong to the pile of playing cards in its own right, but at most to belong to it in view of the way in which we have chosen to regard it; and even then not in such a way that we can simply assign the Number to it as a predicate. What we choose to call a complete pack is obviously an arbitrary decision, in which the pile of playing cards has no say. But itis when we examine the pile in the light of this decision, that we discover perhaps that we can call it two complete packs. Anyone who did not know what we call a complete pack would probably discover in the pile any other + +Number you like before hitting on two. + +§ 23. To the question: What is it that the number belongs to as a property? Mill^ replies as follows: the name of a number connotes, "of course, some property belonging to the + +^ Op. cit., Bk. in, cap. xxiv, § j. + +30 agglomeration of things which we call by the name; and that property is the characteristic manner in which the agglomeration is made up of, and may be separated into, parts." + +Here the definite article in the phrase "the characteristic manner" is a mistake right away; for there are very various manners in which an agglomeration can be separated into parts, and we cannot say that one alone would be characteristic. For example, a bundle of straw can be separated into parts by cutting all the straws in half, or by splitting it up into single straws, or by dividing it into two bundles. Further, is a heap of a hundred grains of sand made up of parts in exactly the same way as a bundle of loo straws? And yet we have the same number. The number word "one", again, in the expression "one straw" signally fails to do justice to the way in which the straw is made up of cells or molecules. Still more difficulty is presented by the number o. Besides, need the straws form any sort of bundle at all in order to be numbered? Must we literally hold a rally of all the blind in Germany before we can attach any sense to the expression "the number of blind in Germany"? Are a thousand grains of wheat, when once they have been scattered by the sower, a thousand grains of wheat no longer? Do such things really exist as agglomerations of proofs of a theorem, or agglomerations of events? And yet these too can be numbered. Nor does it make any difference whether the events occur together or thousands of years + +apart. + +§ 24. This brings us to another reason for refusing to class number along with colour and solidity: it is applicable + +over a far wider range. + +MiLL^ maintains that the truth that whatever is made up of parts is made up of parts of those parts holds good for natural phenomena of every sort, since all admit of being + +Op. cit., Bk. Ill, cap. xxiv, § 5. + +51 numbered. But cannot still far more than this be numbered? LoCKE^ says: "Number applies itself to men, angels, actions, thoughts—everything that either doth exist or can be imagined." Leibniz^ rejects the view of the schoolmen that number is not applicable to immaterial things, and calls number a sort of immaterial figure, which results from the union of things of any sorts whatsoever, for example of God, an angel, a man and motion, which together are four. For which reason he holds that number is of supreme universality and belongs to metaphysics. In another passage^ he says: "Some things cannot be weighed, as having no force and power; some things cannot be measured, by reason of having no parts; but there is nothing which cannot be numbered. Thus number is, as it were, a kind of metaphysical figure." + +It would indeed be remarkable if a property abstracted from external things could be transferred without any change of sense to events, to ideas and to concepts. The effect would be just like speaking of fusible events, or blue ideas, or salty + +concepts or tough judgements. + +It does not make sense that what is by nature sensible should occur in what is non-sensible. When we see a blue surface, we have an impression of a unique sort, which corresponds to the word "blue"; this impression we recogni2e again, when we catch sight of another blue surface. In order to suppose that there is in the same way, when we look at a triangle, something sensible corresponding to the word "three", we should have to commit ourselves to finding that same thing again in three concepts too; so that something non-sensible would have in it something sensible. It may + +^ Baumann, op. cit., Vol. i, p. 409. [Essay, Bk. II, cap. xvi, § i]. \* Baumann, op. cit.. Vol. II, pp. 2-5 [Erdmann edn., p. 8]. Baumann, op. cit.. Vol. II, p. 56 [Erdmann edn., p. 162]. + +32 certainly be granted that a sensible impression of a sort does correspond to the word "triangular", but then the word must be taken as a whole. The three in it we do not see directly; rather, we see something upon which can fasten an intellectual activity of ours leading to a judgement in which the number 5 occurs. How is it after all that we do become acquainted with, let us say, the Number of figures of the syllogism as drawn up by Aristotle? Is it perhaps with our eyes? What we see is at most certain symbols for the syllogistic figures, not the figures themselves. How are we to be able to see their Number, if they themselves remain invisible? However, it may be argued that it is enough to see the symbols; their number is identical with the number of the figures. But then, how do we know this? For that, we must have already ascertained the number of the figures by some other means. Or is the proposition "The Number of figures of the syllogism is four" only another way of putting the proposition that "The Number of symbols for figures of the syllogism is four?" Of course it is not. There is no intention of saying anything about the symbols; no one wants to know anything about them, except in so far as some property of theirs directly mirrors some property in what they symbolize. Besides, the same thing can, without any logical fallacy, be symbolized by several different symbols, so that there is not even any need for the number of symbols to coincide with the number of + +things symbolised. + +§ 25. While for Mill the number is something physical, for Locke and Leibniz it exists only as a notion.\* Mill^ is, of course, quite right that two apples are physically different from three apples, and two horses from one horse; that they are a different visible and tangible phenomenon. ^ But are + +\* Op. cit., Bk. Ill, cap. xxiv, § 5. + +\* Strictly speaking we should add: provided that they are a phenomenon at all. For if someone has one horse in Germany and one in America (and no others), then he does possess two horses; yet these two horses do not form a phenomenon,—only each one of the two by itself could be so described. + +\* [in der Idee] + +33 we to infer from this that their twoness or threeness is something physical? One pair of boots may be the same visible and tangible phenomenon as two boots. Here we have a dif ference in number to which no physical difference corresponds; for two and one pair are by no means the same thing, as Mill seems oddly to believe. How is it possible, after all, for two concepts to be physically distinguishable from three concepts? To quote Berkeley^: "It ought to be considered that number ... is nothing fixed and settled, really existing in things themselves. It is entirely the creature of the mind, considering, either an idea by itself, or any combination of ideas to which itgives one name, and so makes itpass for a unit. According as the mind variously combines its ideas, the unit varies; and as the unit, so the number, which isonly a collection of units, doth also vary. We call a window one, a chimney one, and yet a house in which there are many windows, and many chimneys, hath an equal right to be called + +one, and many houses go to the making of one city." + +Is number something subjective? + +§ 26. This line of thought may easily lead us to regard number as something subjective. It looks as though the way in which number originates in us may prove the key to its essential nature. The matter would thus become one for a psychological enquiry. This is indeed what Lipschitz^ is thinking of when he writes: "Anyone who proposes to make a survey of a number of things, will begin with some one particular thing and proceed by continually adding a new one to those previously selected." This seems to describe much better how we acquire say the intuition of a constellation than how we construct numbers. The intention to make a + +^ Baumann, op. cit., Vol. II, p. 428 \New Theory of Vision, % 109]. \* Op. cit., p. 1. I take it that Lipschitz means to refer to a mental process. + +54 survey is not essential; for it will scarcely be maintained that it becomes any easier to survey a herd after we have learned + +how many head it comprises. + +No description of this kind of the mental processes which precede the forming of a judgement of number\*, even if more to the point than this one, can ever take the place of a genuine definition of the concept. It can never be adduced in proof of any proposition of arithmetic; it acquaints us with none of the properties of numbers. For number isno whit more an object of psychology or a product of mental processes than, let us say, the North Sea is. The objectivity of the North Sea is not affected by the fact that it is a matter of our arbitrary choice which part of all the water on the earth's surface we mark off and elect to call the "North Sea". This is no reason for deciding to investigate the North Sea by psychological methods. In the same way number, too, is something objective. If we say "The North Sea is 10,000 square miles in extent" then neither by "North Sea" nor by "10,000" do we refer to any state of or process in our minds: on the contrary, we assert something quite objective, which isindependent of our ideas and everything of the sort. If we should happen to wish, on another occasion, to draw the boundaries of the North Sea differently or to understand something different by "10,000", that would not make false the same content that was previously true: what we should perhaps rather say is, that a false content had now taken the place of a true, without in any way depriving + +its predecessor of its truth. + +The botanist means to assert something just as factual when he gives the Number of a flower's petals as when he gives their colour. The one depends on our arbitrary choice just as little as the other. There does, therefore, exist a certain similarity between Number and colour; it consists, however, not in our becoming acquainted with them both in external things through the senses, but in their being both objective. \* [For Frege, a "judgement of number" {Zahlurtheil), like its verbal expression, a "statement of number" {Zahlangabe), is one as to hoo) many of something there + +are.] + +33 I distinguish what I call objective from what is handleable or spatial or actual. The axis of the earth is objective, so is the centre of mass of the solar system, but I should not call them actual in the way the earth itself is so. We often speak of the equator as an imaginary line; but it would be wrong to call it an imaginary line in the dyslogistic sense; it is not a creature of thought, the product of a psychological process, but is only recogni2ed or apprehended by thought. If to be recognized were to be created, then we should be able to say nothing positive about the equator for any period earlier than the date + +of its alleged creation. + +Space, according to Kant, belongs to appearance. For other rational beings it might take some form quite different from that in which we know it. Indeed, we cannot even know whether it appears the same to one man as to another; for we caimot, in order to compare them, lay one man's intuition of space beside another's. Yet there is something objective in it all the same; everyone recognizes the same geometrical axioms, even if only by his behaviour, and must do so if he is to find his way about the world. What is objective in it is what is subject to laws, what can be conceived and judged, what is expressible in words. What ispurely intuitable is not communicable. To make this clear, let us suppose two rational beings such that projective properties and relations are all they can intuite—the lying of three points on a line, of four points on a plane, and so on; and let what the one intuites as a plane appear to the other as a point, and vice versa, so that what for the one is the line joining two points for the other is the line of intersection of two planes, and so on with the one intuition always dual to the other. In these circumstances they could understand one another quite well and would never realize the difference between their intuitions, since in projective geometry every proposition has its dual counterpart; any disagreements over points of aesthetic appreciation would not + +36 be conclusive evidence. Over all geometrical theorems they would be in complete agreement, only interpreting the words differently in terms of their respective intuitions. With the word "point", for example, one would connect one intuition and the other another. We can therefore still say that this word has for them an objective meaning, provided only that by this meaning we do not understand any of the peculiarities of their respective intuitions. And in this sense the axis of the earth + +too is objective. + +The word "white" ordinarily makes us think of a certain sensation, which is, of course, entirely subjective; but even in ordinary everyday speech, it often bears, I think, an objective sense. When we call snow white, we mean to refer to an objective quality which we recognize, in ordinary daylight, by a certain sensation. If the snow isbeing seen in a coloured light, we take that into account in our judgement and say, for instance, "It appears red at present, but it is white." Even a colour-blind man can speak of red and green, in spite of the fact that he does not distinguish between these colours in his sensations; he recognizes the distinction by the fact that others make it,or perhaps by making a physical experiment. Often, therefore, a colour word does not signify our subjective sensation, which we cannot know to agree with anyone else's (for obviously our calling things by the same name does not guarantee as much), but rather an objective quality. It is in this way that I understand objective to mean what is independent of our sensation, intuition and imagination, and of all construction of mental pictures out of memories of earlier sensations, but not what is independent of the reason,—for what are things independent of the reason? To answer that would be as much as to judge without judging, or to wash the fur + +without wetting it. + +§ 27. For that reason I cannot agree with Schloemilch^ + +^ Handbuch der algebraischen Analysis, p. i + +37 either, when he calls number the idea of the position of an item in a series.^ If number were an idea, then arithmetic would be psychology. But arithmetic is no more psychology than, say, astronomy is. Astronomy is concerned, not with ideas of the planets, but with the planets themselves, and by the same token the objects of arithmetic are not ideas either. If the number two were an idea, then it would have straight away to be private to me only. Another man's idea is, ex vi termini, another idea. We should then have it might be many millions of twos on our hands. We should have to speak of my two and your two, of one two and all twos. If we accept latent or unconscious ideas, we should have unconscious twos among them, which would then return subsequently to consciousness. As new generations of children grew up, new generations of twos would continually be being born, and in the course of millennia these might evolve, for all we could tell, to such a pitch that two of them would make five. Yet, in spite of all this, it + +^ Another possible objection is, that on this theory the same idea of a position in a series would have always to appear whenever the same number occurred, which obviously does not happen. My arguments would be beside the point if he meant by idea an objective notion [Ideey, but in that case what distinction would there be between the idea of the position and the position + +itself? + +An idea in the subjective sense is what is governed by the psychological laws of association; it is of a sensible, pictorial character. An idea in the objective sense belongs to logic and isin principle non-sensible, although the word which means an objective idea is often accompanied by a subjective idea, which nevertheless is not its meaning. Subjective ideas are often demonstrably different in different men, objective ideas are the same for all. Objective ideas can be divided into objects and concepts. I shall myself, to avoid confusion, use "idea" only in the subjective sense. It is because Kant associated both meanings with the word that his doctrine assumed such a very subjective, idealist complexion, and his true view was made so difficult to discover. The distinction here drawn stands or falls with that between psychology and logic. If only these themselves + +were to be kept always rigidly distinct I + +38 would still be doubtful whether there existed the infinite number of numbers that we ordinarily suppose. 10^°, perhaps, might be only an empty symbol, and there might exist no idea + +at all, in any being whatever, to answer to the name. + +Weird and wonderful, as we see, are the results of taking seriously the suggestion that number is an idea. And we are driven to the conclusion that number is neither spatial and physical, like Mill's piles of pebbles and gingersnaps, nor yet subjective like ideas, but non-sensible and objective. Now objectivity cannot, of course, be based on any sense impression, wliich as an affection of our mind is entirely + +subjective, but only, so far as I can see, on the reason. + +It would be strange if the most exact of all the sciences had to seek support from psychology, which isstill feeling its + +way none too surely. + +The set theory of Number. + +§ 28. Some writers define Number as a set or multitude or plurality. All these views suffer from the drawback that the concept will not then cover the numbers o and i. Moreover, these terms are utterly vague: sometimes they approximate in meaning to "heap" or "group" or "agglomeration", referring to a juxtaposition in space, sometimes they are so used as to be practically equivalent to "Number", only vaguer. No analysis of the concept of Number, therefore, is to be found in a definition of this kind. Thomae^ requires for the formation of number that item-sets which differ be given different names. By this he evidently means to refer to a process of bringing out more sharply the characteristics of the sets in question, of which the giving of names is only the external sign. The question is, just what is this process like? + +\* Elementare Tbeorie der analytiscben Functionen, p. i. + +39 Obviously, the notion of number would not result if, instead of "5 stars", "5 fingers" and "7 stars", we tried introducing names in which there were no recognizable common elements. It is not a matter simply of assigning names, but of symbolizing in its own right the numerical element. For this, we must needs have come to recognize that element in its peculiarity. + +Furthermore, it should be noted that there are two different views. Some call number a set of things or objects; others, following Euclid^, define it as a set of units. This last + +expression demands a separate discussion. + +in. Views on unity and one\*. Does the number word ^^one" standfor a property of objects? + +§ 29. In the definitions which Euclid gives at the beginning of Book VII of the Elements, he seems to mean by the word "fiovas" sometimes an object to be numbered, sometimes a property of such an object, and sometimes the number one. We can translate it consistently by the German "Einheit", but only because that word itself shifts over the + +same variety of meanings. + +According to Schroder^: "Each of the things to be numbered is called a unit." We may well wonder why we must first bring the things under the concept of unity, instead of simply defining number right away as a set of things, which would throw us back once again onto the first of the two views. The most obvious answer is that in calling the things units we are supposed to be adding to our description of them; under the influence of the grammatical form, we are regarding "one" ^ Movds cVti, KaO\* fjv CKaarov twv ovrwv €v Aeyerat. 'Apidfios Se to €k fiovdScjv avyKilfxevov ttXtjOos. ["A unit is that by virtue of which each of the things that exist is called one. A number is a multitude composed of units."] + +\* Op. dt., p. 5. + +\* [It is not possible in English to do entire justice to the ambiguities of the German Einheit, which covers both "unit" and "unity", not to mention "oneness". Moreover Einheit is a verbal derivative of Ein (whereas "unit/y" is not derived directly from "one"), and derivatives of either word can be described alike as derivatives of Ein or "one". These facts make §§ 29, 32 and 37, in par- + +ticular, more plausible in German than in English.] + +40 as a word for a property and taking "one city" in the same way as "wise man". In that case a unit would be an object characterized by the property "one" and would stand to "one" in the same relation as "a sage" to the adjective "wise". Now reasons have already been given as conclusive against the view that number is a property of things; but there are several further arguments against the present suggestion in particular. It must strike us immediately as remarkable that every single thing should possess this property. It would be incomprehensible why we should still ascribe it expressly to a thing at all. It is only in virtue of the possibility of something not being wise that it makes sense to say "Solon is wise." The content of a concept diminishes as its extension increases; if its exten sion becomes all-embracing, its content must vanish altogether. It is not easy to imagine how language could have come to invent a word for a property which could not be of the slightest use for adding to the description of any object whatsoever. + +If it were correct to take "one man" in the same way as "wise man", we should expect to be able to use "one" also as a grammatical predicate, and to be able to say "Solon was one" just as much as "Solon was wise". It is true that "Solon was one" can actually occur, but not in a way to make itintelligible on its own in isolation. It may, for example, mean "Solon was a wise man", if "wise man" can be supplied from the context. In isolation, however, it seems that "one" cannot be a predicate.^ This is even clearer if we take the plural. Whereas we can combine "Solon was wise" and "Thales was wise" into "Solon and Thales were wise", we cannot say "Solon and Thales were one". But it is hard to see why this + +^ Usages do occur which appear to contradict this; but if we look more closely we shall find that some general term has to be supplied, or else that "one" is not being used as a number word—that what itis intended to assert is the + +character (not of being unique, but) of being unitary. + +41 should be impossible, if "one" were a property both of Solon + +and of Thales in the same way that "wise" is. + +§ 30. In line with this is the fact that no one has ever been able to give a definition of the property "one". Leibniz^ indeed says that "By one is meant whatever we grasp in one act of the understanding," but this is to define "one" in terms of itself. Besides, surely we can also grasp what is many in one act of the underscanding? Leibniz admits as much in the same passage. Baumann^ does no better when he says: "That is one, which we apprehend as one", and further: "Whatever we take as a point, or refuse to take as further subdivided into parts, that we regard as one; but every one of outer in tuition, whether empirical or pure, can also be regarded as a many. Every idea is one when isolated in contrast with another; but in itself it can again be distinguished into a many." This sweeps away every limit to the application of the concept imposed by the nature of the facts, and everything is made dependent on our way of regarding them. I ask once more: How can it make sense to ascribe the property "one" to any object whatever, when every object, according as to how we look at it, can be either one or not one? How can a science which bases its claim to fame precisely on being as definite and accurate as possible repose on a concept as hazy as this is? + +§31. Now although Baumann^ bases the concept of one on inner intuition, he refers nevertheless, in the passage just cited, to certain criteria for being one, namely being undivided and being isolated. If this were correct, then we should have to expect animals, too, to be capable of having some sort of idea of unity. Can it be that a dog staring at the moon does have an idea, however ill-defined, of what we signify by the + +\* Baumann, op. cit.. Vol. II, p. 2 (Erdmann edn., p. 8). + +» Op. cit.. Vol. II, p. 669. 3 Op. cit.. Vol. II, p. 669. + +42 word "one"? This is hardly credible—and yet it certainly distinguishes individual objects: another dog, its master, a stone it is playing with, these certainly appear to the dog every bit as isolated, as self-contained, as undivided, as they do to us. It will notice a difference, no doubt, between being set on by several other dogs and being set on by only one, but this is what Mill calls the physical difference. We need to know specifically: is the dog conscious, however dimly, of that common element in the two situations which we express by the word "one", when, for example, it first is bitten by one larger dog and then chases one cat? This seems to me unlikely. I infer, therefore, that the notion of unity is not, as Locke^ holds, "suggested to the understanding by every object without us, and every idea within", but becomes known to us through the exercise of those higher intellectual powers which distinguish men from brutes. Consequently, such properties of things as being undivided or being isolated, which animals perceive quite as well as we do, cannot be what isessential in + +our concept. + +§ 32. Still, we may suspect that they have some sort of connexion with it. Language indicates as much by forming "united" as a derivative from "one". The more the internal contrasts within a thing fade into insignificance by comparison with the contrasts between it and its environment, and the more the internal connexions among its elements overshadow its connexions with its environment, the more natural it becomes for us to regard it as a distinct object. For a thing to be "united" means that it has a property which causes us, when we think of it, to sever it from its environment and consider it on its own. In the same way we can explain how the French "uni" comes to mean "even" or "smooth". The word "unity" too, is used in a similar manner, when we speak of the political + +^ Baumann, op. cit.. Vol. I, p. 409 [Essay, Bk. II, cap. vii, § 7]. + +45 unity of a country or the unity of a work of art.^ But in this sense "unity" is connected not so much with "one" as with "united" or "unitary". For when we say the Earth has one moon, we do not mean to point out that our satellite is isolated, or self-contained, or undivided; rather, we are contrasting the satellite system of the Earth with that of Venus or Mars or Jupiter. So far as being isolated goes, or being undivided, the moons of Jupiter could stand up quite well to our moon, + +and in that sense they are every bit as unitary. + +§ 33. Some writers go still further, and demand something not merely undivided but indivisible. G. Kopp^ calls whatever is thought of as self-contained and incapable of dissection, whether we become acquainted with it through the senses or otherwise, an individual; and individuals which are to be numbered he calls ones, evidently using "one" here in the sense of "unit". Baumann too, when arguing for his view that external things do not present us with strict units on the ground that we are free to treat them as many, gives as a criterion of a strict unit that it must be incapable of dissection. Obviously, by tightening up its internal cohesion without limit, they hope to arrive at a criterion for their unit which is independent of any arbitrary way of regarding things. This attempt collapses because we are then left with practically nothing fit to be called a unit and to be numbered. The result is that we at once begin to retrace our steps, by giving as the criterion not that the thing itself should be incapable of dissect ion in fact, but that we should think of it as such. This brings us back once again to our way of regarding things, with all its fluctuations. And is it really of any advantage to think of things as being what they are not? On the contrary, any ^ On the history of the word "unit" cf. Eucken, Geschichte der philosophischen + +Terminologie, pp. 122-23, ^3^> 220. \* Schularithmetik, pp. 5-6, Eisenach 1867. + +44 conclusions drawn from a false assumption are liable to be false; while if there are no conclusions to be drawn from our unit's being incapable of dissection, why bother to assume that it is? If it does no harm, and in fact is actually necessary, to take our strict units none too strictly, what was the point of being strict? Unless perhaps all that was meant was that we should not think of the possibilities of dissection—as though lack of thought could get us anywhere I Besides, there are cases where we simply cannot avoid thinking of them, where a conclusion is actually based on the way in which a unit is made up of parts, as for instance in the problem: If there are 24 hours in one day, how many are there in three days? + +Are units identical'^ with one another? + +§ 34. Every attempt to define "one" as a property having thus failed, we must finally abandon the view that in designating a thing a imit we are adding to our description of it. We come back once again to our question: Why do we call things units, if "unit" is only another name for thing, if any and every thing is a unit or can be regarded as one? E. Schroder^ gives as the reason, that the word is used for ascribing to the items that are to be numbered the necessary identity. But to begin with it is not easy to see why the words "thing" and "object" could not indicate this just as well. And further, it is natural to ask: Why do we ascribe identity to objects that are to be numbered? And is it only ascribed to them, or are they really identical? In any case, no two objects are ever completely identical. On the other hand, of course, we can practically always engineer some respect in which any two objects whatever agree. And with that we are back once more at our arbitrary way of regarding things, unless we are willing, regardless of truth, to ascribe to things an identity going beyond any they actually possess. In actual fact, many writers + +^ Op. cit., p. 5. + +\* [gleich. See footnote on p. He above.] + +45 do call units identical without any qualification. Hobbes' states that: "Number in the absolute sense in mathematics presupposes units identical\* one with another out of which it is formed." Hume^ holds the component parts of quantity and number to be entirely similar. Thomae^ calls the individual member of his set a unit, and says in so many words that units are identical with each other—though we might with as much or even more justice say that the individual members of his set must be different from each other. Now what has this alleged identity to do with number? The properties which serve to distinguish things from one another are, when we are considering their Number, immaterial and beside the point. That iswhy we want to keep them out of it. But we shall not succeed along the present lines. For suppose that we do, as Thomae demands, "abstract from the peculiarities of the individual members of a set of items", or "disregard, in considering separate things, those characteristics which serve to distinguish them". In that event we are not left, as Lip-SCHITZ maintains, with "the concept of the Number of the things considered"; what we get is rather a general concept under which the things in question fall. The things themselves do not in the process lose any of their special characteristics. If, for example, in considering a white cat and a black cat, I disregard the properties which serve to distingmsh them, then I get presumably the concept "cat". Even if I proceed to bring them both under this concept and call them, I suppose, units, the white one still remains white just the same, and the black black. I may not think about their colours, or I may propose to make no inference from their difference in this respect, but for all that the cats do not become colourless and they remain different precisely as before. The concept "cat", no doubt, which we have arrived at by abstraction, \* Baumann, op. cit.. Vol. I, p. 242 [op. cit.. Dial. I, p. 16 = Molesworth + +edn., p. 18]. + +Baumann, op. cit.. Vol. II, p. 568 [Enquiry concerning Human Understanding, + +Sect. XII, part iii, § 131]. Op. cit., p. I. + +\* [aequales] + +46 no longer includes the special characteristics of either, but of + +it, for just that reason, there is only one. + +§ 35. We cannot succeed in making different things identical simply by dint of operations with concepts. But even if we did, we should then no longer have things in the plural, but only one thing; for, as Descartes^ says, the number (or better, the plurality) in things arises from their diversity. And as E, Schroder^ justly observes: "That things should be numbered is a reasonable demand only where the objects submitted appear clearly distinguishable from one another (for example, spatially and temporally separated) and isolated in contrast with one another." It does actually happen at times that too great similarity, for instance of the uprights in a railing, does make numbering difficult. W. S. Jevons' makes this point with unusual force: "Number is but another name for diversity. Exact identity is unity, and with difference arises plurality." And again (p. 157)\*: "It has often been said that units are units in respect of being perfectly similar to each other; but though they may be perfectly similar in some respects, they must be different in at least one point, otherwise they would be incapable of plurality. If three coins were so similar that they occupied the same place at the same time, + +they would not be three coins, but one." + +§ 36. However, the view that units must be different comes up, as soon transpires, against fresh difficulties. Jevons defines a unit as "any object of thought which can be dis criminated from every other object treated as a unit in the same problem." But this is to define unit in terms of itself, + +Baumann, op. cit.. Vol. I, p. 103 [Principia, Part I, § 60]. + +" Op. cit., p. 5. + +^ Op. cit., p. 156 [1874 edn., p. 175]. + +\* [1874 edn., p. 176] + +47 and the qualifying clause "which can be discriminated from every other object" fails to describe it any more precisely, because it goes without saying: we call them other objects simply and solely because we can discriminate them from the first mentioned. Jevons^ goes on: "Whenever I use the symbol + +5 I really mean + +1 + 1 + 1 + 1 + I, and it is perfectly understood that each of these units is distinct from each other. If requisite I might mark them thus i'+ i"+ i"'+ i""+ I " Certainly it is requisite to mark them differently, if they are different: otherwise the utmost confusion must result. For if a difference simply in the position in which the i appears were to be made to mean of itself a difference in the unit, this convention would have to be laid down as a rule without any exception, or else we should never know whether i + i was to be taken to mean 2 or i. Accordingly, we should have to give up the equation 1 = 1 and we should never, to our embarrassment, be able to mark the same thing twice. That obviously will not do. If, however, we adopt the alternative plan, of assigning different symbols to different things, it is hard to see why we still retain in our symbols a common + +element; why not write, instead of + +i'+ i"+ i"'+ i""+ I , + +simply + +a+ b-]- c-\- d-]- e} Yet the case for identical units has already been finally abandoned as hopeless, and it helps not at all to point out that they are to some extent similar. So our one slips through our fingers; we are left with the objects in all their particularity. + +The symbols + +I', I", I'" tell the tale of our embarrassment. We must have identity + +^ Op. cit., p. 162 [1874 edn., p. 182]. + +48 hence the i; but we must have difference—hence the strokes; only unfortunately, the latter undo the work of the former. § 37. In other writers we meet with the same difficulty. In LocKE^ we read: "By the repeating ... of the idea of an unit, and joining it to another unit, we make thereof one collective idea, marked by the name two. And whosoever can do this and proceed on, still adding one more to the last collective idea which he had of any number, and give a name to it, may count." Leibniz^ defines number as i and i and i or as units. Hesse^ writes: "Anyone who can form for himself an idea of the unit which in algebra is expressed by the symbol i, .. . can go on to conceive a second unit as good as the first, and then further units of the same sort. The union of the second with the first into a single whole yields the + +number 2." + +In these passages, the relation between the meanings of the words "unit" and "one" should be noticed. Leibniz understands by unitas a concept under which this one and that one and the other one fall, or as he also puts it: "Abstractum ab uno est Unitas". Locke and Hesse seem to use unit and one to mean the same. Indeed Leibniz, in the last analysis, does so too; for when he calls each individual object falling under his concept of unitas a unum, this word is being used to signify not the individual object but the concept under which + +they all fall. + +§ 38. However, if confusion is not to become worse confounded, it is advisable to observe a strict distinction + +^ Baumann, op. cit.. Vol. I, pp. 410-11 [Essay, Bk. II., cap, xvi, § 5]. + +\* Baumann, op. cit.. Vol. II, p. 3 [Erdmann edn., p. 53]. + +^ Vier Species [Leipzig 1872], p. 2. + +49 between unit and one. When we speak of "the number one", we indicate by means of the definite article a definite and unique object of scientific study. There are not divers numbers one, but only one. In i we have a proper name, which as such does not admit of a plural any more than "Frederick the Great" or "the chemical element gold". It is no accident, nor is it a notational inexactitude, that we write i without any strokes to mark differences. Jevons would rewrite the equation 3 2 = 1 + +in some such way as this: + +(i' + i" + I'") — (i" + I'") = I'. + +But what would be the remainder of + +Certainly not i '. It follows, therefore, that on his view there would be not only distinct ones but also distinct twos and so on; for i""+ i'"" could not be substituted for i"+ i'". This puts us in a position to see quite clearly that number is not an agglomeration of things. Arithmetic would come to a dead stop, if we tried to introduce in place of the number one, which is always the same, different distinct things, however similar the symbols for them; yet to make the symbols identical would be, of course, a mistake, and surely we cannot suppose that the mainspring of arithmetic is a piece of faulty notation. It is therefore impossible to regard ias a symbol for different distinct objects, for Iceland, Aldebaran, Solon, and so on. The absurdity can be best brought out by taking the case of an equation which has three roots, namely 2, 5 and + +4. Suppose now with Jevons we write for 3 + +i'+ i"+ I'"; and let us take i 'and i " and i '" to be units, that is, still following Jevons, to be the objects currently under consideration. It follows that i' would here mean 2, and i" 5, and i'" 4. Then would it not be more intelligible, instead of i '-|- i " + + +50 2+5+4? Only concept words can form a plural. If, therefore, we speak of "units", we must be using the word not as equivalent to the proper name "one", but as a concept word. If this term "unit" means "object to be numbered", then number cannot be defined as units. But if we understand by "unit" a concept which includes under it the number one and nothing else, a plural makes no sense, and it becomes impossible once more to define number, with Leibniz, as units, or as i and i and i; for if "and" isused as in "Bunsen and Kirchhof", then i and i and I is not 3 but i, just as gold and gold and gold is never + +anything else but gold. The plus symbol in + +1+1+1=3 must, therefore, be interpreted differently from the "and" which we use in symbolizing a collection or a "collective + +idea". + +§ 39. We are faced, therefore, with the following + +difficulty: + +If we try to produce the number by putting together different distinct objects, the result is an agglomeration in which the objects contained remain still in possession of precisely those properties which serve to distinguish them from one another; and that is not the number. But if we try to do it in the other way, by putting together identicals, the result runs perpetually together into one and we never reach a plurality. + +If we use I to stand for each of the objects to be numbered, we make the mistake of assigning the same symbol to different things. But if we provide the iwith differentiating strokes, it + +becomes unusable for arithmetic. + +The word "unit" is admirably adapted to conceal this difficulty; and that is the real, though no doubt unconscious, reason why we prefer it to the words "object" and "thing". We start by calling the things to be numbered "units", without detracting from their diversity; then subsequently the concept + +51 of putting together (or collecting, or uniting, or annexing, or whatever we choose to call it) transforms itself into that of arithmetical addition, while the concept word "unit" changes unperceived into the proper name "one". And there we have our identity. If I annex to the letter a first an n and then a d, anyone can easily see that that is not the number 5. If, however, I bring the letters ^, n and d under the concept "unit", and now, instead of "^ and n and d'\ say "a unit and a unit and a further unit" or "i and i and i", we are quite prepared to believe that this does give us the number 3 . The difficulty is so well hidden under the word "unit", that those who have any suspicion of its existence must surely be few at most. + +Here, indeed, is an artful manipulation of language worthy of Mill's censure; for this is no outward manifestation of an inward process of thought, but only the illusion of one. Here we really do have the impression that words devoid of thought must possess some mysterious power, if what is different is to be made identical simply by being called a + +unit. + +Attempts to overcome the difficulty. + +§ 40. We consider next some detailed views which repre sent attempts to overcome this difficulty, although they have not always been produced with that end clearly and con- + +sciously in view. + +The first suggestion is to call for assistance on a certain property of time and space, as follows. One point of space, considered by itself, is absolutely indistinguishable from another, and so is a straight line, or a plane, or one of a number of congruent bodies or areas or line-segments: they are distinguishable only when conjoined as elements in a single + +52 total intuition. Here, therefore, we seem to get identity combined with distinguishability. With the parts of time, the same applies. This is presumably why Hobbes^ holds it for hardly conceivable that the identity of units should result from anything but the division of the continuum. As Thomae^ puts it: "If we consider a set of individuals or units in space and number them one after the other, for which time is necessary, then, abstract as we will, there remain always as discriminating marks of the units their different positions in + +space and in the order of succession in time." + +The first doubt that strikes us about any such view is that then nothing would be numerable except what is spatial and temporal. Leibniz^ long ago rebutted the view of the schoolmen that number results from the mere division of the con tinuum and cannot be applied to immaterial things. Baumann\* dissociates number emphatically from time: he claims that the concept of the unit is thinkable even apart from time. Jevons^ writes: "Three coins are three coins, whether we count them successively or regard them all simultaneously. In many cases neither time nor space is the ground of difference, but pure quality alone enters. We can discriminate, for instance, the weight, inertia, and hardness of gold as three qualities, though none of these is before or after the other, either in space or time. Every means of discrimination may be a source of plurality." I would add that, if the objects numbered do not follow one after another in actual fact, but it is only that they are numbered one after another, then time cannot be the ground of discrimination between them. For, if we are to be able to number them one after another, we must already be in posses- + +^ Baumann, op. cit.. Vol. I, p. 242 [loc. cit., p. 45© above]. + +Op. cit., p. I. + +Baumann, op. cit.. Vol. II, p. 2 [loc. cit., p. 316 above]. + +Op. cit.. Vol. II, p. 668. \* Op. cit., p. 157 [1874 edn., p. 176]. + +55 sion of distinguishing marks. Time isonly a psychological necessity for numbering, it has nothing to do with the concept of number. We do represent objects which are non-spatial and non-temporal by spatial or temporal points, and this may perhaps be of advantage in carrying out the procedure of numbering; but it presupposes, fundamentally, that the concept of number is applicable to the non-spatial and the non- + +temporal. + +§ 41. But further, supposing we do disregard all dis tinguishing marks except those of space and time, do we then really succeed in combining distinguishability with identity? Not at all. We are not one step nearer a solution. Whether the objects are so much more similar or so much less is beside the point, if they have still to be kept separate in the end. I cannot here symbolize the individual points, or lines or whatever itmay be, all alike by i, any more than for purposes of geometry Ican call them one and all A; in the one case as in the other, it is essential to distinguish between them. It is only considered in themselves, and neglecting their spatial relations, that points of space are identical with one another; if I am to think of them together, I am bound then to consider them in their collocation in space, or else they fuse irretriev ably together into one. Now points taken together as a group may perhaps fall into some pattern or other like a constellation or may equally arrange themselves somehow or other on a straight line; and a group of identical segments may lie perhaps with their end-points adjacent so as to combine into a single segment or perhaps at a distance from one another. Patterns produced in this way can be completely different while the number of their elements remains the same. So that here once again we should have different distinct fives, sixes, and so forth. Points of time, again, are separated by time intervals, long or short, equal or unequal. All these are relationships which have absolutely nothing to do with number as such. Pervading them all is an admixture of some special element, which number in its general form leaves far behind. Even a single moment itself has something sui generis, which serves to + +54 distinguish it from, say, a point of space, and of which there + +is no trace in the concept of number. + +§ 42. Another way out is to invoke instead of spatial or temporal order a more generalized concept of series, but this too fails of its object; for their positions in the series cannot be the basis on which we distinguish the objects, since they must already have been distinguished somehow or other, for us to have been able to arrange them in a series. Any such arrangement always presupposes relations between the objects, whether spatial or temporal or logical relations, or relations of pitch or what not, which serve to lead us on from one object to the next and which are necessarily bound up with + +distinguishing between them. + +When Hankel^ speaks of our thinking or putting a thing once or twice or three times, this too seems to be an attempt to combine in the things to be numbered distinguishability with identity. But itis obvious too at once that it is not successful; for his ideas or intuitions of the same object must, if they are not to coalesce into one, be different in some way or other. Moreover we are, I imagine, entitled to speak of 45 million Germans without having first to have thought or put an average German 45 million times, which might be somewhat + +tedious. + +§ 43. It is probably in order to avoid the difficulties which Jevons runs into through making each symbol i mean one of the objects numbered, that E. Schroder allows it only to copy the object. The consequence is that he gives a defini tion not of number but only of numerals. To give his own words^: "To arrive at a symbol capable of expressing how many + +> ^ Op. cit., p. I. \* Op. cit., pp. 5 fF. + +55 of such units^ are present, we direct our attention upon each one of them in turn once, and copy it by a stroke (a one), thus, I ;these ones we put in a row side by side, only linking them up to each other by the symbol + (plus) because otherwise III, for example, would be read, following the usual number notation, as one hundred and eleven. In this way we + +get a symbol such as: + +I + I + I + I + I, + +the composition of which we can describe by saying: + +\*v4 natural number is a sum of ones' ." + +This passage shows that for Schroder number is a symbol. What the symbol expresses, which is what I have been calling number, is taken, with the words "how many of such units are present", as already known. Even by the word "one" he understands the symbol i, not its meaning. The symbol + is introduced solely to serve as a visible mark, without any content of its own, for linking up the other symbols; only later does he define addition. He could indeed have put what he means more briefly by saying that we write down side by side as many symbols i as we have objects to be numbered, and link them up by the symbol +. Nought + +would be expressed by writing down nothing. + +§ 44. To avoid carrying over into number the distin guishing marks of the things numbered, Jevons^ invokes abstraction: "There will now be little difficulty in forming a clear notion of the nature of numerical abstraction. It consists in abstracting the character of the difference from which plurality arises, retaining merely the fact. When I speak of + +> ^ Objects to be numbered. 2 Op. cit., p. 158 [1874 edn., p. 177]. + +56 three men I need not at once specify the marks by which each may be known from each. Those marks must exist if they are really three men and not one and the same, and in speaking of them as many I imply the existence of the requisite diiferences. + +Abstract number, then, is the emptyform of difference.^'' + +How are we to interpret this? Either we can abstract from the distinguishing properties of things before uniting them into a whole: or we can first form a whole and then abstract from the distinguishing properties. By the first method we should never get so far as to distinguish the things at all, and consequently could not retain the fact of the existence of the differences either; the second method seems to be what Jevons intends. But by it we should never, it seems to me, arrive at a number like 10,000, for it is beyond our powers to grasp so many differences at once and retain the fact of their existence; while to go through them one after another is not enough, for the number would never be complete. We do our numbering in time, of course; but that does not give us the number itself, it only tells us the number of whatever it is we are numbering. Moreover, to tell us how to abstract is not, + +in any case, to defiine for us what abstraction is. + +What are we to understand by "the empty form of differ- + +ence"? Perhaps some proposition like + +"tf is different from ^" where a and h are left indefinite? Can this proposition be, say, + +the number 2? But does the proposition + +"The Earth has two poles" + +mean the same as + +"The North Pole is different from the South"? Obviously not. The second proposition could be true without the first being so, and vice versa. And for the number 10,000 + +we should then have as many as + +57 ijOoo . 999 I . 2 + +such propositions, each stating a difference. + +With the numbers o and i in particular, what Jevons says simply will not work. What is it, in fact, that we are supposed to abstract from, in order to get, for example, from the moon to the number i? By abstraction we do indeed get certain concepts, viz. satellite of the Earth, satellite of a planet, non-self-luminous heavenly body, heavenly body, body, object. But in this series i is not to be met with; for it is no concept that the moon could fall under. In the case of o, we have simply no object at all from which to start our process of abstracting. It is no good objecting that o and i are not numbers in the same sense as 2 and 3. What answers the question How many? isnumber, and if we ask, for example, "How many moons has this planet?'', we are quite as much prepared for the answer o or ias for 2 or 3, and that without having to understand the question differently. No doubt there is something unique about o, and about i too; but the same is true in principle of every whole number, only the bigger the number the less obvious it is. To make out of this a difference in kind is utterly arbitrary. What will not work with o and i cannot be essential to the concept of number. + +Finally, by taking number to arise in this manner we do not by any means remove the difficulty encountered when we + +were considering the symbolization of 5 by + +I'-f I" 4- i"'-f i""+ I'"". This notation agrees well with what Jevons says about the formation of number by abstraction; the strokes above the line, that is, indicate that a difference exists, without however specifying of what sort. But the mere existence of the dif ference is already enough, as we have seen, to produce on Jevons' view different distinct ones and twos and threes. + +58 which is utterly incompatible with the existence of arith metic. • + +Solution of the difficulty. § 45. It is time now to survey what has been so far established and the questions which still remain unanswered. Number is not abstracted from things in the way that colour, weight and hardness are, nor is it a property of things in the sense that they are. But when we make a statement of number\*, what isthat of which we assert something? This + +question remained unanswered. + +Number is not anything physical, but nor is it anything + +subjective (an idea). + +Number does not result from the annexing of thing to thing. It makes no difference even if we assign a fresh name + +after each act of annexation. + +The terms "multitude", "set" and "plurality" are unsuitable, owing to their vagueness, for use in defining number. In considering the terms one and unit, we left unanswered the question: How are we to curb the arbitrariness of our ways of regarding things, which threatens to obliterate every + +distinction between one and many? + +Being isolated, being undivided, being incapable of dissection—none of these can serve as a criterion for what we + +express by the word "one". + +If we call the things to be numbered units, then the + +assertion that units are identical is, if made without qualification, false. That they are identical in this respect or that is true enough but of no interest. It is actually necessary that the things to be numbered should be different if number is + +to get beyond i. + +We were thus forced, it seemed, to ascribe to units two + +contradictory qualities, namely identity and distinguish- + +ability. + +A distinction must be drawn between one and unit. The word "one", as the proper name of an object of mathe- + +\* [See n. on p. 346 supra.] + +59 matical study, does not admit of a plural. Consequently, it is nonsense to make numbers result from the putting together of ones. The plus symbol in i + i = 2 cannot mean such a + +putting together. + +§ 46. It should throw some light on the matter to consider number in the context of a judgement which brings out its basic use. While looking at one and the same external phenomenon, I can say with equal truth both "It is a copse" and "It is five trees", or both "Here are four companies" and "Here are 500 men". Now what changes here from one judgement to the other is neither any individual object, nor the whole, the agglomeration of them, but rather my terminology. But that is itself only a sign that one concept has been substituted for another. This suggests as the answer to the first of the questions left open in our last paragraph, that the content of a statement of number is an assertion about a concept. This is perhaps clearest with the number o. If I say "Venus has o moons", there simply does not exist any moon or agglomeration of moons for anything to be asserted of; but what happens is that a property is assigned to the concept "moon of Venus", namely that of including nothing under it. If I say "the King's carriage is drawn by four horses", then I assign the number four to the concept "horse that draws the + +King's carriage". + +It may be objected that a concept like "inhabitant of Germany" would then possess, in spite of there being no change in its defining characteristics, a property which varied from year to year, if statements of the number of inhabitants did really assert a property of it. In reply to this, it is enough to point out that objects too can change their properties without that preventing us from recognizing them as the same. In this case, however, we can actually give the explanation more precisely. The fact is that the concept "inhabitant of Germany" contains a time-reference as a variable element in it, or, to put it mathematically, is a function of the time. + +6o Instead of "a is an inhabitant of Germany" we can say "a inhabits Germany", and this refers to the current date at the time. Thus in the concept itself there is already something fluid. On the other hand, the number belonging to the concept "inhabitant of Germany at New Year 1883, Berlin time" is + +the same for all eternity. + +§ 47. That a statement of number should express something factual independent of our way of regarding things can surprise only those who think a concept is something subjective like an idea. But this is a mistaken view. If, for example, we bring the concept of body under that of what has weight, or the concept of whale under that of mammal, we are asserting something objective; but if the concepts themselves were subjective, then the subordination of one to the other, being a relation between them, would be subjective too, just as a relation between ideas is. It is true that at first sight the + +proposition + +"All whales are mammals" + +seems to be not about concepts but about animals; but if we ask which animal then are we speaking of, we are unable to point to any one in particular. Even supposing a whale is before us, our proposition still does not state anything about it. We cannot infer from it that the animal before us is a mammal without the additional premiss that it is a whale, as to which our proposition says nothing. As a general principle, it is impossible to speak of an object without in some way designating or naming it; but the word "whale" is not the name of any individual creature. If it be replied that what we are speaking of is not, indeed, an individual definite object, but nevertheless an indefinite object, I suspect that "indefinite object" is only another term for concept, and a poor one at that, being + +6i self-contradictory. However true it may be that our proposition can only be verified by observing particular animals, that proves nothing as to its content; to decide what it is about, we do not need to know whether itis true or not, nor for what reasons we believe it to be true. If, then, a concept is something objective, an assertion about a concept can have for its + +part a factual content. + +§ 48. Several examples given earlier gave the false impression that different numbers may belong to the same thing. This is to be explained by the fact that we were there taking objects to be what has number. As soon as we restore possession to the rightful owner, the concept, numbers reveal themselves as no less mutually exclusive in their own sphere + +than colours are in theirs. + +We now see also why there is a temptation to suggest that we get the number by abstraction from the things. What we do actually get by such means isthe concept, and in this we then discover the number. Thus abstraction does genuinely often precede the formation of a judgement of number. It would be an analogous confusion to maintain that the way to acquire the concept of fire risk is to build a frame house, with timber gables, thatched roof and leaky chimneys. + +The concept has a power of collecting together far superior to the unifying power of synthetic apperception. By means of the latter it would not be possible to join the inhabitants of Germany together into a whole; but we can certainly bring them all under the concept "inhabitant of Germany" and + +number them. + +The wide range of applicability of number also now becomes explicable. Not without reason do we feel it puzzling that we should be able to assert the same predicate of physical and mental phenomena aUke, of the spatial and temporal and of the non-spatial and non-temporal. But then, this simply is not what occurs with statements of number any more than elsewhere; numbers are assigned only to the concepts, vmder + +62 which are brought both the physical and mental alike, both the spatial and temporal and the non-spatial and non-temporal. + +§ 49. Corroboration for our view is to be found in Spinoza,^ where he writes: "I answer that a thing is called one or single simply with respect to its existence, and not with respect to its essence; for we only think of things in terms of number after they have first been reduced to a common genus. For example, a man who holds in his hand a sesterce and a dollar will not think of the number two unless he can cover his sesterce and his dollar with one and the same name, viz., piece of silver, or coin; then he can affirm that he has two pieces of silver, or two coins; since he designates by the name piece of silver or coin not only the sesterce but also the dollar." Unfortunately, he goes on: "From this it is clear, therefore, that nothing is called one or single except when some other thing has first been conceived which, as has been said, matches it", and he holds further that we carmot properly call God one or single, because it would be impossible for us to form an abstract concept of his essence. Here he makes the mistake of supposing that a concept can only be acquired by direct abstraction from a number of objects. We can, on the contrary, arrive at a concept equally well by starting from defining characteristics; and in such a case it is possible for nothing to fall under it. If this did not happen, we should never be able to deny existence, and so the assertion of existence + +too would lose all content. + +§ 50. E. Schroder^ calls attention to the fact that, if we are to be able to speak of the frequency of a thing, the name of the thing concerned must always be a generic name^ a general concept word or notio communis; "So soon, that is, as we picture an object complete—with all its properties and in + +^ Baumann, op. cit.. Vol. I, p. 169 [Epistolae doctorum quorundam virorum. + +No. 50 ad']. Jelles]. « Op. cit., p. 6. + +65 all its relations, it will present itself as unique in the universe, and there will no longer be anything to match it. The name of the object takes on at once the character of a proper name {nomen proprium), and the object itself cannot be thought of as one which is found more than once. But observe that this holds good not only of concrete objects, but generally of anything and everything, even where the idea of it arises through abstractions^ provided only that this idea contains in it sufficient elements to constitute the thing concerned a completely determinate thing. . .". For a thing to be numbered "first becomes possible in so far as, for that purpose, we dis regard or abstract from some of its peculiar characteristics and relations, which distinguish it from all other things; this has the effect of turning what was the name of the thing + +into a concept applicable to more than one thing." + +§ 51. What is true in this account is wrapped up in such distorted and misleading language, that we are obliged to straighten it out and sort the wheat from the chaff. To start with, it will not do to call a general concept word the name of a thing. That leads straight to the illusion that the number is a property of a thing. The business of a general concept word isprecisely to signify a concept. Only when conjoined with the definite article or a demonstrative pronoun can it be counted as the proper name of a thing, but in that case it ceases to count as a concept word. The name of a thing is a proper name. An object, again, is not found more than once, but rather, more than one object falls under the same concept. That a concept need not be acquired by abstraction from the things which fall under it has already been pointed out in criticizing Spinoza. Here Iwill add that a concept does not cease to be a concept simply because only one single thing falls under it, which thing, accordingly, is completely determined by it. It is to concepts of just this kind (for example, satellite of the Earth) that the number i belongs. + +64 which is a number in the same sense as 2 and 3. With a concept the question is always whether anything, and if so what, falls under it. With a proper name such questions make no sense. We should not be deceived by the fact that language makes use of proper names, for instance Moon, as concept words, and vice versa; this does not affect the distinction between the two. As soon as a word is used with the indefinite article or in the plural without any article, it is a concept word. § 52. Further confirmation of the view that number is assigned to concepts is to be found in idiom; just as in English we can speak of "three barrel", so in German we speak generally of "ten man", "four mark" and so on. The use of the singular here may indicate that the concept is intended, not the thing. The advantage of this way of speaking is particularly noticeable in the case of the number o. Elsewhere, it must be admitted, our ordinary language does assign number not to concepts but to objects: we speak of "the number of the bales" just as we do of "the weight of the bales". Thus on the face of it we are talking about objects, whereas really we are intending to assert something of a concept. This usage is confusing. The construction in "four thoroughbred horses" fosters the illusion that "four" modifies the concept "thoroughbred horse" in just the same way as "thoroughbred" modifies the concept "horse." Whereas in fact only "thoroughbred" is a characteristic used in this way; the word "four" is used to + +assert something of a concept. + +§ 53. By properties which are asserted of a concept I naturally do not mean the characteristics which make up the concept. These latter are properties of the things which fall under the concept, not of the concept. Thus "rectangular" is not a property of the concept "rectangular triangle"; but the proposition that there exists no rectangular equilateral rectilinear triangle does state a property of the concept "rectangular equilateral rectilinear triangle"; it assigns to it + +the number nought. + +65 In this respect existence is analogous to number. Affirmation of existence is in fact nothing but denial of the number nought. Because existence is a property of concepts the ontological argument for the existence of God breaks down. But oneness\* is not a component characteristic of the concept "God" any more than existence is. Oneness cannot be used in the definition of this concept any more than the solidity of a house, or its commodiousness or desirability, can be used in building it along with the beams, bricks and mortar. However, it would be wrong to conclude that it is in principle impossible ever to deduce from a concept, that is, from its component characteristics, anything which is a property of the concept. Under certain conditions this is possible, just as we can occasionally infer the durability of a building from the type of stone used in building it. It would therefore be going too far to assert that we can never infer from the component characteristics of a concept to oneness or to existence; what is true is, that this can never be so direct a matter as it is to assign some component of a concept as a property to an object + +falling under it. + +It would also be wrong to deny that existence and oneness can ever themselves be component characteristics of a concept. What is true is only that they are not components of those particular concepts to which language might tempt us to ascribe them. If, for example, we collect under a single concept all concepts under which there falls only one object, then oneness is a component characteristic of this new concept. Under it would fall, for example, the concept "moon of the Earth", though not the actual heavenly body called by this name. In this way we can make one concept fall under another higher or, so to say, second order concept. This relationship, however, should not be confused with the subordination of + +species to genus. + +§ 54. It now becomes possible to give a satisfactory definition of the term "unit". E. Schroder writes, on p. 7 of his text book already referred to: "This generic name or \* [I.e. the character of being single or unique, called by theologians "unity".] + +66 concept will be called the denomination of the number formed by the method given, and constitutes, in effect, what ismeant + +by its unit." + +Why not, in fact, adopt this very apt suggestion, and call a concept the unit relative to the Number which belongs to it? We can then achieve a sense for the assertions made about the unit, that it is isolated from its environment and isindivisible. For it is the case that the concept, to which the number isassigned, does in general isolate in a definite manner what falls under it. The concept "letters in the word three" isolates the / from the hy the h from the r, and so on. The concept "syllables in the word three" picks out the word as a whole, and as indivisible in the sense that no part of itfalls any longer under that same concept. Not all concepts possess this quality. We can, for example, divide up something falling under the concept "red" into parts in a variety of ways, without the parts thereby ceasing to fall under the same concept "red". To a concept of this kind no finite number will belong. The proposition asserting that units are isolated and indivisible + +can, accordingly, be formulated as follows: + +Only a concept which isolates what falls under it in a definite manner, and which does not permit any arbitrary division of it into parts, can be a unit relative to a finite + +Number. + +It will be noticed, however, that "indivisibility" here + +has a special meaning. + +We can now easily solve the problem of reconciling the identity of units with their distinguishability. The word "unit" is being used here in a double sense. The units are identical if the word has the meaning just explained. In the proposition "Jupiter has four moons", the unit is "moon of Jupiter". Under this concept falls moon I, and likewise also moon n, and moon III too, and finally moon IV. Thus we can say: the unit to which I relates is identical with the unit to which n relates, and so on. This gives us our identity. + +67 But when we assert the distinguishability of units, we mean + +that the things numbered are distinguishable. + +IV. The concept of Number. + +Every individual number is a self-subsistent object. + +§55. Now that we have learned that the content of a statement of number is an assertion about a concept, we can try to complete the Leibnizian definitions of the individual + +numbers by giving the definitions of o and of i. + +It is tempting to define o by saying that the number o belongs to a concept if no object falls under it. But this seems to amount to replacing o by "no", which means the same. The following formulation is therefore preferable: the number o belongs to a concept, if the proposition that a does not fall under that concept is true universally, whatever + +a may be. + +Similarly we could say: the number i belongs to a concept F, if the proposition that a does not fall under F is not true universally, whatever a may be, and if from the propositions "^ falls under F" and "b falls under F" + +it foUows universally that a and b are the same. + +It remains still to give a general definition of the step from any given number to the next. Let us try the following formulation: the number {n -\- 1) belongs to a concept F, if there is an object a falling under F and such that the number + +n belongs to the concept "falUng under F, but not a". + +§ 56. These definitions suggest themselves so spontaneously in the light of our previous results, that we shall have to go into the reasons why they cannot be reckoned satisfactory. The most likely to cause misgivings is the last; for strictly + +speaking we do not know the sense of the expression "the + +68 number n belongs to the concept G" any more than we do that of the expression "the number (« -f i) belongs to the concept F". We can, of course, by using the last two defini- + +tions together, say what ismeant by + +"the number i + i belongs to the concept F" + +and then, using this, give the sense of the expression + +"the number i + i + i belongs to the concept F" and so on; but we can never—to take a crude example decide by means of our definitions whether any concept has the number Julius Caesar belonging to it, or whether that same familiar conqueror of Gaul is a number or is not. Moreover we cannot by the aid of our suggested definitions prove that, if the number a belongs to the concept F and the number b belongs to the same concept, then necessarily a = b. Thus we should be unable to justify the expression "the number which belongs to the concept F", and therefore should find it impossible in general to prove a numerical identity, since we should be quite unable to achieve a determinate number. It is only an illusion that we have defined o and i; in reality we have + +only fixed the sense of the phrases + +"the number o belongs to" "the number i belongs to"; but we have no authority to pick out the o and i here as self subsistent objects that can be recognized as the same again. + +§ 57. It is time to get a clearer view of what we mean by our expression "the content of a statement of number is an assertion about a concept". In the proposition "the number o belongs to the concept F", o is only an element in the predicate (taking the concept F to be the real subject). For this reason I have avoided calling a number such as o or i or 2 2iproperty of a concept. Precisely because it forms only an element in what isasserted, the individual number shows itself for what it is, a self-subsistent object. I have already drawn attention above to the fact that we speak of "the number i", where the definite article serves to class it as an object. In arithmetic this self- + +69 subsistence comes out at every turn, as for example in the identity i -{- i = z. Now our concern here is to arrive at a concept of number usable for the purposes of science; we should not, therefore, be deterred by the fact that in the language of everyday life number appears also in attributive constructions. That can always be got round. For example, the proposition "Jupiter has four moons" can be converted into "the number of Jupiter's moons is four". Here the word "is" should not be taken as a mere copula, as in the proposition "the sky is blue". This is shown by the fact that we can say: "the number of Jupiter's moons isthe number four, or 4" Here "is" has the sense of "is identical with" or "is the same as". So that what we have is an identity, stating that the expression "the number of Jupiter's moons" signifies the same object as the word "four". And identities are, of all forms of proposition, the most typical of arithmetic. It is no objection to this account that the word "four" contains nothing about Jupiter or moons. No more is there in the name "Columbus" anything about discovery or about America, yet for all that it is the same man that we call Columbus and the discoverer of + +America. + +§ 5 8. A possible criticism is, that we are not able to form of this object which we are calling Four or the Number of Jupiter's moons any sort of idea^ at all which would make it something self-subsistent. But that is not the fault of the self subsistence we have ascribed to the number. It is easy, I know, to suppose that in our idea of four dots on a die there is to be found something which corresponds to the word "four"; but that is a misapprehension. We have only to think of a green field, and try whether the idea alters when we replace the indefinite article by the number word "one"; nothing fresh is added—whereas with the word "green", there really is in the idea something which corresponds to it. If we + +^ "Idea" in the sense of something like a picture. + +70 imagine the printed word "gold", we shall not immediately think of any number in connexion with it. If we now ask ourselves how many letters it contains, the number 4 is the result; yet the idea does not become in consequence any more definite, but may remain completely unaltered. Where we discover the number is precisely in the freshly added concept "letter in the word gold". In the case of the four dots on the die, the matter is rather more obscured, because the concept thrusts itself upon us so immediately, owing to the similarity of the dots, that we scarcely notice its intervention. We can form no idea of the number either as a self-subsistent object or as a property in an external thing, because it is not in fact either anything sensible or a property of an external thing. But the point is clearest in the case of the number o; we shall try in vain to form an idea of o visible stars. We can, of course, think of a sky entirely overcast with clouds; but in this there is nothing to. correspond to the word "star" or to o. All we succeed in imagining is a situation where the natural judgement + +to make would be: No star is now to be seen. + +§ 59. It may be that every word calls up some sort of idea in us, even a word like "only"; but this idea need not correspond to the content of the word; it may be quite different in different men. The sort of thing we do is to imagine a situation where some proposition in which the word occurs would be called for; or it may happen that the spoken word + +recalls the written word to our memory. + +Nor does this happen only in the case of particles. There is not the slightest doubt that we can form no idea of our distance from the sun. For even although we know the rule that we must multiply a measuring rod so and so many times, we still fail in every attempt to construct by its means a picture approximating even faintly to what we want. Yet this is no + +71 reason for doubting the correctness of the calculation which established the distance, not does it prevent us in any way from taking that distance as a fact upon which to base further + +inferences. + +§ 60. Even so concrete a thing as the Earth we are unable to imagine as we know it to be; instead, we content ourselves with a ball of moderate size, which serves us as a symbol for the Earth, though we know quite well it is very different from it. Thus even although our idea often fails entirely to coincide with what we want, we still make judgements about an object such as the Earth with considerable + +certainty, even where its size is in point. + +Time and time again we are led by our thought beyond the scope of our imagination, without thereby forfeiting the support we need for our inferences. Even if, as seems to be the case, it is impossible for men such as we are to think without ideas, it is still possible for their connexion with what we are thinking of to be entirely superficial, arbitrary + +and conventional. + +That we can form no idea of its content is therefore no + +reason for denying all meaning to a word, or for excluding it from our vocabulary. We are indeed only imposed on by the opposite view because we will, when asking for the meaning of a word, consider it in isolation, which leads us to accept an idea as the meaning. Accordingly, any word for which we can find no corresponding mental picture appears to have no content. But we ought always to keep before our eyes a complete proposition. Only in a proposition have the words really a meaning. It may be that mental pictures float before us all the while, but these need not correspond to the logical elements in the judgement. It is enough if the proposition taken as a whole has a sense; it is this that confers on its parts + +also their content. + +This observation is destined, I believe, to throw light + +72 on quite a number of difficult concepts, among them that of the infinitesimal/ and its scope is not restricted to mathematics + +either. + +The self-subsistence which I am claiming for number is not to be taken to mean that a number word signifies something when removed from the context of a proposition, but only to preclude the use of such words as predicates or + +attributes, which appreciably alters their meaning. + +§ 6i. But, it will perhaps be objected, even if the Earth is really not imaginable, it is at any rate an external thing, occupying a definite place; but where is the number 4? It is neither outside us nor within us. And, taking those words in their spatial sense, that is quite correct. To give spatial co-ordinates for the number 4 makes no sense; but the only conclusion to be drawn from that is, that 4 is not a spatial object, not that it is not an object at all. Not every object has a place. Even our ideas^ are in this sense not within us (beneath our skin); beneath the skin are nerve-ganglia, blood corpuscles and things of that sort, but not ideas. Spatial predicates are not applicable to them: an idea is neither to the right nor to the left of another idea; we cannot give distances between ideas in millimetres. If we still say they are within us, then we intend by this to signify that they are subjective. + +Yet even granted that what is subjective has no position + +in space, how is it possible for the number 4, which isobjective, not to be anywhere? Now I contend that there is no contradiction in this whatever. It is a fact that the number 4 is exactly the same for everyone who deals with it; but that has nothing to do with being spatial. Not every objective + +object\* has a place. + +^ The problem here is not, as might be thought, to produce a segment bounded by two distinct points whose length is dx, but rather to define the + +sense of an identity of the type + +df{x) = g(x)dx \* Understanding this word in its purely psychological, not in its psycho- + +physical, sense. + +\* [objektives Gegenstand] + +To obtain the concept of Number^ we mustfix the sense of a numerical identity. + +§ 62. How, then, are numbers to be given to us, if we cannot have any ideas or intuitions of them? Since it is only in the context of a proposition that words have any meaning, our problem becomes this : To define the sense of a proposition in which a number word occurs. That, obviously, leaves us still a very wide choice. But we have already settled that number words are to be understood as standing for self subsistent objects. And that is enough to give us a class of propositions which must have a sense, namely those which express our recognition of a number as the same again. If we are to use the symbol a to signify an object, we must have a criterion for deciding in all cases whether h is the same as <7, even if it is not always in our power to apply this criterion. In our present case, we have to define the sense of the + +proposition + +"the number which belongs to the concept F is the same as that which belongs to the concept G"; + +that is to say, we must reproduce the content of this proposition in other terms, avoiding the use of the expression + +"the Number which belongs to the concept F". In doing this, we shall be giving a general criterion for the identity of numbers. When we have thus acquired a means of arriving at a determinate number and of recognizing it again as the same, we can assign it a number word as its proper + +name. + +§ 65. HuMfii long ago mentioned such a means: "When two numbers are so combined as that the one has always an unit answering to every unit of the other, we pronounce them equal." This opinion, that numerical equality or identity + +\* Baumann, op. cit.. Vol. II, p. 565 Treatise, Bk. I, Part iii. Sect. i]. + +74 must be defined in terms of one-one correlation, seems in recent years to have gained widespread acceptance among mathematicians.^ But it raises at once certain logical doubts and difficulties, which ought not to be passed over without + +examination. + +It is not only among numbers that the relationship of identity is found. From which it seems to follow that we ought not to define it specially for the case of numbers. We should expect the concept of identity to have been fixed first, and that then, from it together with the concept of Number, it must be possible to deduce when Numbers are identical with one another, without there being need for this purpose of + +a special definition of numerical identity as well. + +As against this, it must be noted that for us the concept of Number has not yet been fixed, but is only due to be deter mined in the light of our definition of numerical identity. Our aim is to construct the content of a judgement which can be taken as an identity such that each side of it is a number. We are therefore proposing not to define identity specially for this case, but to use the concept of identity, taken as already known, as a means for arriving at that which isto be regarded as being identical. Admittedly, this seems to be a very odd kind of definition, to which logicians have not yet paid enough attention; but that it is not altogether unheard of, may be + +shown by a few examples. + +§ 64. The judgement "line a is parallel to line Z?", or, + +using symbols, + +can be taken as an identity. If we do this, we obtain the concept of direction, and say: "the direction of line a is identical with the direction of Une V. Thus we replace the symbol / / by + +\* Cf. E. Schroder, op. cit., pp. 7-8; E. Kossak, Die Elemente der Arithmelik, Program>fi des Friedrichs-Werder'schen Gymnasiums, Berlin 1872, p. i6; G. Cantor, + +Grundlagen einer allgemeimn Alannichfaltigkeitsleijre, Leipzig 1883. + +75 the more generic symbol =, through removing what isspecific in the content of the former and dividing it between a and h. We carve up the content in a way different from the original way, and this yields us a new concept. Often, of course, we conceive of the matter the other way round, and many authorities define parallel lines as lines whose directions are identical. The proposition that "straight lines parallel to the same straight line are parallel to one another" can than be very conveniently proved by invoking the analogous proposition about things identical with the same thing. Only the trouble is, that this is to reverse the true order of things. For surely everything geometrical must be given originally in intuition. But now I ask whether anyone has an intuition of the direction of a straight line. Of a straight line, certainly; but do we distinguish in our intuition between this straight line and something else, its direction? That is hardly plausible. The concept of direction is only discovered at all as a result of a process of intellectual activity which takes its start from the intuition. On the other hand, we do have an idea of parallel straight lines. Our convenient proof is only made possible by surreptitiously assuming, in our use of the word "direction", what was to be proved; for if it were false that "straight lines parallel to the same straight line are parallel to one another", + +then we could not transform a \ \h into an identity. + +We can obtain in a similar way from the parallelism of planes a concept corresponding to that of direction in the case of straight lines; I have seen the name "orientation"\* used for this. From geometrical similarity is derived the concept of shape, so that instead of "the two triangles are similar" we say "the two triangles are of identical shape" or "the shape of the one is identical with that of the other". It is possible to derive yet another concept in this way, to which no name has yet been given, from the collincation of geometrical forms. + +\* \Stellmg\ + +76 § 65 . Now in order to get, for example, from parallelism^ to the concept of direction, let us try the following definition: + +The proposition + +"line a is parallel to line Z>" + +is to mean the same as + +"the direction of line a is identical with the direction of line ^". This definition departs to some extent from normal practice, in that it serves ostensibly to adapt the relation of identity, taken as already known, to a special case, whereas in reality it is designed to introduce the expression "the direction of line a^\ which only comes into it incidentally. It is this that gives rise to a second doubt—are we not liable, through using such methods, to become involved in conflict with the well-known laws of identity? Let us see what these are. As analytic truths they should be capable of being derived from the concept itself alone. Now Leibniz's^ definition is as + +follows: + +"Things are the same as each other, of which one can be substituted for the other without loss of truth".\* This I propose to adopt as my own definition of identity. Whether we use "the same", as Leibniz does, or "identical", is not of any importance. "The same" may indeed be thought to refer to complete agreement in all respects, "identical"\*\* only to agreement in this respect or that; but we can adopt a form of expression such that this distinction vanishes. For example, instead of "the segments are identical in length", we can say "the length of the segments is identical" or "the same", and instead of "the surfaces are identical in colour", "the colour of the surfaces is identical". And this is the way in which the word has been used in the examples above. ^ I have chosen to discuss here the case of parallelism, because I can express myself less clumsily and make myself more easily understood. The argument can readily be transferred in essentials to apply to the case of numerical identity, \* iVo« imlegans specimen demonstrandi in abstractis (Erdmann edn., p. 94). + +\* [Eadem sunt, quorum unum potest substitui alter! salva veritaie.\ \*\* [Still more "equal" or "similar", which the German gleich can also mean.] + +77 Now, it is actually the case that in universal substitutability + +all the laws of identity are contained. + +In order, therefore, to justify our proposed definition of the direction of a line, we should have to show that it is + +possible, if line a is parallel to line h, to substitute + +"the direction of ^" + +everywhere for + +"the direction of a". This task is made simpler by the fact that we are being taken initially to know of nothing that can be asserted about the direction of a line except the one thing, that it coincides with the direction of some other line. We should thus have to show only that substitution was possible in an identity of this one type, or in judgement-contents containing such identities as constituent elements.^ The meaning of any other type of assertion about directions would have first of all to be defined, and in defining it we can make it a rule always to see that it must remain possible to substitute for the direction of any line + +the direction of any line parallel to it. + +§ 66. But there is still a third doubt which may make us + +suspicious of our proposed definition. In the proposition + +"the direction of a is identical with the direction of ^" the direction of ^ plays the part of an object,^ and our definition affords us a means of recognizing this object as the same again, in case it should happen to crop up in some other guise, say as the direction of h. But this means does not provide for all \* In a hypothetical judgement, for example, an identity of directions might + +occur as antecedent or consequent. + +\* This is shown by the definite article. A concept is for me that which can be predicate of a singular judgement-content, an object that which can be sub- + +ject of the same. If in the proposition + +"the direction of the axis of the telescope is identical with the direction of the Earth's axis" we take the direction of the axis of the telescope as subject, then the predicate is "identical with the direction of the Earth's axis". This is a concept. But the direction of the Earth's axis is only an element in the predicate; it, since it can + +also be made the subject, is an object. + +78 cases. It will not, for instance, decide for us whether England is the same as the direction of the Earth's axis—if I may be forgiven an example which looks nonsensical. Naturally no one is going to confuse England with the direction of the Earth's axis; but that is no thanks to our definition of direction. + +That says nothing as to whether the proposition + +"the direction of a is identical with ^" should be affirmed or denied, except for the one case where q is given in the form of "the direction of ^". What we lack is the concept of direction; for if we had that, then we could lay it down that, if q is not a direction, our proposition is to be denied, while if it is a direction, our original definition will decide whether itis to be denied or affirmed. So the temptation + +is to give as our definition: + +^ is a direction, if there is a line h whose direction is q. But then we have obviously come round in a circle. For in order to make use of this definition, we should have to know + +already in every case whether the proposition + +"^ is identical with the direction of V + +was to be affirmed or denied. + +§ 67. If we were to try saying: ^ is a direction if it is introduced by means of the definition set out above, then we should be treating the way in which the object q is introduced as a property of ^, which it is not. The definition of an object does not, as such, really assert anything about the object, but only lays down the meaning of a symbol. After this has been done, the definition transforms itself into a judgement, which does assert about the object; but now it no longer introduces the object, it is exactly on a level with other asser tions made about it. If, moreover, we were to adopt this way out, we should have to be presupposing that an object can only be given in one single way; for otherwise it would not follow, from the fact that q was not introduced by means of our defini tion, that it could not have been introduced by means of it. All identities would then amount simply to this, that whatever + +79 is given to us in the same way is to be reckoned as the same. This, however, is a principle so obvious and so sterile as not to be worth stating. We could not, in fact, draw from it any conclusion which was not the same as one of our premisses. Why is it, after all, that we are able to make use of identities with such significant results in such divers fields? Surely it is rather because we are able to recognize something as the same + +again even although it is given in a different way. + +§ 68. Seeing that we cannot by these methods obtain any concept of direction with sharp limits to its application, nor therefore, for the same reasons, any satisfactory concept of Number either, let us try another way. If line a is parallel to line ^, then the extension of the concept "line parallel to line a" is identical with the extension of the concept "line parallel to line V; and conversely, if the extensions of the two concepts just named are identical, then a is parallel to h. Let us + +try, therefore, the following type of definition: + +the direction of line a is the extension of the concept + +"parallel to line ^"; + +the shape of triangle / is the extension of the concept + +"similar to triangle /". + +To apply this to our own case of Number, we must substitute for lines or triangles concepts, and for parallelism or similarity the possibility of correlating one to one the objects which fall under the one concept with those which fall under the other. For brevity, I shall, when this condition is satisfied, speak of the concept F being equal"^ to the concept G; but I must ask that this word be treated as an arbitrarily selected symbol, whose meaning is to be gathered, not from its + +etymology, but from what ishere laid down. My definition is therefore as follows: + +the Number which belongs to the concept F is the + +\* [Gleick(ablig—an invented word, literally "identinumerate" or "taut arithmic" ; but these are too clumsy for constant use. Other translators have used "equinumerous"; "equinumerate" would be better. Later writers have used "similar" in this connexion (but as a predicate of "class" not of "concept").] + +extension^ of the concept "equal to the concept + +F". + +§ 69. That this definition is correct will perhaps be hardly evident at first. For do we not think of the extensions of concepts as something quite different from numbers? How we do think of them emerges clearly from the basic assertions + +we make about them. These are as follows: 1. that they are identical, + +2. that one is wider than the other. + +But now the proposition: + +the extension of the concept "equal to the concept F" is identical with the extension of the concept "equal + +to the concept G" is true if and only if the proposition + +"the same number belongs to the concept F as to the concept G" + +is also true. So that here there is complete agreement. + +Certainly we do not say that one number iswider than another, in the sense in which the extension of one concept is wider than that of another; but then it is also quite impos- + +sible for a case to occur where + +the extension of the concept "equal to the concept F" + +would be wider than + +^ I believe that for "extension of the concept" we could write simply "con- + +cept". But this would be open to the two objections: + +1. that this contradicts my earlier statement that the individual numbers are objects, as is indicated by the use of the definite article in expressions like "the number two" and by the impossibility of speaking of ones, twos, etc. in the plural, as also by the fact that the number constitutes only an element + +in the predicate of a statement of number; + +2. that concepts can have identical extensions without themselves co- + +inciding. + +I am, as it happens, convinced that both these objections can be met; but to do this would take us too far afield for present purposes. I assume that it is known + +what the extension of a concept is. + +the extension of the concept "equal to the concept G". + +For on the contrary, when all concepts equal to G are also equal to F, then conversely also all concepts equal to F are equal to G. "Wider" as used here must not, of course, be + +confused with "greater" as used of numbers. + +Another type of case is, I admit, conceivable, where the extension of the concept "equal to the concept F" might be wider or less wide than the extension of some other concept, which then could not, on our definition, be a Number; and it is not usual to speak of a Number as wider or less wide than the extension of a concept; but neither is there anything to prevent us speaking in this way, if such a case should + +ever occur. + +Our definition completed and its worth proved. + +§ 70. Definitions show their worth by proving fruitful. Those that could just as well be omitted and leave no link missing in the chain of our proofs should be rejected as + +completely worthless. + +Let us try, therefore, whether we can derive from our definition of the Number which belongs to the concept F any of the well-known properties of numbers. We shall confine + +ourselves here to the simplest. + +For this it is necessary to give a rather more precise account still of the term "equality". "Equal" we defined in terms of one-one correlation, and what must now be laid down is how this latter expression is to be understood, since it might easily be supposed that it had something to do with + +intuition. + +We will consider the following example. If a waiter wishes to be certain of laying exactly as many knives on a table as plates, he has no need to count either of them; all he + +82 has to do is to lay immediately to the right of every plate a knife, taking care that every knife on the table lies immediately to the right of a plate. Plates and knives are thus correlated one to one, and that by the identical spatial relationship. + +Now if in the proposition + +"a lies immediately to the right of A" we conceive first one and then another object inserted in place of a and again of Ay then that part of the content which remains unaltered throughout this process constitutes the essence of the relation. What we need is a generalization of + +this. + +If from a judgement-content which deals with an object a and an object b we subtract a and b, we obtain as remainder a relation-concept which is, accordingly, incomplete at two + +points. If from the proposition + +"the Earth is more massive than the Moon" we subtract "the Earth", we obtain the concept "more massive than the Moon". If, alternatively, we subtract the object, "the Moon", we get the concept "less massive than the Earth". But if we subtract them both at once, then we are left with a relation-concept, which taken by itself has no [assertible] sense any more than a simple concept has: it has always to be completed in order to make up a judgement-content. It can however be completed in different ways: instead of Earth and Moon I can put, for example. Sun and Earth, and + +this eo ipso effects the subtraction. + +Each individual pair of correlated objects stands to the relation-concept much as an individual object stands to the concept under which itfalls—we might call them the subject of the relation-concept. Only here the subject is a composite one. Occasionally, where the relation in question is convertible, this fact achieves verbal recognition, as in the proposi- + +83 tion "Peleus and Thetis were the parents of Achilles".^ But not always. For example, it would scarcely be possible to put the proposition "the Earth is bigger than the Moon" into other words so as to make "the Earth and the Moon" appear as a composite subject; the "and" must always indicate that the two things are being put in some way on a level. + +However, this does not affect the issue. + +The doctrine of relation-concepts is thus, like that of simple concepts, a part of pure logic. What is of concern to logic is not the special content of any particular relation, but only the logical form. And whatever can be asserted of this, is true analytically and known a priori. This is as true + +of relation-concepts as of other concepts. + +Just as + +"tf falls under the concept F\*\* is the general form of a judgement-content which deals with + +an object a, so we can take + +"a stands in the relation ^ to b" as the general form of a judgement-content which deals with + +an object a and an object b. + +§ 71. If now every object which falls under the concept F stands in the relation ^ to an object falling under the concept G, and if to every object which falls under G there stands in the relation j> an object falling under F, then the objects falling under F and under G are correlated with each other + +by the relation <^. + +It may still be asked, what is the meaning of the expres- + +sion + +"every object which falls under F stands in the relation + +^ to an object falling under G" + +in the case where no object at all falls under F. I understand + +this expression as follows: + +^ This type of case should not be confused with another, in which the "and" joins the subjects in appearance only, but in reality joins two propositions. + +"^faUs under F" and "tf does not stand in the relation ^ to any object falling under G" cannot, whatever be signified by a, both be true together; so that either the first proposition is false, or the second is, or both are. From this it can be seen that the proposition "every object which falls under F stands in the relation (j) to an object falling under G" is, in the case where there is no object falling under F, true; for in that case the first proposition + +"a faUs under F" + +is always false, whatever a may be. + +In the same way the proposition + +"to every object which falls under G there stands in + +the relation ^ an object falling under F" + +means that the two propositions + +''a faUs under G" and "no object falling under F stands to a in the relation ^" + +cannot, whatever a may be, both be true together. + +§ 72. We have thus seen when the objects falling under the concepts F and G are correlated with each other by the relation ^. But now in our case, this correlation has to be one-one. By this I understand that the two following + +propositions both hold good: + +I . If J stands in the relation to a, and if d stands in the relation ^ to e, then generally, whatever d, a and e may + +be, a is the same as e. + +z. li d stands in the relation to a^ and if b stands in the relation <^ to ^, then generally, whatever d, i and a may be, + +d is the same as b. + +This reduces one-one correlation to purely logical + +85 relationships, and enables us to give the following defini- + +tion: + +the expression + +"the concept F is equal to the concept G" + +is to mean the same as the expression + +"there exists a relation a concept such that « is the Number + +which belongs to it". + +Thus the concept of Number receives its definition, apparently, indeed, in terms of itself, but actually without any fallacy, since "the Number which belongs to the concept + +F" has already been defined. + +§ 73. Our next aim must be to show that the Number which belongs to the concept F is identical with the Number which belongs to the concept G if the concept F is equal to the concept G. This sounds, of course, like a tautology. But it is not; the meaning of the word "equal" is not to be inferred from its etymology, but taken to be as I defined it + +above. + +On our definition [of "the Number which belongs to the concept F"], what has to be shown isthat the extension of the concept "equal to the concept F" is the same as the extension of the concept "equal to the concept G", if the concept F is equal to the concept G. In other words: it is to be proved that, for F equal to G, the following two propositions hold + +good universally: + +if the concept H is equal to the concept F, + +then it is also equal to the concept G; + +and if the concept H is equal to the concept G, + +then it is also equal to the concept F. + +The first proposition amounts to this, that there exists a relation which correlates one to one the objects falling under the concept H with those falling under the concept G, if there exists a relation ^ which correlates one to one the objects falling under the concept F with those falling under the concept G and if there exists also a relation iji which correlates one to one the objects falling under the concept H with those falling under the concept F. The following arrangement + +of letters will make this easier to grasp: + +Hi[,FG. Such a relation can in fact be given: it is to be found in + +the judgement-content + +"there exists an object to which cstands in the relation + +ip and which stands to b in the relation <^", if we subtract from it c and b—take them, that is, as the terms of the relation. It can be shown that this relation is one-one, and that it correlates the objects falling under the concept H + +with those falling under the concept G. + +A similar proof can be given of the second proposition also.i And with that, I hope, enough has been indicated of my methods to show that our proofs are not dependent at any point on borrowings from intuition, and that our definitions + +can be used to some purpose. + +§ 74. We can now pass on to the definitions of the + +individual numbers. + +^ And likewise of the converse: If the number which belongs to the concept F is the same as that which belongs to the concept G, then the concept F is + +equal to the concept G. + +8? Since nothing falls under the concept "not identical + +with itself", I define nought as follows + +o is the Number which belongs to the concept "not + +identical with itself". + +Some may find it shocking that I should speak of a concept in this connexion. They will object, very likely, that it contains a contradiction and is reminiscent of our old friends the square circle and wooden iron. Now I believe that these old friends are not so black as they are painted. To be of any use is, I admit, the last thing we should expect of them; but at the same time, they cannot do any harm, if only we do not assume that there is anything which falls under them—and to that we are not committed by merely using them. That a concept contains a contradiction is not always obvious without investigation; but to investigate it we must first possess it and, in logic, treat it just like any other. All that can be demanded of a concept from the point of view of logic and with an eye to rigour of proof is only that the limits to its application should be sharp, that we should be able to decide definitely about every object whether it falls under that concept or not. But this demand is completely satisfied by concepts which, like "not identical with itself", contain a contradiction; for of every object we know that it does not fall under any + +such concept.^ + +On my use of the word "concept", + +"a falls under the concept F" is the general form of a judgement-content which deals with \* The definition of an object in terms of a concept under which itfalls is a very different matter. For example, the expression "the largest proper fraction" has no content, since the definite article claims to refer to a definite object. On the other hand, the concept "fraction smaller than iand such that no fraction smaller than one exceeds it in magnitude" is quite unexceptionable: in order, indeed, to prove that there exists no such fraction, we must make use of just this concept, despite its containing a contradiction. If, however, we wished to + +88 an object a and permits of the insertion for a of anything + +whatever. And in this sense + +"tf falls under the concept 'not identical with itself' " + +has the same meaning as + +"tf IS not identical with itself" or "^ is not identical with «". I could have used for the definition of nought any other concept under which no object falls. But I have made a point of choosing one which can be proved to be such on purely logical grounds; and for this purpose "not identical with it self" is the most convenient that offers, taking for the defini tion of "identical" the one from Leibniz given above [(§ 65)], + +which is in purely logical terms. + +§ 75. Now it must be possible to prove, by means of what has already been laid down, that every concept under which no object falls is equal to every other concept under which no object falls, and to them alone; from which it follows that o is the Number which belongs to any such concept, and that no object falls under any concept if the number which + +belongs to that concept is o. + +If we assume that no object falls under either the concept F or the concept G, then in order to prove them equal we have to find a relation ^ which satisfies the following condi- + +tions: + +every object which falls under V stands in the relation ^ to an object which falls under G\ and to every object which falls under G there stands in the relation ^ an + +object falling under V. + +use this concept for defining an object falling under it, it would, of course, be + +necessary first to show two distinct things: + +1. that some object falls under this concept; 2, that only one object falls under it. + +Now since the first of these propositions, not to mention the second, is false, + +it follows that the expression "the largest proper fraction" is senseless. + +89 In view of what has been said above [(§71)] on the meaning of these expressions, it follows, on our assumption [that no object falls under either concept], that these conditions are satisfied by every relation whatsoever, and therefore among others by identity, which is moreover a one-one relation; for it meets both the requirements laid down [in + +§ 72] above. + +If, to take the other case, some object, say a, does fall + +under G, but still none falls under F, then the two proposi- + +tions + +"^ faUs under G" and "no object falling under F stands to a in the relation (^" are both true together for every relation ^; for the first is made true by our first assumption and the second by our second assumption. If, that is, there exists no object falling under F, then a fortiori there exists no object falling under F which stands to a in any relation whatsoever. There exists, therefore, no relation by which the objects falling under F can be correlated with those falling under G so as to satisfy our definition [of equality], and accordingly the concepts F and + +G are unequal. + +§ 76. I now propose to define the relation in which every two adjacent members of the series of natural numbers + +stand to each other. The proposition: + +"there exists a concept F, and an object falling under itX, such that the Number which belongs to the concept F is « and the Number which belongs to the concept 'falling under F but not identical with x' is w" + +is to mean the same as + +"» follows in the series of natural numbers directly + +after m". + +I avoid the expression "« is the Number following next after w", because the use of the definite article cannot be justified until we have first proved two propositions.^ For + +^ See note on p. 8 ye f. + +90 the same reason I do not yet say at this point ''n = m -\- i/\* for to use the symbol = is likewise to designate {m -\- i) an + +object. + +§ 77. Now in order to arrive at the number i,we have first of all to show that there is something which follows in + +the series of natural numbers directly after o. + +Let us consider the concept—or, if you prefer it, the predicate—"identical with o". Under this falls the number o. But under the concept "identical with o but not identical with o", on the other hand, no object falls, so that o is the Number which belongs to this concept. We have, therefore, a concept "identical with o" and an object faUing under it o, of which + +the following propositions hold true: + +the Number which belongs to the concept "identical with o" isidentical with the Number which belongs to + +the concept "identical with o"; + +the Number which belongs to the concept "identical + +with o but not identical with o" is o. + +Therefore, on our definition [(§ 76)], the Number which belongs to the concept "identical with o" follows in the + +series of natural numbers directly after o. + +Now if we give the following definition: + +I is the Number which belongs to the concept "identical + +with o", + +we can then put the preceding conclusion thus: + +I follows in the series of natural numbers directly + +after o. + +It is perhaps worth pointing out that our definition of the number i does not presuppose, for its objective legitimacy, any matter of observed fact.^ It is easy to get confused over this, seeing that certain subjective conditions must be satisfied if we are to be able to arrive at the definition, and that sense experiences are what prompt us to frame it.^ All this, how- + +^ Non-general proposition. + +\* Cf. B. Erdmann, Die Axtome der Geometrie, p. 164. + +91 ever, may be perfectly correct, without the propositions so arrived at ceasing to be a priori. One such condition is, for example, that blood of the right quality must circulate in the brain in sufficient volume—at least so far as we know; but the truth of our last proposition does not depend on this; it still holds, even if the circulation stops; and even if all rational beings were to take to hibernating and fall asleep simultaneously, our proposition would not be, say, cancelled for the duration, but would remain quite unaffected. For a proposition to be true is just not the same thing as for it to + +be thought. + +§ 78. I proceed to give here a list of several propositions to be proved by means of our definitions. The reader will easily see for himself in outline how this can be done. + +1. If ^ follows in the series of natural numbers directly + +after o, then a is = i + +2. If I is the Number which belongs to a concept, then there exists an object which falls under that concept. + +3 + +If Iis the Number which belongs to a concept F; then, if the object x falls under the concept F and if j falls under the concept F, x is =j; that is, x is the same asj. 4. If an object falls under the concept F, and if it can be inferred generally from the propositions that x falls under the concept F and that j falls under the concept F that X is =J, then i is the Number which belongs to the + +concept F. + +5 + +The relation of w to « which is established by the proposi- + +tion: + +"« follows in the series of natural numbers directly + +after m" + +is a one-one relation. + +There is nothing in this so far to state that for every Number there exists another Number which follows directly after it, or after which it directly follows, in the + +series of natural numbers. + +92 6. Every Number except o follows in the series of natural + +numbers directly after a Number. + +§ 79. Now in order to prove that after every Number («) in the series of natural numbers a Number directly follows, we must produce a concept to which this latter Number belongs. + +For this we shall choose the concept + +"member of the series of natural numbers ending + +with «", + +which requires first to be defined. + +To start with, let me repeat in slightly different words + +the definition of following in a series given in my Begriffs- + +schrijt {Concept Writing: The proposition + +> 'if every object to which x stands in the relation falls under the concept F, and if from the proposition that d falls under the concept F it follows universally, whatever d may be, that every object to which d stands in the relation ^ falls under the concept F, then y falls under the concept F, whatever concept F may be" + +is to mean the same as + +"y follows in the ^-series after x" + +and again the same as + +"x comes in the ^-series before j". + +§ 80. It will not be time wasted to make a few comments on this. First, since the relation ^ has been left indefinite, the series is not necessarily to be conceived in the form of a spatial and temporal arrangement, although these cases are not + +excluded. + +Next, there may be those who will prefer some other definition as being more natural, as for example the following: if starting from x we transfer our attention continually from one object to another to which itstands in the relation <^, and if by this procedure we can finally reachj, then we say thatjy + +follows in the ^-series after x, + +93 Now this describes a way of discovering that j follows, it does not define what ismeant byj's following. Whether, as our attention shifts, we reach j may depend on all sorts of subjective contributory factors, for example on the amount of time at our disposal or on the extent of our familiarity with the things concerned. Whetherj follows in the ^-series after x has in general absolutely nothing to do with our attention and the circumstances in which we transfer it; on the contrary, it is a question of fact, just as much as it is a fact that a green leaf reflects light rays of certain wave-lengths whether or not these fall into my eye and give rise to a sensation, and a fact that a grain of salt is soluble in water whether or not I drop it into water and observe the result, and a further fact that it remains still soluble even when it is utterly impossible for me to make any experiment with it. My definition lifts the matter onto a new plane; it is no longer a question of what issubjectively possible but of what is objectively definite. For in literal fact, that one proposition follows from certain others is something objective, something independent of the laws that govern the movements of our attention, and something to which it is immaterial whether we actually draw the conclusion or not. What I have provided is a criterion which decides in every case the question Does itfollow after?, wherever it can be put; and however much in particular cases we may be prevented by extraneous difficulties from actually reaching a decision, that is irrelevant + +to the fact itself. + +We have no need always to run through all the members of a series intervening between the first member and some given object, in order to ascertain that the latter does follow after the former. Given, for example, that in the (^-series b follows after a and c after b, then we can deduce from our definition that c follows after a^ without even knowing the + +intervening members of the series. + +Only by means of this definition of following in a series is it possible to reduce the argument from « to (« + i), which on the face of it is peculiar to mathematics, to the general + +laws of logic. + +§ 8 1. If now we have for our relation + +(f> the relation of + +m ton established by the proposition + +"« follows in the series of natural numbers directly + +after ;»," + +then we shall say instead of "^-series" "series of natural + +numbers". + +I add the following further definition: + +The proposition + +"j follows in the ^-series after x orjis the same as x" + +is to mean the same as + +"j is a member of the .^-series beginning with x" + +and again the same as + +"x is a member of the ^-series ending withj/". It follows that tf is a member of the series of natural numbers ending with », if « either follows in the series of + +natural numbers after a or is identical with ^.^ + +§ 82. It is now to be shown that—subject to a condition still to be specified—the Number which belongs to the + +concept + +"member of the series of natural numbers ending with «" follows in the series of natural numbers directly after «. And in thus proving that there exists a Number which follows in the series of natural numbers directly after «, we shall have proved at the same time that there is no last member of this series. Obviously this proposition cannot be established + +on empirical lines or by induction. + +To give the proof in full here would take us too far afield. I can only indicate briefly the way it goes. It is to be proved + +that + +I. if a follows in the series of natural numbers directly after + +^, and if it is true of d that: + +\* If « is not a Number, then « itself is the only member of the series of natural + +numbers ending with «,—if that is not too shocking a way of putting it. + +95 the Number which belongs to the concept + +"member of the series of natural numbers ending with d" + +follows in the series of natural numbers directly after J, + +then it is also true of a that: + +the Number which belongs to the concept + +"member of the series of natural numbers ending with a^\* follows in the series of natural numbers directly after a. + +It is then to be proved, secondly, that what isasserted of d and of a in the propositions just stated holds for the number o. And finally it is to be deduced that it also holds for « if « is a member of the series of natural numbers beginning with o. The argument here is an application of the definition I have + +given [(§§ 79, 81)] of the expression + +"j follows in the series of natural numbers after x", taking for our concept F what is asserted above [in i .] of ^ + +and a conjointly, but with o and n substituted for d and a. + +§ 83. In order to prove the proposition i. of the last paragraph, we must show that a is the Number which belongs to the concept "member of the series of natural numbers ending with a, but not identical with ^". And for this, again, it is necessary to prove that this concept has an extension identical with that of the concept "member of the series of natural numbers ending with d'\ For this we need the proposition that no object which isa member of the series of natural numbers beginning with o can follow in the series of natural numbers after itself. And this must once again be proved by means of our definition of following in a series, on the lines + +indicated above. + +^ E. Schroder (op. cit., p. 63) seems to regard this proposition as a con sequence of a system of notation which could conceivably be different. Here once more we must be struck by the drawback which vitiates his whole treat- + +96 It is this that obliges us to attach a condition to the proposition that the Number which belongs to the concept + +"member of the series of natural numbers ending + +with «" + +follows in the series of natural numbers directly after n,— + +the condition, namely, that « must be a member of the series of natural numbers beginning with o. For this there is a + +convenient abbreviation, which Idefine as follows: + +the proposition + +"« is a member of the series of natural numbers begin- + +ning with o" is to mean the same as + +"« is a finite Number". + +We can thus formulate the last proposition above as follows: no finite Number follows in the series of natural + +numbers after itself. + +Infinite Numbers. § 84. Contrasted with the finite Numbers are the infinite Numbers. The Number which belongs to the concept "finite Number" is an infinite Number. Let us symbolize it by, say, 00 j. If it were a finite Number, it could not follow in the series of natural numbers after itself. But itcan be shown that this is + +what 00 1 does. + +About the infinite Number ooi so defined there is nothing mysterious or wonderful. "The Number which belongs to the concept F is 00 ^" means no more and no less than this: that there exists a relation which correlates one to one the objects falling under the concept F with the finite Numbers. In terms ment of this matter,—that we do not really know whether the number is a symbol and if so what its meaning is, or whether the number itself is the meaning of the symbol. He is not entided to infer, from the fact that we arrange for our symbols to differ so that the same one never recurs, that the meanings of those + +97 of our definitions this has a perfectly clear and unambiguous sense; and that is enough to justify the use of the symbol oo and to assure it of a meaning. That we cannot form any idea of an infinite Number is of absolutely no importance; the same is equally true of finite Numbers. So regarded, our Number ooi, has a character as definite as that of any finite Number; it can be recognized again beyond doubt as the same, and can be + +distinguished from every other. + +§85. It is only recently that infinite Numbers have been introduced, in a remarkable work by G. Cantor.^ I heartily share his contempt for the view that in principle only finite Numbers ought to be admitted as actual. Perceptible by the senses these are not, nor are they spatial—any more than fractions are, or negative numbers, or irrational or complex numbers; and if we restrict the actual to what acts on our senses or at least produces effects which may cause sense perceptions as near or remote consequences, then naturally no number of any of these kinds is actual. But it is also true that we have no need at all to appeal to any such sense-perceptions in proving our theorems. Any name or symbol that has been introduced in a logically unexceptionable manner can be used in our enquiries without hesitation, and here our + +Number 00 1 is as sound as 2 or 3. + +While in this I agree, as I believe, with Cantor, my + +terminology diverges to some extent from his. For my Number he uses "power", while his concept^ of Number has reference to arrangement in an order. Finite Numbers, + +^ Op. cit., p. 746 above. + +\* This expression may seem to conflict with my earlier insistence on the objective nature of concepts; but all that I mean is subjective here is his use + +of the word. + +98 certainly, emerge as independent nevertheless of sequence in series, but not so transfinite Numbers. But now in ordinary use the word "Number" and the question "how many?" have no reference to arrangement in a fixed order. Cantor's Number gives rather the answer to the question: "the how-manyeth member in the succession is the last member?" So that it seems to me that my terminology accords better with ordinary usage. If we extend the meaning of a word, we should take care that, so far as possible, no general proposition is invali dated in the process, especially one so fundamental as that which asserts of Number its independence of sequence in series. For us, because our concept of Number has from the outset covered infinite numbers as well, no extension of + +its meaning has been necessary at all. + +§ 86. To obtain his infinite Numbers Cantor introduces the relation-concept of following in a succession, which differs from my "following in a series". On his account we should get a succession if, for example, we arranged the finite positive whole numbers in an order such that the odd numbers followed one another just as they do, among themselves, in the series of natural numbers, and similarly the even numbers, but with the further stipulation that every even number was to follow after every odd number. In this succession o, for instance, would follow after 13. But no number would come directly before o. Now this is a situation which cannot arise on my definition of following in the series. It can be strictly proved, without appeal to any axiom borrowed from intuition, that ifj follows in the ^-series after x then there exists an object which comes in that series directly before j'. Now it looks to me as though precise definitions of following in the succession and of Number in Cantor's sense are still wanting. Thus Cantor appeals to the rather mysterious "inner intuition", where he ought to have made an effort to find, and indeed could actually have found, a proof from definitions. For I think I can anticipate how his two concepts could have been made precise. At any rate, nothing in what I have said is + +99 intended to question in any way their legitimacy or their fertility. On the contrary, I find special reason to welcome in Cantor's investigations an extension of the frontiers of science, because they have led to the construction of a purely arithmetical route to higher transfinite Numbers (powers). + +V. Conclusion. + +§ 87. I hope I may claim in the present work to have made it probable that the laws of arithmetic are analytic judgements and consequendy a priori. Arithmetic thus becomes simply a development of logic, and every proposition of arithmetic a law of logic, albeit a derivative one. To apply arithmetic in the physical sciences is to bring logic to bear on observed facts ;^ calculation becomes deduction. The laws of number will not, as Baumann^ thinks, need to stand up to practical tests if they are to be applicable to the external world; for in the external world, in the whole of space and all that therein is, there are no concepts, no properties of concepts, no numbers. The laws of number, therefore, are not really applicable to external things; they are not laws of nature. They are, however, applicable to judgements holding good of things in the external world: they are laws of the laws of nature. They assert not connexions between phenomena, but connexions between judgements; and among judgements + +are included the laws of nature. + +§ 88. Kant^ obviously—as a result, no doubt, of defining them too narrowly—underestimated the value of analytic judgements, though it seems that he did have some inkling + +^ Observation itself already includes within it a logical activity. + +\* Op. cit., Vol. II, p. 670. + +» Op. cit.. Vol. Ill, pp. 39 ff. [Original edns., A6 ff./Bio ff.]. + +lOO of the wider sense in which I have used the term.^ On the basis of his definition, the division of judgements into analytic and synthetic is not exhaustive. What he is thinking of is the universal affirmative judgement; there, we can speak of a subject concept and ask—as his definition requires—whether the predicate concept is contained in it or not. But how can we do this, if the subject is an individual object? Or if the judgement is an existential one? In these cases there can simply be no question of a subject concept in Kant's sense. He seems to think of concepts as defined by giving a simple list of characteristics in no special order; but of all ways of forming concepts, that is one of the least fruitful. If we look through the definitions given in the course of this book, we shall scarcely find one that is of this description. The same is true of the really fruitful definitions in mathematics, such as that of the continuity of a function. What we find in these is not a simple list of characteristics; every element in the defini tion is intimately, I might almost say organically, connected with the others. A geometrical illustration will make the distinction clear to intuition. If we represent the concepts (or their extensions) by figures or areas in a plane, then the concept defined by a simple list of characteristics corresponds to the area common to all the areas representing the defining characteristics; it is enclosed by segments of their boundary lines. With a definition like this, therefore, what we do—in terms of our illustration—is to use the lines already given in a new way for the purpose of demarcating an area.^ Nothing essentially new, however, emerges in the process. But the more fruitful type of definition is a matter of drawing boundary lines that were not previously given at all. What we shall be able to infer from it, cannot be inspected in advance; here, ^ On p. 43 [B14] he says that a synthetic proposition can only be seen to be true by the law of contradiction, if another synthetic proposition is pre- + +supposed. + +• Similarly, if the characteristics are joined by "or". + +lOI we are not simply taking out of the box again what we have just put into it. The conclusions we draw from it extend our knowledge, and ought therefore, on Kant's view, to be regarded as synthetic; and yet they can be proved by purely logical means, and are thus analytic. The truth is that they are contained in the definitions, but as plants are contained in their seeds, not as beams are contained in a house. Often we need several definitions for the proof of some proposition, which consequently is not contained in any one of them alone, yet + +does follow purely logically from all of them together. + +§ 89. I must also protest against the generality of Kant's^ dictum: without sensibility no object would be given to us. Nought and one are objects which cannot be given to us in sensation. And even those who hold that the smaller numbers are intuitable, must at least concede that they cannot be given in intuition any of the numbers greater than 1000 1000 1000^ about which nevertheless we have plenty of information. Perhaps Kant used the word "object" in a rather different sense; but in that case he omits altogether to allow for nought or one, or for our 00 j,—for these are not concepts either, and even of a concept Kant requires that we + +should attach its object to it in intuition. + +I have no wish to incur the reproach of picking petty quarrels with a genius to whom we must all look up with grateful awe; I feel bound, therefore, to call attention also to the extent of my agreement with him, which far exceeds any disagreement. To touch only upon what is immediately relevant, I consider Kant did great service in drawing the distinction between synthetic and analytic judgements. In calling the truths of geometry synthetic and a priori, he + +\* Op. cit.. Vol. Ill, p. 82 [Original edns., A51/B75.] + +102 revealed their true nature. And this is still worth repeating, since even to-day it is often not recognized. If Kant was wrong about arithmetic, that does not seriously detract, in my opinion, from the value of his work. His point was, that there are such things as synthetic judgements a priori; whether they are to be found in geometry only, or in arithmetic + +as well, is of less importance. + +§ 90. I do not claim to have made the analytic character of arithmetical propositions more than probable, because it can still always be doubted whether they are deducible solely from purely logical laws, or whether some other type of premiss is not involved at some point in their proof without our noticing it. This misgiving will not be completely allayed even by the indications I have given of the proof of some of the propositions; it can only be removed by producing a chain of deductions with no link missing, such that no step in it is taken which does not conform to some one of a small number of principles of inference recognized as purely logical. To this day, scarcely one single proof has ever been conducted on these lines; the mathematician rests content if every transi tion to a fresh judgement is self-evidently correct, without enquiring into the nature of this self-evidence, whether it is logical or intuitive. A single such step is often really a whole compendium, equivalent to several simple inferences, and into it there can still creep along with these some element from intuition. In proofs as we know them, progress is by jumps, which is why the variety of types of inference in mathematics appears to be so excessively rich; for the bigger the jump, the more diverse are the combinations it can represent of simple inferences with axioms derived from intuition. Often, nevertheless, the correctness of such a transition is immediately self-evident to us, without our ever becoming conscious of the subordinate steps condensed within it; whereupon, since it does not obviously conform to any of the recognized types of logical inference, we are prepared to accept its self-evidence forthwith as intuitive, and the conclusion itself as a synthetic + +I03 truth—and this even when obviously it holds good of much + +more than merely what can be intuited. + +On these lines our synthetic based on intuition cannot possibly be cut cleanly away from our analytic. Nor shall we succeed in compiling with certainty a complete set of axioms of intuition, such that from them alone we can derive, by means of the laws of logic, every proof in mathematics. + +§ 91. The demand is not to be denied: every jump must be barred from our deductions. That it is so hard to satisfy must be set down to the tediousness of proceeding step by step. Every proof which iseven a little complicated threatens to become inordinately long. And moreover, the excessive variety of logical forms that has gone into the shaping of our language makes it difficult to isolate a set of modes of inference which is both sufficient to cope with all cases and easy to take + +in at a glance. + +To minimize these drawbacks, I invented my concept writing. It is designed to produce expressions which are shorter and easier to take in, and to be operated like a calculus by means of a small number of standard moves, so that no step is permitted which does not conform to the rules which are laid down once and for all.^ It is impossible, therefore, for any premiss to creep into a proof without being noticed. In this way I have, without borrowing any axiom from intuition, given a proof of a proposition^ which might at first sight be taken for synthetic, which I shall here formulate as follows: If the relation of every member of a series to its successor is one- or many-one, and if m andj follow in that series after X, then either J comes in that series before m^ or it coincides + +with m, or it follows after m. + +^ It is designed, however, to be capable of expressing not only the logical + +form, like Boole's notation, but also the content of a proposition. + +From this proof it can be seen that propositions which extend our knowledge can have analytic judgements for their + +content.1 + +Other numbers. + +§ 92. Up to now we have restricted our treatment to the [natural] Numbers. Let us now take a look at the other kinds of numbers, and try to make some use in this wider + +field of what we have learned in the narrower. + +Hankel,2 in an attempt to make clear the sense of asking whether some particular type of number is possible, writes + +as follows: + +"Number to-day is no longer a thing, a substance, existing in its own right apart from the thinking subject and the objects which give rise to it, a self-subsistent element in the sort of way it was for the Pythagoreans. The question whether some number exists can therefore only be understood as referring to the thinking subject or to the objects thought about, relations between which the numbers represent. As impossible in the strict sense the mathematician counts only what is logically impossible, that is, self-contradictory. That numbers which are impossible in this sense cannot be admitted, needs no proof. But if the numbers concerned are logically possible, if their concept is clearly and fully defined and there- ^ This proof will certainly still be found far too lengthy, a disadvantage which may, perhaps, be thought to be more than outweighed by the practically absolute certainty that it contains no mistake and no gap. My aim at that time was to reduce everything to the smallest possible number of the simplest possible logical laws. Consequently, I made use of only one principle of deduction. However, even at that time Inoted in my Preface, p. vii, that for'the further application of my writing it would be imperative to admit more such principles. This can be done without loosening any link in the chain of deduction, and it is possible to achieve in this way a remarkable degree of compression. + +\* Op. cit., pp. 6-7. + +I05 fore free from contradiction, then the question whether they exist can amount only to this: Does there exist in reality or in the actual world given to us in intuition a substratum for these numbers, do there exist objects in which they—relations, that is, for the mind, of the type defined—can become pheno- + +menal?" + +§ 93. Hankel's first sentence leaves it doubtful whether he holds that numbers exist in the thinking subject, or in the objects which give rise to them, or in both. In the spatial sense they are, in any case, neither inside nor outside either the subject or any object. But, of course, they are outside the subject in the sense that they are not subjective. Whereas each individual can feel only his own pain or desire or hunger, and can experience only his own sensations of sound and colour, numbers can be objects in common to many individuals, and they are in fact precisely the same for all, not merely more or less similar mental states in different minds. In making the question of the existence of numbers refer to the thinking subject, Hankel seems to make ita psychological question, which it is not in any way. Mathematics is not concerned with the nature of our mind, and the answer to any question whatsoever in psychology must be for mathe- + +matics a matter of complete indifference. + +§ 94. Further, exception must be taken to the statement that the mathematician counts as impossible only what isself contradictory. A concept is still admissible even though its defining characteristics do contain a contradiction: all that we are forbidden to do, is to presuppose that something falls under it. But even if a concept contains no contradiction, we still cannot infer that for that reason something falls under it. If such concepts were not admissible, how could we ever prove that a concept does not contain any contradiction? It is by no means always obvious; it does not follow that because we see no contradiction there is none there, nor does a clear and full definition afford any guarantee against + +io6 it. Hankel^ proves that any closed field of complex numbers of higher order than the ordinary, if made subject to all the laws of addition and multiplication, contains a contradiction. Now that is something that needs to be proved; it is not seen immediately. Before his proof was given, anyone could always, by using a number system of that type, have arrived at remarkable results, nor would they have been any worse founded than the theory of determinants, if, with Hankel,^ we base that on alternate numbers; for who can assure us that there is not some hidden contradiction in the concept of these numbers also? And moreover, even if we could exclude this possibility generally for as many alternate units as we please, it would still not follow that such units exist. Yet that is precisely what we need. We will take an example + +from Euclid's Elements, Book I, Theorem i8: + +In any triangle the greater side subtends the greater + +angle. + +To prove this, Euclid cuts off from the greater side AC + +a segment AD equal to the lesser side AB, making use for this purpose of a previously given construction. The proof would collapse, if there were no such point as D, and it is not enough that we discover no contradiction in the concept "point on AC whose distance from A is equal to B's". Euclid proceeds to join BD. That there exists such a line is still + +another proposition on which the proof depends. + +§ 95. Strictly, of course, we can only establish that a + +concept is free from contradiction by first producing something that falls under it. The converse inference is a fallacy, and one into which Hankel falls. Referring to [the operation of finding X from] the equation x -\- b — c [(subtraction)] he + +says :^ + +^ Op. cit., pp. 106-7. \* op. cit., § 35, pp. 121-4. + +Op. cit., p. 5. Similarly E. Kossak, op. cit., p. 17 adfiti. + +I07 "It is obvious that, for h > c, there is no number x in the series i, 2, 3, . . • which solves our problem; the subtraction is then impossible. There is nothing, however, to prevent us from regarding the difference {c — h) in this case as a symbol which solves the problem and which is to be operated with exactly as if it were a figure number in the series i, 2, 3 . . ." Nevertheless, there is something to prevent us from regarding (2 — 3) without m.ore ado as a symbol which solves the problem; for an empty symbol is precisely no solution; without some content it is merely ink or print on paper, as which it possesses physical properties but not that of making 2 when increased by 3. Really, it would not be a symbol at all, + +and to use it as one would be a mistake in logic. Even for Ob^lx. is not the symbol ('V — ^") that solves the problem, + +but its content. + +§ 96. We might just as well say this: among numbers hitherto known there is none which satisfies the simultaneous + +equations + +X + I = 2 x+ 2 = I, + +but there is nothing to prevent us from introducing a symbol which solves the problem. Ah, but there is, it will be repUed: to satisfy both the equations simultaneously involves a contradiction. Certainly, if we are requiring a real number or an ordinary complex number to satisfy them; but then all we have to do is to widen our number system, to create numbers which do meet these new requirements. Then we can wait and see whether anyone succeeds in producing a contradiction in them. Who can tell what may not be possible with our new numbers? Naturally {c — b) cannot then remain one-valued; but then 's^a likewise, if we wish to introduce negative numbers, has to cease to be one-valued; and with complex + +numbers log a too becomes many-valued. + +And why not create still further numbers which permit + +the summation of diverging series? But that will do,—even + +io8 the mathematician cannot create things at will, any more than the geographer can; he too can only discover what is there + +and give it a name. + +This is the error that infects the formalist theory of fractions and of negative and complex numbers.^ It is made a postulate that the familiar rules of calculation shall still hold, where possible, for the newly-introduced numbers, and from this their general properties and relations are deduced. If no contradiction is anywhere encountered, the introduction of the new numbers is held to be justified, as though it were impossible for a contradiction still to be lurking somewhere nevertheless, and as though freedom from contradiction + +amounted straight away to existence. + +§ 97. That this mistake is so easily made is due, of course, to the failure to distinguish clearly between concepts and objects. Nothing prevents us from using the concept "square root of —i"; but we are not entitled to put the definite article in front of itwithout more ado and take the expression "the square root of —i" as having a sense. Given that /^ = —i, we can give a proof of the formula expressing the sine of any multiple of the angle a in terms of sin a and cos a; but we ought not to forget that this proposition continues to imply the condition that /2 = —i, which we are not entitled to drop without remark. If there existed nothing at all of which the square was —i, then for all our proof was worth the formula might not be correct,^ since the condition /^ = —i, on which its validity patently depends, would never be fulfilled. It would be as though in a geometrical proof we had made use of an auxiliary line which is quite impossible to construct. + +§ 98. Hankel\* introduces two sorts of operation, which he calls lytic and thetic, and which he defiines by means of + +^ Cantor's infinite Numbers are in like case. + +\* It might always be possible to prove itstrictly in some other way. + +\* Op. cit., p. 18. + +I09 certain properties that they are to possess. There is nothing against this, so long as it is only not presupposed that operations of these sorts and objects such as their results would be exist.\* Later^ he symboli2es an operation which is thetic, one-valued\* and associative by {a + ^), and the corresponding lytic, and likewise one-valued\*, operation by {a — h"). An operation which etc.? But which one? Any we care to choose? Then that is not a definition of {a -f- ^); and besides, what if none such exists? If the word "addition" had as yet no meaning, it would be quite in order logically to say: we propose to call an operation of this sort an addition; but what we cannot say is: we propose to call an operation of this sort the operation of addition, and to symbolize it by {a -\- b). For ithas not yet been established that there is one and only one such operation. We cannot define by putting on one side of our identity the indefinite article and on the other the definite. Hankel, however, goes on to speak next without more ado of "the modulus of the operation", without having proved that there + +is one and only one modulus. + +§ 99. In a word, this purely formalist theory is not sufficient. What isvaluable in it is simply this. We can prove that if any operation possesses certain properties, such as that of being associative or commutative, then certain propositions hold good of it. So that if we go on to show that addition and multiplication, which are already known to us, possess these properties, we can then proceed immediately to assert our propositions of addition and multiplication, without repeating the proof at length for each case individually. Thus it is only after we have applied our formal theory to operations given from elsewhere, that we arrive at the familiar propositions of arithmetic. But we have not the slightest right to suppose that we can use it as a method for introducing addition and multiplication. It does not give 1 This Hankel really docs already by using the identity 6(c, b)= a. + +\* Op. cit., p. 29. + +\* [Literally 'perfectly one-valued', a term defined by Hankel.] + +no their actual definitions, but only lays down the lines for them. We may say: the name "addition" is to be given only to an operation which is thetic, one-valued and associative, but there is nothing at all in this as yet to say which operation it is that is to be so called. So far as this goes, there is nothing to stop us calling multiplication addition and symbolizing it by {a + b), nor could anyone say definitely whether 2+3 was 5 or 6. + +§ 100. If we abandon this purely formal method of + +treatment, we may fasten instead on the circumstance that, simultaneously with the introduction of new numbers, the meanings of the words "sum" and "product" are extended. We take some object, let us say the Moon, and proceed by definition: Let the Moon multiplied by itself be —i. This gives us a square root of —i in the shape of the Moon. There seems to be nothing wrong with this definition, since the meaning hitherto assigned to multiplication says nothing as to the sense of a product such as the Moon into the Moon, so that as we now come to extend its meaning we can make it, for the Moon, whatever we choose. But we need also the product of a real number into the square root of —i. So let us choose instead as our square root of —i the time-interval of one second, and let this be symbolized by /. Thus 3/ will mean the time-interval of 3 seconds, and so on.^ What object shall we then symbolize by, say, 2 + 3/? What meaning should be assigned to the plus symbol in this case? Now this must be ^ We should be equally entitled to choose as further square roots of —1 a certain quantum of electricity, a certain surface area, and so on; but then we should naturally have to use different symbols to signify these different roots. That we are able, apparently, to create in this way as many square roots of as we please, is not so astonishing when we reflect that the meaning of the square root of —1 is not something which was already unalterably fixed before we tnade these choices, but is decided for the first time by and along with them. + +Ill laid down generally for all such cases, which clearly is not going to be easy. However, let us just assume that we have successfully secured a sense for all symbols of the form a + hi^ and a sense such that the familiar laws of addition hold good of it. What we should then have to do would be to lay it + +down further that in general + +{a + hi) {c + di) =ac—bd+i {ad + be), + +thus defining the extended meaning of multiplication. + +§ loi. We should now be able to prove the formula for cos (« a), if we knew that from the identity of complex numbers the identity of their real parts can be inferred. That would have to result from the sense of ^ + bi, which we are here taking to have been made available. Our proof of the formula would thus hold only for complex numbers and their sums and products in the sense fixed by us. Now since for real integral n and real a / disappears completely from the identity in the formula, we are tempted to conclude therefore that it is quite immaterial whether / means a second or a milli metre or anything else, provided only that our laws of addition and multiplication hold good; everything depends on that, and the rest we need not bother about. Well, perhaps it is indeed possible to assign a whole variety of different meanings to a -{- bi, and to sum and product, all of them such that those laws continue to hold good; but it is not immaterial whether we can or cannot find some such a sense for those expressions. § 1 02. It is common to proceed as if a mere postulation were equivalent to its own fulfilment. We postulate that it shall be possible in all cases to carry out the operation of subtraction,^ or of division, or of root extraction, and suppose that with that we have done enough. But why do we not postulate that through any three points it shall be possible to draw a straight line? Why do we not postulate that all the laws + +\* Cp. Kossak, op. cit., p. 17. + +112 of addition and multiplication shall continue to hold for a three-dimensional complex number system just as they do for real numbers? Because this postulate contains a contradiction. Very well then, what we have to do first is to prove that these other postulates of ours do not contain any contradiction. Until we have done that, all rigour, strive for it as we will, is + +so much moonshine. + +In a geometrical theorem where a constructed line is used for the proof, the auxiliary line does not occur in the theorem. Perhaps more than one such line is possible, as for instance where we can select a point at will. But however much we can dispense with each and any of them individually, still the cogency of our proof depends on its being possible to draw some line of the required character. Merely to postulate it is not enough. So in our case likewise, it is not immaterial to the cogency of our proof whether "<2 + ^/" has a sense or is nothing more than printer's ink. It will not get us anywhere simply to require that it have a sense, or to say that it is to have the sense of the sum of a and hi^ when we have not previously defined what "sum" means in this case and when we have given no justification for the use of the definite article. § 103. Against the particular sense we have proposed to assign to "/" many objections can of course be brought. By it, we are importing into arithmetic something quite foreign to it, namely time. The second stands in absolutely no intrinsic relation to the real numbers. Propositions proved by the aid of complex numbers would become a posteriori judgements, or rather, at any rate, synthetic, unless we could find some other sort of proof for them or some other sense for /.We must at least first make the attempt to show that all + +propositions of arithmetic are analytic. + +Kossak's^ account of complex number—"the composite + +^ Op. cit., p. 17. + +113 idea of heterogeneous groups of identical elements"^ appears to avoid importing anything foreign, but this appear ance is only due to the vagueness of his terminology. We are given no answer at all to the question, what does i+ ^ really mean? Is it the idea of an apple and a pear, or the idea of toothache and gout? Not both at once, at any rate, because then I + / would not be always identical with i + i- The temptation is to say: it depends on the special meaning we assign to it. Very well then, Kossak's statement once again does not yet give us any definition at all of complex number, it only lays down the general lines to proceed along. But we need more; we must know definitely what "/" means, and if we do proceed along his lines and try saying it means the idea of a pear, we shall once again be introducing something foreign + +into arithmetic. + +What is commonly called the geometrical representation of complex numbers has at least this advantage over the proposals so far considered, that in it i and /' do not appear as wholly unconnected and different in kind: the segment taken to represent / stands in a regular relation to the segment which represents i . Though I may add that, strictly, it is not correct that I here means a certain segment and ; a segment perpendicular to it of the same length; on the contrary, "i" means in all contexts the same. A complex number, on this interpretation, shows how the segment taken as its representation is reached, starting from a given segment (the unit segment), by means of operations of multiplication, division, and rotation.2 However, even this accoimt seems to make every theorem whose proof has to be based on the existence of a complex number dependent on geometrical intuition and so + +synthetic. + +\* Cf. for the term "idea" § 27, for "group" what issaid about "agglomeration" in § 23 and § 25, and for the identity of the elements §§ 34-39. + +\* For simplicity I neglect incommensurables here. + +114 § 104. How are complex numbers to be given to us then, and fractions and irrational numbers? If we turn for assistance to intuition, we import something foreign into arithmetic; but if we only define the concept of such a number by giving its characteristics, if we simply require the number to have certain properties, then there is still no guarantee that anything falls under the concept and answers to our requirements, and yet it is precisely on this that proofs must be + +based. + +Well, how do things stand with the [natural] Numbers? Have we really no right to speak of 1000 ^^>^ ^^^ until such time as that many objects have been given to us in intuition? Is it, till then, an empty symbol? Not at all. It has a perfectly definite sense, even although, psychologically speaking and having regard to the shortness of human life, it is impossible for us ever to become conscious of that many objects;^ in spite of that, 1000 1000 ^°°<' is still an object, whose properties we can come to know, even though it is not intuitable. To convince ourselves of this, we have only to show, introducing the symbol a\*\* for the n^ power of a, that for positive integral a and « this expression always refers to one and only one positive whole number. To give the proof of this in detail would take us too far afield for present purposes. A general idea of the way it goes can be gathered from the method used to define nought in § 74, one in § 77, and the infinite Number ooj in § 84, and from the outline of the proof that after every finite Number in the series of natural numbers a Number directly + +follows (§§ 82-3). + +In the same way with the definitions of fractions, complex numbers and the rest, everything will in the end come down to the search for a judgement-content which can be trans formed into an identity whose sides precisely are the new ^ A simple calculation shows that millions of years would not be time enough + +for that. + +115 numbers. In other words, what we must do is fix the sense of a recognition-judgement for the case of these numbers. In doing so, we must not forget the doubts raised by such transformations, which we discussed in §§ 63-68. If we follow the same procedure as we did there, then the new numbers are given + +to us as extensions of concepts. + +§ 105. On this view of numbers^ the charm of work on + +arithmetic and analysis is, it seems to me, easily accounted for. We might say, indeed, almost in the well-known words: the reason's proper study is itself. In arithmetic we are not concerned with objects which we come to know as something alien from without through the medium of the senses, but with objects given directly to our reason and, as its nearest kin, + +utterly transparent to it.^ + +And yet, or rather for that very reason, these objects are not subjective fantasies. There is nothing more objective than + +the laws of arithmetic. + +§ 106. Let us cast a final brief glance back over the course of our enquiry. After establishing that number is neither a collection of things nor a property of such, yet at the same time is not a subjective product of mental processes either, we concluded that a statement of number asserts something objective of a concept. We attempted next to define the individual numbers o, i, etc., and the step from one number to the next in the number series. Our first attempt broke down, because we had defined only the predicate which we said was + +^ It too might be called formalist. However, it is completely different from the + +view criticized above under that name. + +\* By this I do not mean in the least to deny that without sense impressions we should be as stupid as stones, and should know nothing either of numbers or of anything else; but this psychological proposition is not of the slightest concern to us here. Because of the ever-present danger of confusing two + +fundamentally different questions, I make this point once more. + +ii6 asserted of the concept, but had not given separate definitions of o or I, which are only elements in such predicates. This resulted in our being unable to prove the identity of numbers. It became clear that the number studied by arithmetic must be conceived not as a dependent attribute, but substantivally.\* Number thus emerged as an object that can be recogni2ed again, although not as a physical or even a merely spatial object, nor yet as one of which we can form a picture by means of our imagination. We next laid down the fundamental principle that we must never try to define the meaning of a word in isolation, but only as it is used in the context of a proposition: only by adhering to this can we, as I believe, avoid a physical view of number without slipping into a psychological view of it. Now for every object there is one type of proposition which must have a sense, namely the recognitionstatement, which in the case of numbers is called an identity. Statements of number too are, we saw, to be considered as identities. The problem, therefore, was now this: to fix the sense of a numerical identity, that is, to express that sense without making use of number words or the word "number". The content of a recognition-judgement concerning numbers we found to be this, that it is possible to correlate one to one the objects falling under a concept F with those falling under a concept G. Accordingly, our definition had to lay it down that a statement of this possibility means the same as a numerical identity. We recalled similar cases: the definition of direction derived from parallelism of lines, that of shape + +derived from similarity of figures, and so on. + +§ 107. The question then arose: when are we entitled to regard a content as that of a recognition-judgement? For this a certain condition has to be satisfied, namely that it \* The distinction corresponds to that between "blue" and "the colour of the + +"7 must be possible in every judgement to substitute without loss of truth the right-hand side of our putative identity for its left-hand side. Now at the outset, and until we bring in further definitions, we do not know of any other assertion concerning either side of such an identity except the one, that they are identical. We had only to show, therefore, that the + +substitution is possible in an identity. + +One doubt, however, still remained, which was this. A recognition-statement must always have a sense. But now if we treat the possibility of correlating one to one the objects falling under the concept F with the objects falling under the concept G as an identity, by putting for it: "the Number which belongs to the concept F is identical with the Number which belongs to the concept G", thus introducing the expression "the Number which belongs to the concept F'\ this gives us a sense for the identity only if both sides of it are of the form just mentioned. A definition like this is not enough to enable us to decide whether an identity is true or false if only one side of it is of this form. We were thus led + +to give the definition: + +The Number which belongs to the concept F is the extension of the concept "concept equal to the concept F", where a concept F is called equal to a concept G if there exists the possibility of one-one correlation referred to above. + +In this definition the sense of the expression "extension of a concept" is assumed to be known. This way of getting over the difficulty cannot be expected to meet with universal approval, and many will prefer other methods of removing the doubt in question. I attach no decisive importance even + +to bringing in the extensions of concepts at all. + +§ 1 08. It now still remained to define one-one correlation; this we reduced to purely logical relationships. Next, we + +ii8 first gave an outline of the proof of the proposition: the number which belongs to the concept F is identical with the number which belongs to the concept G, if the concept F is equal to the concept G; and then gave definitions of nought, of the expression "« follows in the series of natural numbers directly after ^", and of the number i, showing that ifollows in the series of natural numbers directly after o. After adducing a number of propositions which can easily be proved at this stage, we proceeded to go rather more closely into the following proposition, from which we learn that the number series + +is infinite: + +After every number there follows in the series of natural + +numbers a number. + +This led us to the concept "member of the series of natural numbers ending with «", with the aim of showing that the Number belonging to this concept foUows in the series of natural numbers directly after n. We began by defining this in terms of the following of an objectj after an object X in a series in general ^. The sense of this expression too was reduced to purely logical relationships. And by this means we succeeded in showing that the inference from « to (n -\- I ), which is ordinarily held to be peculiar to mathematics, is really based on the universal principles of inference + +in logic. + +Now to prove that the number series is infinite, we needed to make use of the proposition that no finite number follows in the series of natural numbers after itself. And so we arrived at the concepts of finite and infinite number. We showed that fundamentally the latter is no less logically justified than the former. For the sake of comparison, Cantor's infinite Numbers and his "following in the succession" were referred to, and at the same time the divergence in his ter- + +minology was pointed out, + +§ 109. From all the preceding it thus emerged as a very probable conclusion that the truths of arithmetic are analytic and a priori; and we achieved an improvement on the view of + +119 Kant. We saw further what isstill needed to raise this probability to a certainty, and indicated the path which must lead + +to that goal. + +Finally, we made use of our results in a critique of a formalist theory of negative, fractional, irrational and complex numbers, which made the inadequacy of the theory evident. We came to see that its error lies in taking it as proved that a concept is free from contradiction if no contradiction has revealed itself, and in taking freedom from contradiction in a concept as sufficient guarantee in itself that something falls under it. This theory imagines that all we need do is make postulates; that these are satisfied then goes without saying. It conducts itself like a god, who can create by his mere word whatever he wants. It had also to be censured for passing off as a definition what is only a guide towards a definition, and one which, if we followed it, would lead to the introduction into arithmetic of foreign elements; these do not, it is true, obtrude into the words of the "definition", but only because it + +remains a mere guide. + +The formalists are thus in danger of relapsing into an a posteriori or at any rate a synthetic theory, however high on the summits of abstraction they may seem to themselves to be + +floating. + +Now we, from our previous treatment of the positive whole numbers, have seen that it is possible to avoid all importation of external things and geometrical intuitions into arithmetic, without, for all that, falling into the error of the formalists. Here, just as there, it is a matter of fixing the content of a recognition-] udgement. 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"previous_order": 0 + } + } + ], + "debug_data_path": "debug_data/gottlob-frege-the-foundations-of-arithmetic" + } +} \ No newline at end of file diff --git a/lit-marker2/hannah-arendt-between-past-and-future/hannah-arendt-between-past-and-future.md b/lit-marker2/hannah-arendt-between-past-and-future/hannah-arendt-between-past-and-future.md new file mode 100644 index 0000000000000000000000000000000000000000..37b773488b84fd37fec7a51aa356e781540f749e --- /dev/null +++ b/lit-marker2/hannah-arendt-between-past-and-future/hannah-arendt-between-past-and-future.md @@ -0,0 +1,2957 @@ +BET.ENPAST + +AND FUTURE + +EIGHT EXERCISES IN POLITICAL THOUGHT HANNAH ARENDT For those seeking to understand our times Hannah Arendt has become a guide and an inspiration. Her penetrating observations of the modern world, based on a profound knowledge of the past, constitute a major + +contribution to political philosophy. + +In this enlarged edition of a book first published in 1961, she describes the crisis, or rather series of crises, that we face as a result of the breakdown of tradition. That tradition, our heritage from Rome, no longer relieves us of the necessity of thought by supplying usable, ready-made answers. It has ceased to bridge the gap between past and future. And so this gap, once visible only to those few who made thinking their business, has become a tangible reality and perplexity to us all. It has become a pressing and inescap- + +able fact of politics. + +The modern world has not been trained for the task of re-examining its basic words and concepts. Fundamental thinking has never been a general requirement. Faced now with the imperative need for it, as the traditional key words of politics-justice, reason, responsibility, virtue, glory, truth, stature-lose their meaning, we see crises developing in every direction, and no way of meeting them. + +In fact, we lack the very concepts with which + +to envisage our problems. + +It is to this task of fundamental thinking that Hannah Arendt addresses herself, showing how we can distill once more the vital essence of traditional concepts by discovering their real origins, and how, by exercise of the intelligence, we can appraise our present position and regain a frame of reference for + +the future. + +For this edition she has added two new full-length essays, one on the conflict between truth and politics, springing from the controversy after publication of her Eichmann in Jerusalem, and the other debating whether the conquest of space has increased or diminished the stature of man. To participate in these eight exercises is to associate, in action, with one of the most original and + +fruitful minds of our times. + +HANNAH ARENDT is University Professor of Political Philosophy in the Graduate Faculty of the New School for Social Research and a Visiting Fellow of the Committee on Social Thought at the University of Chicago. She is the author of The Origins of Totalitarianism, The Human Condition, Eichmann in Jerusa- + +lem, and On Revolution. + +THE VIKING PRESS Publishers of The Viking Portable Library and Guide to American Graduate Schools 625 Madison Avenue, New York, N.Y. 10022 PRINTED IN U.S.A. + +BE T WEEN PAS T AND FU TURE + +Also by Hannah Arendt + +ORIGINS OF TOTALITARIANISM + +THE HUMAN CONDITION + +ON REVOLUTION + +EI CHMANN IN JERUS ALEM + +MEN IN DARK TIMES + +Hannah Arendt + +BETWEEN PAST + +AND FUTURE + +Eiaht Exercises in + +Political Thouaht + +Copyright 1954, © 1956, 1957, 1958, 1960, 196 1, 1963, 1967, 1968 + +by Hannah Arendt + +All rights reserved + +Published in 1961 by The Viking Press, Inc. 625 Madison Avenue, New York, N.Y. 10022 + +Reissued with additional text in 1968 in a hardbound edition and a + +Viking Compass edition + +Published simultaneously in Canada by The Macmillan Company of Canada Limited + +Part of Chapter III was first published in Nomos 1: Authority, edited by Carl J. Friedrich for the American Society of Political and Legal Philosophy, copyright © 1958 by the President and Fellows of Harvard College, published by The Liberal Arts Press, a division of The Bobbs-Merrill Company, Inc. Part of Chapter VI was fi1st published in Daedalus, copyright © 1960 by the American Academy of Arts and Sciences, and other chapters in Chicago Review, Partisan Review, and + +Review of Politics. + +No part of this book may be reproduced in any form without permission from The Viking Press, Inc. + +Library of Congress catalog card number : 68-28022 + +Printed in U.S.A. + +For Heinrich after twenty-five years ACKNO WLED GMENT S + +The essays in this book are revised and enlarged versions of those which appeared in the following magazines : American Scholar, Chicago Review, Daedalus, Nomos, Partisan Review, The Review of Politics. "Truth and Politics" originally appeared in The New Yorker. "The Crisis in Education" was translated from the German + +by Denver Lindley. + +CON TEN TS + +PREFACE: The Gap between Past and Future 3 + +I. Tradition and the Modern Age 17 + +2. The Concept of History: ANCIENT AND + +MODERN 41 + +3· What Is Authority? 91 + +4· What Is Freedom? 143 + +5· The Crisis in Education 173 + +6. The Crisis in Culture: ITS SOCIAL AND ITS + +POLITICAL SIGNIFICANCE 197 + +7· Truth and Politics 227 + +8. The Conquest of Space and the Stature of + +Man 265 + +BE T WEEN PA ST AND FU TURE + +PREFACE: + +THE GAP BETWEEN + +PAST AND FUTURE + +Notre heritage n'est precede d'aucun testament-"our inheritance was left to us by no testament"-this is perhaps the strangest of the strangely abrupt aphorisms into which Rene Char, French poet and writer, compressed the gist of what four years in the resistance had come to mean to a whole generation of European writers and men of letters.1 The collapse of France, to them a totally unexpected event, had emptied, from one day to the next, the political scene of their country, leaving it to the puppet-like antics of knaves or fools, and they who as a matter of course had never participated in the official business of the Third Republic were sucked into politics as though with the force of a vacuum. Thus, without premonition and probably against their conscious inclinations, they had come to constitute willy-nilly a public realm where-without the paraphernalia of officialdom and hidden from the eyes of friend and foe-all relevant business in the affairs of the + +It did not last long. After a few short years they were liberated from what they originally had thought to be a "burden" and thrown back into what they now knew to be the weightless irrelevance of their personal affairs, once more separated from "the world of reality" by an epaisseur triste, the "sad opaqueness" of a private life centered about nothing but itself. And if they refused "to go back to [their] very beginnings, to [their] most indigent behavior," they could only return to the old empty strife of conflicting ideologies which after the defeat of the common enemy once more occupied the political arena to split the former comrades-in-arms into innumerable cliques which were not even factions and to engage them in the endless polemics and intrigues of a paper war. What Char had foreseen, clearly anticipated, while the real fight was still on-"If I survive, I know that I shall have to break with the aroma of these essential years, silently reject (not repress) my treasure" + +-had happened. They had lost their treasure. + +What was this treasure? As they themselves understood it, it seems to have consisted, as it were, of two interconnected parts: they had discovered that he who "joined the Resistance, found himself," that he ceased to be "in quest of [himself] without mastery, in naked unsatisfaction," that he no longer suspected himself of "insincerity," of being "a carping, suspicious actor of life," that he could afford "to go naked." In this nakedness, stripped of all masks-of those which society assigns to its members as well as those which the individual fabricates for himself in his psychological reactions against society-they had been visited for the first time in their lives by an apparition of freedom, not, to be sure, because they acted against tyranny and things worse than tyranny -this was true for every soldier in the Allied armies-but because they had become "challengers," had taken the initiative upon themselves and therefore, without knowing or even noticing it, had begun to create that public space between themselves where freedom could appear. "At every meal that we eat together, freedom is invited to sit down. The chair remains vacant, but the place is + +the last to lose their treasure. The history of revolutions-from the summer of 1776 in Philadelphia and the summer of 1789 in Paris to the autumn of 1956 in Budapest-which politically spells out the innermost story of the modern age, could be told in parable form as the tale of an age-old treasure which, under the most varied circumstances, appears abruptly, unexpectedly, and disappears again, under different mysterious conditions, as though it were a fata morgana. There exist, indeed, many good reasons to believe that the treasure was never a reality but a mirage, that we deal here not with anything substantial but with an apparition, and the best of these reasons is that the treasure thus far has remained nameless. Does something exist, not in outer space but in the world and the affairs of men on earth, which has not even a name? Unicorns and fairy queens seem to possess more reality than the lost treasure of the revolutions. And yet, if we turn our eyes to the beginnings of this era, and especially to the decades preceding it, we may discover to our surprise that the eighteenth century on both sides of the Atlantic possessed a name for this treasure, a name long since forgotten and lost-one is tempted to say-even before the treasure itself disappeared. The name in America was "public happiness," which, with its overtones of "virtue" and "glory," we understand hardly better than its French counterpart, "public freedom"; the difficulty for us is that in both instances the + +emphasis was on "public." + +However that may be, it is the namelessness of the lost treasure to which the poet alludes when he says that our inheritance was left us by no testament. The testament, telling the heir what will rightfully be his, wills past possessions for a future. Without testament or, to resolve the metaphor, without tradition-which selects and names, which hands down and preserves, which indicates where the treasures are and what their worth is-there seems to be no willed continuity in time and hence, humanly speaking, neither past nor future, only sempiternal change of the world and the biological cycle of living creatures in it. Thus the treasure was lost not because of historical circumstances and the adversity of reality but because no tradition had foreseen its appearance or its + +reality, because no testament had willed it for the future. The loss, at any rate, perhaps inevitable in terms of political reality, was consummated by oblivion, by a failure of memory, which befell not only the heirs but, as it were, the actors, the witnesses, those who for a fleeting moment had held the treasure in the palms of their hands, in short, the living themselves. For remembrance, which is only one, though one of the most important, modes of thought, is helpless outside a pre-established framework of reference, and the human mind is only on the rarest occasions capable of retaining something which is altogether unconnected. Thus the first who failed to remember what the treasure was like were precisely those who had possessed it and found it so strange that they did not even know how to name it. At the time this did not bother them; if they did not know their treasure, they knew well enough the meaning of what they did and that it was beyond victory and defeat: "Action that has a meaning for the living has value only for the dead, completion only in the minds that inherit and question it." The tragedy began not when the liberation of the country as a whole ruined, almost automatically, the small hidden islands of freedom that were doomed anyhow, but when it turned out that there was no mind to inherit and to question, to think about and to remember. The point of the matter is that the "completion," whicn indeed every enacted event must have in the minds of those who then are to tell the story and to convey its meaning, eluded them; and without this thinking completion after the act, without the articulation accomplished by remembrance, there simply was + +no story left that could be told. + +There is nothing in this situation that is altogether new. We arc only too familiar with the recurring outbursts of passionate exasperation with reason, thought, and rational discourse which are the natural reactions of men who know from their own experiences that thought and reality have parted company, that reality has become opaque for the light of thought and that thought, no longer bound to incident as the circle remains bound to its focus, is liableeither to become altogether meaningless or to rehash old verities which have lost all concrete relevance. Even the anticipating rec- + +ognition of the predicament has by now become familiar. When Tocqueville returned from the New World, which he so superbly knew how to describe and to analyze that his work has remained a classic and survived more than a century of radical change, he was well aware of the fact that what Char called the "completion" of act and event had still eluded him; and Char's "Our inheritance was left to us by no testament" sounds like a variation of Tocqueville's "Since the past has ceased to throw its light upon the future, the mind of man wanders in obscurity." 2 Yet the only exact description of this predicament is to be found, as far as I know, in one of those parables of Franz Kafka which, unique perhaps in this respect in literature, are real 7rapa{3o>..a[, thrown alongside and around the incident like rays of light which, however, do not illuminate its outward appearance but possess the power of X rays to lay bare its inner structure that, in our case, consists of the + +hidden processes of the mind. + +Kafka's parable reads as follows : 3 + +He has two antagonists: the first presses him from behind, from the origin. The second blocks the road ahead. He gives battle to both. To be sure, the first supports him in his fight with the second, for he wants to push him forward, and in the same way the second supports him in his fight with the first, since he drives him back. But it is only theoretically so. For it is not only the two antagonists who are there, but he himself as well, and who really knows his intentions? His dream, though, is that some time in an unguarded moment -and this would require a night darker than any night has ever been yet-he will jump out of the fighting line and be promoted, on account of his experience in fighting, to the position of umpire over his antagonists in their fight with + +each other. + +The incident which this parable relates and penetrates follows, in the inner logic of the matter, upon the events whose gist we found contained in Rene Char's aphorism. It begins, in fact, at precisely the point where our opening aphorism left the sequence of events hanging, as it were, in mid-air. Kafka's fight begins when the + +course of action has run its course and when the story which was its outcome waits to be completed "in the minds that inherit and question it." The task of the mind is to understand what happened, and this understanding, according to Hegel, is man's way of reconciling himself with reality; its actual end is to be at peace with the world. The trouble is that if the mind is unable to bring peace and to induce reconciliation, it finds itself immediately engaged in + +its own kind of warfare. + +However, historically speaking, this stage in the development of the modem mind was preceded, at least in the twentieth century, by two, r.ather than one, previous acts. Before the generation of Rene Char, whom we have chosen here as its representative, found itself thrown out of literary pursuits into the commitments of action, another generation, only slightly older, had turned to politics for the solution of philosophic perplexities and had tried to escape from thought into action. It was this older generation which then became the spokesmen and creators of what they themselves called existentialism; for existentialism, at least in its French version, is primarily an escape from the perplexities of modem philosophy into the unquestioning commitment of action. And since, under the circumstances of the twentieth century, the so-called intellectuals-writers, thinkers, artists, men of letters, and the like--could find access to the public realm only in time of revolution, the revolution came to play, as Malraux once noticed (in Man's Fate), "the role which once was played by eternal life": it "saves those that make it." Existentialism, the rebellion of the philosopher against philosophy, did not arise when philosophy turned out to be unable to apply its own rules to the realm of political affairs; this failure of political philosophy as Plato would have understood it is almost as old as the history of Western philosophy and metaphysics ; and it did not even arise when it turned out that philosophy was equally unable to perform the task assigned to it by Hegel and the philosophy of history, that is, to understand and grasp conceptually historical reality and the events that made the modern world what it is. The situation, however, became desperate when the old metaphysical questions were shown to be meaning- + +less; that is, when it began to dawn upon modern man that he had come to live in a world in which his mind and his tradition of thought were not even capable of asking adequate, meaningful questions, let alone of giving answers to its own perplexities. In this predicament action, with its involvement and commitment, its being engagee, seemed to hold out the hope, not of solving any problems, but of making it possible to live with them without be- + +coming, as Sartre once put it, a salaud, a hypocrite. + +The discovery that the human mind had ceased, for some mysterious reasons, to function properly forms, so to speak, the first act of the story with which we are concerned here. I mentioned it here, however briefly, because without it the peculiar irony of what was to follow would be lost on us. Rene Char, writing during the last months of the Resistance, when liberation-which in our context meant liberation from action-loomed large, concluded his reflections with an appeal to thought for the prospective survivors no less urgent and no less passionate than the appeal to action of those who preceded him. If one were to write the intellectual history of our century, not in the form of successive generations, where the historian must be literally true to the sequence of theories and attitudes, but in the form of the biography of a single person, aiming at no more than a metaphorical approximation to what actually happened in the minds of men, this person's mind would stand revealed as having been forced to turn full circle not once but twice, first when he escaped from thought into action, and then again when action, or rather having acted, forced him back into thought. Whereby it would be of some relevance to notice that the appeal to thought arose in the odd in-between period which sometimes inserts itself into historical time when not only the later historians but the actors and witnesses, the living themselves, become aware of an inte-rval in time which is altogether determined by things that are no longer and by things that are not yet. In history, these intervals have shown more than once that they may + +We now may return to Kafka, who·in the logic of these matters, though not in their chronology, occupies the last and, as it were, + +the most advanced position. (The riddle of Kafka, who in more than thirty-five years of growing posthumous fame has established himself as one of the foremost writers' writers, is still unsolved; it consists primarily in a kind of breath-taking reversal of the established relationship between experience and thought. While we find it a matter of course to associate richness of concrete detail and dramatic action with the experience of a given reality and to ascribe to mental processes abstract pallor as the price exacted for their order and precision, Kafka, by sheer force of intelligence and spiritual imagination, created out of a bare, "abstract" minimum of experience a kind of thought-landscape which, without losing in precision, harbors all the riches, varieties, and dramatic elements characteristic of "real" life. Because thinking to him was the most vital and the liveliest part of reality, he developed this uncanny gift of anticipation which even today, after almost forty years full of unprecedented and unforeseeable events, does not cease to amaze us.) The story in its utter simplicity and brevity records a mental phenomenon, something which one may call a thought-event. The scene is a battleground on which the forces of the past and the future clash with each other; between them we find the man whom Kafka calls "he," who, if he wants to stand his ground at all, must give battle to both forces. Hence, there are two or even three fights going on simultaneously: the fight between "his" antagonists and the fight of the man in between with each of them. However, the fact that there is a fight at all seems due exclusively to the presence of the man, without whom the forces of the past and of the future, one suspects, would have + +neutralized or destroyed each other long ago. + +The first thing to be noticed is that not only the future-"the wave of the future"-but also the past is seen as a force, and not, as in nearly all our metaphors, as a burden man has to shoulder and of whose dead weight the living can or even must get rid in their march into the future. In the words of Faulkner, "the past is never dead, it is not even past." This past, moreover, reaching all the way back into the origin, does not pull back but presses forward, and it is, contrary to what one would expect, the future + +which drives us back into the past. Seen from the viewpoint of man, who always lives in the interval between past and future, time is not a continuum, a flow of uninterrupted succession; it is broken in the middle, at the point where "he" stands; and "his" standpoint is not the present as we usually understand it but rather a gap in time which "his" constant fighting, "his" making a stand against past and future, keeps in existence. Only because man is inserted into time and only to the extent that he stands his ground does the flow of indifferent time break up into tenses; it is this insertion-the beginning of a beginning, to put it into Augustinian terms-which splits up the time continuum into forces which then, because they are focused on the particle or body that gives them their direction, begin fighting with each + +other and acting upon man in the way Kafka describes. + +Without distorting Kafka's meaning, I think one may go a step further. Kafka describes how the insertion of man breaks up the unidirectional flow of time but, strangely enough, he does not change the traditional image according to which we think of time as moving in a straight line. Since Kafka retains the traditional metaphor of a rectilinear temporal movement, "he" has barely enough room to stand and whenever "he" thinks of striking out on "his" own "he" falls into the dream of a region over and above the fighting-line-and what else is this dream and this region but the old dream which Western metaphysics has dreamed from Parmenides to Hegel of a timeless, spaceless, suprasensuous realm as the proper region of thought? Obviously what is missing in Kafka's description of a thought-event is a spatial dimension where thinking could exert itself without being forced to jump out of human time altogether. The trouble with Kafka's story in all its magnificence is that it is hardly possible to retain the notion of a rectilinear temporal movement if its unidirectional flow is broken up into antagonistic forces being directed toward and acting upon man. The insertion of man, as he breaks up the continuum, cannot but cause the forces to deflect, however lightly, from their original direction, and if this were the case, they would no longer clash head on but meet at an angle. In other words, the gap where + +what the physicists call a parallelogram of forces. + +Ideally, the action of the two forces which form the parallelogram of forces where Kafka's "he" has found his battlefield should result in a third force, the resultant diagonal whose origin would be the point at which the forces clash and upon which they act. This diagonal force would in one respect differ from the two forces whose result it is. The two antagonistic forces are both unlimited as to their origins, the one coming from an infinite past and the other from an infinite future; but though they have no known beginning, they have a terminal ending, the point at which they clash. The diagonal force, on the contrary, would be limited as to its origin, its starting-point being the clash of the antagonistic forces, but it would be infinite with respect to its ending by virtue of having resulted from the concerted action of two forces whose origin is infinity. This diagonal force, whose origin is known, whose direction is determined by past and future, but whose eventual end lies in infinity, is the perfect metaphor for the activity of thought. lf Kafka's "he" were able to exert his forces along this diagonal, in perfect equidistance from past and future, walking along this diagonal line, as it were, forward and backward. with the slow, ordered movements which are the proper motion for trains of thought, he would not have jumped out of the fightingline and be above the melee as the parable demands, for this diagonal, though pointing toward the infinite, remains bound to and is rooted in the present; but he would have discoveredpressed as he was by his antagonists into the only direction from which he could properly see and survey what was most his own, what had come into being only with his own, self-inserting appearance-the enormous, ever-changing time-space which is created and limited by the forces of past and future; he would have found the place in time which is sufficiently removed from past and future to offer "the umpire" a position from which to judge the + +But, one is tempted to add, this is "only theoretically so." What is much more likely to happen-and what Kafka in other stories + +and parables has often described-is that the "he," unable to find lhe diagonal which would lead him out of the fighting-line and into the space ideally constituted by the parallelogram of forces, will "die of exhaustion," worn out under the pressure of constant fighting, oblivious of his original intentions, and aware only of the existence of this gap in time which, as long as he lives, is the ground on which he must stand, though it seems to be a battle- + +field and not a home. + +To avoid misunderstandings : the imagery I am using here to indicate metaphorically and tentatively the contemporary conditions of thought can be valid only within the realm of mental phenomena. Applied to historical or biographical time, none of these metaphors can possibly make sense because gaps in time do not occur there. Only insofar as he thinks, and that is insofar as he is ageless-a "he" as Kafka so rightly calls him, and not a "somebody"--does man in the full actuality of his concrete being live in this gap of time between past and future. The gap, I suspect, is not a modern phenomenon, it is perhaps not even a historical datum but is coeval with the existence of man on earth. It may well be the region of the spirit or, rather, the path paved by thinking, this small track of non-time which the activity of thought beats within the time-space of mortal men and into which the trains of thought, of remembrance and anticipation, save whatever they touch from the ruin of historical and biographical time. This small non-time-space in the very heart of time, unlike the world and the culture into which we are born, can only be indicated, but cannot be inherited and handed down from the past; each new generation, indeed every new human being as he inserts himself between an infinite past and an infinite future, must discover and ploddingly + +pave it anew. + +The trouble, however, is that we seem to be neither equipped nor prepared for this activity of thinking, of settling down in the gap between past and future. For very long times in our history, actually throughout the thousands of years that followed upon the foundation of Rome and were determined by Roman concepts. this gap was bridged over by what, since the Romans, we have + +called tradition. That this tradition has worn thinner and thinner as the modern age progressed is a secret to nobody. When the thread of tradition finally broke, the gap between past and future ceased to be a condition peculiar only to the activity of thought and restricted as an experience to those few who made thinking their primary business. It became a tangible reality and perplexity + +for all; that is, it became a fact of political relevance. + +Kafka mentions the experience, the fighting experience gained by "him" who stands his ground between the clashing waves of past and future. This experience is an experience in thinkingsince, as we saw, the whole parable concerns a mental phenomenon-and it can be won, like all experience in doing something, only through practice, through exercises. (In this, as in other respects, this kind of thinking is different from such mental processes as deducing, inducing, and drawing conclusions whose logical rules of non-contradiction and inner consistency can be learned once and for all and then need only to be applied.) The following six essays are such exercises, and their only aim is to gain experience in how to think; they do not contain prescriptions on what to think or which truths to hold. Least of all do they intend to retie the broken thread of tradition or to invent some newfangled surrogates with which to fill the gap between past and future . Throughout these exercises the problem of truth is kept in abeyance; the concern is solely with how to move in this gap-the only region perhaps where truth eventually will appear. More specifically, these are exercises in political thought as it arises out of the actuality of political incidents (though such incidents are mentioned only occasionally), and my assumption is that thought itself arises out of incidents of living experience and must remain bound to them as the only guideposts by which to take its bearings. Since these exercises move between past and future, they contain criticism as well as experiment, but the experiments do not attempt to design some sort of utopian future, and the critique of the past, of traditional concepts, does not intend to "debunk." Moreover, the critical and the experimental parts of the following essays are not sharply divided, although, + +roughly speaking, the first three chapters are more critical than experimental and the last five chapters are more experimental than critical. This gradual shift of emphasis is not arbitrary, because there is an element of experiment in the critical interpretation of the past, an interpretation whose chief aim is to discover the real origins of traditional concepts in order to distill from them anew their original spirit which has so sadly evaporated from the very key words of political language-such as freedom and justice, authority and reason, responsibility and virtue, power and glory-leaving behind empty shells with which to settle almost all accounts, regardless of their underlying phenomenal reality. + +It seems to me, and I hope the reader will agree, that the essay as a literary form has a natural affinity to the exercises I have in mind. Like all collections of essays, this book of exercises obviously could contain more or fewer chapters without for that reason changing its character. Their unity-which to me is the justification of publishing them in book form-is not the unity of a whole but of a sequence of movements which, as in a musical suite, are written in the same or related keys. The sequence itself is determined by content. In this respect, the book is divided into three parts. The first part deals with the modem break in tradition and with the concept of history with which the modem age hoped to replace the concepts of traditional metaphysics. The second part discusses two central and interrelated political concepts, authority and freedom; it presupposes the discussion of the first part in the sense that such elementary and direct questions as What is authority? What is freedom? can arise only if no answers, handed down by tradition, are available and valid any longer. The four essays of the last part, finally, are frank attempts at applying the kind of thinking that was tried out in the first two parts of the book to immediate, topical problems with which we are daily confronted, not, to be sure, in order to find definite solutions but in the hope of clarifying the issues and gaining some assurance in confronting spe- + +TRADITION AND + +THE MODERN AGE + +I + +0 UR tradition of political thought had its definite beginning in the teachings of Plato and Aristotle. I believe it came to a no less definite end in the theories of Karl Marx. The beginning was made when, in The Republic's allegory of the cave, Plato described the sphere of human affairs-all that belongs to the living together of men in a common world-in terms of darkness. confusion, and deception which those aspiring to true being must turn away from and abandon if they want to discover the clear sky of eternal ideas. The end came with Marx's declaration that philosophy and its truth are located not outside the affairs of men and their common world but precisely in them, and can be "realized" only in the sphere of living together, which he called "society," through the emergence of "socialized men" ( vergesellschaftete Menschen). Political philosophy necessarily implies the attitude of the philosopher toward politics; its tradition began with the philosopher's turning away from politics and then returning + +in order to impose his standards on human affairs. The end came when a philosopher turned away from philosophy so as to "realize" it in politics. This was Marx's attempt, expressed first in his decision (in itself philosophical) to abjure philosophy, and second in his intention to "change the world" and thereby the philosophiz- + +ing minds, the "consciousness" of men. + +The beginning and the end of the tradition have this in common: that the elementary problems of politics never come as clearly to light in their immediate and simple urgency as when they are first formulated and when they receive their final challenge. The beginning, in Jacob Burckhardt's words, is like a "fundamental chord" which sounds in its endless modulations through the whole history of Western thought. Only beginning and end are, so to speak, pure or unmodulated; and the fundamental chord therefore never strikes its listeners more forcefully and more beautifully than when it first sends its harmonizing sound into the world and never more irritatingly and jarringly than when it still continues to be heard in a world whose soundsand thought-it can no longer bring into harmony. A random remark which Plato made in his last work: "The beginning is like a god which as long as it dwells among men saves arl things" -&.pm yap Kat fho<; EV av8pw7rOL<; iopvp.lv7J uwCn 7rclVTa 1 \*-is true of our tradition; as long as its beginning was alive, it could save all things and bring them into harmony. By the same token, it became destructive as it came to its end-to say nothing of the aftermath of confusion and helplessness which came after the tradition ended + +and in which we live today. + +In Marx's philosophy, which did not so much turn Hegel upside down as invert the traditional hierarchy of thought and action, of contemplation and labor, and of philosophy and politics, the beginning made by Plato and Aristotle proves its vitality by leading Marx into flagrantly contradictory statements, mostly in that part of his teachings usually called utopian. The most important are his prediction that under conditions of a "socialized humanity" the "state will wither away," and that the productivity of labor + +will become so great that labor somehow will abolish itself, thus guaranteeing an almost unlimited amount of leisure time to each member of the society. These statements, in addition to being predictions, contain of course Marx's ideal of the best form of society. As such they are not utopian, but rather reproduce the political and social conditions of the same Athenian city-state which was the model of experience for Plato and Aristotle, and therefore the foundation on which our tradition rests. The Athenian polis functioned without a division between rulers and ruled, and thus was not a state if we use this term, as Marx did, in accordance with the traditional definitions of forms of government, that is, one-man rule or monarchy, rule by the few or oligarchy, and rule by the majority or democracy. Athenian citizens, moreover, were citizens only insofar as they possessed leisure time, had that freedom from labor which Marx predicts for the future. Not only in Athens but throughout antiquity and up to the modern age, those who labored were not citizens and those who were citizens were first of all those who did not labor or who possessed more than their labor power. This similarity becomes even more striking when we look into the actual content of Marx's ideal society. Leisure time is seen to exist under the condition of statelessness, or under conditions where, in Lenin's famous phrase which renders Marx's thought very precisely, the administration of society has become so simplified that every cook is qualified to take over its machinery. Obviously, under such circumstances the whole business of politics, Engels' simplified "administration of things," could be of interest only to a cook, or at best to those "mediocre minds" whom Nietzsche thought best qualified for taking care of public affairs.2 This, to be sure, is very different from actual conditions in antiquity, where, on the contrary, political duties were considered so difficult and timeconsuming that those engaged in them could not be permitted to undertake any tiring activity. (Thus, for instance, the shepherd could qualify for citizenship but the peasant could not; the painter, but not the sculptor, was still recognized as something more than a f3avavuo<;;, the distinction being drawn in either case simply by + +applying the criterion of effort and fatigue.) It is against the timeconsuming political life of an average full-fledged citizen of the Greek polis that the philosophers, especially Aristotle, established their ideal of O")(oA�, of leisure time, which in antiquity never meant freedom from ordinary labor, a matter of course anyhow, but time + +free from political activity and the business of the state. + +In Marx's ideal society these two different concepts are inextricably combined: the classless and stateless society somehow realizes the general ancient conditions of leisure from labor and, at the same time, leisure from politics. This is supposed to come about when the "administration of things" has taken the place of government and political action. This twofold leisure from labor as well as politics had been for the philosophers the condition of a {3lo<> fhwp7JTU, a life devoted to philosophy and knowledge in the widest sense of the word. Lenin's cook, in other words, lives in a society providing her with as much leisure from labor as the free ancient citizens enjoyed in order to devote their time to 1TOALTru(tT8aL, as well as as much leisure from politics as the Greek philosophers had demanded for the few who wanted to devote all their time to philosophizing. The combination of a stateless (apolitical) and almost Iaborless society loomed so large in Marx's imagination as the very expression of an ideal humanity because of the traditional connotation of leisure as O")(oA� and otium, that is, a life devoted + +to aims higher than work or politics. + +Marx himself regarded his so-called utopia as simple prediction, and it is true that this part of his theories corresponds to certain developments which have come fully to light only in our time. Government in the old sense has given way in many respects to administration, and the constant increase in leisure for the masses is a fact in all industrialized countries. Marx clearly perceived certain trends inherent in the era ushered in by the Industrial Revolution, although he was wrong in assuming that these trends would assert themselves only under conditions of socialization of the means of production. The hold which the tradition had over him lies in his viewing this development in an idealized light, and in understanding it in terms and concepts having their origin in + +an altogether different historical period. This blinded him to the authentic and very perplexing problems inherent in the modern world and gave his accurate predictions their utopian quality. But the utopian ideal of a classless, stateless, and laborless society wa� born out of the marriage of two altogether non-utopian elements: the perception of certain trends in the present which could no longer be understood in the framework of the tradition, and the traditional concepts and ideals by which Marx himself understood and + +integrated them. + +Marx's own attitude to the tradition of political thought was one of conscious rebellion. In a challenging and paradoxical mood he therefore framed certain key statements which, containing his political philosophy, underlie and transcend the strictly scientific part of his work (and as such curiously remained the same throughout his life, from the early writings to the last volume of Das Kapital) . Crucial among them are the following: "Labor created man" (in a formulation by Engels, who, contrary to an opinion current among some Marx scholars, usually rendered Marx's thought adequately and succinctly) .3 "Violence is the midwife of every old society pregnant with a new one," hence: violence is the midwife of history (which occurs in both the writings of Marx and of Engels in many variations) .4 Finally, there is the famous last thesis on Feuerbach: "The philosophers have only interpreted the world differently; the point is, however, to change it," which, in the light of Marx's thought, one could render more adequately as: The philosophers have interpreted the world long enough; the time has come to change it. For this last statement is in fact only a variation of another, occurring in an early manuscript: "You cannot aufheben [i.e., elevate, conserve, and abolish in the Hegelian sense] philosophy without realizing it." In the later work the same attitude to philosophy appears in the prediction that the working class will be the only legitimate heir of classical philosophy. None of these statements can be understood in and by itself. Each acquires its meaning by contradicting some traditionally accepted truth whose plausibility up to the beginning of the modern + +age had been beyond doubt. "Labor created man" means first that labor and not God created man; second, it means that man, insofar as he is human, creates himself, that his humanity is the result of his own activity; it means, third, that what distinguishes man from :mimal, his differentia specifica, is not reason, but labor, that he \s not an animal rationale, but an animal laborans,· it means, fourth, that it is not reason, until then the highest attribute of man, but labor, the traditionally most despised human activity, which contains the humanity of man. Thus Marx challenges the traditional God, the traditional estimate of labor, and the traditional glorifica- + +tion of reason. + +That violence is the midwife of history means that the hidden forces of development of human productivity, insofar as they depend upon free and conscious human action, come to light only through the violence of wars and revolutions. Only in those violent periods does history show its true face and dispel the fog of mere ideological, hypocritical talk. Again the challenge to tradition is clear. Violence is traditionally the u.ftima ratio in relationships between nations and the most disgraceful of domestic actions, being always considered the outstanding characteristic of tyranny. (The few attempts to save violence from disgrace, chiefly by Machiavelli and Hobbes, are of great relevance for the problem of power and quite illuminative of the early confusion of power with violence, but they exerted remarkably little influence on the tradition of political thought prior to our own time.) To Marx, on the contrary, violence or rather the possession of the means of violence is the constituent element of all forms of government; the state is the instrument of the ruling class by means of which it oppresses and exploits, and the whole sphere of political action is character- + +ized by the use of violence. + +The Marxian identification of action with violence implies another fundamental challenge to tradition which may be more difficult to perceive, but of which Marx, who knew Aristotle very well, must have been aware. The twofold Aristotelian definition of man as a 'wov 1roAtTucov and a 'wov .\oyov lxov, a being attaining his highest possibility in the faculty of speech and the life in a polis, + +was designed to distinguish the Greek from the barbarian and the free man from the slave. The distinction was that Greeks, living together in a polis, conducted their affairs by means of speech, through persuasion ( 7rtt8nv), and not by means of violence, through mute coercion. Hence, when free men obeyed their government, or the laws of the polis, their obedience was called 1rn8apx£a, a word which indicates clearly that obedience was obtained by persuasion and not by force. Barbarians were ruled by violence and slaves forced to labor, and since violent action and toil are alike in that they do not need speech to be effective, barbarians and slaves were avev ..\oyov, that is, they did not live with each other primarily by means of speech. Labor was to the Greeks essentially a nonpolitical, private affair, but violence was related to and established a contact, albeit negative, with other men. Marx's glorification of violence therefore contains the more specific denial of ..\oyo�, of speech, the diametrically opposite and traditionally most human form of intercourse. Marx's theory of ideological superstructures ultimately rests on this anti-traditional hostility to speech and the concomitant glorification of violence. + +For traditional philosophy it would have been a contradiction in terms to "realize philosophy" or to change the world in accordance with philosophy-and Marx's statement implies that change is preceded by interpretation, so that the philosophers' interpretation of the world has indicated how it should be changed. Philosophy might have prescribed certain rules of action, though no great philosopher ever took this to be his most important concern. Essentially, philosophy from Plato to Hegel was "not of this world," whether it was Plato describing the philosopher as the man whose body only inhabits the city of his fellow men, or Hegel admitting that, from the point of view of common sense, philosophy is a world stood on its head, a verkehrte Welt. The challenge to tradition, this time not merely implied but directly expressed in Marx's statement, lies in the prediction that the world of common human affairs, where we orient ourselves and think in common-sense terms, will one day become identical with the realm of ideas where the philosopher moves, or that philosophy, which has always been + +everybody. + +These three statements are framed in traditional terms which they, however, explode; they are formulated as paradoxes and meant to shock us. They are in fact even more paradoxical and led Marx into greater perplexities than he himself had anticipated. Each contains one fundamental contradiction which remained insoluble in his own terms. If labor is the most human and most productive of man's activities, what will happen when, after the revolution, "labor is abolished" in "the realm of freedom," when man has succeeded in emancipating himself from it? What productive and what essentially human activity will be left? If violence is the midwife of history and violent action therefore the most dignified of all forms of human action, what will happen when, after the conclusion of class struggle and the disappearance of the state, no violence will even be possible? How will men be able to act at all in a meaningful, authentic way? Finally, when philosophy has been both realized and abolished in the future so- + +ciety, what kind of thought will be left? + +Marx's inconsistencies are well known and noted by almost all Marx scholars. They usually are summarized as discrepancies "between the scientific point of view of the historian and the moral point of view of the prophet" (Edmund Wilson) , between the historian seeing in the accumulation of capital "a material means for the increase of productive forces" (Marx) and the moralist who denounced those who performed "the historical task" (Marx) as exploiters and dehumanizers of man. This and similar inconsistencies are minor when compared with the fundamental contradiction between the glorification of labor and action (as against contemplation and thought) and of a stateless, that is, actionless and (almost) laborless society. For this can be neither blamed on the natural difference between a revolutionary young Marx and the more scientific insights of the older historian and economist, nor resolved through the assumption of a dialectical movement wl::.i�h ;!eccs the negative or evil to produce the positive or the + +Such fundamental and flagrant contradictions rarely occur in second-rate writers, in whom they can be discounted. In the work of great authors they lead into the very center of their work and are the most important clue to a true understanding of their problems and new insights. In Marx, as in the case of other great authors of the last century, a seemingly playful, challenging, and paradoxical mood conceals the perplexity of having to deal with new phenomena in terms of an old tradition of thought outside of whose conceptual framework no thinking seemed possible at all. It is as though Marx, not unlike Kierkegaard and Nietzsche, tried desperately to think against the tradition while using its own conceptual tools. Our tradition of political thought began when Plato discovered that it is somehow inherent in the philosophical experience to turn away from the common world of human affairs; it ended when nothing was left of this experience but the opposition of thinking and acting, which, depriving thought of reality and + +action of sense, makes both meaningless. + +II + +The strength of this tradition, its hold on Western man's thought, has never depended on his consciousness of it. Indeed, only twice in our history do we encounter periods in which men are conscious and over-conscious of the fact of tradition, identifying age as such with authority. This happened, first, when the Romans adopted classical Greek thought and culture as their own spiritual tradition and thereby decided historically that tradition was to have a permanent formative influence on European civilization. Before the Romans such a thing as tradition was unknown; with them it became and after them it remained the guiding thread through the past and the chain to which each new generation knowingly or unknowingly was bound in its understanding of the world and its own experience. Not until the Romantic period do we again encounter an exalted consciousness and glorification of tradition. (The discovery of antiquity in the Renaissance was a + +first attempt to break the fetters of tradition, and by going to the sources themselves to establish a past over which tradition would have no hold.) Today tradition is sometimes considered an essentially romantic concept, but Romanticism did no more than place the discussion of tradition on the agenda of the nineteenth century; its glorification of the past only served to mark the moment when the modern age was about to change our world and general circumstances to such an extent that a matter-of-course + +reliance on tradition was no longer possible. + +The end of a tradition does 'l.Ot necessarily mean that traditional concepts have lost their power over the minds of men. On the contrary, it sometimes seems that this power of well-worn notions and categories becomes more tyrannical as the tradition loses its living force and as the memory of its beginning recedes; it may even reveal its full coercive iorce only alter its end has come and men no longer even rebel against it. This at least seems to be the lesson of the twentieth-century aftermath of formalistic and compulsory thinking, which came after Kierkegaard, Marx, and Nietzsche had challenged the basic assumptions of traditional religion, traditional political thought, and traditional metaphysics by consciously inverting the traditional hierarchy of concepts. However, neither the twentieth-century aftermath nor the nineteenth-century rebellion against tradition actually caused the break in our history. This sprang from a chaos of mass-perplexities on the political scene and of mass-opinions in the spiritual sphere which the totalitarian movements, through terror and ideology, crystallized into a new form of government and domination. Totalitarian domination as an established fact, which in its unprecedentedness cannot be comprehended through the usual categories of political thought, and whose "crimes" cannot be judged by traditional moral standards or punished within the legal framework of our civilization, has broken the continuity of Occidental history. The break in our tradition is now an accomplished fact. It is neither the result of anyone's deliberate choice nor subject to + +patterns of thought which had ruled the West for more than two thousand years may have foreshadowed this event and certainly can help to illuminate it, but they did not cause it. The event itself marks the division between the modem age-rising with the natural sciences in the seventeenth century, reaching its political climax in the revolutions of the eighteenth, and unfolding its general implications after the Industrial Revolution of the nineteenth-and the world of the twentieth century, which came into existence through the chain of catastrophes touched off by the First World Wru:. To hold the thinkers of the modem age, especially the nineteenth-century rebels against tradition, responsible for the structure and conditions of the twentieth century is even more dangerous than it is unjust. The implications apparent in the actual event of totalitarian domination go far beyond the most radical or most adventurous ideas of any of these thinkers. Their greatness lay in the fact that they perceived their world as one invaded by new problems and perplexities which our tradition of thought was unable to cope with. In this sense their own departure from tradition, no matter how emphatically they proclaimed it (like children whistling louder and louder because they are lost in the dark), was no deliberate act of their own choosing either. What frightened them about the dark was its silence, not the break in tradition. This break, when it actually occurred, dispelled the darkness, so that we can hardly listen any longer to the overloud, "pathetic" style of their writing. But the thunder of the eventual explosion has also drowned the preceding ominous silence that still answers us whenever we dare to ask, not "What + +are we fighting against" but "What are we fighting for?" + +Neither the silence of the tradition nor the reaction of thinkers against it in the nineteenth century can ever explain what actually happened. The non-deliberate character of the break gives it an irrevocability which only events, never thoughts, can have. The rebellion against tradition in the nineteenth century remained strictly within a traditional framework; and on the level of mere thought, which could hardly be concerned then with more than the essentially negative experiences of foreboding, apprehension, + +reconsideration of the past, was possible. + +Kierkegaard, Marx, and Nietzsche stand at the end of the tradition, just before the break came. Their immediate predecessor was Hegel. He it was who for the first time saw the whole of world history as one continuous development, and this tremendous achievement implied that he himself stood outside all authority-claiming systems and beliefs of the past, that he was held only by the thread of continuity in history itself. The thread of historical continuity was the first substitute for tradition; by means of it, the overwhelming mass of the most divergent values, the most contradictory thoughts and conflicting authorities, all of which had somehow been able to function together, were reduced to a unilinear, dialectically consistent development actually designed to repudiate not tradition as such, but the authority of all traditions. Kierkegaard, Marx, and Nietzsche remained Hegelians insofar as they saw the history of past philosophy as one dialectically developed whole; their great merit was that they radicalized this new approach toward the past in the only way it could still be further developed, namely, in questioning the conceptual hierarchy which had ruled Western philosophy since Plato and which Hegel had still taken + +for granted. + +Kierkegaard, Marx, and Nietzsche are for us like guideposts to a past which has lost its authority. They were the first who dared to think without the guidance of any authority whatsoever; yet, for better and worse, they were still held by the categorical framework of the great tradition. In some respects we are better off. We need no longer be concerned with their scorn for the "educated philistines," who all through the nineteenth century tried to make up for the loss of authentic authority with a spurious glorification of culture. To most people today this culture looks like a field of ruins which, far from being able to claim any authority, can hardly command their interest. This fact may be deplorable, but implicit in it is the great chance to look upon the past with eyes undistracted by any tradition, with a directness which has disappeared + +submitted to the authority of Greek thought. + +III + +The destructive distortions of the tradition were all caused by men who had experienced something new which they tried almost instantaneously to overcome and resolve into something old. Kierkegaard's leap from doubt into belief was a reversal and a distortion of the traditional relationship between reason and faith. It was the answer to the modern loss of faith, not only in God but in reason as well, which was inherent in Descartes' de omnibus dubitandum est, with its underlying suspicion that things may not be as they appear and that an evil spirit may willfully and forever hide truth from the minds of man. Marx's leap from theory into action, and from contemplation into labor, came after Hegel had transformed metaphysics into a philosophy of history and changed the philosopher into the historian to whose backward glance eventually, at the end of time, the meaning of becoming and motion, not of being and truth, would reveal itself. Nietzsche's leap from the nonsensuous transcendent realm of ideas and measurements into the sensuousness of life, his "inverted Platonism" or "trans-valuation of values," as he himself would call it, was the last attempt to tum away from the tradition, and it succeeded only in turning + +tradition upside down. + +Different as these rebellions against tradition are in content and intention, their results have an ominous similarity : Kierkegaard, jumping from doubt into belief, carried doubt into religion, transformed the attack of modern science on religion into an inner religious struggle, so that since then sincere religious experience has seemed possible only in the tension between doubt and belief, in torturing one's beliefs with one's doubts and relaxing from this torment in the violent affirmation of the absurdity of both the human condition and man's belief. No clearer symptom of this + +modern religious situation can be found than the fact that Dostoevski, perhaps the most experienced psychologist of modern religious beliefs, portrayed pure faith in the character of Myshkin "the idiot," or of Alyosha Karamazov, who is pure in heart because he + +is simple-minded. + +Marx, when he leaped from philosophy into politics, carried the theories of dialectics into action, making political action more theoretical, more dependent upon what we today would call an ideology, than it ever had been before. Since, moreover, his springboard was not philosophy in the old metaphysical sense, but as specifically Hegel's philosophy of history as Kierkegaard's springboard had been Descartes' philosophy of doubt, he superimposed the "law of history" upon politics and ended by losing the significance of both, of action no less than of thought, of politics no less than of philosophy, when he insisted that both were mere + +functions of society and history. + +Nietzsche's inverted Platonism, his insistence on life and the sensuously and materially given as against the suprasensuous and transcendent ideas which, since Plato, had been supposed to measure, judge, and give meaning to the given, endeci in what is commonly called nihilism. Yet Nietzsche was no nihilist but, on the contrary, was the first to try to overcome the nihilism inherent not in the notions of the thinkers but in the reality of modem life. What he discovered in his attempt at "trans-valuation" was that within this categorical framework the sensuous loses its very raison d'etre when it is deprived of its background of the suprasensuous and transcendent. "We abolished the true world: which world has remained? perhaps the world of appearances? . . . But no! together with the true world we abolished the world of appearances." 5 This insight in its elementary simplicity is relevant for all the turning-about operations in which the tradition found its + +end. + +What Kierkegaard wanted was to assert the dignity of faith against modem reason and reasoning, as Marx desired to assert again the dignity of human action against modern historical contemplation and relativization, and as Nietzsche wanted to assert the dignity + +of human life against the impotence of modem man. The traclitional oppositions of fides and intellectus, and of theory and practice, took their respective revenges upon Kierkegaard and Marx, just as the opposition between the transcendent and the sensuously given took its revenge upon Nietzsche, not because these oppositions still had roots in valid human experience, but, on the contrary, because they had become mere concepts, outside of which, + +however, no comprehensive thought seemed possible at all. + +That these three outstanding and conscious rebellions against a tradition which had lost its apx�. its beginning and principle, should have ended in self-defeat is no reason to question the greatness of the enterprises nor their relevance to the understanding of the modern world. Each attempt, in its particular way, took account of those traits of modernity which were incompatible with our tradition, and this even before modernity in all its aspects had fully revealed itself. Kierkegaard knew that the incompatibility of modem science with traditional beliefs does not lie in any specific scientific findings, all of which can be integrated into religious systems and absorbed by religious beliefs for the reason that they will never be able to answer the questions which religion raises. He knew that this incompatibility lay, rather, in the conflict between a spirit of doubt and distrust which ultimately can trust only what it has made itself, and the traditional unquestioning confidence in what has been given and appears in its true being to man's reason and senses. Modem science, in Marx's words, would "be superfluous if the appearance and the essence of things coincided." 6 Because our traditional religion is essentially a revealed religion and holds, in harmony with ancient philosophy, that truth is what reveals itself, that truth is revelation (even though the meanings of this revelation may be as different as the philosophers' aA�lhw and o�Awcno; are from the early Christians' eschatological expectations for an a?ToKaAvtfno; in the Second Corning) , 7 modem science has become a much more formidable enemy of religion than traditional philosophy, even in its most rationalistic versions, ever could be. Yet Kierkegaard's attempt to save faith from the onslaught of modernity made even religion modern, that is, subject + +to doubt and distrust. Traditional beliefs disintegrated into absurdity when Kierkegaard tried to reassert them on the assumption that man cannot trust the truth-receiving capacity of his + +reason or of his senses. + +Marx knew that the incompatibility between classical political thought and modern political conditions lay in the accomplished fact of the French and Industrial Revolutions, which together had raised labor, traditionally the most despised of all human activities, to the highest rank of productivity and pretended to be able to assert the time-honored ideal of freedom under unheard-of conditions of universal equality. He knew that the question was only superficially posed in the idealistic assertions of the equality of man, the inborn dignity of every human being, and only superficially answered by giving laborers the right to vote. This was not a problem of justice that could be solved by giving the new class of workers its due, after which the old order of suum cuique would be restored and function as in the past. There is the fact of the basic incompatibility between the traditional concepts making labor itself the very symbol of man's subjection to necessity, and the modern age which saw labor elevated to express man's positive freedom, the freedom of productivity. It is from the impact of labor, that is to say, of necessity in the traditional sense, that Marx endeavored to save philosophical thought, deemed by the tradition to be the freest of all human activities. Yet when he proclaimed that "you cannot abolish philosophy without realizing it," he began subjecting thought also to the inexorable despotism of + +necessity, to the "iron law" of productive forces in society. + +Nietzsche's devaluation of values, like Marx's labor theory of value, arises from the incompatibility between the traditional "ideas," which, as transcendent units, had been used to recognize and measure human thoughts and actions, and modern society, which had dissolved all such standards into relationships between its members, establishing them as functional "values." Values are social commodities that have no significance of their own but, like other commodities, exist only in the ever-changing relativity of social linkages and commerce. Through this relativization both the + +things which man produces for his use and the standards according to which he lives undergo a decisive change: they become entities of exchange, and the bearer of their "value" is society and not man, who produces and uses and judges. The "good" loses its character as an idea, the standard by which the good and the bad can be measured and recognized; it has become a value which can be exchanged with other values, such as those of expediency or of power. The holder of values can refuse this exchange and become an "idealist," who prices the value of "good" higher than the value of expediency; but this does not make the "value" of good any + +less relative. + +The term "value" owes its origin to the sociological trend which even before Marx was quite manifest in the relatively new science of classical economy. Marx was still aware of the fact, which the social sciences have since forgotten, that nobody "seen in his isolation produces values," but that products "become values only in their social relationship." 8 His distinction between "use value" and "exchange value" reflects the distinction between things as men use and produce them and their value in society, and his insistence on the greater authenticity of use values, his frequent description of the rise of exchange value as a kind of original sin at the beginning of market production reflect his own helpless and, as it were, blind recognition of the inevitability of an impending "devaluation of all values." The birth of the social sciences can be located at the moment when all things, "ideas" as well as material objects, were equated with values, so that everything derived its existence from and was related to society, the bonum and malum no less than tangible objects. In the dispute as to whether capital or labor is the source of values, it is generally overlooked that at no time prior to the incipient Industrial Revolution was it held that values, and not things, are the result of man's productive capacity, or was everything that exists related to society and not to man "seen in his isolation." The notion of "socialized men," whose emergence Marx projected into the future classless society, is in fact the underlying assumption of classical as well as Marxian econ- + +It is therefore only natural that the perplexing question which has plagued all later "value-philosophies," where to find the one supreme value by which to measure all others, should first appear in the economic sciences which, in Marx's words, try to "square the circle-to find a commodity of unchanging value which would serve as a constant standard for others." Marx believed he had found this standard in labor-time, and insisted that use values "which can be acquired without labor have no exchange value" (though they retain their "natural usefulness") , so that the earth itself is of "no value"; it does not represent "objectified labor." 11 With this conclusion we come to the threshold of a radical nihilism, to that denial of everything given of which the nineteenth-century rebellions against tradition as yet knew little and which arises only in twenti- + +eth-century society. + +Nietzsche seems to have been unaware of the origin as well as of the modernity of the term "value" when he accepted it as a key notion in his assault on tradition. But when he began to devaluate the current values of society, the implications of the whole enterprise quickly became manifest. Ideas in the sense of absolute units had become identified with social values to such an extent that they simply ceased to exist once their value-character, their social status, was challenged. Nobody knew his way better than Nietzsche through the meandering paths of the modern spiritual labyrinth, where recollections and ideas of the past are hoarded up as though they had always been values which society depreciated whenever it needed better and newer commodities. Also, he was well aware of the profound nonsense of the new "value-free" science which was soon to degenerate into scientism and general scientific superstition and which never, despite all protests to the contrary, had anything in common with the Roman historians' attitude of sine ira et studio. For while the latter demanded judgment without scorn and truthfinding without zeal, the wertfreie Wissenschaft, which could no longer judge because it had lost its standards of judgment and could no longer find truth because it doubted the existence of truth, imagined that it could produce meaningful results if only it abandoned the last remnants of those absolute standards. And when Nietzsche + +proclaimed that he had discovered "new and higher values,'' he was the first to fall prey to delusions which he himself had helped to destroy, accepting the old traditional notion of measuring with transcendent units in its newest and most hideous form, thereby again carrying the relativity and exchangeability of values into the very matters whose absolute dignity he had wanted to assert-power and + +life and man's love of his earthly existence. + +IV + +Self-defeat, the result of all three challenges to tradition in the nineteenth century, is only one and perhaps the most superficial thing Kierkegaard, Marx, and Nietzsche have in common. More important is the fact that each of their rebellions seems to he concentrated on the same ever-repeated subject: Against the alleged abstractions of philosophy and its concept of man as an animal rationale, Kierkegaard wants to assert concrete and suffering men; Marx confirms that man's humanity consists of his productive and active force, which in its most elementary aspect he calls laborpower; and Nietzsche insists on life's productivity, on man's will and will-to-power. In complete independence of one another-none of them ever knew of the others' existence-they arrive at the conclusion that this enterprise in terms of the tradition can be achieved only through a mental operation best described in the images and similes of leaps, inversions, and turning concepts upside down: Kierkegaard speaks of his leap from doubt into belief; Marx turns Hegel, or rather "Plato and the whole Platonic tradition" (Sidney Hook) , "right side up again," leaping "from the realm of necessity into the realm of freedom"; and Nietzsche understands his philosophy as "inverted Platonism" and "transformation of all values." The turning operations with which the tradition ends bring the beginning to light in a twofold sense. The very assertion of one side of the opposites-fides against inteliectus, practice against theory, sensuous, perishable life against permanent, unchanging, suprasen· suous truth-necessarily brings to light the repudiated opposire anc! + +shows that both have meaning and significance only in this opposition. Furthermore, to think in terms of such opposites is not a matter of course, but is grounded in a first great turning operation on which all others ultimately are based because it established the opposites in whose tension the tradition moves. This first turning-about is Plato's 7rEptaywy� rij<; tfrt>xij,, the turning-about of the whole human being, which he tells-as though it were a story with beginning and end and not merely a mental operation-in the parable of the cave + +in The Republic. + +The story of the cave unfolds in three stages : the first turningabout takes place in the cave itself when one of the inhabitants frees himself from the fetters which chain the cave dwellers' "legs and necks" so that "they can only see before them," their eyes glued to the screen on which shadows and images of things appear; he now turns around to the rear of the cave, where an artificial fire illuminates the things in the cave as they really are. There is, second, the turning from the cave to the clear sky, where the ideas appear as the true and eternal essences of the things in the cave, illuminated by the sun, the idea of ideas, enabling man to see and the ideas to shine forth. Finally, there is the necessity of returning to thf. cave, of leaving the realm of eternal essences and moving again in the realm of perishable things and mortal men. Each of these turnings is accomplished by a loss of sense and orientation: the eyes accustomed to the shadowy appearances on the screen are blinded by the fire in the cave; the eyes then adjusted to the dim light of the artificial fire are blinded by the light that illuminates the ideas; finally, the eyes adjusted to the light of the sun must readjust to the dimness of + +the cave. + +Behind these turnings-about, which Plato demands only of the philosopher, the lover of truth and light, lies another inversion indicated generally in Plato's violent polemics against Homer and the Homeric religion, and in particular in the construction of his story as a kind of reply to and reversal of Homer's description of Hades in the eleventh book of the Odyssey. The parallel between the image!ii of the cave and Hades (the shadowy, unsubstantial, senseless movements of the soul in Homer's Hades correspond to the ignorance and + +senselessness of the bodies in the cave) is unmistakable because it is stressed by Plato's use of the words £iow.\ov, image, and uKla, shadow, which are Homer's own key words for the description of life after death in the underworld. The reversal of the Homeric "position" is obvious; it is as though Plato were saying to him: Not the life of bodyless souls, but the life of the bodies takes place in an underworld; compared to the sky and the sun, the earth is like Hades; images and shadows are the objects of bodily senses, not the surroundings of bodyless souls; the true and real is not the world in which we move and live and which we have to part from in death, but the ideas seen and grasped by the eyes of the mind. In a sense, Plato's 7Ttptaywy� was a turning-about by which everything that was commonly believed in Greece in accordance with the Homeric religion came to stand on its head. It is as though the underworld of Hades had risen to the surface of the earth.10 But this reversal of Homer did not actually turn Homer upside down or downside up, since the dichotomy within which such an operation alone can take place is almost as alien to Plato's thought, which did not yet operate with predetermined opposites, as it is alien to the Homeric world. (No turning about of the tradition can therefore ever land us in the original Homeric "position," which seems to have been Nietzsche's error; he probably thought that his inverted Platonism could lead him back into pre-Platonic modes of thought.) It was solely for political purposes that Plato set forth his doctrine of ideas in the form of a reversal of Homer; but thereby he established the framework within which such turning operations are not far-fetched possibilities but predetermined by the conceptual structure itself. The development of philosophy in late antiquity in the various schools, which fought one another with a fanaticism unequaled in the pre-Christian world, consists of turnings-about and shifting emphases on one of two opposite terms, made possible by Plato's separation of a world of mere shadowy appearance and the world of eternally true idP.as. He himself had given the first example in the turning from the cave to the sky. When Hegel finally, in a last gigantic effort, had gathered together into one. consistent self-developing whole the various strands of traditional philosophy as they had developed from + +Plato's original concept, the same splitting up into two conflicting schools of thought, though on a much lower level, took place, and right-wing and left-wing, idealistic and materialistic Hegelians could + +for a short while dominate philosophical thought. + +The significance of Kierkegaard's, Marx's, and Nietzsche's challenges to the tradition-though none of them would have been possible without the synthesizing achievement of Hegel and his concept of history-is that they constitute a much more radical turningabout than rhe mere upside-down operations with their weird oppositions between sensualism and idealism, materialism and spiritualism, and even immanentism and transcendentalism imply. If Marx had been merely a "materialist" who brought Hegel's "idealism" down to earth, his influence would have been as short-lived and limited to scholarly quarrels as that of his contemporaries. Hegel's basic as�umption was that the dialectical movement of thought is identical with the dialectical movement of matter itself. Thus he hoped to bridge the abyss which Descartes had opened between man, defined as res cogitans, and the world, defined as res extensa, between cognition and reality, thinking and being. The spiritual homelessness of modern man finds its first expressions in this Cartesian perplexity and the Pascalian answer. Hegel claimed that the discovery of the dialectical movement as a universal law, ruling both man's reason and human affairs and the inner "reason" of natural events, accomplished even more than a mere correspondence between intellectus and res, whose coincidence pre-Cartesian philosophy had defined as truth. By introducing the spirit and its selfrealization in movement, Hegel believed he had demonstrated an ontological identity of matter and idea. To Hegel, therefore, it would have been of no great importance whether one started this movement from the viewpoint of consciousness, which at one moment begins to "materialize," or whether one chose as starting point matter, which, moving in the direction of "spiritualization," becomes conscious of itself. (How little Marx doubted these fundamentals of his teacher appears from the role he ascribed to self-consciousness in the form of class-consciousness in history.) In other words, Marx was no more a "dialectical materialist" than Hegel was a + +"dialectical idealist"; the very concept of dialectical movement, as Hegel conceived it as a universal law, and as Marx accepted it, makes the terms "idealism" and "materialism" as philosophical systems meaningless. Marx, especially in his earlier writings, is quite conscious of this and knows that his repudiation of the tradition and of Hegel does not lie in his "materialism," but in his refusal to assume that the difference between man and animal life is ratio, or thought, that, in Hegel's words, "man is essentially spirit"; for the young Marx man is essentially a natural being endowed with the faculty of action (ein tiitiges Naturwesen), and his action remains "natural" because it consists of laboring-the metabolism between man and nature.11 His turning-about, like Kierkegaard's and Nietzsche's, goes to the core of the matter; they all question the traditional hierarchy of human capabilities, or, to put it another way, they ask again what the specifically human quality of man is; they do not intend to build systems or W eltanschauungen on this or that premise. + +Since the rise of modem science, whose spirit is expressed in the Cartesian philosophy of doubt and mistrust, the conceptual framework of the tradition has not been secure. The dichotomy between contemplation and action, the traditional hierarchy which ruled that truth is ultimately perceived only in speechless and actionless seeing, could not be upheld under conditions in which science became active and did in order to know. When the trust that things appear as they really are was gone, the concept of truth as revelation had become doubtful, and with it the unquestioning faith in a revealed God. The notion of "theory" changed its meaning. It no longer meant a system of reasonably connected truths which as such had been not made but given to reason and the senses. Rather it became the modern scientific theory, which is a working hypothesis, changing in accordance with the results it produces and depending for its validity not on what it "reveals" but on whether it "works." By the same process, Plato's ideas lost their autonomous power to illuminate the world and the universe. First they became what they had been for Plato only in their relationship to the political realm, standards and measurements, or the regulating, limiting forces of + +man's own reasoning mind, as they appear in Kant. Then, after the priority of reason over doing, of the mind's prescribing its rules to the actions of men, had been lost in the transformation of the whole world by the Industrial Revolution-a transformation the success of which seemed to prove that man's doings and fabrications prescribe their rules to reason-these ideas finally became mere values whose validity is determined not by one or many men but by society as a + +whole in its ever-changing functional needs. + +These values in their ex- and inter-changeability are the only "ideas" left to (and understood by) "socialized men." These are men who have decided never to leave what to Plato was "the cave" of everyday human affairs, and never to venture on their own into a world and a life which, perhaps, the ubiquitous functionalization of modern society has deprived of one of its most elementary characteristics-the instilling of wonder at that which is as it is. This very real development is reflected and foreshadowed in Marx's political thought. Turning the tradition upside down within its own framework, he did not actually get rid of Plato's ideas, though he did record the darkening of the clear sky where those ideas, as well as ID?JlJ \l'tll�r presences, had once become visible to t!le eyes of + +men. + +THE CONCEP T + +OF HISTORY + +Ancient and Modern + +1: History and Nature + +T ET us begin with Herodotus, whom Cicero called pater historiae and who has remained father of Western history.1 He tells us in the first sentence of the Persian Wars that the purpose of his enterprise is to preserve that which owes its existence to men, Ta yulflJ-L£va l� d.v8pw1rwv, lest it be obliterated by time, and to bestow upon the glorious, wondrous deeds of Greeks and barbarians sufficient praise to assure their remembrance by posterity and thus make their glory + +shine through the centuries. + +This tells us a great deal and yet does not tell us enough. For us, concern with immortality is not a matter of course, and Herodotus, since this was a matter of course to him, does not tell us much about it. His understanding of the task of history-to save human deeds from the futility that comes from oblivion-was rooted in the Greek concept and experience of nature, which comprehended all things + +that come into being by themselves without assistance from men or gods-the Olympian gods did not claim to have created the world 2 -and therefore are immortal. Since the things of nature are everpresent, they are not likely to be overlooked or forgotten; ana since they are forever, they do not need human remembrance for their further existence. All living creatures, man not excepted, are contained in this realm of being-forever, and Aristotle explicitly assures us that man, insofar as he is a natural being and belongs to the species of mankind, possesses immortality; through the recurrent cycle of life, nature assures the same kind of being-forever to things that are born and die as to things that are and do not change. "Being for living creatures is Life," and being-forever ( or 1rpayp.am, as distinguished from 1rot-'lcm, fabrication, can never outlast the moment of their realization, would never leave any trace without the help of remembrance. The task of the poet and + +historiographer (both of whom Aristotle still puts in the same category because their subject is 1rpa�t�) 6 consists in making something lasting out of remembrance. They do this by translating 1rpii.�t> and >..i�t>, action and speech, into that kind of 1ro£71ut> or fabrication + +which eventually becomes the written word. + +History as a category of human existence is of course older than the written word, older than Herodotus, older even than Homer. Not historically but poetically speaking, its beginning lies rather in the moment when Ulysses, at the court of the king of the Phaeacians, listened to the story of his own deeds and sufferings, to the story of his life, now a thing outside l·1imself, an "object" for all to see and to hear. What had been sheer occurrence now became "history." But the transformation of single events and occurrences into history was essentially the same "imitation of action" in words which was later employed in Greek tragedy,i where, as Burckhardt once remarked, "external action is hidden from the eye" through the reports of messengers, even though there was no objection at all to showing the horrible.8 The scene where Ulysses listens to the story of his own life is paradigmatic for both history and poetry; the "reconciliation with reality," the catharsis, which, according to Aristotle, was the essence of tragedy, and, according to Hegel, was the ultimate purpose of history, came about through the tears of remembrance. The deepest human motive for history and poetry appears here in unparalleled purity : since listener, actor, and sufferer are the same person, ali motives of sheer curiosity and lust for new information, which, of course, have always played a large role in both historical inquiry and aesthetic pleasure, are naturally absent in Ulysses himself, who would have been bored rather than moved + +if history were only news and poetry only entertainment. + +Such distinctions and reflections may seem commonplace to modern ears. Implied in them, however, is one great and painful paradox which contributed (perhaps more than any other single factor) to the tragic aspect of Greek culture in its greatest manifestations. The paradox is that, on the one hand, everything was seen and measured against the background of the things that are forever, while, on the other, true human greatness was understood, at least by the pre- + +Platonic Greeks, to reside in deeds and words, and was rather re� resented by Achilles, "the doer of great deeds and the speaker of great words," than by the maker and fabricator, even the poet and writer. This paradox, that greatness was understood in terms of permanence while human greatness was seen in precisely the most futile and least lasting activities of men, has haunted Greek poetry and historiography as it has perturbed the quiet of the philosophers. The early Greek solution of the paradox was poetic and nonphilosophical. It consisted in the immortal fame which the poets could bestow upon word and deed to make them outlast not only the futile moment of speech and action but even the mortal life of their agent. Prior to the Socratic school-with the possible exception of Hesiod-we encounter no real criticism of immortal fame; even Heraclitus thought that it was the greatest of all human aspirations, and while he denounced with violent bitterness the political conditions in his native Ephesus, it never would have occurred to him to condemn the realm of human affairs as such or doubt its + +potential greatness. + +The change, prepared by Parmenides, came about with Socrates and reached its culminat4>n in Plato's philosophy, whose teaching regarding a potential immortality of mortal men become authoritative for all philosophy schools in antiquity. To be sure, Plato was still confronted with the same paradox and he seems to have been the first who considered "the desire to become famous and not to lie in the end without a name" on the same level as the natural desire for children through which nature secures the immortality of the species, though not the d.Oavau-{a of the individual person. In his political philosophy, therefore, he proposed to substitute the latter for the former, as though the desire for immortality through fame could as well be fulfilled when men "are immortal because they leave children's children behind them, and partake of immortality through the unity of a sempiternal becoming"; when he declared the begetting of children to be a law he obviously hoped this would be sufficient for the "common man's" natural yearning for deathlessness. For neither Plato nor Aristotle any longer believed that mortal men could "immortalize" (d.Oavart{ftv, in the Aristotelian + +terminology, an activity whose object is by no means necessarily one's own self, the immortal fame of the name, but includes a variety of occupations with immortal things in general) through great deeds and words.9 They had discovered, in the activity of thought itself, a hidden human capacity for turning away from the whole realm of human affairs which should not be taken too seriously by men (Plato) because it was patently absurd to think that man is the highest being there is (Aristotle ). While begetting might be enough for the many, to "immortalize" meant for the philosopher to dwell in the neighborhood of those things which are forever, to be there and present in a state of active attention, but without doing anything, without performance of deeds or achievement of works. Thus the proper attitude of mortals, once they had reached the neighborhood of the immortal, was actionless and even speechless contemplation: the Aristotelian voii<>, the highest and most human capacity of pure vision, cannot translate into words what it beholds, 10 and the ultimate truth which the vision of ideas disclosed to Plato is likewise an app7JTov, something which cannot be caught in words.11 Hence the old paradox was resolved by the philosophers by denying to man not the capacity to "immortalize," but the capability of measuring himself and his own deeds against the everlasting greatness of the cosmos, of matching, as it were, the immortality of nature and the gods with an immortal greatness of his own. The solution clearly comes about at the expense of "the doer of great deeds and the + +speaker of great word!.." + +The distinction between the poets and historians on one side and the philosophers on the other was that the former simply accepted the common Greek concept of greatness. Praise, from which came glory and eventually everlasting fame, could be bestowed only upon things already "great," that is, things that possessed an emerging, shining quality which distinguished them from all others and made glory possible. The great was that which deserved immortality, that which should be admitted to the company of things that lasted forever, surrounding the futility of mortals with their unsurpassable majesty. Through history men almost became the equals of nature, and only those events, deeds, or words that rose by themselves to + +the ever-present challenge of the natural universe were what we would call historical. Not only the poet Homer and not only the storyteller Herodotus, but even Thucydides, who in a much more sober mood was the first to set standards for historiography, tells us explicitly in the beginning of the Peloponnesian War that he wrote his work because of the war's "greatness," because "this was the greatest movement yet known in history, not only of the Hellenes, but of a large part of the barbarian world . . . almost mankind." The concern with greatness, so prominent in Greek poetry and historiography, is based on the most intimate connection between the concepts of nature and history. Their common denominator is immortality. Immortality is what nature possesses without effort and without anybody's assistance, and immortality is what the mortals therefore must try to achieve if they want to live up to the world into which they were born, to live up to the things which surround them and to whose company they are admitted for a short while. The connection between history and nature is therefore by no means an opposition. History receives into its remembrance those mortals who through deed and word have proved themselves worthy of nature, and their everlasting fame means that they, despite their mortality, may remain in the company of the things that last forever. + +Our modern concept of history is no less intimately connected with our modern concept of nature than the corresponding and very different concepts which stand at the beginning of our history. They too can be seen in their full significance only if their common root is discovered. The nineteenth-century opposition of the natural and historical sciences, together with the allegedly absolute objectivity and precision of the natural scientists, is today a thing of the past. The natural sciences now admit that with the experiment, testing natural processes under prescribed conditions, and with the observer, who in watching the experiment becomes one of its conditions, a "subjective" factor is introduced into the "objective" proc- + +The most important new result of nuclear physics was the recognition of the possibility of applying quite different types + +of natural laws, without contradiction, to one and the same physical event. This is due to the fact that within a system of laws which are based on certai-n fundamental ideas only certain quite definite ways of asking questions make sense, and thus, that such a system is separated from others which allow + +different questions to be put.12 + +In other words, the experiment "being a question put before nature" ( Galileo) ,13 the answers of science will always remain replies to questions asked by men; the confusion in the issue of "objectivity" was to assume that there could be answers without questions and results independent of a question-asking being. Physics, we know today, is no less a man-centered inquiry into what is than historical research. The old quarrel, therefore, between the "subjectivity" of historiography and the "objectivity" of physics has lost + +much of its relevance.14 + +The modern historian as a rule is not yet aware of the fact that the natural scientist, against whom he had to defend his own "sci� entific standards" for so many decades, finds himself in the same position, and he is quite likely to state and restate in new, seemingly more scientific terms the old distinction between a science of nature and a science of history. The reason is that the problem of objectivity in the historical sciences is more than a mere technical, scientific perplexity. Objectivity, the "extinction of the self" as the condition of "pure vision" (das reine Sehen der Dinge-Ranke ) meant the historian's abstention from bestowing either praise or blame, together with an attitude of perfect distance with which he would follow the course of events as they were revealed in his documentary sources. To him the only limitation of this attitude, which Droysen once denounced as "eunuchic objectivity," 15 lay in the necessity of selecting material from a mass of facts which, compared with the limited capacity of the human mind and the limited time of human life, appeared infinite. Objectivity, in other words, meant noninterference as well as nondiscrimination. Of these two, nondiscrimination, abstention from praise and blame, was obviously much easier to achieve than noninterference; every selection of material in a sense interferes with history, and all criteria for selection put the + +historical course of events under certain man-made conditions, which are quite similar to the conditions the natural scientist prescribes to + +natural processes in the experiment. + +We have stated here the problem of objectivity in modern terms, as it arose during the modern age, which believed it had discovered in history a "new science" which then would have to comply to the standards of the "oJder" science of nature. This, however, was a self-misunderstanding. Modern natural science developed quickly into an even "newer" science than history, and both sprang, as we shall see, from exactly the same set of "new" experiences with the exploration of the universe, made at the beginning of the modern age. The curious and still confusing point about the historical sciences was that they did not take their standards from the natural sciences of their own age, but harked back to the scientific and, in the last analysis, philosophical attitude which the modern age had just begun to liquidate. Their scientific standards, culminating in the "extinction of the self," had their roots in Aristotelian and medieval natural science, which consisted mainly in observing and cataloguing observed facts. Before the rise of the modern age it was a matter of course that quiet, actionless, and selfless contemplation of the miracle of being, or of the wonder of God's creation, should also be the proper attitude for the scientist, whose curiosity about the particular had not yet parted company with the wonder before the general from which, according to the ancients, sprang philosophy\_ With the modern age this objectivity lost its fundament and therefore was constantly on the lookout for new justifications. For the historical sciences the old standard of objectivity could make sense only if the historian believed that history in its entirety was either a cyclical phenomenon which could be grasped as a whole through contemplation (and Vico, following the theories of late antiquity, was still of this opinion) or that it was guided by some divine providence for the salvation of mankind, whose plan was revealed, whose beginnings and ends were known, and therefore could be again contemplated as a whole. Both these concepts, however, were actually quite alien to the new consciousness of history in the modern age; they were only the old traditional framework into which. + +the new experiences were pressed and from which the new science had risen. The problem of scientific objectivity, as the nineteenth <:entury posed it, owed so much to historical self-misunderstanding and philosophical confusion that the real issue at stake, the issue of impartiality, which is indeed decisive not only for the "science" of history but for all historiography from poetry and storytelling on- + +ward, has become difficult to recognize. + +Impartiality, and with it all true historiography, came into the world when Homer decided to sing the deeds of the Trojans no less than those of the Achaeans, and to praise the glory of Hector no less than the greatness of Achilles. This Homeric impartiality, as it is echoed by Herodotus, who set out to prevent "the great and wonderful actions of the Greeks and the barbarians from losing their due meed of glory," is still the highest type of objectivity we know. Not only does it leave behind the common interest in one's own side and one's own people which, up to our own days, characterizes almost all national historiography, but it also discards the alternative of victory or defeat, which modems have felt expresses the "objective" judgment of history itself, and does not permit it to interfere with what is judged to be worthy of immortalizing praise. Somewhat later, and most magnificently expressed in Thucydides, there appears in Greek historiography still another powerful element that contributes to historical objectivity. It could come to the foreground only after long experience in polis-life, which to an incrediby large extent consisted of citizens talking with one another. In this incessant talk the Greeks discovered that the world we have in common is usually regarded from an infinite number of different standpoints, to which correspond the most diverse points of view. In a sheer inexhaustible flow of arguments, as the Sophists presented them to the citizenry of Athens, the Greek learned to exchange his own viewpoint, his own "opinion"-the way the world appeared and opened up to him (SoKfi pm, "it appears to me," from which comes So�a, or "opinion")-with those of his fellow citizens. Greeks learned to understand-not to understand one another as individual persons, but to look upon the same world from one another's standpoint, to see the same in very different and frequently opposing aspects. The + +speeches in which Thucydides makes articulate the standpoints and interests of the warring parties are still a living testimony to the + +extraordinary degree of this objectivity. + +What has obscured the modern discussion of objectivity in the historical sciences and prevented its ever touching the fundamental issues involved seems to be the fact that none of the conditions of either Homeric impartiality or Thucydidean objectivity are present in the modern age. Homeric impartiality rested upon the assumption that great things are self-evident, shine by themselves; that the poet (or later the historiographer ) has only to preserve their glory, which is essentially futile, and that he would destroy, instead of preserving, if he were to forget the glory that was Hector's. For the short duration of their existence great deeds and great words were, in their greatness, as real as a stone or a house, there to be seen and heard by everybody present. Greatness was easily recognizable as that \Vhich by itself aspired to immortality-that is, negatively speaking, as a heroic contempt for all that merely comes and passes away, for all individual life, one's own included. This sense of greatness could not possibly survive intact into the Christian era for the very simple reason that, according to Christian teachings, the relationship between life and world is the exact opposite to that in Greek and Latin antiquity: in Christianity neither the world nor the everrecurring cycle of life is immortal, only the single living individual. It is the world that will pass away; men will live forever. The Christian reversal is based, in its turn, upon the altogether different teachings of the Hebrews, who always held that life itself is sacred, more sacred than anything else in the world, and that man is the supreme + +being on earth. + +Connected with this inner conviction of the sacredness of life as such, which has remained with us even after security of the Christian faith in life after death has passed away, is the stress on the all-importance of self-interest, still so prominent in all modern political philosophy. In our context this means that the Thucydidean type of objectivity, no matter how much it may be admired, no longer has any basis in real political life. Since we have made life our supreme and foremost concern, we have no room left for an activity + +based on contempt for one's own life-interest. Selflessness may still be a religious or a moral virtue; it can hardly be a political one. Under these conditions objectivity lost its validity in experience, was divorced from real life, and became that "lifeless" academic affair + +which Droysen rightly denounced as being eunuchic. + +Moreover, the birth of the modern idea of history not only coincided with but was powerfully stimulated by the modern age's doubt of the reality of an outer world "objectively" given to human perception as an unchanged and unchangeable object. In our context the most important consequence of this doubt was the emphasis on sensation qua sensation as more "real" than the "sensed" object and, at any rate, the only safe ground of experience. Against this subjectivization, which is but one aspect of the still growing worldalienation of man in the modern age, no judgments could hold out: they were all reduced to the level of sensations and ended on the level of the lowest of all sensations, the sensation of taste. Our vocabulary is a telling testimony to this degradation. All judgments not inspired by moral principle (which is felt to be old-fashioned) or not dictated by some self-interest are considered matters of "taste," and this in hardly a different sense from what we mean by saying that the preference for clam chowder over pea soup is a matter of taste. This conviction, the vulgarity of its defenders on the theoretical level notwithstanding, has disturbed the conscience of the historian much more deeply because it has much deeper roots in the general spirit of the modern age than the allegedly superior + +scientific standards of his colleagues in the natural sciences. + +Unfortunately it is in the nature of academic quarrels that methodological problems are likely to overshadow more fundamental issues. The fundamental fact about the modern concept of history is that it arose in the same sixteenth and seventeenth centuries which ushered in the gigantic development of the natural sciences. Foremost among the characteristics of that age, which are still alive and present in our own world, is the world-alienation of man, which I mentioned before and which is so difficult to perceive as a basic condition of our whole life because out of it, and partly at least out of its despair, did arise the tremendous structure of the human + +artifice we inhabit today, in whose framework we have even discovered the means of destroying it together with all non-man-made + +things on earth. + +The shortest and most fundamental expression this world-alienation ever found is contained in Descartes' famous de omnibus dubitandum est, for this rule signifies something altogether different from the skepticism inherent in the self-doubt of all true thought. Descartes came to his rule because the then recent discoveries in the natural sciences had convinced him that man in his search for truth and knowledge can trust neither the given evidence of the senses, nor the "innate truth" of the mind, nor the "inner light of reason." This mistrust of the human capacities has been ever since one of the most elementary conditions of the modern age and the modern world; but it did not spring, as is usually assumed, from a sudden mysterious dwindling of faith in God, and its cause was originally not even a suspicion of reason as such. Its origin was simply the highly justified loss of confidence in the truth-revealing capacity of the senses. Reality no longer was disclosed as an outer phenomenon to human sensation, but had withdrawn, so to speak, into the sensing of the sensation itself. It now turned out that without confidence in the senses neither faith in God nor trust in reason could any longer be secure, because the revelation of both divine and rational truth had always been implicitly understood to follow the awe-inspiring simplicity of man's relationship with the world: I open my eyes and behold the vision, I listen and hear the sound, I move my body and touch the tangibility of the world. If we begin to doubt the fundamental truthfulness and reliability of this relationship, which of course does not exclude errors and illusions but, on the contrary, is the condition of their eventual correction, none of the traditional metaphors for suprasensual truth-be it the eyes of the mind which can see the sky of ideas or the voice of conscience listened to by the human heart-can any longer carry its meaning. The fundamental experience underlying Cartesian doubt was the discovery that the earth, contrary to all direct sense experience, revolves around the sun. The modern age began when man, with + +the help of the telescope, turned his bodily eyes toward the universe, about which he had speculated for a long time-seeing with the eyes of the mind, listening with the ears of the heart, and guided by the inner light of reason-and learned that his senses were not fitted for the universe, that his everyday experience, far from being able to constitute the model for the reception of truth and the acquisition of knowledge, was a constant source of error and delusion. After this deception-whose enormity we find difficult to realize because it was centuries before its full impact was felt everywhere and not only in the rather restricted milieu of scholars and philosopherssuspicions began to haunt modern man from all sides. But its most immediate consequence was the spectacular rise of natural science, which for a long time seemed to be liberated by the discovery that our senses by themselves do not tell the truth. Henceforth, sure of the unreliability of sensation and the resulting insufficiency of mere observation, the natural sciences turned toward the experiment, which, by directly interfering with nature, assured the development + +whose progress has ever since appeared to be limitless. + +Descartes became the father of modern philosophy because he generalized the experience of the preceding as well as his own generation, developed it into a new method of thinking, and thus became the first thinker thoroughly trained in that "school of suspicion" which, according to Nietzsche, constitutes modern philosophy. Suspicion of the senses remained the core of scientific pride until in our time it has turned into a source of uneasiness. The trouble is that "we find nature behaving so differently from what we observe in the visible and palpable bodies of our surroundings that no model shaped after our large-scale experiences can ever be 'true' "; at this point the indissoluble connection between our thinking and our sense perception takes its revenge, for a model that would leave sense experience altogether out of account and, therefore, be completely adequate to nature in the experiment is not only ''practically inaccess!ble but not even thinkable." 16 The trouble, in other words. 1s not that the modern physical universe cannot be visualized, for this is a matter of course under the assumption that nanm: do�s not + +reveal itself to the human senses; the uneasiness begins when nature turns out to be inconceivable, that is, unthinkat.Je in terms of pure + +reasoning as well. + +The dependence of modern thought upon factual discoveries of the natural sciences shows itself most clearly in the seventeenth century. It is not always admitted as readily as by Hobbes, who attributed his philosophy exclusively to the results of the work of Copernicus and Galileo, Kepler, Gassendi, and Mersenne, and who denounced all past philosophy as nonsense with a violence matched perhaps only by Luther's contempt for the "stulti philosophi." One does not need the radical extremism of Hobbes's conclusion, not that man may be evil by nature, but that a distinction between good and evil makes no sense, and that reason, far from being an inner light disclosing truth, is a mere "faculty of reckoning with consequences"; for the basic suspicion that man's earthbound experience presents a caricature of truth is no less present in Descartes' fear that an evil spirit may rule the world and withhold truth forever from the mind of a being so manifestly subject to error. In its most harmless form, it permeates English empiricism, where the meaningfulness of the sensibly given is dissolved into data of sense perception, disclosing their meaning only through habit and repeated experiences, so that in an extreme subjectivism man is ultimately imprisoned in a non-world of meaningless sensations that no reality and no truth can penetrate. Empiricism is only seemingly a vindication of the senses; actually it rests on the assumption that only common-sense arguing can give them meaning, and it always starts with a declaration of non-confidence in the truth- or reality-revealing capacity of the senses. Puritanism and empiricism, in fact, are only two sides of the same coin. The same fundamental suspicion finally inspired Kant's gigantic effort to re-examine the human faculties in such a way that the question of a Ding an sich, that is the truthrevealing faculty of experience in an absolute sense, could be left + +Of much more immediate consequence for our concept of history was the positive version of subjectivism which arose from the same predicament : Although it seems that man is unable to recognize + +the given world which he has not made himself, he nevertheless must be capable of knowing at least what he made himself. This pragmatic attitude is already the fully articulated reason why Vico turned his attention to history and thus became one of the fathers of modern historical consciousness. He said: Geometrica demonstramus quia facimus; si physica demonstrare possemus, faceremusY ("Mathematical matters we can prove because we ourselves make them; to prove the physical, we would have to make it.") Vico turned to the sphere of history only because he still believed it impossible "to make nature." No so-called humanist considerations inspired his turning away from nature, but solely the belief that history is "made" by men just as nature is "made" by God; hence historical truth can be known by men, the makers of history, but physical truth is reserved for the Maker of the universe. + +It has frequently been asserted that modern science was born when attention shifted from the search after the "what" to the investigation of "how." This shift of emphasis is almost a matter of course if one assumes that man can know only what he has made himself, insofar as this assumption in turn implies that I "know" a thing whenever I understand how it has come into being. By the same token, and for the same reasons, the emphasis shifted from interest in things to interest in processes, of which things were soon to become almost accidental by-products. Vico lost interest in nature because he assumed that to penetrate the mystery of Creation it would be necessary to understand the creative process, whereas all previous ages had taken it for granted that one can very well understand the universe without ever knowing how God created it, or, in the Greek version, how the things that are by themselves came into being. Since the seventeenth century the chief preoccupation of all scientific inquiry, natural as well as historical, has been with processes; but only modern technology (and no mere science, no matter how highly developed), which began with substituting mechanical processes for human activities-laboring and working-and ended with starting new natural processes, would have been wholly adequate to Vico's ideal of knowledge. Vico, who is regarded by many as the father of modern history, would hardly have turned to history + +under modern conditions. He would have turned to technology; for our technology does indeed what Vico thought divine action did in the realm of nature and human action in the realm of history. + +In the modern age history emerged as something it never had been before. It was no longer composed of the deeds and sufferings of men, and it no longer told the story of events affecting the lives of men; it became a man-made process, the only all-comprehendin!! process which owed its existence exclusively to the human race. Today this quality which distinguished history from nature is also a thing of the past. We know today that though we cannot "make" nature in the sense of creation, we are quite capable of starting new natural processes, and that in a sense therefore we "make nature." to the extent, that is, that we "make history." It is true we have reached this stage only with the nuclear discoveries, where natural forces are let loose, unchained, so to speak, and where the natural processes which take place would never have existed without direct interference of human action. This stage goes far beyond not only the pre-modern age, when wind and water were used to substitute for and multiply human forces, but also the industrial age, with its steam engine and internal-combustion motor, where nJtural forces were imitated and utilized as man-made means of production. + +The contemporary decline of interest in the humanities, and especially in the study of history, which seems inevitable in all completely modernized countries, is quite in accord with the first impulses that led to modern historical science. What is definitely out of place today is the resignation which led Vico into the study of history. We can do in the natural-physical realm what he thought we could do only in the realm of history. We have begun to act into nature as we used to act into history. If it is merely a question of processes, it has turned out that man is as capable of starting natural processes which would not have come about without human interference as he is of starting something new in the field of human + +Since the beginning of the twentieth century, technology has emerged as the meeting ground of the natural and historical sciences, and although hardly a single great scientific discovery has ever beeo + +made for pragmatic, technical, or practical purposes (pragmatism in the vulgar sense of the word stands refuted by the factual record of scientific development), this final outcome is in perfect accord with the innermost intentions of modern science. The comparatively new social sciences, which so quickly became to history what technology had been to physics, may use the experiment in a much cruder and less reliable way than do the natural sciences, but the method is the same : they too prescribe conditions, conditions to human behavior, as modern physics prescribes conditions to natural processes. If their vocabulary is repulsive and their hope to close the alleged gap between our scientific mastery of nature and our deplored impotence to "manage" human affairs through an engineering science of human relations sounds frightening, it is only because they have decided to treat man as an entirely natural being whose life process can be handled the same way as all other proc- + +esses. + +In this context, however, it is important to be aware how decisively the technological world we live in, or perhaps begin to live in, differs from the mechanized world as it arose with the Industrial Revolution. This difference corresponds essentially to the difference between action and fabrication. Industrialization still consisted primarily of the mechanization of work processes, the improvement in the making of objects, and man's attitude to nature still remained that of homo faber, to whom nature gives the material out of which the human artifice is erected. The world we have now come to live in, however, is much more determined by man acting into nature, creating natural processes and directing them into the human artifice and the realm of human affairs, than by building and preserving + +the human artifice as a relatively permanent entity. + +Fabrication is distinguished from action in that it has a definite beginning and a predictable end : it comes to an end with its end product, which not only outlasts the activity of fabrication but from then on has a kind of "life" of its own. Action, on the contrary, as the Greeks were the first to discover, is in and by itself utterly futile; it never leaves an end product behind itself. If it has any consequences at all, they consist in principle in an endless new chain of + +happenings whose eventual outcome the actor is utterly incapable of knowing or controlling beforehand. The most he may be able to do is to force things into a certain direction, and even of this he can never be sure. None of these characteristics is present in fabrication. Compared with the futility and fragility of human action, the world fabrication erects is of lasting permanence and tremendous solidity. Only insofar as the end product of fabrication is incorporated into the human world, where its use and eventual "history" can never be entirely predicted, does even fabrication start a process whose outcome cannot be entirely foreseen and is therefore beyond the control of its author. This means only that man is never exclusively homo faber, that even the fabricator remains at the same time an acting being, who starts processes wherever he goes and with + +whatever he does. + +Up to our own age human action with its man-made processes was confined to the human world, whereas man's chief preoccupation with regard to nature was to use its material in fabrication, to build with it the human artifice and defend it against the overwhelming force of the elements. The moment we started natural processes of our own-and splitting the atom is precisely such a man-made natural process-we not only increased our power over nature, or became more aggressive in our dealings with the given forces of the earth, but for the first time have taken nature into the human world as such and obliterated the defensive boundaries between natural elements and the human artifice by which all previous civilizations + +were hedged in.11l + +The dangers of this acting into nature are obvious if we assume that the aforementioned characteristics of human action are part and parcel of the human condition. Unpredictability is not lack of foresight, and no engineering management of human affairs will ever be able to eliminate it, just as no training in prudence can ever lead to the wisdom of knowing what one does. Only total conditioning, that is, the total abolition of action, can ever hope to cope with unpredictability. And even the predictability of human behavior which political terror can enforce for relatively long periods of time is hardly able to change the very essence of human affairs once and + +for all; it can never be sure of its own future. Human action, like all strictly political phenomena, is bound up with human plurality, which is one of the fundamental conditions of human life insofar as it rests on the fact of natality, through which the human world is constantly invaded by strangers, newcomers whose actions and reactions cannot be foreseen by those who are already there and are going to leave in a short while. If, therefore, by starting natural processes, we have begun to act into nature, we have manifestly begun to carry our own unpredictability into that realm which we used to think of as ruled by inexorable laws. The "iron law" of history was always only a metaphor borrowed from nature; and the fact is that this metaphor no longer convinces us because it has turned out that natural science can by no means be sure of an unchallengeable rule of law in nature as soon as men, scientists and technicians, or simply builders of the human artifice, decide to inter- + +fere and no longer leave nature to herself. + +Technology, the ground on which the two realms of history and nature have met and interpenetrated each other in our time, points back to the connection between the concepts of nature and history as they appeared with the rise of the modern age in the sixteenth and seventeenth centuries. The connection lies in the concept of process : both imply that we think and consider everything in terms of processes and are not concerned with single entities or individual occurrences and their special separate causes. The key words of modern historiography-"development" and "progress"-were, in the nineteenth century, also the key words of the then new branches of natural science, particularly biology and geology, one dealing with animal life and the other even with non-organic matter in terms of historical processes. Technology, in the modern sense, was preceded by the various sciences of natural history, the history of biological life, of the earth, of the universe. A mutual adjustment of terminology of the two branches of scientific inquiry had taken place before the quarrel between the natural and historical sciences preoccupied the scholarly world to such an extent that it confused + +developments in the natural sciences. They have brought us back to the common origin of both nature and history in the modern ag�:: and demonstrate that their common denominator lies indeed in the concept of process-no less than the common denominator of nature and history in antiquity lay in the concept of immortality. But the experience which underlies the modern age's notion of process, unlike the experience underlying the ancient notion of immortality, is by no means primarily an experience which man made in the world surrounding him; on the contrary, it sprang from the despair of ever experiencing and knowing adequately all that is given to man and not made by him. Against this despair modern man summoned up the full measure of his own capacities ; despairing of ever finding truth through mere contemplation, he began to try out his capacities for action, and by doing so he could not help becoming aware that wherever man acts he starts processes. The notion of process does not denote an objective quality of either history or nature; it is the inevitable result of human action. The first result of men's acting into history is that history becomes a process, and the most cogent argument for men's acting into nature in the guise of scientific inquiry is that today, in Whitehead's formulation, "nature + +is a process." + +To act into nature, to carry human unpredictability into a realm where we are confronted with elemental forces which we shall perhaps never be able to control reliably, is dangerous enough. Even more dangerous would it be to ignore that for the first time in our history the human capacity for action has begun to dominate all others-the capacity for wonder and thought in contemplation no less than the capacities of homo faber and the human animal laborans. This, of course, does not mean that men from now on will no longer be able to fabricate things or to think or to labor. Not the capabilities of man, but the constellation which orders their mutual relationships can and does change historically. Such changes can best be observed in the changing self-interpretations of man throughout history, which, though they may be quite irrelevant for the ultimate "what" of human nature, are still the briefest and most succinct witnesses to the spirit of whole epochs. Thus, schematically + +speaking, Greek classic antiquity agreed that the highest form of human life was spent in a polis and that the supreme human capacity was speech-,wov 1f0ALTI.Kov and 'wov .\oyov €xov, in Aristotle's famous twofold definition; Rome and medieval philosophy defined man as the animal rationale; in the initial stages of the modern age, man was thought of primarily as homo faber, until, in the nineteenth century, man was interpreted as an animal laborans whose metabolism with nature would yield the highest productivity of which human life is capable. Against the background of these schematic definitions, it would be adequate for the world we have come to live in to define man as a being capable of action; for this capacity seems to have + +become the center of all other human capabilities. + +It is beyond doubt that the capacity to act is the most dangerous of all human abilities and possibilities, and it is also beyond doubt that the self-created risks mankind faces today have never been faced before. Considerations like these are not at all meant to offer solutions or to give advice. At best, they might encourage sustained and closer reflection on the nature and the intrinsic potentialities of action, which never before has revealed its greatness and its + +dangers so openly. + +II: History and Earthly Immortality + +The modern concept of process pervading history and nature alike separates the modern age from the past more profoundly than any other single idea. To our modern way of thinking nothing is meaningful in and by itself, not even history or nature taken each as a whole, and certainly not particular occurrences in the physical order or specific historical events. There is a fateful enormity in this state of affairs. Invisible processes have engulfed every tangible thing, every individual entity that is visible to us, degrading them into functions of an over-all process. The enormity of this change is likely to escape us if we allow ourselves to be misled by such generalities as the disenchantment of the world or the alienation of man, genera!ities that often involve a romanticized notion of the + +past. What the concept of process implies is that the concrete and the general, the single thing or event and the universal meaning, have parted company. The process, which alone makes meaningful whatever it happens to carry along, has thus acquired a monopoly + +of universality and significance. + +Certainly nothing more sharply distinguishes the modern concept of history from that of antiquity. For this distinction does not hinge on whether or not antiquity had a concept of world history or an idea of mankind as a whole. What is much more relevant is that Greek and Roman historiography, much as they differ from each other, both take it for granted that the meaning or, as the Romans would say, the lesson of each event, deed, or occurrence is revealed in and by itself. This, to be sure, does not exclude either causality or the context in which something occurs; antiquity was as aware of these as we are. But causality and context were seen in a light provided by the event itself, illuminating a specific segment of human affairs ; they were not envisaged as having an independent existence of which the event would be only the more or less accidental though adequate expression. Everything that was done or happened contained and disclosed its share of "general" meaning within the confines of its individual shape and did not need a developing and engulfing process to become significant. Herodotus wanted "to say what is" (A.iynv Ta lovm) because saying and writing stabilize the futile and perishable, "fabricate a memory" for it, in the Greek idiom : p.v�p.11v 71'0Lfiu8aL; yet he never would have doubted that each thing that is or was carries its meaning within hself and needs only the word to make it manifest (.\oyoLc; o11A.ovv, "to disclose through words"), to "display the great deeds in public," a7roon�Lc; ;pywv ,.uya.\wv. The flux of his narrative is sufficiently loose to leave room for many stories, but there is nothing in this flux indicative that the + +general bestows meaning and significance on the particular. + +For this shift of emphasis it is immaterial whether Greek poetry and historiography saw the meaning of the event in some surpassing greatness justifying its remembrance by posterity, or whether the Romans conceived of history as a storehouse of examples taken from actual political behavior, demonstrating what tradition, the + +authority of ancestors, demanded from each generation and what the past had accumulated for the benefit of the present. Our notion of historical process overrules both concepts, bestowing upon mere time-sequence an importance and dignity it never had before. + +Because of this modern emphasis upon time and time-sequence, it has often been maintained that the origin of our historical consciousness lies in the Hebrew-Christian tradition, with its rectilinear time-concept and its idea of a divine providence giving to the whole of man's historical time the unity of a plan of salvation-an idea which indeed stands as much in contrast to the insistence on individual events and occurrences of classical antiquity as to the cyclical time-speculations of late antiquity. A great deal of evidence has been cited in support of the thesis that the modern historical conscious· ness has a Christian religious origin and came into being through a secularization of originally theological categories. Only our religious tradition, it is said, knows of a beginning and, in the Christian version, an end of the world; if human life on earth follows a divine plan of salvation, then its mere sequence must harbor a significance independent of and transcending all single occurrences. Therefore, the argument runs, a "well-defined outline of world history" did not appear prior to Christianity, and the first philosophy of history is presented in Augustine's De Civitate Dei. And it is true that in Augustine we find the notion that history itself, namely that which has meaning and makes sense, can be separated from the single historical events related in chronological narrative. He states explicitly that "although the past institutions of men are related in historical narrative, history itself is not to be counted among human + +institutions." 19 + +This similarity between the Christian and the modern concept of history is deceptive, however. It rests on a comparison with the cyclical history-speculations of late antiquity and overlooks the classical history-concepts of Greece and Rome. The comparison is supported by the fact that Augustine himself, when he refuted pagan time-speculations, was primarily concerned with the cyclical timetheories of his own era, which indeed no Christian could accept because of the absolute uniqueness of Christ's life and death on + +earth : "Once Christ died for our sins; and rising from the dead, he dieth no more." 20 What modem interpreters are liable to forget ts that Augustine claimed this uniqueness of event, which sounds so familiar to our ears, for this one event only-the supreme event in human history, when eternity, as it were, broke into the course of earthly mortality; he never claimed such uniqueness, as we do, for ordinary secular events. The simple fact that the problem of history arose in Christian thought only with Augustine should make us doubt its Christian origin, and this all the more as it arose, in terms of Augustine's own philosophy and theology, because of an accident. The fall of Rome, occurring in his lifetime, was interpreted by Christians and pagans alike as a decisive event, and it was to the refutation of this belief that Augustine devoted thirteen years of his life. The point, as he saw it, was that no purely secular event could or should ever be of central import to man. His lack of interest in what we call history was so great that he devoted only one book of the Civitas Dei to secular events; and in commissioning his friend and pupil Orosius to write a "world history" he had no more in + +mind than a "true compilation of the evils of the world." 21 + +Augustine's attitude toward secular history is essential!y no different from that of the Romans, albeit the emphasis is inverted: history remains a storehouse of examples, and the location of events in time within the secular course of history remains without importance. Secular history repeats itself, and the only story in which unique and unrepeatable events take place begins with Adam and ends with the birth and death of Christ. Thereafter secular powers rise and fall as in the past and will rise and fall until the world's end, but no fundamentally new truth will ever again be revealed by such mundane events, and Christians are not supposed to attach particular significance to them. In all truly Christian philosophy man is a "pilgrim on earth," and this fact alone separates it from our own historical consciousness. To the Christian, as to the Roman, the significance of secular events lay in their having the character of examples likely to repeat themselves, so that action could follow certain standardized patterns. (This, incidentally, is also very far removed from the Greek notion of the heroic deed, related by poets + +and historians, which serves as a kind of yardstick with which to measure one's own capacities for greatness. The difference between the faithful following of a recognized example and the attempt to measure oneself against it is the difference between Roman-Christian morality and what has been called the Greek agonal spirit, which did not know any "moral" considerations but only an a££ aptonvEtv, an unceasing effort always to be the best of all.) For us, on the other hand, history stands and falls on the assumption that the process in its very secularity tells a story of its own and that, + +strictly speaking, repetitions cannot occur. + +Even more alien to the modern concept of history is the Christian notion that mankind has a beginning and an end, that the world was created in time and will ultimately perish, like all things temporal. Historical consciousness did not arise when the creation of the world was taken as the starting point for chronological enumeration, by the Jews in the Middle Ages; nor did it arise in the sixth century when Dionysus Exiguus began counting time from the birth of Christ. We know of similar schemes of chronology in Oriental civilization, and the Christian calendar imitated the Roman practice of counting time from the year of the foundation of Rome. In stark contrast stands the modem computation of historical dates, introduced only at the end of the eighteenth century, that takes the birth of Christ as a turning point from which to count time both backward and forward. This chronological reform is presented in the textbooks as a mere technical improvement, needed for scholarly purposes to facilitate the exact fixing of dates in ancient history without referring to a maze of different time-reckonings. In more recent times, Hegel inspired an interpretation which sees in the modern time system a truly Christian chronology because the birth of Christ now seems to have become the turning point of world + +history.22 + +Neither of these explanations is satisfactory. Chronological reforms for scholarly purposes have occurred many times in the past without being accepted in everyday life, precisely because they were invented for scholarly convenience only and did not correspond to any changed time-concept in society at large. The decisive thing + +in our system is not that the birth of Christ now appears as the turning point of world history, for it had been recognized as such and with greater force many centuries before without any similar effect upon our chronology, but rather that now, for the first time, the history of mankind reaches back into an infinite past to which we can add at will and into which we can inquire further as it stretches ahead into an infinite future. This twofold infinity of past and future eliminates all notions of beginning and end, establishing mankind in a potential earthly immortality. What at first glance looks like a Christianization of world history in fact eliminates all religious time-speculations from secular history. So far as secular history is concerned we live in a process which knows no beginning and no end and which thus does not permit us to entertain eschatological expectations. Nothing could be more alien to Christian thought + +than this concept of an earthly immortality of mankind. + +The great impact of the notion of history upon the consciousness of the modern age came relatively late, not before the last third of the eighteenth century, finding with relative quickness its climactic consummation in Hegel's philosophy. The central concept of Hegelian metaphysics is history. This alone places it in the sharpest possible opposition to all previous metaphysics, which, since Plato, had looked for truth and the revelation of eternal Being everywhere except in the realm of human affairs--rcl. Twv av6ptJ1rwv 7rpa:yf14Taof which Plato speaks with such contempt precisely because no permanence could be found in it and therefore it could not be expected to disclose truth. To think, with Hegel, that truth resides and reveals itself in the time-process itself is characteristic of all modem historical consciousness, however it expresses itself, in specifically Hegelian terms or not. The rise of the humanities in the nineteenth century was inspired by the same feeling for history and is hence clearly distinguished from the recurrent revivals of antiquity that took place in previous periods. Men now began to read, as Meinecke pointed out, as nobody had ever read before. They "read in order to force from history the ultimate truth it could offer to God-seeking people"; but this ultimate truth was no longer supposed to reside + +in a single book, whether the Bible or some substitute for it. History itself was considered such a book, the book "of the human soul + +in times and nations," as Herder defined it.23 + +Recent historical research has shed much new light on the transitional period between the Middle Ages and modem times, with the result that the modern age, previously assumed to have begun with the Renaissance, has been traced back into the very heart of the Middle Ages. This greater insistence on an unbroken continuity, valuable though it is, has one drawback, that by trying to bridge the gulf separating a religious culture from the secular world we live in, it bypasses, rather than solves, the great riddle of the sudden undeniable rise of the secular. If by "secularization" one means no more than the rise of the secular and the concomitant eclipse of a transcendent world, then it is undeniable that modern historical consciousness is very intimately connected with it. This, however, in no way implies the doubtful transformation of religious and transcendent categories into immanent earthly aims and standards on which the historians of ideas have recently insisted. Secularization means first of all simply the separation of religion and politics, and this affected both sides so fundamentally that nothing is less likely to have taken place than the gradual transformation of religious categories into secular concepts which the defenders of unbroken continuity try to establish. The rooson they can succeed to some extent in convincing us lies in the nature of ideas in general rather than in the period with which they deal; the moment one separates an idea entirely from its basis in real experience, it is not difficult to establish a connection between it and almost any other idea. In other words, if we assume that something like an independent realm of pure ideas exists, all notions and concepts cannot but be interrelated, because then they all owe their origin to the same source : a human mind seen in its extreme subjectivity, forever playing with its own images, unaffected by experience and with no relationship to the world, whether the world is conceived as nature or as history. However, if we understand by secularization an event that can be dated in historical time rather than a change of ideas, then the question is not whether Hegel's "cunning of reason" was a secular- + +ization of divine providence or whether Marx's classless society represents a secularization of the Messianic Age. The fact is that the separation of church and state occurred, eliminating religion from public life, removing all religious sanctions from politics, and causing religion to lose that political element it had acquired in the centuries when the Roman Catholic Church acted as the heir of the Roman Empire. (It does not follow that this separation converted religion into an entirely "private affair." This type of privacy in religion comes about when a tyrannical regime prohibits the public functioning of churches, denying the believer the public space in which he can appear with others and be seen by them. The publicsecular domain, or the political sphere, properly speaking, comprehends and has room for the public-religious sphere. A believer can be a member of a church and at the same time act as a citizen in the larger unit constituted by all belonging to the City.) This secularization was frequently brought about by men who did not doubt in the least the truth of traditional religious teaching (even Hobbes died in mortal fear of "hell-fire," and Descartes prayed to the Holy Virgin) and nothing in the sources justifies us in considering all those who prepared or helped to establish a new independent secular sphere as secret or unconscious atheists. All that we can say is that, whatever their faith or lack of it, it was without influence on the secular. Thus the political theorists of the seventeenth century accomplished secularization by separating political thinking from theology, and by insisting that the rules of natural law provided a basis for the body politic even if God did not exist. It was the same thought which made Grotius say that "even God cannot cause two times two not to make four." The point was not to deny the existence of God but to discover in the secular realm an independent, im- + +manent meaning which even God could not alter. + +It has been pointed out before that the most important consequence of the rise of the secular realm in the modern age was that belief in individual immortality-whether it be the immortality of the soul or, more importantly, the resurrection of the body-lost its politically binding force. Now indeed "it was inevitable that earthly posterity should once again become the principal substance + +of hope," but it does not follow from this that a secularization of the belief in a hereafter occurred or that the new attitude was essentially nothing but "a redisposition of the Christian ideas which it seeks to displace." 24 What actually happened was that the problem of politics regained that grave and decisive relevance for the existence of men which it had been lacking since antiquity because it was irreconcilable with a strictly Christian understanding of the secular. For Greeks and Romans alike, all differences notwithstanding, the foundation of a body politic was brought about by man's need to overcome the mortality of human life and the futility of human deeds. Outside the body politic, man's life was not only and not even primarily insecure, i.e., exposed to the violence of others; it was without meaning and dignity because under no circumstances could it leave any traces behind it. That was the reason for the curse laid by Greek thinking on the whole sphere of private life, the "idiocy" of which consisted in its being concerned solely with survival, just as it was the reason for Cicero's contention that only through building and preserving political communities could human virtue attain to the ways of the gods.25 In other words, the secularization of the modern age once more brought to the fore that activity which Aristotle had called &.Oavar£C£tv, a term for which we have no ready equivalent in our living languages. The reason I mention this word again is that it points to an activity of "immortalizing" rather than to the object which is to become immortal. To strive for immortality can mean, as it certainly did in early Greece, the immortalization of oneself through famous deeds and the acquisition of immortal fame; it can also mean the addition to the human artifice of something more permanent than we are ourselves; and it can mean, as it did with the philosophers, the spending of one's life with things immortal. In any event, the word designated an activity and not a belief, and what the activity required was an imperishable space guaranteeing that "immortalizing" would not be in vain.26 To us, who have been accustomed to the idea of immortality only through the lasting appeal of works of art and perhaps through the relative permanence we ascribe to all great civilizations, it may appear implausible that the drive toward immortality should lie at + +the foundation of political communities.27 To the Greeks, howevet, the latter might very well have been much more taken for granted than the former. Did not Pericles think that the highest praise he could bestow upon Athens was to claim that it no longer needed "a Homer or others of his craft," but that, thanks to the polis, Athenians everywhere would leave "imperishable monuments" behind them? 28 What Homer had done was to immortalize human deeds,29 and the polis could dispense with the service of "others of his craft" because it offered each of its citizens that public-political space that it assumed would confer immortality upon his acts. The growing apolitism of the philosophers after Socrates' death, their demand to be freed from political activities and their insistence on performing a nonpractical, purely theoretical MJavartCnv outside the sphere of political life had philosophical as well as political causes, but among the political ones was certainly the increasing decay of polis life, making even the permanence, let alone immortality, of this par- + +ticular body politic more and more doubtful. + +The apolitism of ancient philosophy foreshadowed the much more radical anti-political attitude of early Christianity, which, however, in its very extremism survived only so long as the Roman Empire provided a stable body politic for all nations and all religions. During these early centuries of our era the conviction that things earthly are perishable remained a religious matter and was the belief of those who wanted to have nothing to do with political affairs. This changed decisively with the crucial experience of the fall of Rome, the sacking of the Eternal City, after which no age ever again believed that any human product, least of all a political structure, could endure forever. As far as Christian thought was concerned, this was a mere reaffirmation of its beliefs. It was of no great relevance, as Augustine pointed out. To Christians only individual men were immortal, but nothing else of this world, neither mankind as a whole nor the earth itself, least of all the human artifice. Only by transcending this world could immortalizing activities be performed, and the only institution that could be justified within the secular realm was the Church, the Civitas Dei on earth, to which had fallen the burden of political responsibility and into which all genuinely + +political impulses could be drawn. That this transformation of Christianity and its earlier anti-political impulses into a great and stable political institution was possible at all without complete perversion of the Gospel is almost wholly due to Augustine, who, though hardly the father of our concept of history, is probably the spiritual author and certainly the greatest theorist of Christian politics. What was decisive in this respect was that he, still firmly rooted in the Roman tradition, could add to the Christian notion of an everlasting life the idea of a future civitas, a Civitas Dei, where men even in the hereafter would continue to live in a community. Without this reformulation of Christian thoughts through Augustine, Christian politics might have remained what they had been in the early centuries, a contradiction in terms. Augustine could solve the dilemma because the language itself came to his help: in Latin the word "to live" had always coincided with inter homines esse, "to be in the company of men," so that an everlasting life in Roman interpretation was bound to mean that no man would ever have to part from human company even though in death he had to leave the earth. Thus the fact of the plurality of men, one of the fundamental prerequisites of political life, bound human "nature" even under the conditions of individual immortality, and was not among the characteristics which this "nature" had acquired after Adam's fall and which made politics in the mere secular sense a necessity for the sinful life on earth. Augustine's conviction that some kind of political life must exist even under conditions of sinlessness, and indeed sanctity, he summed up in one sentence : Socialis est vita sanctorum, even the life of the saints + +is a life together with other men.30 + +If the insight into the perishability of all human creations had no great relevance for Christian thought and could even in its greatest thinker be in accord with a conception of politics beyond the secular realm, it became very troublesome in the modern age when the secular sphere of human life had emancipated itself from religion. The separation of religion and politics meant that no matter what an individual might believe as a member of a church, as a citizen he acted and behaved on the assumption of human mortality. lJobbes's + +fear of hell-fire did not influence m the least his construction of government as the Leviathan, a mortal god to overawe all men. Politically speaking, within the secular realm itself secularization meant nothing more or less than that men once more had become mortals. If this led them to a rediscovery of antiquity, which we call humanism, and in which Greek and Roman sources spoke again a much more familiar language corresponding to experiences much more similar to their own, it certainly did not allow them in practice to mold their behavior in accordance with either the Greek or the Roman example. The ancient trust in the world's being more permanent than individual men and in political structures as a guarantee of earthly survival after death did not return, so that the ancient opposition of a mortal life to a more or less immortal world failed them. Now both life and world had become perishable, mortal, and + +futile. + +Today we find it difficult to grasp that this situation of absolute mortality could be unbearable to men. However, looking back upon the development of the modem age up to the beginning of our own, the modern world, we see that centuries passed before we became accustomed to the notion of absolute mortality, so that the thought of it no longer bothers us and the old alternative between an individual immortal life in a mortal world and a mortal life in an immortal world has ceased to be meaningful. In this respect, however, as in many others, we differ from all previous ages. Our concept of history, though essentially a concept of the modem age, owes its existence to the transition period when religious confidence in immortal life had lost its influence upon the secular and the new indifference toward the question of immortality had not yet been + +born. + +If we leave aside the new indifference and stay within the limits of the traditional alternative, bestowing immortality either upon life or upon the world, then it is obvious that d.8avaTiCnv, immortalizing, as an activity of mortal men, can be meaningful only if there is no guarantee of life in the hereafter. At that moment, however, it becomes almost a necessity as long as there is any concern with immortality whatsoever. It was therefore in the course of its search + +for a strictly secular realm of enduring permanence that the modern age discovered the potential immortality of mankind. This is what is manifestly expressed in our calendar; it is the actual content of our concept of history. History, stretching into the twofold infinity of past and future, can guarantee immortality on earth in much the same way as the Greek polis or the Roman republic had guaranteed that human life and human deeds, insofar as they disclosed something essential and something great, would receive a strictly human and earthly permanence in this world. The great advantage of this concept has been that the twofold infinity of the historical process establishes a time-space in which the very notion of an end is virtually inconceivable, whereas its great disadvantage, compared with ancient political theory, seems to be that permanence is entrusted to a flowing process, as distinguished from a stable structure. At the same time the immortalizing process has become independent of cities, states, and nations ; it encompasses the whole of mankind, whose history Hegel was consequently able to see as one uninterrupted development of the Spirit. Therewith mankind ceases to be only a species of nature, and what distinguishes man from the animals is no longer merely that he has speech (Aoyov £xwv) , as in the Aristotelian definition, or that he has reason, as in the medieval definition (animal rationale ): his very life now distinguishes him, the one thing that in the traditional definition he was supposed to share with the animals. In the words of Droysen, who was perhaps the most thoughtful of the nineteenth-century historians : "What their species is for animals and plants . . . that is + +history for human beings." 31 + +III: History and Politics + +While it is obvious that our historical consciousness would never have been possible without the rise of the secular realm to a new dignity, it was not so obvious that the historical process would eventually be called upon to bestow the necessary new meaning and significance upon men's deeds and sufferings on earth. And indeed, + +at the beginning of the modern age everything pointed to an elevation of political action and political life, and the sixteenth and seventeenth centuries, so rich in new political philosophies, were still quite unaware of any special emphasis on history as such. Their concern, on the contrary, was to get rid of the past rather than to rehabilitate the historical process. The distinguishing trait of Hobbes's philosophy is his single-minded insistence on the future and the resulting teleological interpretation of thought as well as of action. The conviction of the modern age that man can know only that which he himself has made seems to be in accordance with a glorification of action rather than with the basically contemplative attitude of the + +historian and of historical consciousness in general. + +Thus one of the reasons for Hobbes's break with traditional philosophy was that while all previous metaphysics had followed Aristotle in holding that the inquiry into the first causes of everything that is comprises the chief task of philosophy, it was Hobbes's contention that, on the contrary, the task of philosophy was to guide purposes and aims and to establish a reasonable teleology of action. So important was this point to Hobbes that heinsisted that animals too are capable of discovering causes and that therefore this cannot be the true distinction between human and animal life ; he found the distinction instead in the ability to reckon with "the effects of some present or past cause . . . of which I have not at any time seen any sign but in man only." 32 The modem age not only produced at its very start a new and radical political philosophy-Hobbes is only one example, though perhaps the most interesting-it also produced for the first time philosophers willing to orient themselves according to the requirements of the political realm; and this new political orientation is present not only in Hobbes but, mutatis mutandis, in Locke and Hume as well. It can be said that Hegel's transformation of metaphysics into a philosophy of history was preceded by an attempt to get rid of metaphysics for the sake of a phi- + +In any consideration of the modern concept of history one of the crucial problems is to explain its sudden rise during the last third + +of the eighteenth century and the concomitant decrease of interest in purely political thinking. (Vico must be said to be a forerunner whose influence was not felt until more than two generations after his death. ) Where a genuine interest in political theory still survived it ended in despair, as in Tocqueville, or in the confusion of politics with history, as in Marx. For what else but despair could have inspired Tocqueville's assertion that "since the past has ceased to throw its light upon the future the mind of man wanders in obscurity"? This is actually the conclusion of the great work in which he had "delineated the society of the modem world" and in the i-ntroduction to which he had proclaimed that "a new science of politics is needed for a new world." 33 And what else but confusion -a merciful confusion for Marx himself and a fatal one for his followers--could have led to Marx's identification of action with + +"the making of history"? + +Marx's notion of "making history" had an influence far beyond the circle of convinced Marxists or determined revolutionaries. Although it is closely connected with Vico's idea that history was made by man, as distinguished from "nature," which was made by God, the difference between them is still decisive. For Vico, as later for Hegel, the importance of the concept of history was primarily theoretical. It never occurred to either of them to apply this concept directly by using it as a principle of action. Truth they conceived of as being revealed to the contemplative, backward-directed glance of the historian, who, by being able to see the process as a whole, is in a position to overlook the "narrow aims" of acting men, concentrating instead on the "higher aims" that realize themselves behind their backs (Vico) . Marx, on the other hand, combined this. notion of history with the teleological political philosophies of the earlier stages of the modem age, so that in his thought the "higher aims"-which according to the philosophers of history revealed themselves only to the backward glance of the historian and philosopher--could become intended aims of political action. The point is that Marx's political philosophy was based not upon an analysis of action and acting men but, on the contrary, on the Hegelian con- + +cern with history. It was the historian and the philosopher of history who were politicalized. By the same token, the age-old identification of action with making and fabricating was supplemented and perfected, as it were, through identifying the contemplative gaze of the historian with the contemplation of the model (the (tOoo; or "shape" from which Plato had derived his "ideas" ) that guides the craftsmen and precedes all making. And the danger of these combinations did not lie in making immanent what was formerly transcendent, as is often alleged, as though Marx attempted to establish on earth a paradise formerly located in the hereafter. The danger of transforming the unknown and unknowable "higher aims" into planned and willed intentions was that meaning and meaningfulness were transformed into ends-which is what happened when Marx took the Hegelian meaning of all history-the progressive unfolding and actualization of the idea of Freedom-to be an end of human action, and when he furthermore, in accordance with tradition, viewed this ultimate "end" as the end-product of a manufacturing process. But neither freedom nor any other meaning can ever be the product of a human activity in the sense in which the table is clearly + +the end-product of the carpenter's activity. + +The growing meaninglessness of the modem world is perhaps nowhere more clearly foreshadowed than in this identification of meaning and end. Meaning, which can never be the aim of action and yet, inevitably, will rise out of human deeds after the action itself has come to an end, was now pursued with the same machinery of intentions and of organized means as were the particular direct aims of concrete action-with the result that it was as though meaning itself had departed from the world of men and men were left with nothing but an unending chain of purposes in whose progress the meaningfulness of all past achievements was constantly canceled out by future goals and intentions. It is as though men were stricken suddenly blind to fundamental distinctions such as the distinction between meaning and end, between the general and the particular, or, grammatically speaking, the distinction between "for the sake of ••. " and "in order to ... " (as though the carpenter, for in- + +stance, forgot that only his particular acts in making a table are performed in the mode of "in order to," but that his whole life as a carpenter is ruled by something quite different, namely an encompassing notion "for the sake of" which he became a carpenter in the first place) . And the moment such distinctions are forgotten and meanings are degraded into ends, it follows that ends themselves are no longer safe because the distinction between means and ends is no longer understood, so that finally all ends turn and are degraded + +into means. + +In this version of deriving politics from history, or rather, political conscience from historical consciousness-by no means restricted to Marx in particular, or even to pragmatism in general-we can easily detect the age-old attempt to escape from the frustrations and fragility of human action by construing it in the image of making. What distinguishes Marx's own theory from all others in which the notion of "making history" has found a place is only that he alone realized that if one takes history to be the object of a process of fabrication or making, there must come a moment when this "object" is completed, and that if one imagines that one can "make history," one cannot escape the consequence that there will be an end to history. Whenever we hear of grandiose aims in politics, such as establishing a new society in which justice will be guaranteed forever, or fighting a war to end all wars or to make the whole world safe for democracy, we are moving in the realm of this kind of think- + +ing. + +In this context, it is important to see that here the process of history, as it shows itself in our calendar's stretching into the infinity of the past and the future, has been abandoned for the sake of an altogether different kind of process, that of making something which has a beginning as well as an end, whose laws of motion, therefore, can be determined (for instance as dialectical movement) and whose innermost content can be discovered (for instance as class struggle ). This process, however, is incapable of guaranteemg men any kind of immortality because its end cancels out and makes unimportant whatever went before : in the classless society the best mankind can + +do with history is to forget the whole unhappy affair, whose on!' purpose was to abolish itself. It cannot bestow meaning on particular occurrences either, because it has dissolved all of the particular into means whose meaningfulness ends the moment the end-product . is finished: single events and deeds and sufferings have no more . meaning here than hammer and nails have with respect to the + +finished table. + +We know the curious ultimate meaninglessness arising from all the strictly utilitarian philosophies that were so common and so characteristic of the earlier industrial phase of the modern age, when men, fascinated by the new possibilities of manufacturing, thought of everything in terms of means and ends, i.e., categories whose validity had its source and justification in the experience of producing use-objects. The trouble lies in the nature of the categorical framework of ends and means, which changes every attained end immediately into the means to a new end, thereby, as it were, destroying meaning wherever it is applied, until in the midst of the seemingly unending utilitarian questioning, What is the use of . . . ? in the midst of the seemingly unending progress where the aim of today becomes the means of a better tomorrow, the one question arises which no utilitarian thinking can ever answer : "And + +what is the use of use?" as Lessing once succinctly put it. + +This meaninglessness of all truly utilitarian philosophies could escape Marx's awareness because he thought that after Hegel in his dialectics had discovered the law of all movements, natural and historical, he himself had found the spring and content of this law in the historical realm and thereby the concrete meaning of the story history has to tell. Class struggle-to Marx this formula seemed to unlock all the secrets of history, just as the law of gravity had appeared to unlock all the secrets of nature. Today, after we have been treated to one such history-construction after another, to one such formula after another, the question for us is no longer whether this or that particular formula is correct. In all such attempts what is considered to be a meaning is in fact no more than a pattern, and within the limitations of utilitarian thought nothing but patterns can + +make sense, because only patterns can be "made," whereas meanings cannot be, but, like truth, will only disclose or reveal themselves. Marx was only the first-and still the greatest, among historiansto mistake a pattern for a meaning, and he certainly could hardly have been expected to realize that there was almost no pattern into which the events of the past would not have fitted as neatly and consistently as they did into his own. Marx's pattern at least was based on one important historical insight; since then we have seen historians freely imposing upon the maze of past facts almost any pattern they wish, with the result that the ruin of the factual and particular through the seemingly higher validity of general "meanings" has even undermined the basic factual structure of all histori- + +cal process, that is, chronology. + +Moreover, Marx construed his pattern as he did because of his concern with action and impatience with history. He is the last of those thinkers who stand at the borderline between the modern age's earlier interest in politics and its later preoccupation with history. One might mark the point where the modern age abandoned its earlier attempts to establish a new political philosophy for its rediscovery of the secular by recalling the moment at which the French Revolutionary calendar was given up, after one decade, and the Revolution was reintegrated, as it were, into the historical process with its twofold extension toward infinity. It was as though it was conceded that not even the Revolution, which, along with the promulgation of the American Constitution, is still the greatest event in modem political history, contained sufficient independent meaning in itself to begin a new historical process. For the Republican calendar was abandoned not merely because of Napoleon's wish to rule an empire and to be considered the equal of the crowned heads of Europe. The abandonment also implied the refusal, despite the re-establishment of the secular, to accept the conviction of the ancients that political actions are meaningful regardless of their h!storical location, and especially a repudiation of the Roman faith m the sacredness of foundations with the accompanying custom of numbering time from the foundation date. Indeed, the French Revolu- + +tion, which was inspired by the Roman spirit and appeared to the world, as Marx liked to say, in Roman dress, reversed itself in more + +than one sense. + +An equally important landmark in the shift from the earlier concern with politics to the later concern with history is encountered in Kant's political philosophy. Kant, who had greeted in Rousseau "the Newton of the moral world," and had been greeted by his contemporaries as the theorist of the Rights of Man,34 still had great difficulty in coping with the new idea of history, which had probably come to his attention in the writings of Herder. He is one of the last philosophers to complain in earnest about the "meaningless course of human affairs," the "melancholy haphazardness" of historical events and developments, this hopeless, senseless "mixture of error and violence," as Goethe once defined history. Yet Kant also saw what others had seen before him, that once you look at history in its entirety (im Grossen) , rather than at single events and the everfrustrated intentions of human agents, everything suddenly makes sense, because there is always at least a story to tell. The process as a whole appears to be guided by an "intention of nature" unknown to acting men but comprehensible to those who come after them. By pursuing their own aims without rhyme or reason men seem to + +be led by "the guiding thread of reason." 35 + +It is of some importance to notice that Kant, like Vico before him, was already aware of what Hegel later called "the cunning of reason" (Kant occasionally called it "the ruse of nature" ). He even had some rudimentary insight into historical dialectics, as when he pointed out that nature pursues its over-all aims through "the antagonism of men in society . . . without which men, good-natured like the sheep they tend, would hardly know how to give a higher value to their own existence than is possessed by their cattle." This shows to what extent the very idea of history as a process suggests that in their actions men are led by something of which they are not necessarily conscious and which finds no direct expression in the action itself. Or, to put it another way, it shows how extremely useful the modern concept of history proved to be in giving the secular political realm a meaning which it otherwise seemed to be devoid of. In + +Kant, in contrast to Hegel, the motive for the modern escape from politics into history is still quite clear. It is the escape into the "whole," and the escape is prompted by the meaninglessness of the particular. And since Kant's primary interest was still in the nature and principles of political (or, as he would say, moral ) action, he was able to perceive the crucial drawback of the new approach, the one great stumbling block which no philosophy of history and no concept of progress can ever remove. In Kant's own words : "It will always remain bewildering . . . that the earlier generations seem to carry on their burdensome business only for the sake of the later . . . and that only the last should have the good fortune to dwell + +in the [completed] building." 36 + +The bewildered regret and great diffidence with which Kant resigned himself to introducing a concept of history into his political philosophy indicates with rare precision the nature of the perplexities which caused the modern age to shift its emphasis from a theory of politics-apparently so much more appropriate to its belief in the superiority of action to contemplation-to an essentially contemplative philosophy of history. For Kant was perhaps the only great thinker to whom the question "What shall I do?" was not only as relevant as the two other questions of metaphysics, "What can I know?" and "What may I hope?" but formed the very center of his philosophy. Therefore he was not troubled, as even Marx and Nietzsche were still troubled, by the traditional hierarchy of contemplation over action, the vita contemplativa over the vita activa; his problem was rather another traditional hierarchy which, because it is hidden and rarely articulate, has proved much more difficult to overcome, the hierarchy within the vita activa itself, where the acting of the statesman occupies the highest position, the making of the craftsman and artist an intermediary, and the laboring which provides the necessities for the functioning of the human organism the lowest. (Marx was later to reverse this hierarchy too, although he wrote explicitly only about elevating action over contemplation and changing the world as against interpreting it. In the course of this reversal he had to upset the traditional hierarchy within the vita activa as well, by putting the lowest of human activities, the activity + +oi labor. into the highest place. Action now appeared to be no more than a function of "the productive relationships" of mankind brought about by labor. ) It is true that traditional philosophy often pays only lip service to the estimate of action as the highest activity of man, preferring the so much more reliable activity of making, so that the hierarchy within the vita activa has hardly ever been fully articulated. It is a sign of the political rank of Kant's philosophy that the old perplexities inherent in action were brought to the fore + +again. + +However that may be, Kant could not but become aware of the fact that action fulfilled neither of the two hopes the modern age was bound to expect from it. If the secularization of our world implies the revival of the old desire for some kind of earthly immortality, then human action, especially in its political aspect, must appear singularly inadequate to meet the demands of the new age. From the point of view of motivation, action appears to be the least interesting and most futile of all human pursuits : "Passions, private aims, and the satisfaction of selfish desires, are . . . the most effective springs of action," 37 and "the facts of known history," taken by themselves, "possess neither a common basis nor continuity nor coherence" (Vico) . From the viewpoint of achievement, on the other hand, action appears at once to be more futile and more frustrating than the activities of laboring and of producing objects. Human deeds, unless they are remembered, are the most futile and perishable things on earth; they hardly outlast the activity itself and certainly by themselves can never aspire to that permanence which even ordinary useobjects possess when they outlast their maker's life, not to mention works of art, which speak to us over the centuries. Human action, projected into a web of relationships where many and opposing ends are pursued, almost never fulfills its original intention; no act can ever be recognized by its author as his own with the same happy certainty with which a piece of work of any kind can be recognized by its maker. Whoever begins to act must know that he has started something whose end he can never foretell, if only because his own deed has already changed everything and made it even more unpredictable. That is what Kant had in mind when he spoke of the + +"melancholy haphazardness" (trostlose Ungefiihr) which is so striking in the record of political history. "Action: one does not know its origin, one does not know its consequences :-therefore, does action possess any value at all?'' 38 Were not the old philosophers right, and was it not madness to expect any meaning to arise out of the realm + +of human affairs? + +For a long time it seemed that these inadequacies and perplexities within the vita activa could be solved by ignoring the peculiarities of action and by insisting upon the "meaningfulness" of the process of history in its entirety, which seemed to give to the political sphere that dignity and final redemption from "melancholy haphazardness" so obviously required. History-based on the manifest assumption that no matter how haphazard single actions may appear in the present and in their singularity, they inevitably lead to a sequence of events forming a story that can be rendered through intelligible narrative the moment the events are removed into the past-became the great dimension in which men could become "reconciled" with reality (Hegel ), the reality of human affairs, i.e., of things which owe their existence exclusively to men. Moreover, since history in its modern version was conceived primarily as a process, it showed a peculiar and inspiring affinity to action, which, indeed, in contrast to all other human activities, consists first of all of starting processes -a fact of which human experience has of course always been aware, even though the preoccupation of philosophy with making as the model of human activity has prevented the elaboration of an articulate terminology and precise description. The very notion of process, which is so highly characteristic of modern science, both natural and historical, probably had its origin in this fundamental experience of action, to which secularization lent an emphasis such as it had not known since the very early centuries of Greek culture, even before the rise of the polis and certainly before the victory of the Socratic school. History in its modern version could come to terms with this experience ; and though it failed to save politics itself from the old disgrace, though the single deeds and acts constituting the realm of politics, properly speaking, were left in limbo, it has at least bestowed upon the record of past events that share of + +earthly immortality to which the modern age necessarily aspired. but which its acting men no longer dared to claim from posterity. + +Epilogue + +Today the Kantian and Hegelian way of becoming reconciled to reality through understanding the innermost meaning of the entire historical process seems to be quite as much refuted by our experience as the simultaneous attempt of pragmatism and utilitarianism to "make history" and impose upon reality the preconceived meaning and law of man. While trouble throughout the modern age has as a rule started with the natural sciences and has been the consequence of experience gained in the attempt to know the universe, this time the refutation rises simultaneously out of the physical and political fields. The trouble is that almost every axiom seems to lend itself to consistent deductions and this to such an extent that it is as though men were in a position to prove almost any hypothesis they might choose to adopt, not only in the field of purely mental constructions like the various over-all interpretations of history which are all equally well supported by facts, but in the natural sciences + +as well.39 + +As far as natural science is concerned, this brings us back to the previously quoted statement by Heisenberg (pp. 48--49 ), whose consequence he once formulated in a different context as the paradox that man, whenever he tries to learn about things which neither are himself nor owe their existence to him, will ultimately encounter nothing but himself, his own constructions, and the patterns of his own actions.40 This is no longer a question of academic objectivity. It cannot be solved by the reflection that man as a question-asking being naturally can receive only answers to match his own questions. If nothing more was involved, then we would be satisfied that different questions put "to one and the same physical event" reveal different but objectively equally "true" aspects of the same phenomenon, just as the table around which a number of people have takea + +their places is seen by each of them in a different aspect, without •hereby ceasing to be the object common to all of them. One could even imagine that a theory of theories, like the old mathesis universalis, might eventually be able to determine how many such questions are possible or how many "different types of natural law" can be applied to the same natural universe without contra- + +diction. + +The matter would become somewhat more serious if it turned out that no question exists at all which does not lead to a consistent set of answers-a perplexity we mentioned earlier when we discussed the distinction between pattern and meaning. In this instance the very distinction between meaningful and meaningless questions would disappear together with absolute truth, and the consistency we would be left with could just as well be the consistency of an asylum for paranoiacs or the consistency of the current demonstrations of the existence of God. However, what is really undermining the whole modem notion that meaning is contained in the process as a whole, from which the particular occurrence derives its intelligibility, is that not only can we prove this, in the sense of consistent deduction, but we can take almost any hypothesis and act upon it, with a sequence of results in reality which not only make sense but work. This means quite literally that everything is possible not only + +in the realm of ideas but in the field of reality itself. + +In my studies of totalitarianism I tried to show that the totalitarian phenomenon, with its striking anti-utilitarian traits and its strange disregard for factuality, is based in the last analysis on the conviction that everything is possible-and not just permitted, morally or otherwise, as was the case with early nihilism. The totalitarian systems tend to demonstrate that action can be based on any hypothesis and that, in the course of consistently guided action, the particular hypothesis will become true, will become actual, factual reality. The assumption which underlies consistent action can be as mad as it pleases; it will always end in producing facts which are then "objectively" true. What was originally nothing but a hypothesis, to be proved or disproved by actual facts, will in the course of consistent + +action always turn into a fact, never to be disproved. In other words. the axiom from which the deduction is started does not need to be, as traditional metaphysics and logic supposed, a self-evident truth; it does not have to tally at all with the facts as given in the objective world at the moment the action starts ; the process of action, if it is consistent, will proceed to create a world in which the assumption + +becomes axiomatic and self-evident. + +The frightening arbitrariness with which we are confronted whenever we decide to embark upon this type of action, which is the exact counterpart of consistent logical processes, is even more obvious in the political than in the natural realm. But it is more difficult to convince people that this holds true for past history. The historian, by gazing backward into the historical process, has been so accustomed to discovering an "objective" meaning, independent of the aims and awareness of the actors, that he is liable to overlook what actually happened in his attempt to discern some objective trend. He will, for example, overlook the particular characteristics of Stalin's totalitarian dictatorship in favor of the industrialization of the Soviet empire or of the nationalistic aims of traditional Russian + +foreign policy. + +Within the natural sciences things are not essentially different, but they appear more convincing because they are so far removed from the competence of the layman and his healthy, stubborn common sense, which refuses to see what it cannot understand. Here too, thinking in terms of processes, on the one hand, and the conviction, on the other, that I know only what I have myself made, has led to the complete meaninglessness inevitably resulting from the insight that I can choose to do whatever I want and some kind of "meaning" will always be the consequence. In both instances the perplexity is that the particular incident, the observable fact or single occurrence of nature, or the reported deed and event of history, have ceased to make sense without a universal process in which they are supposedly embedded; yet the moment man approaches this process in order to escape the haphazard character of the particular, in order to find meaning-order and necessity-his effort is rebutted by the answer from all sides : Any order, any necessity, any mea.u- + +ing you wish to impose will do. This is the clearest possible demonstration that under these conditions there is neither necessity nor meaning. It is as though the "melancholy haphazardness" of the particular had now caught up with us and were pursuing us into the very region where the generations before us had fled in order to escape it. The decisive factor in this experience, both in nature and in history, is not the patterns with which we tried to "explain," and which in the social and historical sciences cancel each other out more quickly, because they can all be consistently proved, than they do in the natural sciences, where matters are more complex and for this technical reason less open to the irrelevant arbitrariness of irresponsible opinions. These opinions, to be sure, have an altogether different source, but are liable to becloud the very relevant issue of contingency, with which we are everywhere confronted today. What is decisive is that our technology, which nobody can accuse of not functioning, is based on these principles, and that our social techniques, whose real field of experimentation lies in the totalitarian countries, have only to overcome a certain time-lag to be able to do for the world of human relations and human affairs as much as has + +already been done for the world of human artifacts. + +The modern age, with its growing world-alienation, has led to a situation where man, wherever he goes, encounters only himself. All the processes of the earth and the universe have revealed themselves either as man-made or as potentially man-made. These processes, after having devoured, as it were, the solid objectivity of the given, ended by rendering meaningless the one over-all process which originally was conceived in order to give meaning to them, and to act, so to speak, as the eternal time-space into which they could all flow and thus be rid of their mutual conflicts and exclusiveness. This is what happened to our concept of history, as it happened to our concept of nature. In the situation of radicai world-alienation, neither history nor nature is at all conceivable. This twofold loss of the world-the loss of nature and the loss of human artifice in the widest sense, which would include all history-has left behind it a society of men who, without a common world which would at once relate and separate them, either live in desperate lonely separa- + +tion or are pressed together into a mass. For a mass-society is nothing more than that kind of organized living which automatically establishes itself among human beings who are still related to one another but have lost the world once common to all of + +them. + +WHAT IS AUTHORITY? + +I + +I + +N order to avoid misunderstanding, it might have been wiser to ask in the title : What was-and not what is-authority? For it is my contention that we are tempted and entitled to raise this question because authority has vanished from the modern world. Since we can no longer fall back upon authentic and undisputable experiences common to all, the very term has become clouded by controversy and confusion. Little about its nature appears self-evident or even comprehensible to everybody, except that the political scientist may still remember that this concept was once fundamental to political theory, or that most will agree that a constant, ever-widening and deepening crisis of authority has accompanied the development + +of the modem world in our century. + +This crisis, apparent since the inception of the century, is political in origin and nature. The rise of political movements intent upon replacing the party system, and the development of a new totalitarian form of government, took place against a background of a more or less general, more or less dramatic breakdown of all traditional authorities. Nowhere was this breakdown the direct result + +of the regimes or movements themselves; it rather seemed as though totalitarianism, in the form of movements as well as of regimes, wa!> best fitted to take advantage of a general political and social atmosphere in which the party system had lost its prestige and the govern- + +ment's authority was no longer recognized. + +The most significant symptom of the crisis, indicating its depth and seriousness, is that it has spread to such prepolitical areas as child-rearing and education, where authority in the widest sense has always been accepted as a natural necessity, obviously required as much by natural needs, the helplessness of the child, as by political necessity, the continuity of an established civilization which can be assured only if those who are newcomers by birth are guided through a pre-established world into which they are born as strangers. Because of its simple and elementary character, this form of authority has, throughout the history of political thought, served as a model for a great variety of authoritarian forms of government, so that the fact that even this prepolitical authority which ruled the relations between adults and children, teachers and pupils, is no longer secure signifies that all the old time-honored metaphors and models for authoritarian relations have lost their plausibility. Practically as well as theoretically, we are no longer in a position to know what + +authority really is. + +In the following reflections I assume that the answer to this question cannot possibly lie in a definition of the nature or essence of "authority in general." The authority we have lost in the modern world is no such "authority in general," but rather a very specific form which had been valid throughout the Western World over a long period of time. I therefore propose to reconsider what authority was historically and the sources of its strength and meaning. Yet, in view of the present confusion, it seems that even this limited and tentative approach must be preceded by a few remarks on what authority never was, in order to avoid the more common misunderstandings and make sure that we visualize and consider the same phenomenon and not any number of connected or unconnected is- + +taker for �orne form of power or violence. Yet authority precludes the use of external means of coercion; where force is used, authority itself has failed. Authority, on the other hand, is incompatible with persuasion, which presupposes equality and works through a process of argumentation. Where arguments are used, authority is left in abeyance. Against the egalitarian order of persuasion stands the authoritarian order, which is always hierarchical. If authority is to be defined at all, then, it must be in contradistinction to both coercion by force and persuasion through arguments. (The authoritarian relation between the one who commands and the one who obeys rests neither on common reason nor on the power of the one who commands; what they have in common is the hierarchy itself, whose rightness and legitimacy both recognize and where both have their predetermined stable place.) This point is of historical importance; one aspect of our concept of authority is Platonic in origin, and when Plato began to consider the introduction of authority into the handling of public affairs in the polis, he knew he was seeking an alternative to the common Greek way of handling domestic affairs, which was persuasion ( 7rd0nv) as well as to the common way of + +handling foreign affairs, which was force and violence ({3[a). + +Historically, we may say that the loss of authority is merely the final, though decisive, phase of a development which for centuries undermined primarily religion and tradition. Of tradition, religion, and authority-whose interconnectedness we shall discuss laterauthority has proved to be the most stable element. With the loss of authority, however, the general doubt of the modern age also invaded the political realm, where things not only assume a more radical expression but become endowed with a reality peculiar to the political realm alone. What perhaps hitherto had been of spiritual significance only for the few now has become a concern of one and all. Only now, as it were after the fact, the loss of tradition and + +of religion have become political events of the first order. + +When I said that I did not wish to discuss "authority in general," but only the very specific concept of authority which has been dominant in our history, I wished to hint at some distinctions which we are liable to neglect when we speak too sweepingly of the crisis of + +our time, and which I may perhaps more easily explain in terms of the related concepts of tradition and religion. Thus the undeniable loss of tradition in the modem world does not at all entail a loss of the past, for tradition and past are not the same, as the believers in tradition on one side and the believers in progress on the other would have us believe-whereby it makes little difference that the former deplore this state of affairs while the latter extend their congratulations. With the loss of tradition we have lost the thread which safely guided us through the vast realms of the past, but this thread was also the chain fettering each successive generation to a predetermined aspect of the past. It could be that only now will the past open up to us with unexpected freshness and tell us things no one has yet had ears to hear. But it cannot be denied that without a securely anchored tradition-and the loss of this security occurred several hundred years ago-the whole dimension of the past has also been endangered. We are in danger of forgetting, and such an oblivionquite apart from the contents themselves that could be lost-would mean that, humanly speaking, we would deprive ourselves of one dimension, the dimension of depth in human existence. For memory and depth are the same, or rather, depth cannot be reached by man + +except through remembrance. + +It is similar with the loss of religion. Ever since the radical criticism of religious beliefs in the seventeenth and eighteenth centuries, it has remained characteristic of the modem age to doubt religious truth, and this is true for believers and nonbelievers alike. Since Pascal and, even more pointedly, since Kierkegaard, doubt has been carried into belief, and the modem believer must constantly guard his beliefs against doubts; not the Christian faith as such, but Christianity (and Judaism, of course) in the modem age is ridden by paradoxes and absurdity. And whatever else may be able to survive absurdity-philosophy perhaps can-religion certainly cannot. Yet this loss of belief in the dogmas of institutional religion need not necessarily imply a loss or even a crisis of faith, for religion and faith, or belief and faith, are by no means the same. Only belief, but not faith, has an inherent affinity with and is constantly exposed to doubt. But who can deny that faith too, for so xrany centunes se- + +curely protected by religion, its beliefs and its dogmas, has been gravely endangered through what is actually only a crisis of institu- + +tional religion? + +Some simrlar qualifications seem to me to be necessary regarding the modern loss of authority. Authority, resting on a foundation in the past as its unshaken cornerstone, gave the world the permanence and durability which human beings need precisely because they are mortals-the most unstable and futile beings we know of. Its loss is tantamount to the loss of the groundwork of the world, which indeed since then has begun to shift, to change and transform itself with ever-increasing rapidity from one shape into another, as though we were living and struggling with a Protean universe where everything at any moment can become almost anything else. But the loss of worldly permanence and reliability-which politically is identical with the loss of authority--does not entail, at least not necessarily, the loss of the human capacity for building, preserving, and caring for a world that can survive us and remain a place fit to live + +in for those who come after us. + +It is obvious that these reflections and descriptions are based on the conviction of the importance of making distinctions. To stress such a conviction seems to be a gratuitous truism in view of the fact that, at least as far as I know, nobody has yet openly stated that distinctions are nonsense. There exists, however, a silent agreement in most discussions amcng political and social scientists that we can ignore distinctions and proceed on the assumption that everything can eventually be called anything else, and that distinctions are meaningful only to the extent that each of us has the right "to define his terms." Yet does not this curious right, which we have come to grant as soon as we deal with matters of importance-as though it were actually the same as the right to one's own opinion-already indicate that such terms as "tyranny," "authority," "totalitarianism" have simply lost their common meaning, or that we have ceased to live in a common world where the words we have in common possess an unquestionable meaningfulness, so that, short of being condemned to live verbally in an altogether meaningless world, we gmnt + +each other the right to retreat into our own worlds of meaning. and demand only that each of us remain consistent within his own private terminology? If, in these circumstances , we assure ourselves that we still understand each other, we do not mean that together we understand a world common to us all, but that we understand the consistency of arguing and reasoning, of the process of argu- + +mentation in its sheer formality. + +However that may be, to proceed under the implicit assumption that distinctions are not important or, better, that in the social-political-historical realm, that is, in the sphere of human affairs, things do not possess that distinctness which traditional metaphysics used to call their "otherness" (their alteritas), has become the hallmark of a great many theories in the social, political, and historical sciences. Among these, two seem to me to deserve special mention because they touch the subject under discussion in an especially sig- + +nificant manner. + +The first concerns the ways in which, since the nineteenth century, liberal and conservative writers have dealt with the problem of authority and, by implication, with the related problem of freedom in the realm of politics. Generally speaking, it has been quite typical of liberal theories to start from the assumption that "the constancy of progress . . . in the direction of organized and assured freedom is the characteristic fact of modern history" 1 and to look upon each deviation from this course as a reactionary process leading in the opposite direction. This makes them overlook the differences in principle between the restriction of freedom in authoritarian regimes, the abolition of political freedom in tyrannies and dictatorships, and the total elimination of spontaneity itself, that is, of the most general and most elementary manifestation of human freedom, at which only totalitarian regimes aim by means of their various methods of conditioning. The liberal writer, concerned with history and the progress of freedom rather than with forms of government, sees only differences in degree here, and ignores that authoritarian government committed to the restriction of liberty remains tied to the freedom it limits to the extent that it would lose its very substance if it abolished it altogether, that is, would change into tyranny. The same is + +true for the distinction between legitimate and illegitimate power on which all authoritarian government hinges. The liberal writer is apt to pay little attention to it because of his conviction that all power corrupts and that the constancy of progress requires constant + +loss of power, no matter wh:1t its origin may be. + +Behind the liberal identification of totalitarianism with authoritarianism, and the concomitant inclination to see "totalitarian" trends in every authoritarian limitation of freedom, lies an older confusion of authority with tyranny, and of legitimate power with violence. The difference between tyranny and authoritarian government has always been that the tyrant rules in accordance with his own will and interest, whereas even the most draconic authoritarian government is bound by laws. Its acts are tested by a code which was made either not by man at all, as in the case of the law of nature or God's Commandments or the Platonic ideas, or at least not by those actually in power. The source of authority in authoritarian government is always a force external and superior to its own power; it is always this source, this external force which transcends the political realm, from which the authorities derive their "authority," that is, their legitimacy, and against which their power can be + +checked. + +Modern spokesmen of authority, who, even in the short intervals. when public opinion provides a favorable climate for neo-conservatism, remain well aware that theirs is an almost lost cause, are of course eager to point to this distinction between tyranny and authority. Where the liberal writer sees an essentially assured progress in the direction of freedom, which is only temporarily interrupted by some dark forces of the past, the conservative sees a process of doom which started with the dwindling of authority, so that freedom, after it lost the restricting limitations which protected its boundaries, became helpless, defenseless, and bound to be destroyed. (It is hardly fair to say that only liberal political thought is primarily interested in freedom; there is hardly a school of political thought in our history which is not centered around the idea of freedom, much as the concept of liberty may vary with different writers and in different political circumstances. The only exception of any consequence to + +this statement seems to me to be the political philosophy of Thomas Hobbes, who, of course, was anything but a conservative.) Tyranny and totalitarianism are again identified, except that now totalitarian government, if it is not directly identified with democracy, is seen as its almost inevitable result, that is, the result of the disappearance of all traditionally recognized authorities. Yet the differences between tyranny and dictatorship on one side, and totalitarian domination on the other, are no less distinct than those between authoritari- + +anism and totalitarianism. + +These structural differences become apparent the moment we leave the over-all theories behind and concentrate our attention on the apparatus of rule, the technical forms of administration, and the organization of the body politic. For brevity's sake, it may be permitted to sum up the technical-structural differences between authoritarian, tyrannical, and totalitarian government in the image of three different representative models. As an image for authoritarian government, I propose the shape of the pyramid, which is well known in traditional political thought. The pyramid is indeed a particularly fitting image for a governmental structure whose source of authority lies outside itself, but whose seat of power is located at the top, from which authority and power is filtered down to the base in such a way that each successive layer possesses some authority, but less than the one above it, and where, precisely because of this careful filtering process, all layers from top to bottom are not only firmly integrated into the whole but are interrelated like converging rays whose common focal point is the top of the pyramid as well as the transcending source of authority above it. This image, it is true, can be used only for the Christian type of authoritarian rule as it developed through and under the constant influence of the Church during the Middle Ages, when the focal point above and beyond the earthly pyramid provided the necessary point of reference for the Christian type of equality, the strictly hierarchical structure of life on earth notwithstanding. The Roman understanding of political authority, where the source of authority lay exclusively in the past, in the foundation of Rome and the greatness of ancestors, leads into institutional structures whose shape requires a different + +kind of image-about which more later (p. 124) . In any event, an authoritarian form of government with its hierarchical structure is the least egalitarian of all forms; it incorporates inequality and dis- + +tinction as its all-permeating principles. + +All political theories concerning tyranny agree that it belongs strictly among the egalitarian forms of government; the tyrant is the ruler who rules as one against all, and the "all" he oppresses are all equal, namely equally powerless. If we stick to the image of the pyramid, it is as though all intervening layers between top and bottom were destroyed, so that the top remains suspended, supported only by the proverbial bayonets, over a mass of carefully isolated, disintegrated, and completely equal individuals. Classical political theory used to rule the tyrant out of mankind altogether, to call him a "wolf in human shape" (Plato) , because of this position of one against all, in which he had put himself and which sharply distinguished his rule, the rule of one, which Plato still calls indiscriminately p.orapxJa or tyranny, from various forms of kingship or + +{3acnA£ta. + +In contradistinction to both tyrannical and authoritarian regimes, the proper image of totalitarian rule and organization seems to me to be the structure of the onion, in whose center, in a kind of empty space, the leader is located; whatever he does-whether he integrates the body politic as in an authoritarian hierarchy, or oppresses his subjects like a tyrant-he does it from within, and not from without or above. All the extraordinarily manifold parts of the movement: the front organizations, the various professional societies, the party membership, the party bureaucracy, the elite formations and police groups, are related in such a way that each forms the fa�ade in one direction and the center in the other, that is, plays the role of normal outside world for one layer and the role of radical extremism for another. The great advantage of this system is that the movement provides for each of its layers, even under conditions of totalitarian rule, the fiction of a normal world along with a consciousness of being different from and more radical than it. Thus, the sympathizers in the front organizations, whose convictions differ only in intensity from those of the party membership, sur· + +round the whole movement and provide a deceptive fa<;adc of normality to the outside world because of their lack of fanaticism and extremism, while, at the same time, they represent the normal world to the totalitarian movement, whose members come to believe that their convictions differ only in degree from those of other people, so that they need never be aware of the abyss which separates their own world from that which actually surrounds it. The onion structure makes the system organizationally shock-proof against the + +factuality of the real world.2 + +However, while both liberalism and conservatism fail us the moment we try to apply their theories to factually existing political forms and institutions, it can hardly be doubted that their over-all assertions carry a high amount of plausibility. Liberalism, we saw, measures a process of receding freedom, and conservatism measures a process of receding authority; both call the expected end-result totalitarianism and see totalitarian trends wherever either one or the other is present. No doubt, both can produce excellent documentation for their findings. Who would deny the serious threats to freedom from all sides since the beginning of the century, and the rise of all kinds of tyranny, at least since the end of the First World War? Who can deny, on the other hand, that disappearance of practically all traditionally established authorities has been one of the most spectacular characteristics of the modern world? It seems as though one has only to fix his glance on either of these two phenomena to justify a theory of progress or a theory of doom according to his own taste or, as the phrase goes, according to his own "scale of values." If we look upon the conflicting statements of conservatives and liberals with impartial eyes, we can easily see that the truth is equaily distributed between them and that we are in fact confronted with a simultaneous recession of both freedom and authority in the modern world. As far as these processes are concerned, one can even say that the numerous oscillations in public opinion, which for more than a hundred and fifty years has swung at regular intervals from one extreme to the other, from a liberal mood to a conservative one and back to a more liberal again, at times attempting to reassert authority and at others to reassert freedom, have resulted only in + +further undermining both, confusing the issues, blurring the distinctive lines between authority and freedom, and eventually destroying + +the political meaning of both. + +Both liberalism and conservatism were born in this climate of violently oscillating public opinion, and they are tied together, not only because each would lose its very substance without the presence of its opponent in the field of theory and ideology, but because both are primarily concerned with restoration, with restoring either freedom or authority, or the relationship between both, to its traditional position. It is in this sense that they form the two sides of the same coin, just as their progress-or-doom ideologies correspond to the two possible directions of the historical process as such; if one assumes, as both do, that there is such a thing as a historical process with a definable direction and a predictable end, it obviously + +can land us only in paradise or in hell. + +It is, moreover, in the nature of the very image in which history is usually conceived, as process or stream or development, that everything comprehended by it can change into anything else, that distinctions become meaningless because they become obsolete, submerged, as it were, by the historical stream, the moment they have appeared. From this viewpoint, liberalism and conservatism present themselves as the political philosophies which correspond to the much more general and comprehensive philosophy of history of the nineteenth century. In form and content, they are the political expression of the history-consciousness of the last stage of the modern age. Their inability to distinguish, theoretically justified by the concepts of history and process, progress or doom, testifies to an age in which certain notions, clear in their distinctness to all previous centuries, have begun to lose their clarity and plausibility because they have lost their meaning in the public-political reality- + +without altogether losing their significance. + +The second and more recent theory implicitly challenging the importance of making distinctions is, especially in the social sciences, the almost universal functionalization of all concepts and ideas. Here, as in the example previously quoted, liberalism and conservatism differ not in method, viewpoint, and approach, but only in emphasis + +and evaluation. A convenient instance may be provided by the widespread conviction in the free world today that communism is a new "religion," notwithstanding its avowed atheism, because it fulfills socially, psychologically, and "emotionally" the same function traditional religion fulfilled and still fulfills in the free world. The concern of the social sciences does not lie in what bolshevism as ideology or as form of government is, nor in what its spokesmen have to say for themselves; that is not the interest of the social sciences, and many social scientists believe they can do without the study of what the historical sciences call the sources themselves. Their concern is only with functions, and whatever fulfills the same function can, according to this view, be called the same. It is as though I had the right to call the heel of my shoe a hammer because I, like most + +women, use it to drive nails into the wall. + +Obviously one can draw quite different conclusions from such equations. Thus it would be characteristic of conservatism to insist that after all a heel is not a hammer, but that the use of the heel as a substitute for the hammer proves that hammers are indispensable. In other words, it will find in the fact that atheism can fulfill the same function as religion the best proof that religion is necessary, and recommend the return to true religion as the only way to counter a "heresy." The argument is weak, of course; if it is only a question of function and how a thing works, the adherents of "false religion" can make as good a case for using theirs as I can for using my heel, which does not work so badly either. The liberals, on the contrary, view the same phenomena as a bad case of treason to the cause of secularism and believe that only "true secularism" can cure us of the pernicious influence of both false and true religion on politics. But these conflicting recommendations at the address of free society to return to true religion and become more religious, or to rid ourselves of institutional religion (especially of Roman Catholicism with its constant challenge to secularism) hardly conceal the opponents' agreement on one point: that whatever fulfills the function + +The same argument is frequently used with respect to authority: if violence fulfills the same function as authority-namely, makes + +people obey-then violence is authority. Here again we find those who counsel a return to authority because they think only a reintroduction of the order-obedience relationship can master the problems of a mass society, and those who believe that a mass society can rule itself, like any other social body. Again both parties agree on the one essential point : authority is whatever makes people obey. All those who call modem dictatorships "authoritarian," or mistake totalitarianism for an authoritarian structure, have implicitly equated violence with authority, and this includes those conservatives who explain the rise of dictatorships in our century by the need to find a surrogate for authority. The crux of the argument is always the same : everything is related to a functional context, and the use of violence is taken to demonstrate that no society can exist except in + +an authoritarian framework. + +The dangers of these equations, as I see them, lie not only in the confusion of political issues and in the blurring of the distinctive lines which separate totalitarianism from all other forms of government. I do not believe that atheism is a substitute for or can fulfill the same function as a religion any more than I believe that violence can become a substitute for authority. But if we follow the recommendations of the conservatives, who at this particular moment have a rather good chance of being heard, I am quite convinced that we shall not find it hard to produce such substitutes, that we shall use violence and pretend to have restored authority or that our rediscovery of the functional usefulness of religion will produce a substitute-religion-as though our civilization were not already sufficiently cluttered up with all sorts of pseudo-things and nonsense. Compared with these theories, the distinctions between tyrannical, authoritarian, and totalitarian systems which I have proposed are unhistorical, if one understands by history not the historical space in which certain forms of government appeared as recognizable entities, but the historical process in which everything can always change into something else; and they are anti-functional insofar as the content of the phenomenon is taken to determine both the nature of the political body and its function in society, and not vice-versa. Politically speaking, they have a tendency to assume that in the + +modern world authority has disappeared almost to the vanishing point, and this in the so-called authoritarian systems no less than in the free world, and that freedom-that is, the freedom of movement of human beings-is threatened everywhere, even in free societies, but abolished radically only in totalitarian systems, and not in tyran- + +nies and dictatorships. + +It is in the light of this present situation that I propose to raise the following questions : What were the political experiences that corresponded to the concept of authority and from which it sprang? What is the nature of a public-political world constituted by authority? Is it true that the Platonic-Aristotelian statement that every well-ordered community is constituted of those who rule and those who are ruled was always valid prior to the modern age? Or, to put it differently, what kind of world came to an end after the modern age not only challenged one or another form of authority in different spheres of 1ife but caused the whole concept of authority to lose + +its validity altogether? + +II + +Authority as the one, if not the decisive, factor in human communities did not always exist, though it can look back on a long history, and the experiences on which this concept is based are not necessarily present in all bodies politic. The word and the concept are Roman in origin. Neither the Greek language nor the varied political experiences of Greek history shows any knowledge of authority and the kind of rule it implies.3 This is expressed most clearly in the philosophy of Plato and Aristotle, who, in quite different ways but from the same political experiences, tried to introduce something akin to authority into the public life of the Greek polis. There existed two kinds of rule on which they could fall back and from which they derived their political philosophy, one known to them from the public-political realm, and the other from the private sphere of Greek household and family life. To the polis, absolute rule was known as tyranny, and the chief characteristics of + +the tyrant were that he ruled by sheer violence, had to be protected from the people by a bodyguard, and insisted that his subjects mind their own business and leave to him the care of the public realm. The last characteristic, in Greek public opinion, signified that he destroyed the public realm of the polis altogether "a polis belonging to one man is no polis" 4-and thereby deprived the citizens of that political faculty which they felt was the very essence of freedom. Another political experience of the need for command and obedience might have been provided by the experience in warfare, where danger and the necessity to make and carry out decisions quickly seem to constitute an inherent reason for the establishment of authority. Neither of these political models, however, could possibly serve the purpose. The tyrant remained, for Plato as for Aristotle, the "wolf in human shape,'· and the military commander was too obviously connected with a temporary emergency to be able to serve as model for a permanent insti- + +tution. + +Because of this absence of valid political experience on which to base a claim to authoritarian rule, both Plato and Aristotle, albeit in very different ways, had to rely on examples of human relations drawn from Greek household and family life, where the head of the household ruled as a "despot," in uncontested mastery over the members of his family and the slaves of the household. The despot, unlike the king, the {3arnl..o)>, who had been the leader of household heads and as such primus inter pares, was by definition vested with the power to coerce. Yet it was precisely this characteristic that made the despot unfit for political purposes; his power to coerce was incompatible not only with the freedom of others but with his own freedom as well. Wherever he ruled there was only one relation, that between master and slaves. And the master, according to Greek common opinion (which was still blissfully unaware of Hegelian dialectics ), was not free when he moved among his slaves ; his freedom consisted in his ability to leave the sphere of the household altogether and to move among his equals, freemen. Hence, neither the despot nor the tyrant, the one moving among slaves, the other + +Authority implies an obedience in which men retain their freedom, and Plato hoped to have found such an obedience when, in his old age, he bestowed upon the laws that quality which would make them undisputable rulers over the whole public realm. Men could at least have the illusion of being free because they did not depend upon other men. Yet the rulership of these laws was construed in an obviously despotic rather than an authoritarian manner, the clearest sign of which is that Plato was led to speak of them in terms of private household affairs, and not in political terms, and to say, probably in a variation of Pindar's vop.or; f3aar.>..£V., '1Tavrwv ("a law is king over everything"): vop.o<; 8£U'1TOT7J'> TWV apxovrwv, oi sf apxovT£<; 8oii.\ot TOV vop.ov ("the law is the despot of the rulers, and the rulers are the slaves of the law") .5 In Plato, the despotism originating in the household, and its concomitant destruction of the political realm as antiquity understood it, remained utopian. But it is interesting to note that when the destruction became a reality in the last centuries of the Roman Empire, the change was introduced by the application to public rule of the term dominus, which in Rome (where the family also was "organized like a monarchy") 6 had the same meaning as the Greek "despot." Caligula was the first Roman emperor who consented to be called dominus, that is, to be given a name "which Augustus and Tiberius still had rejected as if it were a malediction and an injury," 7 precisely because it implied a despotism unknown in the political realm, although all too familiar + +in the private, household realm. + +The political philosophies of Plato and Aristotle have dominated all subsequent political thought, even when their concepts have been superimposed upon such greatly different political experiences as those of the Romans. If we wish not only to comprehend the actual political experiences behind the concept of authority-which, at least in its positive aspect, is exclusively Roman-but also to understand authority as the Romans themselves already understood it theoretically and made it part of the political tradition of the West, we shall have to concern ourselves briefly with those features of Greek political philosophy which have so decisively influenced its + +Nowhere else has Greek thinking so closely approached the concept of authority as in Plato's Republic, wherein he confronted the reality of the polis with a utopian rule of reason in the person of the philosopher-king. The motive for establishing reason as ruler in the realm of politics was exclusively political, although the consequences of expecting reason to develop into an instrument of coercion perhaps have been no less decisive for the tradition of Western philosophy than for the tradition of Western politics. The fatal resemblance between Plato's philosopher-king and the Greek tyrant, as well as the potential harm to the political realm that his rule would imply, seems to have been recognized by Aristotle; 8 but that this combination of reason and rule implied a danger to philosophy as well has been pointed out, as far as I know, only in Kant's reply to Plato: "It is not to be expected that kings philosophize or that philosophers become kings, nor is it to be desired, because the possession of power corrupts the free judgment of reason inevitably" 11-although even this reply does not go to the root of + +the matter. + +The reason Plato wanted the philosophers to become the rulers of the city lay in the conflict between the philosopher and the polis, or in the hostility of the polis toward philosophy, which probably had lain dormant for some time before it showed its immediate threat to the life of the philosopher in the trial and death of Socrates. Politically, Plato's philosophy shows the rebellion of the philosopher against the polis. The philosopher announces his claim to rule, but not so much for the sake of the polis and politics (although patriotic motivation cannot be denied in Plato and distinguishes his philosophy from those of his followers in antiquity) as for the sake of + +philosophy and the safety of the philosopher. + +It was after Socrates' death that Plato began to discount persuasion as insufficient for the guidance of men and to seek for something liable to compel them without using external means of violence. Very early in his search he must have discovered that truth, namely, the truths we call self-evident, compels the mind, and that this coercion, though it needs no violence to be effective, is stronger than + +persuasion and argument. The trouble with coercion through reason, however, is that only the few are subject to it, so that the problem arises of how to assure that the many, the people who in their very multitude compose the body politic, can be submitted to the same truth. Here, to be sure, other means of coercion must be found, and here again coercion through violence must be avoided if political life as the Greeks understood it is not to be destroyed.10 This is the central predicament of Plato's political philosophy and has remained a predicament of all attempts to establish a tyranny of reason. In The Republic the problem is solved through the concluding myth of rewards and punishments in the hereafter, a myth which Plato himself obviously neither believed nor wanted the philosophers to believe. What the allegory of the cave story in the middle of The Republic is for the few or for the philosopher the myth of hell at the end is for the many who are not capable of philosophical truth. In the Laws Plato deals with the same perplexity, but in the opposite way; here he proposes a substitute for persuasion, the introduction to the laws in which their intent and purpose are to be explained to + +the citizens. + +In his attempts to find a legitimate principle of coercion Plato was originally guided by a great number of models of existing relations, such as that between the shepherd and his sheep, between the helmsman of a ship and the passengers, between the physician and the patient, or between the master and the slave. In all these instances either expert knowledge commands confidence so that neither force nor persuasion are necessary to obtain compliance, or the ruler and the ruled belong to two altogether different categories of beings, one of which is already by implication subject to the other, as in the cases of the shepherd and his flock or the master and his slaves. All these examples are taken from what to the Greeks was the private sphere of life, and they occur time and again in all the great political dialogues, The Republic, the Statesman, and the l..aws. Nevertheless, it is obvious that the relation between master 'and slave has a special significance. The master, according to the discussion in the Statesman, knows what should be done and gives his orders, while the slave executes them and obeys, so that know- + +ing what to do and actual doing become separate and mutually exclusive functions. In The Republic they are the political characteristics of two different classes of men. The plausibility of these examples lies in the natural inequality prevailing between the ruling and the ruled, most apparent in the example of the shepherd, where Plato himself ironically concludes that no man, only a god, could relate to human beings as the shepherd relates to his sheep. Although it is obvious that Plato himself was not satisfied with these models, for his purpose, to establish the "authority" of the philosopher over the polis, he returned to them time and again, because only in these instances of glaring inequality could rule be exerted without seizure of power and the possession of the means of violence. What he was looking for was a relationship in which the compelling element lies in the relationship itself and is prior to the actual issuance of commands; the patient became subject to the physician's authority when he fell ill, and the slave came under the command of his master + +when he became a slave. + +It is important to bear these examples in mind in order to realize what kind of coercion Plato expected reason to exert in the hands of the king-philosopher. Here, it is true, the compelling power does not lie in the person or in inequality as such, but in the ideas which are perceived by the philosopher. These ideas can be used as measures of human behavior because they transcend the sphere of human affairs in the same way that a yardstick transcends, is outside and beyond, all things whose length it can measure. In the parable of the cave in The Republic, the sky of ideas stretches above the cave of human existence, and therefore can become its standard. But the philosopher who leaves the cave for the pure sky of ideas does not originally do so in order to acquire those standards and learn the "art of measurement" 11 but to contemplate the true essence of Being-{3>-.f.?r€LV d., TO a>-.rjlJf.aTaTOJ!. The basically authoritative element of the ideas, that is, the quality which enables them to rule and compel, is therefore not at all a matter of course. The ideas become measures only after the philosopher has left the bright sky of ideas and returned to the dark cave of human existence. In this part of the story Plato touches upon the deepest reason for the conflict + +between the philosopher and the polis.12 He tells of the philosopher's loss of orientation in human affairs, of the blindness striking the eyes, of the predicament of not being able to communicate what he has seen, and of the actual danger to his life which thereby arises. It is in this predicament that the philosopher resorts to what he has seen, the ideas, as standards and measures, and finally, in fear of + +his life, uses them as instruments of domination. + +For the transformation of the ideas into measures, Plato is helped by an analogy from practical life, where it appears that all arts and crafts are also guided by "ideas," that is, by the "shapes" of objects, visualized by the inner eye of the craftsman, who then reproduces them in reality through imitation.13 This analogy enables him to understand the transcendent character of the ideas in the same manner as he does the transcendent existence of the model, which lies beyond the fabrication process it guides and therefore can eventually become the standard for its success or failure. The ideas become the unwavering, "absolute" standards for political and moral behavior and judgment in the same sense that the "idea" of a bed in general is the standard for making and judging the fitness of all particular manufactured beds. For there is no great differen�e between using the ideas as models and using them, in a somewhat cruder fashion, as actual yardsticks of behavior, and Aristotle in his earliest dialogue, written under the direct influence of Plato, already compares "the most perfect law," that is, the law which is the closest possible approximation to the idea, with "the plummet, the rule, and the compass . . . [which] are outstanding among all + +tools." 14 + +It is only in this context that the ideas relate to the varied multitude of things concrete in the same way as one yardstick relates to the varied multitude of things measurable, or as the rule of reason or common sense relates to the varied multitude of concrete events which can be subsumed under it. This aspect of Plato's doctrine of tdeas had the greatest influence on the Western tradition, and even Kant, though he had a very different and considerably deeper concept of human judgment, still occasionally mentioned this capacity for subsuming as its essential function. Likewise, the essential char- + +acteristic of specifically authoritarian forms of government-that the. source of their authority, which legitimates the exercise of power, must be beyond the sphere of power and, like the law of nature or the commands of God, must not be man-made-goes back to this + +applicability of the ideas in Plato's political philosophy. + +At the same time the analogy relating to fabrication and the arts and crafts offers a welcome opportunity to justify the otherwise very dubious use of examples and instances taken from activities in which some expert knowledge and specialization are required. Here the concept of the expert enters the realm of political action for the first time, and the statesman is understood to be competent to deal with human affairs in the same sense as the carpenter is competent to make furniture or the physician to heal the sick. Closely connected with this choice of examples and analogies is the element of violence, which is so glaringly evident in Plato's utopian republic and actually constantly defeats his great concern for assuring voluntary obedience, that is, for establishing a sound foundation for what, since the Romans, we call authority. Plato solved his dilemma through rather lengthy tales about a hereafter with rewards and punishments, which he hoped would be believed literally by the many and whose usage he therefore recommended to the attention of the few at the close of most of his political dialogues. In view of the enormous influence these tales have exerted upon the images of hell in religious thought, it is of some importance to note that they were originally designed for purely political purposes. In Plato they are simply an ingenious device to enforce obedience upon those who are not subject to the compelling power of reason, without + +actually using external violence. + +It is of greater relevance in our context, however, that an element of violence is inevitably inherent in all activities of making, fabricating, and producing, that is, in all activities by which men confront nature directly, as distinguished from such activities as action and speech, which are primarily directed toward human beings. The building of the human artifice always involves some violence done to nature-we must kill a tree in order to have lumber, and we must violate this material in order to build a table. In the few + +instances where Plato shows a dangerous preference for the tyran-· nical form of government, he is carried to this extreme by his own analogies. This, obviously, is most tempting when he speaks about 'the right way to found new communities, because this foundation can be easily seen in the light of another "making" process. If the republic is to be made by somebody who is the political equivalent of a craftsman or artist, in accordance with an established rix.•'TJ and the rules and measurements valid in this particular "art," the tyrant + +is indeed in the best position to achieve the purpose.15 + +We have seen that, in the parable of the cave, the philosopher leaves the cave in search of the true essence of Being without a second thought to the practical applicability of what he is going to find. Only later, when he finds himself again confined to the darkness and uncertainty of human affairs and encounters the hostility of his fellow human beings, does he begin to think of his "truth" in terms of standards applicable to the behavior of other people . This discrepancy between the ideas as true essences to be contemplated and as measures to be applied 16 is manifest in the two entirely different ideas which represent the highest idea, the one to which all others owe their existence. We find in Plato either that this suprem� idea is that of the beautiful, as in the Symposion, where it constitutes the topmost rung of the ladder that leads to truth, 17 and in Phaedrus, where Plato speaks of the "lover of wisdom or of beauty" as though these two actually were the same because beauty is what "shines forth most" (the beautiful is f.Kcj>aviurarov) and therefore illuminates everything else ; 18or that the highest idea is the idea of the good, as in The Republic.H' Obviously Plato's choice was based on the current ideal of the KaA.ov K'aya86v, but it is striking that the idea of the good is found only in the strictly political context of The Republic. If we were to analyze the original philosophical experiences underlying the doctrine of ideas (which we cannot do here), it would appear that the idea of the beautiful as the highest idea reflected these experiences far more adequately than the idea of the good. Even in the first books of The Republic 20the philosopher is still defined as a lover of beauty, not of goodness, and only in the sixth book is the idea of good as the highest idea introduced. For the original func- + +tion of the ideas was not to rule or otherwise determine the chaos of human affairs, but, in "shining brightness," to illuminate their darkness. As such, the ideas have nothing whatever to do with politics, political experience, and the problem of action, but pertain exclusively to philosophy, the experience of contemplation, and the quest for the "true being of things." It is precisely ruling, measuring, subsuming, and regulating that are entirely alien to the experiences underlying the doctrine of ideas in its original conception. It seems that Plato was the first to take exception to the political "irrelevance" of his new teaching, and he tried to modify the doctrine of ideas so that it would become useful for a theory of politics. But usefulness could be saved only by the idea of the good, since "good" in the Greek vocabulary always means "good for" or "fit." If the highest idea, in which all other ideas must partake in order to be ideas at all, is that of fitness, then the ideas are applicable by definition, and in the hands of the philosopher, the expert in ideas, they can become rules and standards or, as later in the Laws, they can become laws. (The difference is negligible. What in The Republic is still the philosopher's, the philosopher-king's, direct personal claim to rule, has become reason's impersonal claim to domination in the Laws.) The actual consequence of this political interpretation of the doctrine of ideas would be that neither man nor a god is the measure of all things, but the good itself-a consequence which apparently + +Aristotle, not Plato, drew in one of his earlier dialogues.21 + +For our purposes it i:; essential to remember that the element of rule, as reflected in our present concept of authority so tremendously influenced by Platonic thinking, can be traced to a conflict between philosophy and politics, but not to specifically political experiences, that is, experiences immediately derived from the realm of human affairs. One cannot understand Plato without bearing in mind both his repeated emphatic insistence on the philosophic irrelevance of this realm, which he always warned should not be taken too seriously, and the fact that he himself, in distinction to nearly all philosophers who carne after him, still took human affairs so seriously that he changed the very center of his thought to make it applicable to politics. And it is this ambivalence rather than any formal ex- + +position of his new doctrine of ideas which forms the true content of the parable of the cave in The Republic, which after all is told in the context of a strictly political dialogue searching for the best form of government. In the midst of this search Plato tells his parable, which turns out to be the story of the philosopher in this world, as though he had intended to write the concentrated biography of the philosopher. Hence, the search for the best form of government reveals itself to be the search for the best government for philosophers, which turns out to be a government in which philosophers have become the rulers of the city-a not too surprising solution for + +people who had witnessed the life and death of Socrates. + +Still, the philosopher's rule had to be justified, and it could be justified only if the philosopher's truth possessed a validity for that very realm of human affairs which the philosopher had to tum away from in order to perceive it. Insofar as the philosopher is nothing but a philosopher, his quest ends with the contemplation of the highest truth, which, since it illuminates everything else, is also the highest beauty; but insofar as the philosopher is a man among men, a mortal among mortals, and a citizen among citizens, he must take his truth and transform it into a set of rules, by virtue of which transformation he then may claim to become an actual ruler-the king-philosopher. The lives of the many in the cave over which the philosopher has established his rule are characterized not by contemplation but by >..i�t<;, speech, and 7rpa�t<;, action; it is therefore characteristic that in the parable of the cave Plato depicts the lives of the inhabitants as though they too were interested only in seeing: first the images on the screen, then the things themselves in the dim light of the fire in the cave, until finally those who want to see truth itself must leave the common world of the cave altogether and embark upon their new adventure all by themselves. In other words, the whole realm of human affairs is seen from the viewpoint of a philosophy which assumes that even those who inhabit the cave of human affairs are human only insofar as they too want to see, though they remain deceived by shadows and images. And the rule of the philosopher-king, that is, the domination or human affairs by something outside its own realm, is justified not + +only by an absolute priority of seeing over doing, of contemplation over speaking and acting, but also by the assumption that what makes men human is the urge to see. Hence, the interest of the philosopher and the interest of man qua man coincide; both demand that human affairs, the results of speech and action, must not acquire a dignity of their own but be subjected to the domination of + +something outside their realm. + +III + +The dichotomy between seeing the truth in solitude and remoteness and being caught in the relationships and relativities of human affairs became authoritative for the tradition of political thought. It is expressed most forcefully in Plato's parable of the cave, and one is therefore somehow tempted to see its origin in the Platonic doctrine of ideas. Historically, however, it was not dependent upon an acceptance of this doctrine, but depended much more upon an attitude which Plato expressed only once, almost casually in a random remark, and which Aristotle later quoted in a famous sentence of Metaphysics almost verbatim, namely that the beginning of all philosophy is 8avJ.LaC£tv, the surprised wonder at everything that is as it is. More than anything else, Greek "theory" is the prolongation and Greek philosophy the articulation and conceptualization of this initial wonder. To be capable of it is what separates the few from the many, and to remain devoted to it is what alienates them from the affairs of men. Aristotle, therefore, without accepting Plato's doctrine of ideas, and even repudiating Plato's ideal state, still followed him in the main not only by separating a "theoretical way of life" ({3{o-;; 8£wp17nKo<;) from a life devoted to human affairs ({3[o., roAtnKo<; }-the first to establish such ways of life in hierarchical order had been Plato in his Phaedrus-but accepted as a matter of course the hierarchical order implied in it. The point in our context is not only that thought was supposed to rule over action, to prescribe principles to action so that the rules of the latter were invariably derived from experiences of the former, but that by way of the + +p:.o,, of identifying activities with ways of life, the principle of rulership was established between men as well. Historically this became the hallmark of the political philosophy of the Socratic school, and the irony of this development is probably that it was precisely this dichotomy between thought and action that Socrates had feared and + +tried to prevent in the polis. + +Thus it is in the political philosophy of Aristotle that we find the second attempt to establish a concept of authority in terms of rulers and the ruled; it was equally important for the development of the tradition of political thought, although Aristotle took a basically different approach. For him reason has neither dictatorial nor tyrannical features, and there is no philosopher-king to regulate human affairs once and for all. His reason for maintaining that "each body politic is composed of those who rule and those who are ruled" does not derive from the superiority of the expert over the layman, and he is too conscious of the difference between acting and making to draw his examples from the sphere of fabrication. Aristotle, as far as I can see, was the first to appeal, for the purpose of establishing rule in the handling of human affairs, to "nature," which "established the difference . . . between the younger and the older ones, destined the ones to be ruled and the others to rule." 22 + +The simplicity of this argument is all the more deceptive since centuries of repetition have degraded it into a platitude. This may be why one usually overlooks its flagrant contradiction of Aristotle's own definition of the polis as also given in Politics: "The polis is a community of equals for the sake of a life which is potentially the best." 23 Obviously the notion of rule in the polis was for Aristotle himself so far from convincing that he, one of the most consistent and least self-contradictory great thinkers, did not feel particularly bound by his own argument. We therefore need not be surprised when we read at the beginning of the Economics (a pseudo-Aristotelian treatise, but written by one of his closest disciples) that the essential difference between a political community (the 17'6..\.,,) and a private household (the oiK£a) is that the latter constitutes a "monarchy," a one-man rule, while the polis, on the contrary, "is composed of many rulers." 2! In order to understand this characteriza· + +tion we must remember first that the words "monarchy" and "tyranny" were used synonymously and in clear contradistinction to kingship; second, that the character of the polis as "composed of many rulers" has nothing to do with the various forms of government that usually are opposed to one-man rule, such as oligarchy, aristocracy, or democracy. The "many rulers" in this context are the household heads, who have established themselves as "monarchs" at horne before they join to constitute the public-political realm of the city. Ruling itself and the distinction between rulers and ruled belong to a sphere which precedes the political realm, and what disinguishes it from the "economic" sphere of the household is that the polis is based upon the principle of equality and knows + +no differentiation between rulers and ruled. + +In this distinction between what we would today call the private and the public spheres, Aristotle only articulates current Greek public opinion, according to which "every citizen belongs to two orders of existence," because "the polis gives each individual ... besides his private life a sort of second life, his bios politikos." 2;; (The latter Aristotle called the "good life," and redefined its content; only this definition, not the differentiation itself, conflicted with common Greek opinion.) Both orders were forms of human living-together, but only the household community was concerned with keeping alive as such and coping with the physical necessities (uvayKaia) involved in maintaining individual life and guaranteeing the survival of the species. In characteristic difference from the modern approach, care for the preservation of life, both of the individual and the species, belonged exclusively in the private sphere of the household, while in the polis man appeared Kar' apdJp.6v, as an individual personality, as we would say today.26 As living beings, concerned with the preservation of life, men are confronted with and driven by necessity. Necessity must be mastered before the political "good life" can begin, and it can be mastered only through domination. Hence the freedom of the "good life" rests on the + +The mastery of necessity then has as its goal the controlling of the necessities of life, which coerce men and hold them in their + +power. But such domination can be accomplished only by controlling and doing violence to others, who as slaves relieve free men from themselves being coerced by necessity. The free man, the citizen of a polis, is neither coerced by the physical necessities of life nor subject to the man-made domination of others. He not only must not be a slave, he must own and rule over slaves. The freedom of the political realm begins after all elementary necessities of sheer living have been mastered by rule, so that domination and subjection, command and obedience, ruling and being ruled, are preconditions for establishing the political realm precisely because they + +are not its content. + +There can be no question that Aristotle, like Plato before him, meant to introduce a kind of authority into the handling of public affairs and the life of the polis, and no doubt for very good political reasons. Yet he too had to resort to a kind of makeshift solution in order to make plausible the introduction into the political realm of a distinction between rulers and ruled, between those who command and those who obey. And he too could take his examples and models only from a prepolitical sphere, from the private realm of the household and the experiences of a slave economy. This leads him into glaringly contradictory statements, insofar as he superimposes on the actions and life in the polis those standards which, as he explains elsewhere, are valid only for the behavior and life in the household community. The inconsistency of his enterprise is apparent even if we consider only the famous example from the Politics previously mentioned, in which the differentiation between rulers and ruled is derived from the natural difference between the younger and the elder. For this example is in itself eminently unsuitable to prove Aristotle's argument. The relation between old and young is educational in essence, and in this education no more is involved than the training of the future rulers by the present rulers. If rule is at all involved here, it is entirely different from political forms of rule, not only because it is limited in time and intent, but because it happens between people who are potentially equals. Yet substitution of education for rule had the most far-reaching consequences. On its grounds rulers have posed as educators and edu- + +cators have been accused of ruling. Then, as well as now, nothing is more questionable than the political relevance of examples drawn from the field of education. In the political realm we deal always with adults who are past the age of education, properly speaking, and politics or the right to participate in the management of public affairs begins precisely where education has come to an end. (Adult education, individual or communal, may be of great relevance for the formation of personality, its full development or greater enrichment, but is politically irrelevant unless its purpose is to supply technical requirements, somehow not acquired in youth, needed for participation in public affairs.) In education, conversely, we always deal with people who cannot yet be admitted to politics and equality because they are being prepared for it. Aristotle's example is nevertheless of great relevance because it is true that the necessity for "authority" is more plausible and evident in child-rearing and education than anywhere else. That is why it is so characteristic of our own time to want to eradicate even this extremely limited and politi- + +cally irrelevant form of authority. + +Politically, authority can acquire an educational character only if we presume with the Romans that under all circumstances ancestors represent the example of greatness for each successive generation, that they are the maiores, the greater ones, by definition. Wherever the model of education through authority, without this fundamental conviction, was superimposed on the realm of politics (and this has happened often enough and still is a mainstay of conservative argument), it served primarily to obscure real or coveted claims to rule and pretended to educate while in reality it wanted + +to dominate. + +The grandiose attempts of Greek philosophy to find a concept of authority which would prevent deterioration of the polis and safeguard the life of the philosopher foundered on the fact that in the realm of Greek political life there was no awareness of authority based on immediate political experience. Hence all prototypes by which subsequent generations understood the content of authority were drawn from specifically unpolitical experiences, stemming either from \he sphere of "making" and the arts, where there must + +be experts and where fitness is the highest criterion, or from the private household community. It is precisely in this politically determined aspect that the philosophy of the Socratic school has exerted its greatest impact upon our tradition. Even today we believe that Aristotle defined man primarily as a political being endowed with speech or reason, which he did only in a political context, or that Plato exposed the original meaning of his doctrine of ideas in The Republic, where, on the contrary, he changed it for political reasons. In spite of the grandeur of Greek political philosophy, it may be doubted that it would have lost its inherent utopian character if the Romans, in their indefatigable search for tradition and authority, had not decided to take it over and acknowledge it as their highest authority in all matters of theory and thought. But they were able to accomplish this integration only because both authority and tradition had already played a decisive role in the political life of the + +Roman republic. + +IV + +At the heart of Roman politics, from the beginning of the republic until virtually the end of the imperial era, stands the conviction of the sacredness of foundation, in the sense that once something has been founded it remains binding for all future generations. To be engaged in politics meant first and foremost to preserve the founding of the city of Rome. This is why the Romans were unable to repeat the founding of their first polis in the settlement of colonies but were capable of adding to the original foundation until the whole of Italy and, eventually, the whole of the Western world were united and administered by Rome, as though the whole world were nothing but Roman hinterland. From beginning to end, the Romans were bound to the specific locality of this one city, and unlike the Greeks, they could not say in times of emergency or overpopulation, "Go and found a new city, for wherever you are you will always be a polis." Not the Greeks, but the Romans, were really rooted in the soil, and the word patria derives its full meaning from Roman his- + +tory. The foundation of a new body politic-to the Greeks an almost commonplace experience-became to the Romans the central, decisive, unrepeatable beginning of their whole history, a unique event. And the most deeply Roman divinities were Janus, the god of beginning, with whom, as it were, we still begin our year, + +and Minerva, the goddess of remembrance. + +The founding of Rome-tanta molis erat Romanam condere gentem ("so great was the effort and toil to found the Roman people" ), as Virgil sums up the ever-present theme of the Aeneid, that all wandering and suffering reach their end and their goal dum conderet urbem ("that he may found the city" )-this foundation and the equally un-Greek experience of the sanctity of house and hearth, as though Homerically speaking the spirit of Hector had survived the fall of Troy and been resurrected on Italian soil, form the deeply political content of Roman religion. In contrast to Greece, where piety depended upon the immediate revealed presence of the gods, here religion literally meant re-ligare: 27 to be tied back, obligated, to the enormous, almost superhuman and hence always legendary effort to lay the foundations, to build the cornerstone, to found for etemity.28 To be religious meant to be tied to the past, and Livy, the great recorder of past events, could therefore say, Mihi vetustas res scribenti nescio quo pacto antiquus fit animus et quaedam religio tenet ("While I write down these ancient events, I do not know through what connection my mind grows old and some religio holds [me]" ). 29 Thus religious and political activity could be considered as almost identical, and Cicero could say, "In no other realm does human excellence approach so closely the paths of the gods (numen) as it does in the founding of new and in the preservation of already founded communities." 30 The binding power of the foundation itself was religious, for the city also offered the gods of the people a permanent home-again unlike Greece, whose gods protected the cities of the mortals and occasionally dwelt in them but had their own horne, far from the abode of men, on Mount + +It is in this context that word and concept of authority originally appeared. The word auctoritas derives from the verb auger-e, "aug- + +ment," and what authority or those in authority constantly augment is the foundation. Those endowed with authority were the elders, the Senate or the patres, who had obtained it by descent and by transmission (tradition) from those who had laid the foundations for all things to come, the ancestors, whom the Romans therefore called the maiores. The authority of the living was always derivative, depending upon the auctores imperii Romani conditoresque, as Pliny puts it, upon the authority of the founders, who no longer were among the living. Authority, in contradistinction to power (potestas) , had its roots in the past, but this past was no less present in the actual life of the city than the power and strength of the living. Moribus antiquis res stat Romana virisque, in the words of Ennius. In order to understand more concretely what it meant to be in authority, it may be useful to notice that the word auctores can be used as the very opposite of the artifices, the actual builders and makers, and this precisely when the word auctor signifies the same thing as our "author." Who, asks Pliny at the occasion of a new theater, should be more admired, the maker or the author, the inventor or the invention?-meaning, of course, the latter in both instances. The author in this case is not the builder but the one who inspired the whole enterprise and whose spirit, therefore, much more than the spirit of the actual builder, is represented in the building itself. In distinction to the artifex, who only made it, he is the actual "author" of the building, namely its founder; with it he has become + +an "augmenter" of the city. + +However, the relation between auctor and artifex is by no means the (Platonic ) relation between the master who gives orders and the servant who executes them. The most conspicuous characteristic of those in authority is that they do not have power. Cum potestas in populo auctoritas in senatu sit, "while power resides in the people, authority rests with the Senate." 31 Because the "authority," the augmentation which the Senate must add to political decisions, is not power, it seems to us curiously elusive and intangible, bearing in this respect a striking resemblance to Montesquieu's judiciary branch of government, whose power he called "somehow nil" (en quelque fafon nulle) and which nevertheless constitutes the highest + +authority in constitutional governments.32 Mommsen called it "more than advice and less than a command, an advice which one may not safely ignore," whereby it is assumed that "the will and the actions of the people like those of children are exposed to error and mistakes and therefore need 'augmentation' and confirmation through the council of elders." 33 The authoritative character of the "augmentation" of the elders lies in its being a mere advice, needing neither the form of command nor external coercion to make itself + +heard.3� + +The binding force of this authority is closely connected with the religiously binding force of the auspices, which, unlike the Greek oracle, does not hint at the objective course of future events but reveals merely divine approval or disapproval of decisions made by men.35 The gods too have authority among, rather than power over, men; they "augment" and confirm human actions but do not guide them. And just as "all auspices were traced back to the great sign by which the gods gave Romulus the authority to found the city," 36 so all authority derives from this foundation, binding every act back to the sacred beginning of Roman history, adding, as it were, to every single moment the whole weight of the past. Gravitas, the ability to bear this weight, became the outstanding trait of the Roman character, just as the Senate, the representation of authority in the republic, could function-in the words of Plutarch ("Life of Lycurgus" )-as "a central weight, like ballast in a ship, which + +always keeps things in a just equilibrium." + +Thus precedents, the deeds of the ancestors and the usage that grew out of them, were always binding.:n Anything that happened was transformed into an example, and the auctoritas maiorum became identical with authoritative models for actual behavior, with the moral political standard as such. This is also why old age, as distinguished from mere adulthood, was felt by the Romans to contain the very climax of human life; not so much because of accumulated wisdom and experience as because the old man had grown closer to the ancestors and the past. Contrary to our concept of growth, where one grows into the future, the Romans felt that growth was directed toward the past. If one wants to relate this + +attitude to the hierarchical order established by authority and to visualize this hierarchy in the familiar image of the pyramid, it is as though the peak of the pyramid did not reach into the height of a sky above (or, as in Christianity, beyond) the earth, but into the + +depth of an earthly past. + +It is in this primarily political context that the past was sanctified through tradition. Tradition preserved the past by handing down from one generation to the next the testimony of the ancestors, who first had witnessed and created the sacred founding and then augmented it by their authority throughout the centuries. As long as this tradition was uninterrupted, authority was inviolate ; and to act without authority and tradition, without accepted, time-honored standards and models, without the help of the wisdom of the founding fathers, was inconceivable. The notion of a spiritual tradition and of authority in matters of thought and ideas is here derived from the political realm and therefore essentially derivative-just as Plato's conception of the role of reason and ideas in politics was derived from the philosophical realm and became derivative in the realm of human affairs. But the historically all-important fact is that the Romans felt they needed founding fathers and authoritative examples in matters of thought and ideas as well, and accepted the great "ancestors" in Greece as their authorities for theory, philosophy, and poetry. The great Greek authors became authorities in the hands of the Romans, not of the Greeks. The way Plato and others before and after him treated Horner, "the educator of all Hellas," was inconceivable in Rome, nor would a Roman philosopher have dared "to raise his hand against his [spiritual] father," as Plato said of himself (in the Sophistes) when he broke with the teaching of + +Parrnenides. + +Just as the derivative character of the applicability of the ideas to politics did not prevent Platonic political thought from becoming the origin of Western political theory, so the derivative character of authority and tradition in spiritual matters did not prevent them from becoming the dominant features of Western philosophic thought for the longer part of our history. In both instances the political origin and the political experiences underlying the theories + +were forgotten, the original conflict between politics and philosophy, between the citizen and the philosopher, no less than the experience of foundation in which the Roman trinity of religion, authority, and tradition had its legitimate source. The strength of this trinity lay in the binding force of an authoritative beginning to which "religious" bonds tied men back through tradition. The Roman trinity not only survived the transformation of the republic into the empire but penetrated wherever the pax Romana created Western civiliza- + +tion on Roman foundations. + +The extraordinary strength and endurance of this Roman spirit --or the extraordinary reliability of the founding principle for the creation of bodies politic-were subjected to a decisive test and proved themselves conspicuously after the decline of the Roman Empire, when Rome's political and spiritual heritage passed to the Christian Church. Confronted with this very real mundane task, the Church became so "Roman" and adapted itself so thoroughly to Roman thinking in matters of politics that it made the death and resurrection of Christ the cornerstone of a new foundation, erecting on it a new human institution of tremendous durability. Thus, after Constantine the Great had called upon the Church to secure for the declining empire the protection of the "most powerful God," the Church was eventually able to overcome the antipolitical and antiinstitutional tendencies of the Christian faith, which had caused so much trouble in earlier centuries, and which are so manifest in the New Testament and in early Christian writings, and seemingly so insurmountable. The victory of the Roman spirit is really almost a miracle; in any event, it alone enabled the Church "to offer men in the membership of the Church the sense of citizenship which neither Rome nor municipality could any longer offer them." 38 Yet, just as Plato's politicalization of the ideas changed Western philosophy and determined the philosophic concept of reason, so the politicalization of the Church changed the Christian religion. The basis of the Church as a community of believers and a public institution was now no longer the Christian faith in resurrection (though this faith remained its content) or the Hebrew obedience to the commands of God, but rather the testimony of the life, of the birth, death, and + +resurrection, of Jesus of Nazareth as a historically recorded evcnt.30 As witnesses to this event the Apostles could become the "founding fathers" of the Church, from whom she would derive her own authority as long as she handed down their testimony by way of tradition from generation to generation. Only when this had happened, one is tempted to say, had the Christian faith become a "religion" not only in the post-Christian sense but in the ancient sense as well; only then, at any rate, could a whole world-as distinguished from mere groups of believers, no matter how large they might have been -become Christian. The Roman spirit could survive the catastrophe of the Roman Empire because its most powerful enemies-those who had laid, as it were, a curse on the whole realm of worldly public affairs and sworn to live in hiding--discovered in their own faith something which could be understood as a worldly event as well and could be transformed into a new mundane beginning to which the world was bound back once more (religare) in a curious mixture of new and old religious awe. This transformation was to a large extent accomplished by Augustine, the only great philosopher the Romans ever had. For the mainstay of his philosophy, Sedis animi est in memoria ("the seat of the mind is in memory" ), is precisely that conceptual articulation of the specifically Roman experience which the Romans themselves, overwhelmed as they were + +by Greek philosophy and concepts, never achieved. + +Thanks to the fact that the foundation of the city of Rome was repeated in the foundation of the Catholic Church, though, of course, with a radically different content, the Roman trinity of religion, authority, and tradition could be taken over by the Christian era. The most conspicuous sign of this continuity is perhaps that the Church, when she embarked upon her great political career in the fifth century, at once adopted the Roman distinction between authority and power, claiming for herself the old authority of the Senate and leaving the power-which in the Roman Empire was no longer in the hands of the people but had been monopolized by the imperial household-to the princes of the world. Thus, at the close of the fifth century, Pope Gelasius I could write to Emperor Anastasi us I: "Two are the things by which this world is chiefly + +ruled : the sacred authority of the Popes and the royal power." 40 The result of the continuity of the Roman spirit in the history of the West was twofold. On one hand, the miracle of permanence repeated itself once more; for within the framework of our history the durability and continuity of the Church as a public institution can be compared only with the thousand years of Roman history in antiquity. The separation of church and state, on the other hand, far from signifying unequivocally a secularization of the political realm and, hence, its rise to the dignity of the classical period, actually implied that the political had now, for the first time since the Romans, lost its authority and with it that element which, at least in Western history, had endowed political structures with durability, + +continuity, and permanence. + +It is true that Roman political thought at a very early date began to use Platonic concepts in order to understand and interpret the specifically Roman political experiences. Yet it seems as though it has been only in the Christian era that Plato's invisible spiritual yardsticks, by which the visible, concrete affairs of men were to be measured and judged, have unfolded their full political effectiveness. Precisely those parts of Christian doctrine which would have had great difficulty in fitting in and being assimilated to the Roman political structure-namely, the revealed commandments and truths of a genuinely transcendent authority which, unlike Plaia's, did not stretch above but was beyond the earthly realm-could be integrated into the Roman foundation legend via Plato. God's revelation could now be interpreted politically as if the standards for human conduct and the principle of political communities, intuitively anticipated by Plato, had been finally revealed directly, so that, in the words of a modern Platonist, it appeared as though Plato's early "orientation toward the unseen measure was now confirmed through the revelation of the measure itself." 41 To the extent that the Catholic Church incorporated Greek philosophy into the structure of its doctrines and dogmatic beliefs, it amalgamated the Roman political concept of authority, which inevitably was based on a beginning, a founding in the past, with the Greek notion of transcending measurements and rules. General and transcendent standards under which the par- + +ticular and immanent could be subsumed were now required for any political order, moral rules for all interhuman behavior, and rational measurements for the guidance of all individual judgment. There is scarcely anything that eventually was to assert itself with greater authority and more far-reaching consequences than the amalgama- + +tion itself. + +Since then it has turned out, and this fact speaks for the stability of the amalgamation, that wherever one of the elements of the Roman trinity, religion or authority or tradition, was doubted or eliminated, the remaining two were no longer secure. Thus, it was Luther's error to think that his challenge of the temporal authority of the Church and his appeal to unguided individual judgment would leave tradition and religion intact. So it was the error of Hobbes and the political theorists of the seventeenth century to hope that authority and religion could be saved without tradition. So, too, was it finally the error of the humanists to think it would be possible to remain within an unbroken tradition of Western civilization without + +religion and without authority. + +v + +Politically the most momentous consequence of the amalgamation of Roman political institutions with Greek philosophic ideas was that it enabled the Church to interpret the rather vague and conflicting notions of early Christianity about life in the hereafter in the light of the Platonic political myths, and thus to elevate to the rank of dogmatic certitude an elaborate system of rewards and punishments for deeds and misdeeds that did not find their just retribution on earth. This happened not before the fifth century, when the earlier teachings of the redemption of all sinners, even of Satan himself (as taught by Origen and still held by Gregory of Nyssa) , and the spiritualizing interpretation of the torments of hell as torments of conscience (also taught by Origen) were declared to be heretical; but it coincided with the downfall of Rome, the disappearance of an assured secular order, the assumption of responsibility + +for secular affairs by the Church, and the emergence of the papacy as a temporal power. Popular and literate notions about a hereafter with rewards and punishments were, of course, widespread then as they had been throughout antiquity, but the original Christian version of these beliefs, consistent with the "glad tidings" and the redemption from sin, was not a threat of eternal punishment and eternal suffering, but, on the contrary, the descensus ad in/eros, Christ's mission to the underworld where he had spent the three days between his death and his resurrection in order to liquidate hell, defeat Satan, and liberate the souls of dead sinners, as he had + +liberated the souls of the living, from death and punishment. + +We find it somewhat difficult to gauge correctly the political, nonreligious origin of the doctrine of hell because the Church incorporated it, in its Platonic version, so early into the body of dogmatic beliefs. It seems only natural that this incorporation in its turn should have blurred the understanding of Plato himself to the point of identifying his strictly philosophic teaching of the immortality of the soul, which was meant for the few, with his political teaching of a hereafter with punishments and rewards, which was clearly meant for the multitude. The philosopher's concern is with the invisible which can be perceived by the soul, which itself is something invisible (a£Loi�) and hence goes to Hades, the place of invisibility (A-io7J>), after death has rid the invisible part of man of his body, the organ of sense perception.42 This is the reason why philosophers always seem "to pursue death and dying" and why philosophy can also be called "the study of death." 43 Those who have no experience with a philosophic truth beyond the range of sense perception, of course, cannot be persuaded of the immortality of a bodyless soul; for them, Plato invented a number of tales to conclude his political dialogues, usually after the argument itself had broken down, as in The Republic, or it had turned out that Socrates' opponent could not be persuaded, as in the Gorgias.44 Of these tales, the Er-myth of The Republic is the most elaborate and has exerted the greatest influence. Between Plato and the secular victory of Christianity in the fifth century, which brought with it the religious sanction of the doctrine of hell (so that from then on this became so general a feature of + +the Christian world that political treatises did not need to mention it specifically), there was hardly an important discussion of political problems-except in Aristotle-which did not conclude with an imitation of the Platonic myth.45 And it is still Plato, as distinguished from the Hebrew and early Christian speculations about an afterlife, who is the true forerunner of Dante's elaborate descriptions; for in Plato we find for the first time not merely a concept of final judgment about eternal life or eternal death, about rewards and punishments, but the geographical separation of hell, purgatory, and paradise, as well as the horribly concrete notions of graduated + +bodily punishment.46 + +The purely political implications of Plato's myths in the last book of The Republic, as well as in the concluding parts of Phaedon and Gorgias, seem to be indisputable. The distinction between the philosophic conviction of the immortality of the soul and the politically desirable belief in an afterlife runs parallel to the distinction in the doctrine of ideas between the idea of the beautiful as the highest idea of the philosopher and the idea of the good as the highest idea of the statesman. Yet while Plato, when applying his philosophy of ideas to the political realm, somehow blurred the decisive distinction between the ideas of the beautiful and of the good, silently substituting the latter for the former in his discussions of politics, the same cannot be said for the distinction between an immortal, invisible, bodyless soul and an afterlife in which bodies, sensitive to pain, will receive their punishment. One of the clearest indications for the political character of these myths is indeed that they, because they imply bodily punishment, stand in flagrant contradiction to his doctrine of the mortality of the body, and of this contradiction Plato himself was by no means unaware.n Moreover, when he came to telling his tales, he used elaborate precautions to make sure that what followed was not truth but a possible opinion of which one better persuaded the multitude "as though it were the truth." 48 Finally, is it not rather obvious, especially in The Republic, that this whole concept of life after death cannot possibly make sense to those who have understood the story of the cave and know that the true under- + +No doubt Plato relied on popular beliefs, perhaps on Orphjc and Pythagorean traditions, for his descriptions of an afterlife, just as the Church, almost a thousand years later, could choose freely which of the then prevalent beliefs and speculations she wanted to lay down as dogma and which to declare as heretical. The distinction between Plato and his predecessors, whoever they may have been, was that he was the first to become aware of the enormous, strictly political potentiality inherent in such beliefs, just as the distinction between Augustine's elaborate teachings about hell, purgatory, and paradise and the speculations of Origen or Clement of Alexandria was that he (and perhaps Tertullian before him) understood to what an extent these doctrines could be used as threats in this world, quite apart from their speculative value about a future life. Nothing, indeed, is more suggestive in this context than that it was Plato who coined the word "theology," for the passage in which the new word is used occurs again in a strictly political discussion, namely in The Republic, when the dialogue deals with the founding of cities.49 This new theological god is neither a living God nor the god of the philosophers nor a pagan divinity; he is a political device, "the measurement of measurements," 50 that is, the standard according to which cities may be founded and rules of behavior laid down for the multitude. Theology, moreover, teaches how to enforce these standards absolutely, even in cases when human justice seems at a loss, that is, in the case of crimes which escape punishment as well as in the case of those for which even the death sentence would not be adequate. For "the main thing" about the hereafter is, as Plato says explicitly, that "for every wrong men had done to anyone they suffered tenfold." 51 To be sure, Plato had no inkling of theology as we understand it, as the interpretation of God's word whose sacrosanct text is the Bible; theology to him was part and parcel of "political science," and specifically that part which + +taught the few how to rule the many. + +Whatever other historical influences may have been at work to elaborate the doctrine of hell, it continued, during antiquity, to be used for political purposes in the interest of the few to retain a moral and political control over the multitude. The point at stake was al- + +ways the same : truth by its very nature is self-evident and therefore cannot be satisfactorily argued out and demonstrated.�2 Hence, belief is necessary for those who lack the eyes for what is at the same time self-evident, invisible, and beyond argument. Platonically speaking, the few cannot persuade the multitude of truth because truth cannot be the object of persuasion, and persuasion is the only way to deal with the multitude. But the multitude, carried away by the irresponsible tales of poets and storytellers, can be persuaded to believe almost anything; the appropriate tales which carry the truth of the few to the multitude are tales about rewards and punishments after death; persuading the citizens of the existence of hell + +will make them behave as though they knew the truth. + +As long as Christianity remained without secular interests and responsibilities, it left the beliefs and speculations about a hereafter as free as they had been in antiquity. Yet when the purely religious development of the new creed had come to an end and the Church had become aware of, and willing to take over, political responsibilities, she found herself confronted with a perplexity similar to the one that had given rise to Plato's political philosophy. Again it had become a question of imposing absolute standards on a realm which is made up of human affairs and relations, whose very essence therefore seems to be relativity; and to this relativity corresponds the fact that the worst man can do to man is to kill him, that is, to bring about what one day is bound to happen to him anyhow. The "improvement" on this limitation, proposed in the hell images, is precisely that punishment can mean more than the "eternal death" which early Christianity thought to be the appropriate reward of sin, namely eternal suffering, compared to which eternal death is + +salvation. + +The introduction of the Platonic hell into the body of Christian dogmatic beliefs strengthened religious authority to the point where it could hope to remain victorious in any contest with secular power. But the price paid for this additional strength was that the Roman concept of authority was diluted, and an element of violence was permitted to insinuate itself into both the very structure of Western + +religious thought and the hierarchy of the Church. How high this price actually was might be gauged by the more than embarrassing fact that men of unquestionable stature-among them Tertullian and even Thomas Aquinas--could be convinced that one of the joys in heaven would be the privilege of watching the spectacle of unspeakable sufferings in hell. Nothing perhaps in the whole development of Christianity throughout the centuries is farther removed from and more alien to the letter and spirit of the teaching of Jesus of Nazareth than the elaborate catalogue of future punishments and the enormous power of coercion through fear which only in the last stages of the modern age have lost their public, political significance. As far as religious thought is concerned, it certainly is a terrible irony that the "glad tidings" of the Gospels, "Life is everlasting," should eventually have resulted not in an increase of joy but of fear on earth, should not have made it easier but harder for man to + +die. + +However that may be, the fact is that the most significant consequence of the secularization of the modem age may well be the elimination from public life, along with religion, of the only political element in traditional religion, the fear of hell. We who had to witness how, during the Hitler and Stalin era, an entirely new and unprecedented criminality, almost unchallenged in the respective countries, was to invade the realm of politics should be the last to underestimate its "persuasive" influence upon the functioning of conscience. And the impact of these experiences is likely to grow when we recall that, in the very age of enlightenment, the men of the French Revolution no less than the founding fathers in America insisted on making the fear of an "avenging God" and hence the belief in "a future state" part and parcel of the new body politic. For the obvious reason why the men of the revolutions of all people should be so strangely out of tune in this respect with the general climate of their age was that precisely because of the new separation of church and state they found themselves in the old Platonic predicament. When they warned against the elimination of the fear of hell from public life because this would pave the way "to make + +murder itself as indifferent as shooting plover, and the extermination of the Rohilla nation as innocent as the swallowing of mites on a morsel of cheese," 53 their words may sound with an almost prophetic ring in our ears; yet they were clearly spoken not out of any dogmatic faith in the "avenging God" but out of mistrust in the na- + +ture of man. + +Thus the belief in a future state of rewards and punishments, consciously designed as a political device by Plato and perhaps no less consciously adopted, in its Augustinian form, by Gregory the Great, was to survive all other religious and secular elements which together had established authority in Western history. It was not during the Middle Ages, when secular life had become religious to such an extent that religion could not serve as a political instrument, but during the modern age that the usefulness of religion for secular authority was rediscovered. The true motives of this rediscovery have been somewhat overshadowed by the various more or less infamous alliances of "throne and altar" when kings, frightened at the prospect of revolution, believed that "the people must not be permitted to lose its religion" because, in Heine's words, Wer sich von seinem Gotte reisst,/ wird endlich auch abtriinnig werden/ von seinen irdischen BehOrden ("who tears himself away from his God will end by deserting his earthly authorities as well") . The point is rather that the revolutionaries themselves preached belief in a future state, that even Robespierre ended by appealing to an "Immortal Legislator" to give sanction to the revolution, that none of the early American constitutions lacked an appropriate provision for future rewards and punishments, that men like John Adams regarded + +them as "the only true foundation of morality." 54 + +It certainly is not surprising that all these attempts at retaining the only element of violence from the crumbling edifice of religion, authority, and tradition, and at using it as safeguard for the new, secular political order should be in vain. And it was by no means the rise of socialism or of the Marxian belief that "religion is the opiate of the people" which put an end to them. (Authentic religion in general and the Christian faith in particular-with its unrelenting stress on the individual and his own role in salvation, which led + +to the elaboration of a catalogue of sins greater than in any other religion--could never be used as tranquilizers. Modern ideologies, whether political or psychological or social, are far better fitted to immunize man's soul against the shocking impact of reality than any traditional religion we know. Compared with the various superstitions of the twentieth century, the pious resignation to God's will seems like a child's pocket-knife in competition with atomic weapons.) The conviction that "good morals" in civil society ultimately depended upon fear and hope for another life may still have appeared to the political men of the eighteenth century no more than good common sense; to those of the nineteenth century it appeared simply scandalous that, for instance, English courts took it for granted "that the oath is worthless of a person who does not believe in a future state," and this not only for political reasons but also because it implies "that they who do believe are only prevented + +from lying . . . by the fear of hell." 55 + +Superficially speaking, the loss of belief in future states is politically, though certainly not spiritually, the most significant distinction between our present period and the centuries before. And this loss is definite. For no matter how religious our world may turn again, or how much authentic faith still exists in it, or how deeply our moral values may be rooted in our religious systems, the fear of hell is no longer among the motives which would prevent or stimulate the actions of a majority. This seems inevitable if secularity of the world involves separation of the religious and political realms of life; under these circumstances religion was bound to lose its political element, just as public life was bound to lose the religious sanction of transcendent authority. In this situation, it would be well to recall that Plato's device of how to persuade the multitude to follow the standards of the few had remained utopian prior to its being sanctioned by religion; its purpose, to establish rule of the few over the many, was too patent to be useful. For the same reason the beliefs in future states withered from the public realm at once when their political usefulness was blatantly exposed by the very fact that they, out of the whole body of dogmatic beliefs, were + +VI + +One thing, however, is particularly striking in this context: while all the models, prototypes, and examples for authoritarian relationships-such as the statesman as healer and physician, as expert, as helmsman, as the master who knows, as educator, as the wise manall Greek in origin, have been faithfully preserved and further articulated until they became empty platitudes, the one political experience which brought authority as word, concept, and reality into our history-the Roman experience of foundation-seems to have been entirely lost and forgotten. And this to such an extent that the moment we begin to talk and think about authority, after all one of the central concepts of political thought, it is as though we were caught in a maze of abstractions, metaphors, and figures of speech in which everything can be taken and mistaken for something else, because we have no reality, either in history or in everyday experience, to which we can unanimously appeal. This, among other things, indicates what could also be proved otherwise, namely that the Greek concepts, once they had been sanctified by the Romans through tradition and authority, simply eliminated from historical consciousness all political experiences which could not be fitted into + +their framework. + +However, this statement is not entirely true. There exists in our political history one type of event for which the notion of founding is decisive, and there is in our history of thought one political thinker in whose work the concept of foundation is central, if not paramount. The events are the revolutions of the modern age, and the thinker is Machiavelli, who stood at the threshold of this age and, though he never used the word, was the first to conceive of a revolu- + +tion. + +Machiavelli's unique position in the history of political thought has little to do with his often praised but by no means unarguable realism, and he was certainly not the father of political science, a role now frequently attributed to him. (If one understands by + +political science political theory, its father certainly is Plato rather than Machiavelli. If one stresses the scientific character of political science, it is hardly possible to date its birth earlier than the rise of all modern science, that is, in the sixteenth and seventeenth centuries. In my opinion the scientific character of Machiavelli's theories is often greatly exaggerated.) His unconcern with moral judgments and his freedom from prejudice are astonishing enough, but they do not strike the core of the matter ; they have contributed more to his fame than to the understanding of his works, because most of his readers, then as today, were too shocked even to read him properly. When he insists that in the public-political realm men "should learn how not to be good," 5G he of course never meant that. they should learn how to be evil. After all, there is scarcely another political thinker who has spoken with such vehement contempt of "methods tby which] one may indeed gain power but not glory." 57 The truth is only that he opposed both concepts of the good which we find in our tradition : the Greek concept of the "good for" or fitness, and the Christian concept of an absolute goodness which is not of this world. Both concepts in his opinion were valid, but only in the private sphere of human life; in the public realm of politics they had no more place than their opposites, unfitness or incompetence and evil. The virtu, on the other hand, which according to Machiavelli is the specifically political human quality, has neither the connotation of moral character as does the Roman virtus, nor that of a morally neutral excellence like the Greek apn�. Virtu is the response, summoned up by man, to the world, or rather to the constellation of fortuna in which the world opens up, presents and offers itself to him, to his virtu. There is no virtu without fortuna and no fortuna without virtu; the interplay between them indicates a harmony between man and world-playing with each other and succeeding together-which is as remote from the wisdom of the statesman as from the excellence, moral or otherwise, of the individual, and the + +His experiences in the struggles of his time taught Machiavelli a deep contempt for all traditions, Christian and Greek, as presented, nurtured, and reinterpreted by the Church. His contempt was leveled + +at a corrupt Church which had corrupted the political life of Italy, but such corruption, he argued, was inevitable because of the Christian character of the Church. What he witnessed, after all, was not only corruption but also the reaction against it, the deeply religious and sincere revival emanating from the Franciscans and Dominicans, culminating in the fanaticism of Savonarola, whom he held in considerable respect. Respect for these religious forces and contempt for the Church together led him to certain conclusions about a basic discrepancy between the Christian faith and politics that are oddly reminiscent of the first centuries of our era. His point was that every contact between religion and politics must corrupt both, and that a noncorrupt Church, though considerably more respectable, would be even more destructive to the public realm than its present corruption. 68 What he did not, and perhaps in his time could not, see was the Roman influence on the Catholic Church, which, indeed, was much less noticeable than its Christian content and its Greek theo- + +retical framework of reference. + +It was more than patriotism and more than the current revival of interest in antiquity that sent Machiavelli to search for the central political experiences of the Romans as they had originally been presented, equally removed from Christian piety and Greek philosophy. The greatness of his rediscovery lies in that he could not simply revive or resort to an articulate conceptual tradition, but had himself to articulate those experiences which the Romans had not conceptualized but rather expressed in terms of Greek philosophy vulgarized for this purpose.59 He saw that the whole of Roman history and mentality depended upon the experience of foundation, and he believed it should be possible to repeat the Roman experience through the foundation of a unified Italy which was to become the same sacred cornerstone for an "eternal" body politic for the Italian nation as the founding of the Eternal City had been for the Italic people. The fact that he was aware of the contemporary beginnings of the birth of nations and the need for a new body politic, for which he therefore used the hitherto unknown term lo stato, has caused him to be commonly and rightfully identified as the father of the modern nation-state and its notion of a "reason of state." + +What is even more striking, though less well known, is that Machiavelli and Robespierre so often seem to speak the same language. When Robespierre justifies terror, "the despotism of liberty against tyranny," he sounds at times as if he were repeating almost word for word Machiavelli's famous statements on the necessity of violence for the founding of new political bodies and for the reform- + +ing of corrupt ones. + +This resemblance is all the more startling since both Machiavelli and Robespierre in this respect go beyond what the Romans themselves had to say about foundation. To be sure, the connection between foundation and dictatorship could be learned from the Romans themselves, and Cicero, for instance, appeals explicitly to Scipio to become dictator rei publicae constituendae, to seize the dictatorship in order to restore the republic.60 Like the Romans, Machiavelli and Robespierre felt founding was the central political action, the one great deed that established the public-political realm and made politics possible; but unlike the Romans, to whom this was an event of the past, they felt that for this supreme "end" all "means," and chiefly the means of violence, were justified. They understood the act of founding entirely in the image of making; the question to them was literally how to "make" a unified Italy or a French republic, and their justification of violence was guided by and received its inherent plausibility from the underlying argument: You cannot make a table without killing trees, you cannot make an omelet without breaking eggs, you cannot make a republic without killing people. In this respect, which was to become so fateful for the history of revolutions, Machiavelli and Robespierre were not Romans, and the authority to which they could have appealed would have been rather Plato, who also recommended tyranny as the government where "change is likely to be easiest and most rapid." 61 It is precisely in this double respect, because of his rediscovery of the foundation experience and his reinterpretation of it in terms of the justification of (violent) means for a supreme end, that Machiavelli may be regarded as the ancestor of modern revolutions, all of which can be characterized by Marx's remark that the French Revolution appeared on the stage of history in Roman costume. Unless + +it is recognized that the Roman pathos for foundation inspired them, it seems to me that neither the grandeur nor the tragedy of Western revolutions in the modern age can be properly understood. For if I am right in suspecting that the crisis of the present world is primarily political, and that the famous "decline of the West" consists primarily in the decline of the Roman trinity of religion, tradition, and authority, with the concomitant undermining of the specifically Roman foundations of the political realm, then the revolutions of the modem age appear like gigantic attempts to repair these foundations, to renew the broken thread of tradition, and to restore, through founding new political bodies, what for so many centuries had endowed the affairs of men with some measure of dignity and greatness. Of these attempts, only one, the American Revolution, has been successful : the founding fathers as, characteristically enough, we still call them, founded a completely new body politic without violence and with the help of a constitution. And this body politic has at least endured to the present day, in spite of the fact that the specifically modem character of the modem world has nowhere else produced such extreme expressions in all nonpolitical spheres of + +life as it has in the United States. + +This is not the place to discuss the reasons for the surprising stability of a political structure under the onslaught of the most vehement and shattering social instability. It seems certain that the relatively nonviolent character of the American Revolution, where violence was more or less restricted to regular warfare, is an important factor in this success. It may also be that the founding fathers, because they had escaped the European development of the nation-state, had remained closer to the original Roman spirit. More important, perhaps, was that the act of foundation, namely the colonization of the American continent, had preceded the Declaration of Independence, so that the framing of the Constitution, falling back on existing charters and agreements, confirmed and legalized an already existing body politic rather than made it anew.62 Thus the actors in the American Revolution were spared the effort of "initiating a new order of things" altogether; that is, they were spared the one action of which Machiavelli once said that "there is nothing + +more difficult to carry out, nor more doubtful of success, nor more dangerous to handle." 63 And Machiavelli surely must have known, for he, like Robespierre and Lenin and all the great revolutionaries whose ancestor he was, wished nothing more passionately than to + +initiate a new order of things. + +However that may be, revolutions, which we commonly regard as radical breaks with tradition, appear in our context as events in which the actions of men are still inspired by and derive their greatest strength from the origiRs of this tradition. They seem to be the only salvation which this Roman-Western tradition has provided for emergencies. The fact that not only the various revolutions of the twentieth century but all revolutions since the French have gone wrong, ending in either restoration or tyranny, seems to indicate that even these last means of salvation provided by tradition have become inadequate. Authority as we once knew it, which grew out of the Roman experience of foundation and was understood in the light of Greek political philosophy, has nowhere been re-established, either through revolutions or through the even less promising means of restoration, and least of all through the conservative moods and trends which occasionally sweep public opinion. For to live in a political realm with neither authority nor the concomitant awareness that the source of authority transcends power and those who are in power, means to be confronted anew, without the religious trust in a sacred beginning and without the protection of traditional and therefore self-evident standards of behavior, by the elementary + +problems of human living-together. + +WHAT IS FREEDOM? + +I + +T + +o raise the question, what is freedom? seems to be a hopeless enterprise. It is as though age-old contradictions and antinomies were lying in wait to force the mind into dilemmas of logical impossibility so that, depending which horn of the dilemma you are holding on to, it becomes as impossible to conceive of freedom or its opposite as it is to realize the notion of a square circle. In its simplest form, the difficulty may be summed up as the contradiction between our consciousness and conscience, telling us that we are free and hence responsible, and our everyday experience in the outer world, in which we orient ourselves according to the principle of causality. In all practical and especially in political matters we hold human freedom to be a self-evident truth, and it is upon this axiomatic assumption that laws are laid down in human communities, that decisions are taken, that judgments are passed. In all fields of scientific and theoretical endeavor, on the contrary, we proceed according to the no less self-evident truth of nihil ex nihilo, of nihil sine causa, that is, on the assumption that even "our own lives are, in the last analysis, subject to causation" and that if + +there should be an ultimately free ego in ourselves, it certainly never makes its unequivocal appearance in the phenomenal world, :and therefore can never become the subject of theoretical ascerlainment. Hence freedom turns out to be a mirage the moment psychology looks into what is supposedly its innermost domain; for "the part which force plays in nature, as the cause of motion, has its counterpart in the mental sphere in motive as the cause of conduct." 1 It is true that the test of causality-the predictability of effect if all causes are known--cannot be applied to the realm of human affairs; but this practical impredictability is no test of freedom, it signifies merely that we are in no position ever to know all causes which come into play, and this partly because of the sheer number of factors involved, but also because human motives, as distinguished from natural forces, are still hidden from all onlookers, from inspection by our fellow men as well as from introspection. The greatest clarification in these obscure matters we owe to Kant and to his insight that freedom is no more ascertainable to the inner sense and within the field of inner experience than it is to the senses with which we know and understand the world. Whether or not causality is operative in the household of nature and the universe, it certainly is a category of the mind to bring order into all sensory data, whatever their nature may be, and thus it makes experience possible. Hence the antinomy between practical freedom and theoretical non-freedom, both equally axiomatic in their respective fields, does not merely concern a dichotomy between science and ethics, but lies in everyday life experiences from which both ethics and science take their respective points of departure. It is not scientific theory but thought itself, in its pre-scientific and prephilosophical understanding, that seems to dissolve freedom on which our practical conduct is based into nothingness. For the moment we reflect upon an act which was undertaken under the assumption of our being a free agent, it seems to come under the sway of two kinds of causality, of the causality of inner motivation on one hand and of the causal principle which rules the outer world on the other. Kant saved freedom from this twofold assault upon it + +by distinguishing between a "pure" or theoretical reason and a "practical reason" whose center is free will, whereby it is important to keep in mind that the free-willing agent, who is practically allimportant, never appears in the phenomenal world, neither in the outer world of our five senses nor in the field of the inner sense with which I sense myself. This solution, pitting the dictate of the will against the understanding of reason, is ingenious enough and may even suffice to establish a moral law whose logical consistency is in no way inferior to natural laws. But it does little to eliminate the greatest and most dangerous difficulty, namely, that thought itself, in its theoretical as well as its pre-theoretical form, makes freedom disappear-quite apart from the fact that it must appear strange indeed that the faculty of the will whose essential activity consists in dictate and command should be the harborer of freedom. To the question of politics, the problem of freedom is crucial, and no political theory can afford to remain unconcerned with the fact that this problem has led into "the obscure wood wherein philosophy has lost its way." 2 It is the contention of the following considerations that the reason for this obscurity is that the phenomenon of freedom does not appear in the realm of thought at all, that neither freedom nor its opposite is experienced in the dialogue between me and myself in the course of which the great philosophic and metaphysical questions arise, and that the philosophical tradition, whose origin in this respect we shall consider later, has distorted, instead of clarifying, the very idea of freedom such as it is given in human experience by transposing it from its original field, the realm of politics and human affairs in general, to an inward domain, the will, where it would be open to self-inspection. As a first, preliminary justification of this approach, it may be pointed out that historically the problem of freedom has been the last of the time-honored great metaphysical questions-such as being, nothingness, the soul, nature, time, eternity, etc.-to become a topic of philosophic inquiry at all. There is no preoccupation with freedom in the whole history of great philosophy from the pre-Socratics up to Plotinus, the last ancient philosopher. And when + +freedom made its first appearance in our philosophical tradition, it was the experience of religious conversion--Qf Paul first and then + +of Augustine-which gave rise to it. + +The field where freedom has always been known, not as a problem, to be sure, but as a fact of everyday life, is the political realm. And even today, whether we know it or not, the question of politics and the fact that man is a being endowed with the gift of action must always be present to our mind when we speak of the problem of freedom; for action and politics, among all the capabilities and potentialities of human life, are the only things of which we could not even conceive without at least assuming that freedom exists, and we can hardly touch a single political issue without, implicitly or explicitly, touching upon an issue of man's liberty. Freedom, moreover, is not only one among the many problems and phenomena of the political realm properly speaking, such as justice, or power, or equality; freedom, which only seldom-in times of crisis or revolution-becomes the direct aim of political action, is actually the reason that men live together in political organization at all. Without it, political life as such would be meaningless. The raison d'etre of politics is freedom, and its field of experience is action. This freedom which we take for granted in all political theory and which even those who praise tyranny must still take into account is the very opposite of "inner freedom," the inward space into which men may escape from external coercion and feel free. This inner feeling remains without outer manifestations and hence is by definition politically irrelevant. Whatever its legitimacy may be, and however eloquently it may have been described in late antiquity, it is historically a late phenomenon, and it was originally the result of an estrangement from the world in which worldly experiences were transformed into experiences within one's own self. The experiences of inner freedom are derivative in that they always presuppose a retreat from the world, where freedom was denied, into an inwardness to which no other has access. The inward space where the self is sheltered against the world must not be mistaken for the heart or the mind, both of which exist and function only in interrelationship with the world. Not the heart and not the mind, + +but inwardness as a place of absolute freedom within one's own self was discovered in late antiquity by those who had no place of their own in the world and hence lacked a worldly condition which, from early antiquity to almost the middle of the nineteenth century, + +was unanimously held to be a prerequisite for freedom. + +The derivative character of this inner freedom, or of the theory that "the appropriate region of human liberty" is the "inward domain of consciousness," 3 appears more clearly if we go back to its origins. Not the modern individual with his desire to unfold, to develop, and to expand, with his justified fear lest society get the better of his individuality, with his emphatic insistence "on the importance of genius" and originality, but the popular and popularizing sectarians of late antiquity, who have hardly more in common with philosophy than the name, are representative in this respect. Thus the most persuasive arguments for the absolute superiority of inner freedom can still be found in an essay of Epictetus, who begins by stating that free is he who lives as he wishes, 4 a definition which oddly echoes a sentence from Aristotle's Politics in which the statement "Freedom means the doing what a man likes" is put in the mouths of those who do not know what freedom is.5 Epictetus then goes on to show that a man is free if he limits himself to what is in his power, if he does not reach into a realm where he can be hindered.6 The "science of living" 7 consists in knowing how to distinguish between the alien world over which man has no power and the self of which he may dispose as he sees + +fit.S + +Historically it is interesting to note that the appearance of the problem of freedom in Augustine's philosophy was thus preceded by the conscious attempt to divorce the notion of freedom from politics, to arrive at a formulation through which one may be a slave in the world and still be free. Conceptually, however, Epictetus's freedom which consists in being free from one's own desires is no more than a reversal of the current ancient political notions, and the political background against which this whole body of popular philosophy was formulated, the obvious decline of freedom in the late Roman Empire, manifests itself still quite + +clearly in the role which such notions as power, domination, and property play in it. According to ancient understanding, man could liberate himself from necessity only through power over other men, and he could be free only if he owned a place, a home in the world. Epictetus transposed these worldly relationships into relationships within man's own self, whereby he discovered that no power is so absolute as that which man yields over himself, and that the inward space where man struggles and subdues himself is more entirely his own, namely, more securely shielded from outside + +interference, than any worldly home could ever be. + +Hence, in spite of the great influence the concept of an inner, nonpolitical freedom has exerted upon the tradition of thought, it seems safe to say that man would know nothing of inner freedom if he had not first experienced a condition of being free as a worldly tangible reality. We first become aware of freedom or its opposite in our intercourse with others, not in the intercourse with ourselves. Before it became an attribute of thought or a quality of the will, freedom was understood to be the free man's status, which enabled him to move, to get away from home, to go out into the world and meet other people in deed and word. This freedom clearly was preceded by liberation : in order to be free, man must have liberated himself from the necessities of life. But the status of freedom did not follow automatically upon the act of liberation. Freedom needed, in addition to mere liberation, the company of other men who were in the same state, and it needed a common public space to meet them-a politically organized world, in other words, into which each of the free men could insert himself by word and deed. Obviously not every form of human intercourse and not every kind of community is characterized by freedom. Where men live together but do not form a body politic-as, for example, in tribal societies or in the privacy of the household-the factors ruling their actions and conduct are not freedom but the necessities of life and concern for its preservation. Moreover, wherever the man-made world does not become the scene for action and speech-as in despotically ruled communities which banish their subjects into the narrowness of the home and thus prevent the rise of a public realm + +-freedom has no worldly reality. Without a politically guaranteed public realm, freedom lacks the worldly space to make its appearance. To be sure it may still dwell in men's hearts as desire or will or hope or yearning; but the human heart, as we all know, is a very dark place, and whatever goes on in its obscurity can hardly be called a demonstrable fact. Freedom as a demonstrable fact and politics coincide and are related to each other like two sides of the + +same matter. + +Yet it is precisely this coincidence of politics and freedom which we cannot take for granted in the light of our present political experience. The rise of totalitarianism, its claim to having subordinated all spheres of life to the demands of politics and its consistent nonrecognition of civil rights, above all the rights of privacy and the right to freedom from politics, makes us doubt not only the coincidence of politics and freedom but their very compatibility. We are inclined to believe that freedom begins where politics ends, because we have seen that freedom has disappeared when so-called political considerations overruled everything else. Was not the liberal credo, "The less politics the more freedom," right after all? Is it not true that the smaller the space occupied by the political, the larger the domain left to freedom? Indeed, do we not rightly measure the extent of freedom in any given community by the free scope it grants to apparently nonpolitical activities, free economic enterprise or freedom of teaching, of religion, of cultural and intellectual activities? Is it not true, as we all somehow believe, that politics is compatible with freedom only because and insofar as it + +guarantees a possible freedom from politics? + +This definition of political liberty as a potential freedom from politics is not urged upon us merely by our most recent experiences; it has played a large part in the history of political theory. We need go no farther than the political thinkers of the seventeenth and eighteenth centuries, who more often than not simply identified political freedom with security. The highest purpose of politics, "the end of government," was the guaranty of security; security, in turn, made freedom possible, and the word "freedom" designated a quintessence of activities which occurred outside the political realm. + +Even Montesquieu, though he had not only a different but a much higher opinion of the essence of politics than Hobbes or Spinoza, could still occasionally equate political freedom with security.u The rise of the political and social sciences in the nineteenth and twentieth centuries has even widened the breach between freedom and politics; for government, which since the beginning of the modern age had been identified with the total domain of the political, was now considered to be the appointed protector not so much of freedom as of the life process, the interests of society and its individuals. Security remained the decisive criterion, but not the individual's security against "violent death," as in Hobbes (where the condition of all liberty is freedom from fear), but a security which should permit an undisturbed development of the life process of society as a whole. This life process is not bound up with freedom but follows its own inherent necessity; and it can be called free only in the sense that we speak of a freely flowing stream. Here freedom is not even the nonpolitical aim of politics, but a marginal phenomenon-which somehow forms the boundary government should not overstep unless life itself and its immediate interests + +and necessities are at stake. + +Thus not only we, who have reasons of our own to distrust politics for the sake of freedom, but the entire modern age has separated freedom and politics. I could descend even deeper into the past and evoke older memories and traditions. The pre-modern secular concept of freedom certainly was emphatic in its insistence on separating the subjects' freedom from any direct share in government; the people's "liberty and freedom consisted in having the government of those laws by which their life and their goods may be most their own : 'tis not for having share in government, that is nothing pertaining to them"-as Charles I summed it up in his speech from the scaffold. It was not out of a desire for freedom that people eventually demanded their share in government or admission to the political realm, but out of mistrust in those who held power over their life and goods. The Christian concept of political freedom, moreover, arose out of the early Christians' suspicion of and hostility against the public realm as such, from whose concerns + +they demanded to be absolved in order to be free. And this Christian freedom for the sake of salvation had been preceded, as we saw before, by the philosophers' abstention from politics as a prerequisite for the highest and freest way of life, the vita contem- + +plativa. + +Despite the enormous weight of this tradition and despite the perhaps even more telling urgency of our own experiences, both pressing into the same direction of a divorce of freedom from politics, I think the reader may believe he has �ead only an old truism when I said that the raison d' etre of politics is freedom and that this freedom is primarily experienced in action. In the following I + +shall do no more than reflect on this old truism. + +II + +Freedom as related to politics is not a phenomenon of the will. We deal here not with the liberum arbitrium, a freedom of choice that arbitrates and decides between two given things, one good and one evil, and whose choice is predetermined by motive which has only to be argued to start its operation-"And therefore, since I cannot prove a lover,/ To entertain these fair well-spoken days,/ I am determined to prove a villain,/ And hate the idle pleasures of these days." Rather it is, to remain with Shakespeare, the freedom of Brutus : "That this shall be or we will fall for it," that is, the freedom to call something into being which did not exist before, which was not given, not even as an object of cognition or imagination, and which therefore, strictly speaking, could not be known. Action, to be free, must be free from motive on one side, from its intended goal as a predictable effect on the other. This is not to say that motives and aims are not important factors in every single act, but they are its determining factors, and action is free to the extent that it is able to transcend them. Action insofar as it is determined is guided by a future aim whose desirability the intellect has grasped before the will wills it, whereby the intellect calls upon the will, since only the will can dictate action-to paraphrase a char- + +acteristic description of this process by Duns Scotus.10 The aim of action varies and depends upon the changing circumstances of the world; to recognize the aim is not a matter of freedom, but of right or wrong judgment. Will, seen as a distinct and separate human faculty, follows judgment, i.e., cognition of the right aim, and then commands its execution. The power to command, to dictate action, is not a matter of freedom but a question of strength or + +weakness. + +Action insofar as it is free is neither under the guidance of the intellect nor under the dictate of the will-although it needs both for the execution of any particular goal-but springs from something altogether different which (following Montesquieu's famous analysis of forms of government) I shall call a principle. Principles do not operate from within the self as motives do--"mine own deformity" or my "fair proportion"-but inspire, as it were, from without; and they are much too general to prescribe particular goals, although every particular aim can be judged in the light of its principle once the act has been started. For, unlike the judgment of the intellect which precedes action, and unlike the command of the will which initiates it, the inspiring principle becomes fully manifest only in the performing act itself; yet while the merits of judgment lose their validity, and the strength of the commanding will exhausts itself, in the course of the act which they execute in cooperation, the principle which inspired it loses nothing in strength or validity through execution. In distinction from its goal, the principle of an action can be repeated time and again, it is inexhaustible, and in distinction from its motive, the validity of a principle is universal, it is not bound to any particular person or to any particular group. However, the manifestation of principles comes about only through action, they are manifest in the world as long as the action lasts, but no longer. Such principles are honor or glory, love of equality, which Montesquieu called virtue, or distinction or excellence-the Greek dE! aptam!m, ("always strive to do your best and to be the best of all" ), but also fear or distrust or hatred. Freedom or its opposite appears in the world whenever such principles are actualized; the appearance of freedom, like the manifestation of + +principles, coincides with the performing act. Men are free-as distinguished from their possessing the gift for freedom-as long as they act, neither before nor after; for to be free and to act are the + +same. + +Freedom as inherent in action is perhaps best illustrated by Machiavelli's concept of virtu, the excellence with which man answers the opportunities the world opens up before him in the guise of fortuna. Its meaning is best rendered by "virtuosity," that is, an excellence we attribute to the performing arts (as distinguished from the creative arts of making), where the accomplishment lies in the performance itself and not in an end product which outlasts the activity that brought it into existence and becomes independent of it. The virtuoso-ship of Machiavelli's virtu somehow reminds us of the fact, although Machiavelli hardly knew it, that the Greeks always used such metaphors as flute-playing, dancing, healing, and seafaring to distinguish political from other activities, that is, that they drew their analogies from those arts in which + +virtuosity of performance is decisive. + +Since all acting contains an element of virtuosity, and because virtuosity is the excellence we ascribe to the performing arts, politics has often been defined as an art. This, of course, is not a definition but a metaphor, and the metaphor becomes completely false if one falls into the common error of regarding the state or government as a work of art, as a kind of collective masterpiece. In the sense of the creative arts, which bring forth something tangible and reify human thought to such an extent that the produced thing possesses an existence of its own, politics is the exact opposite of an art-which incidentally does not mean that it is a science. Political institutions, no matter how well or how badly designed, depend for continued existence upon acting men; their conservation is achieved by the same means that brought them into being. Independent existence marks the work of art as a product of making; utter dependence upon further acts to keep it in existence marks + +The point here is not whether the creative artist is free in the process of creation, but that the creative process is not displayed + +in public and not destined to appear in the world. Hence the element of freedom, certainly present in the creative arts, remains hidden; it is not the free creative process which finally appears and matters for the world, but the work of art itself, the end product of the process . The performing arts, on the contrary, have indeed a strong affinity with politics. Performing artists--dancers, play-actors, musicians, and the like-need an audience to show their virtuosity, just as acting men need the presence of others before whom they can appear; both need a publicly organized space for their "work," and both depend upon others for the performance itself. Such a space of appearances is not to be taken for granted wherever men live together in a community. The Greek polis once was precisely that "form of government" which provided men with a space of appearances where they could act, with a kind of + +theater where freedom could appear. + +To use the word "political" in the sense of the Greek polis is neither arbitrary nor far-fetched. Not only etymologically and not .only for the learned does the very word, which in all European languages still derives from the historically unique organization of the Greek city-state, echo the experiences of the community which first discovered the essence and the realm of the political. It is indeed difficult and even misleading to talk about politics and its innermost principles without drawing to some extent upon the experiences of Greek and Roman antiquity, and this for no other reason than that men have never, either before or after, thought so highly of political activity and bestowed so much dignity upon its realm. As regards the relation of freedom to politics, there is the additional reason that only ancient political communities were founded for the express purpose of serving the free-those who were neither slaves, subject to coercion by others, nor laborers, driven and urged on by the necessities of life. If, then, we understand the political in the sense of the polis, its end or raison d'erre would be to establish and keep in existence a space where freedom as virtuosity can appear. This is the realm where freedom is a worldly reality, tangible in words which can be heard, in deeds which can be seen, and in events which are talked about, remem- + +bered, and turned into stories before they are finally incorporated into the great storybook of human history. Whatever occurs in this space of appearances is political by definition, even when it is not a direct product of action. What remains outside it, such as the great feats of barbarian empires, may be impressive and note- + +worthy, but it is not political, strictly speaking. + +Every attempt to derive the concept of freedom from experiences in the political realm sounds strange and startling because all our theories in these matters are dominated by the notion that freedom is an attribute of will and thought much rather than of action. And this priority is not merely derived from the notion that every act must psychologically be preceded by a cognitive act of the intellect and a command of the will to carry out its decision, but also, and perhaps even primarily, because it is held that "perfect liberty is incompatible with the existence of society," that it can be tolerated in its perfection only outside the realm of human affairs. This current argument does not hold-what perhaps is true-that it is in the nature of thought to need more freedom than does any other activity of men, but rather that thinking in itself is not dangerous, so that only action needs to be restrained: "No one pretends that actions should be as free as opinions." 11 This, of course, belongs among the fundamental tenets of liberalism, which, its name notwithstanding, has done its share to banish the notion of liberty from the political realm. For politics, according to the same philosophy, must be concerned almost exclusively with the maintenance of life and the safeguarding of its interests. Now, where life is at stake all action is by definition under the sway of necessity, and the proper realm to take care of life's necessities is the gigantic and still increasing sphere of social and economic life whose administration has overshadowed the political realm ever since the beginning of the modem age. Only foreign affairs, because the relationships between nations still harbor hostilities and sympathies which cannot be reduced to economic factors, seem to be left as a purely political domain. And even here the prevailing tendency is to consider international power problems and rivalries as ultimately + +Yet just as we, despite all theories and isms, still believe that to say "Freedom is the raison d'etre of politics" is no more than a truism, so do we, in spite of our apparently exclusive concern with life, still hold as a matter of course that courage is one of the cardinal political virtues, although-if all this were a matter of consistency, which it obviously is not-we should be the first to condemn courage as the foolish and even vicious contempt for life and its interests, that is, for the allegedly highest of all goods . . Courage is a big word, and I do not mean the daring of adventure which gladly risks life for the sake of being as thoroughly and intensely alive as one can be only in the face of danger and death. Temerity is no less concerned with life than is cowardice. Courage, which we still believe to be indispensable for political action, and which Churchill once called "the first of human qualities, because it is the quality which guarantees all others," does not gratify our individual sense of vitality but is demanded of us by the very nature of the public realm. For this world of ours, because it existed before us and is meant to outlast our lives in it, simply cannot afford to give primary concern to individual lives and the interests connected with them; as such the public realm stands in the sharpest possible contrast to our private domain, where, in the protection of family and home, everything serves and must serve the security of the life process. It requires courage even to leave the protective security of our four walls and enter the public realm, not because of particular dangers which may lie in wait for us, but because we have arrived in a realm where the concern for life has lost its validity. Courage liberates men from their worry about life for the freedom of the world. Courage is indispensable because in politics not life + +but the world is at stake. + +Ill + +Obviously this notion of an interdependence of freedom and politics stands in contradiction to the social theories of the modern age. Unfortunately it does not follow that we need only to revert + +to older, pre-modern traditions and theories. Indeed, the greatest difficulty in reaching an understanding of what freedom is arises from the fact that a simple return to tradition, and especially to what we are wont to call the great tradition, does not help us. Neither the philosophical concept of freedom as it first arose in late antiquity, where freedom became a phenomenon of thought by which man could, as it were, reason himself Otlt of the world, nor the Christian and modern notion of free will has any ground in political experience. Our philosophical tradition is almost unanimous in holding that freedom begins where men have left the realm of political life inhabited by the many, and that it is not experienced in association with others but in intercourse with one's self-whether in the form of an inner dialogue which, since Socrates, we call thinking, or in a conflict within myself, the inner strife between what I would and what I do, whose murderous dialectics disclosed first to Paul and then to Augustine the equivo- + +calities and impotence of the human heart. + +For the history of the problem of freedom, Christian tradition has indeed become the decisive factor. We almost automatically equate freedom with free will, that is, with a faculty virtually unknown to classical antiquity. For will, as Christianity discovered it, had so little in common with the well-known capacities to desire, to intend, and to aim at, that it claimed attention only after it had come into conflict with them. If freedom were actually nothing but a phenomenon of the will, we would have to conclude that the ancients did not know freedom. This, of course, is absurd, but if one wished to assert it he could argue what I have mentioned before, namely, that the idea of freedom played no role in philosophy prior to Augustine. The reason for this striking fact is that, in Greek as well as Roman antiquity, freedom was an exclusively political concept, indeed the quintessence of the city-state and of citizenship. Our philosophical tradition of political thought, beginning with Parmenides and Plato, was founded explicitly in opposition to this polis and its citizenship. The way of life chosen by the philosopher was understood in opposition to the f3Lo., 7ToAmKo<>, the political way of life. Freedom, therefore, the very center of poli- + +tics as the Greeks understood it, was an idea which almost by definition could not enter the framework of Greek philosophy. Only when the early Christians, and especially Paul, discovered a kind of freedom which had no relation to politics, could the concept of freedom enter the history of philosophy. Freedom became one of the chief problems of philosophy when it was experienced as something occurring in the intercourse between me and myself, and outside of the intercourse between men. Free will and freedom became synonymous notions, 12 and the presence of freedom was experienced in complete solitude, "where no man might hinder the hot contention wherein I had engaged with myself," the deadly conflict which took place in the "inner dwelling" of the soul and the + +dark "chamber of the heart." 13 + +Classical antiquity was by no means inexperienced in the phenomena of solitude; it knew well enough that solitary man is no longer one but two-in-one, that an intercourse between me and myself begins the moment the intercourse between me and my fellow men has been interrupted for no matter what reason. In addition to this dualism which is the existential condition of thought, classical philosophy since Plato had insisted on a dualism between soul and body whereby the human faculty of motion had been assigned to the soul, which was supposed to move the body as well as itself, and it was still within the range of Platonic thought to interpret this faculty as a rulership of the soul over the body. Yet the Augustinian solitude of "hot contention" within the soul itself was utterly unknown, for the fight in which he had become engaged was not between reason and pa�sion, between understanding and Ot�p.o'>, 14 that is, between two different human faculties, but it was a conflict within the will itself. And this duality within the self-same faculty had been known as the characteristic of thought, as the dialogue which I hold with myself. In other words, the two-in-one of solitude which sets the thought process into motion has the exactly opposite effect on the will: it paralyzes and locks it within itself; willing in solitude is always ve/le and nolle, to will and not to + +the more surprisingly as its very essence obviously is to command and be obeyed. Hence it appears to be a "monstrosity" that man may command himself and not be obeyed, a monstrosity which can be explained only by the simultaneous presence of an 1-will and an I-will-not.111 This, however, is already an interpretation by Augustine; the historical fact is that the phenomenon of the will originally manifested itself in the experience that what I would I do not, that there is such a thing as 1-will-and-cannot. What was unknown to antiquity was not that there is a possible 1-know-but-1-will-not, but that 1-will and l-ean are not the same-non hoc est velle, quod posse.16 For the 1-will-and-1-can was of course very familiar to the ancients. We need only remember how much Plato insisted that only those who knew how to rule themselves had the right to rule others and be freed from the obligation of obedience. And it is true that self-control has remained one of the specifically political virtues, if only because it is an outstanding phenomenon of virtuosity where 1-will and l-ean must be so well attuned that they practi- + +cally coincide. + +Had ancient philosophy known of a possible conflict between what I can and what J will, it would certainly have understood the phenomenon of freedom as an inherent quality of the l-ean, or it might conceivably have defined it as the coincidence of 1-will and l-ean; it certainly would not have thought of it as an attribute of the 1-will or 1-would. This assertion is no empty speculation; even the Euripidean conflict between reason and Ovp.o>, both simultaneously present in the soul, is a relatively late phenomenon. More typi<;al, and in our context more relevant, was the conviction that passion may blind men's reason but that once reason has succeeded in making itself heard there is no passion left to prevent man from doing what he knows is right. This conviction still underlies Socrates' teaching that virtue is a kind of knowledge, and our amazement that anybody could ever have thought that virtue was "rational," that it could be learned and taught, arises from our acquaintance with a will which is broken in itself, which wills and wills-not at the same time, much rather than from any superior in- + +In other words, will, will-power, and will-to-power are for us almost identical notions; the seat of power is to us the faculty of the will as known and experienced by man in his intercourse with himself. And for the sake of this will-power we have emasculated not only our reasoning and cognitive faculties but other more "practical" faculties as well. But is it not plain even to us that, in the words of Pindar, "this is the greatest grief: to stand with his feet outside the right and the beautiful one knows [forced away], by necessity"? 17 The necessity which prevents me from doing what I know and will may arise from the world, or from my own body, or from an insufficiency of talents, gifts, and qualities which are bestowed upon man by birth and over which he has hardly more power than he has over other circumstances; all these factors, the psychological ones not excluded, condition the person from the outside as far as the !-will and the 1-know, that is, the ego itself, are concerned; the power that meets these circumstances, that liberates, as it were, willing and knowing from their bondage to necessity is the l-ean. Only where the 1-will and the l-ean coincide does free- + +dom come to pass. + +There exists still another way to check our current notion of free will, born of a religious predicament and formulated in philosophical language, against the older, strictly political experiences of freedom. In the revival of political thought which accompanied the rise of the modern age, we may distinguish between those thinkers who can truly be called the fathers of political "science," since they took their cue from the new discoveries of the natural sciences-their greatest representative is Hobbes-and those who, relatively undisturbed by these typically modern developments, harkened back to the political thought of antiquity, not out of any predilection for the past as such but simply because the separation of church and state, of religion and politics, had given rise to an independent secular, political realm such as had been unknown since the fall of the Roman Empire. The greatest representative of this political secularism was Montesquieu, who, though indifferent to problems of a strictly philosophic nature, was deeply aware of the inadequacy of the Christian and the philosophers' concept of + +freedom for political purposes. In order to get rid of it, he expressly distinguished between philosophical and political freedom, and the difference consisted in that philosophy demands no more of freedom than the exercise of the will ( l' exercice de Ia volonte), independent of circumstances and of attainment of the goals the will has set. Political freedom, on the contrary, consists in being able to do what one ought to will (Ia liberte ne peut consister qu' a pouvoir faire ce que l'on doit vouloir-the emphasis is on pouvoir) .18 For Montesquieu as for the ancients it was obvious that an agent could no longer be called free when he lacked the capacity to do-whereby it is irrelevant whether this failure is caused by + +exterior or by interior circumstances. + +I chose the example of self-control because to us this is clearly a phenomenon of will and of will-power. The Greeks, more than any other people, have reflected on moderation and the necessity to tame the steeds of the soul, and yet they never became aware of the will as a distinct faculty, separate from other human capacities. Historically, men first discovered the will when t.hey experienced its impotence-and not its power, when they said with Paul: "For to will is present with me; but how to perform that which is good I find not." It is the same will of which Augustine complained that it seemed "no monstrousness [for it] partly to will, partly to nill"; and although he points out that this is "a disease of the mind," he also admits that this disease is, as it were, natural for a mind possessed of a will: "For the will commands that there be a will, it commands not something else but itself. . . . Were the will entire, it would not even command itself to be, because it would already be." 19 In other words, if man has a will at all, it must always appear as though there were two wills present in the same man, fighting with each other for power over his mind. Hence, the will is + +both powerful and impotent, free and unfree. + +When we speak of impotence and the limits set to will-power, we usually think of man's powerlessness with respect to the surrounding world. It is, therefore, of some importance to notice that in these early testimonies the will was not defeated by some overwhelming force of nature or circumstances; the contention which + +its appearance raised was neither the conflict between the one against the many nor the strife between body and mind. On the contrary, the relation of mind to body was for Augustine even the outstanding example for the enormous power inherent in the will: "The mind commands the body, and the body obeys instantly; the mind commands itself, and is resisted." 20 The body represents in this context the exterior world and is by no means identical with one's self. It is within one's self, in the "interior dwelling" (interior domus) , where Epictetus still believed man to be an absolute master, that the conflict between man and himself broke out and that the will was defeated. Christian will-power was discovered as an organ of self-liberation and immediately found wanting. It is as though the 1-will immediately paralyzed the l-ean, as though the moment men willed freedom, they lost their capacity to be free. In the deadly conflict with worldly desires and intentions from which will-power was supposed to liberate the self, the most willing seemed able to achieve was oppression. Because of the will's impotence, its incapacity to generate genuine power, its constant defeat in the struggle with the self, in which the power of the l-ean exhausted itself, the will-to-power turned at once into a will-tooppression. I can only hint here at the fatal consequences for political theory of this equation of freedom with the human capacity to will; it was one of the causes why even today we almost automatically equate power with oppression or, at least, with rule over + +others. + +However that may be, what we usually understand by will and will-power has grown out of this conflict between a willing and a performing self, out of the experience of an 1-will-and-cannot, which means that the 1-will, no matter what is willed, remains subject to the self, strikes back at it, spurs it on, incites it further, or is ruined by it. However far the will-to-power may reach out, and even if somebody possessed by it begins to conquer the whole world, the 1-will can never rid itself of the self; it always remains bound to it and, indeed, under its bondage. This bondage to the self distinguishes the 1-will from the 1-think, which also is carried on between me and myself but in whose dialogue the self is not the ob- + +ject of the activity of thought. The fact that the I-will has become so power-thirsty, that will and will-to-power have become practically identical, is perhaps due to its having been first experienced in its impotence. Tyranny at any rate, the only form of government which arises directly out of the I-will, owes its greedy cruelty to an egotism utterly absent from the utopian tyrannies of reason with which the philosophers wished to coerce men and which they con- + +ceived on the model of the I-think. + +I have said that the philosophers first began to show an interest in the problem of freedom when freedom was no longer experienced in acting and in associating with others but in willing and in the intercourse with one's self, when, briefly, freedom had become free will. Since then, freedom has been a philosophical problem of the first order; as such it was applied to the political realm and thus has become a political problem as well. Because of the philosophic shift from action to will-power, from freedom as a state of being manifest in action to the liberum arbitrium, the ideal of freedom ceased to be virtuosity in the sense we mentioned before and became sovereignty, the ideal of a free will, independent from others and eventually prevailing against them. The philosophic ancestry of our current political notion of freedom is still quite manifest in eighteenth-century political writers, when, for instance, Thomas Paine insisted that "to be free it is sufficient [for man] that he wills it," a word which Lafayette applied to the nation-state : "Pour + +qu'une nation soit libre, il suffit qu'elle veuille l'etre." + +Obviously such words echo the political philosophy of Jean-Jacques Rousseau, who has remained the most consistent representative of the theory of sovereignty, which he derived directly from the will, so that he could conceive of political power in the strict image of individual will-power. He argued against Montesquieu that power must be sovereign, that is, indivisible, because "a divided will would be inconceivable." He did not shun the consequences of this extreme individualism, and he held that in an ideal state "the citizens had no communications one with another," that in order to avoid factions "each citizen should think only his own thoughts." In reality Rousseau's theory stands refuted for the + +simple reason that "it is absurd for the will to bind itself for the future"; :!l a community actually founded on this sovereign will would be built not on sand but on quicksand. All political business is, and always has been, transacted within an elaborate framework of ties and bonds for the future-such as laws and constitutions, treaties and alliances-all of which derive in the last instance from the faculty to promise and to keep promises in the face of the essential uncertainties of the future. A state, moreover, in which there is no communication between the citizens and where each man thinks only his own thoughts is by definition a tyranny. That the faculty of will and will-power in and by itself, unconnected with any other faculties, is an essentially nonpolitical and even antipolitical capacity is perhaps nowhere else so manifest as in the absurdities to which Rousseau was driven and in the curious cheer- + +fulness with which he accepted them. + +Politically, this identification of freedom with sovereignty is perhaps the most pernicious and dangerous consequence of the philosophical equation of freedom and free will. For it leads either to a denial of human freedom-namely, if it is realized that whatever men may be, they are never sovereign-or to the insight that the freedom of one man, or a group, or a body politic can be purchased only at the price of the freedom, i.e., the sovereignty, of all others. Within the conceptual framework of traditional philosophy, it is indeed very difficult to understand how freedom and non-sovereignty can exist together or, to put it another way, how freedom could have been given to men under the condition of non-sovereignty. Actually it is as unrealistic to deny freedom because of the fact of human non-sovereignty as it is dangerous to believe that one can be free-as an individual or as a group-only if he is sovereign. The famous sovereignty of political bodies has always been an illusion, which, moreover, can be maintained only by the instruments of violence, that is, with essentially nonpolitical means. Under human conditions, which are determined by the fact that not man but men live on the earth, freedom and sovereignty are so little identical that they cannot even exist simultaneously. Where men wish to be sovereign, as individuals or as organized groups, they + +must submit to the oppression of the will, be this the individual will with which I force myself, or the "general will" of an organized group. If men wish to be free, it is precisely sovereignty they must + +renounce. + +IV + +Since the whole problem of freedom arises for us in the horizon of Christian traditions on one hand, and of an originally antipolitical philosophic tradition on the other, we find it difficult to realize that there may exist a freedom which is not an attribute of the will but an accessory of doing and acting. Let us therefore go back once more to antiquity, i.e., to its political and pre-philosophical traditions, certainly not for the sake of erudition and not even because of the continuity of our tradition, but merely because a freedom experienced in the process of acting and nothing elsethough, of course, mankind never lost this experience altogetherhas never again been articulated with the same classical clarity. However, for reasons we mentioned before and which we cannot discuss here, this articulation is nowhere more difficult to grasp than in the writings of the philosophers. It would of course lead us too far to try to distill, as it were, adequate concepts from the body of non-philosophical literature, from poetic, dramatic, historical, and political writings, whose articulation lifts experiences into a realm of splendor which is not the realm of conceptual thought. And for our purposes this is not necessary. For whatever ancient literature, Greek as well as Latin, has to tell us about these matters is ultimately rooted in the curious fact that both the Greek and the Latin language possess two verbs to designate what we uniformly call "to act." The two Greek words are apxnv: to begin, to lead, and, finally, to rule; and 7rpaTwv : to carry something through. The corresponding Latin verbs are agere: to set something in motion; and gerere, which is hard to translate and somehow means the enduring and supporting continuation of past acts whose results are the res gestae, the deeds and events we call historical. In both instances + +action occurs in two different stages; its first stage is a beginning by which something new comes into the world. The Greek word tip;x.ttv, which covers beginning, leading, ruling, that is, the outstanding qualities of the free man, bears witness to an experience in which being free and the capacity to begin something new coincided. Freedom, as we would say today, was experienced in spontaneity. The manifold meaning of apx.uv indicates the following: only those could begin something new who were already rulers (i.e., household heads who ruled over slaves and family) and had thus liberated themselves from the necessities of life for enterprises in distant lands or citizenship in the polis; in either case, they no longer ruled, but were rulers among rulers, moving among their peers, whose help they enlisted as leaders in order to begin something new, to start a new enterprise; for only with the help of others could the ap;x.wv, the ruler, beginner and leader, really act, 7rpaTTttv, carry through + +whatever he had started to do. + +In Latin, to be free and to begin are also interconnected, though in a different way. Roman freedom was a legacy bequeathed by the founders of Rome to the Roman people; their freedom was tied to the beginning their forefathers had established by founding the city, whose affairs the descendants had to manage, whose consequences they had to bear, and whose foundations they had to "augment." All these together are the res gestae of the Roman republic. Roman historiography therefore, essentially as political as Greek historiography, never was content with the mere narration of great deeds and events; unlike Thucydides or Herodotus, the Roman historians always felt bound to the beginning of Roman history, because this beginning contained the authentic element of Roman freedom and thus made their history political; whatever they had to relate, they started ab urbe condita, with the founda- + +tion of the city, the guaranty of Roman freedom. + +I have already mentioned that the ancient concept of freedom played no role in Greek philosophy precisely because of its exclusively political origin. Roman writers, it is true, rebelled occasionally against the anti-political tendencies of the Socratic school, but their strange lack of philosophic talent apparently prevented + +their finding a theoretical concept of freedom which could have been adequate to their own experiences and to the great institutions of liberty present in the Roman res publica. If the history of ideas were as consistent as its historians sometimes imagine, we should have even less hope of finding a valid political idea of freedom in Augustine, the great Christian thinker who in fact introduced Paul's free will, along with its perplexities, into the history of philosophy. Yet we find in Augustine not only the discussion of freedom as liberum arbitriwn, though this discussion became decisive for the tradition, but also an entirely differently conceived notion which characteristically appears in his only political treatise, in De Civitate Dei. In the City of God Augustine, as is only natural, speaks more from the background of specifically Roman experiences than in any of his other writings, and freedom is conceived there not as an inner human disposition but as a character of human existence in the world. Man does not possess freedom so much as he, or better his coming into the world, is equated with the appearance of freedom in the universe; man is free because he is a beginning and was so created after the universe had already come into existence : [lnitium] ut esset, creatus est homo, ante quem nemo fuit.22 In the birth of each man this initial beginning is reaffirmed, because in each instance something new comes into an already existing world which will continue to exist after each individual's death. Because he is a beginning, man can begin; to be human and to be free are one and the same. God created man in order to introduce into the + +world the faculty of beginning: freedom. + +The strong anti-political tendencies of early Christianity are so familiar that the notion of a Christian thinker's having been the first to formulate the philosophical implications of the ancient political idea of freedom strikes us as almost paradoxical. The only explanation that comes to mind is that Augustine was a Roman as well as a Christian, and that in this part of his work he formulated the central political experience of Roman antiquity, which was that freedom qua beginning became manifest in the act of foundation. Yet I am convinced that this impression would considerab:y change if the sayings of Jesus of Nazareth were taken more se�iously in + +their philosophic implications. We find in these parts of the New Testament an extraordinary understanding of freedom, and particularly of the power inherent in human freedom; but the human capacity which corresponds to this power, which, in the words of the Gospel, is capable of removing mountains, is not will but faith. The work of faith, actually its product, is what the gospels called "miracles," a word with many meanings in the New Testament and difficult to understand. We can neglect the difficulties here and refer only to those passages where miracles are clearly not supernatural events but only what all miracles, those performed by men no less than those performed by a divine agent, always must be, namely, interruptions of some natural series of events, of some automatic process, in whose context they constitute the wholly unex- + +pected. + +No doubt human life, placed on the earth, is surrounded by automatic processes-by the natural processes of the earth, which, in turn, are surrounded by cosmic processes, and we ourselves are driven by similar forces insofar as we too are a part of organic nature. Our political life, moreover, despite its being the realm of action, also takes place in the midst of processes which we call historical and which tend to become as automatic as natural or cosmic processes, although they were started by men. The truth is that automatism is inherent in all processes, no matter what their origin may be-which is why no single act, and no single event, can ever, once and for all, deliver and save a man, or a nation, or mankind. It is in the nature of the automatic processes to which man is subject, but within and against which he can assert himself through action, that they can only spell ruin to human life. Once man-made, historical processes have become automatic, they are no less ruinous than the natural life process that drives our organism and which in its own terms, that is, biologically, leads from being to non-being, from birth to death. The historical sciences know only too well such cases of petrified and hopelessly declining civilizations where doom seems foreordained, like a biological necessity, and since such historical processes of stagnation can last and creep on for centuries, they even occupy by far the largest + +been relatively short in the history of mankind. + +What usually remains intact in the epochs of petrification and foreordained doom is the faculty of freedom itself, the sheer capacity to begin, which animates and inspires all human activities and is the hidden source of production of all great and beautiful things. But so long as this source remains hidden, freedom is not a worldly, tangible reality; that is, it is not political. Because the source of freedom remains present even when political life has become petrified and political action impotent to interrupt automatic processes, freedom can so easily be mistaken for an essentially nonpolitical phenomenon; in such circumstances, freedom is not experienced as a mode of being with its own kind of "virtue" and virtuosity, but as a supreme gift which only man, of all earthly creatures, seems to have received, of which we can find traces and signs in almost all his activities, but which, nevertheless, develops fully only when action has created its own worldly space where it can come out of + +hiding, as it were, and make its appearance. + +Every act, seen from the perspective not of the agent but of the process in whose framework it occurs and whose automatism it interrupts, is a "miracle"-that is, something which could not be expected. If it is true that action and beginning are essentially the same, it follows that a capacity for performing miracles must likewise be within the range of human faculties. This sounds stranger than it actually is. It is in the very nature of every new beginning that it breaks into the world as an "infinite improbability," and yet it is precisely this infinitely improbable which actually constitutes the very texture of everything we call real. Our whole existence rests, after all, on a chain of miracles, as it were-the coming into being of the earth, the development of organic life on it, the evolution of mankind out of the animal species. For from the viewpoint of the processes in the universe and in nature, and their statistically overwhelming probabilities, the coming into being of the earth out of cosmic processes, the formation of organic life out of inorganic processes, the evolution of man, finally, out of the processes of organic life are all "infinite improbabilities," they are + +"miracles" in everyday language. It is because of this element of the "miraculous" present in all reality that events, no matter how well anticipated in fear or hope, strike us with a shock of surprise once they have come to pass. The very impact of an event is never wholly explicable; its factuality transcends in principle all anticipation. The experience which tells us that events are miracles is neither arbitrary nor sophisticated; it is, on the contrary, most natural and, indeed, in ordinary life almost commonplace. Without this commonplace experience, the part assigned by religion to supernatural miracles would be well-nigh incomprehensible. + +I chose the example of natural processes which are interrupted by the advent of some "infinite improbability" in order to illustrate that what we call real in ordinary experience has mostly come into existence through coincidences which are stranger than fiction. Of course the example has its limitations and cannot be simply applied to the realm of human affairs. It would be sheer superstition to hope for miracles, for the "infinitely improbable," in the context of automatic historical or political processes, although even this can never be completely excluded. History, in contradistinction to nature, is full of events; here the miracle of accident and infinite improbability occurs so frequently that it seems strange to speak of miracles at all. But the reason for this frequency is merely that historical processes are created and constantly interrupted by human initiative, by the initium man is insofar as he is an acting being. Hence it is not in the least superstitious, it is even a counsel of realism, to look for the unforeseeable and unpredictable, to be prepared for and to expect "miracles" in the political realm. And the more heavily the scales are weighted in favor of disaster, the more miraculous will the deed done in freedom appear; for it is disaster, not salvation, which always happens automatically and + +therefore always must appear to be irresistible. + +Objectively, that is, seen from the outside and without taking into account that man is a beginning and a beginner, the chances that tomorrow will be like yesterday are always overwhelming. Not quite so overwhelming, to be sure, but very nearly so as the chances were that no earth would ever rise out of cosmic occur- + +rences, that no life would develop out of inorganic processes, and that no man would emerge out of the evolution of animal life. The decisive difference between the "infinite improbabilities" on which the reality of our earthly life rests and the miraculous character inherent in those events which establish historical reality is that, in the realm of human affairs, we know the author of the "miracles." It is men who perform them-men who because they have received the twofold gift of freedom and action can establish a reality of + +their own. + +THE CRISIS IN + +EDUCATION + +I + +T + +HE general crisis that has overtaken the modem world everywhere and in almost every sphere of life manifests itself differently in each country, involving different areas and taking on different forms. In America, one of its most characteristic and suggestive aspects is the recurring crisis in education that, during the last decade at least, has become a political problem of the first magnitude, reported on almost daily in the newspapers. To be sure, no great imagination is required to detect the dangers of a constantly progressing decline of elementary standards throughout the entire school system, and the seriousness of the trouble has been properly underlined by the countless unavailing efforts of the educational authorities to stem the tide. Still, if one compares this crisis in education with the political experiences of other countries in the twentieth century, with the revolutionary turmoil after the First World War, with concentration and extermination camps, or even with the profound malaise which, appearances of prosperity to the contrary not- + +withstanding, has spread throughout Europe ever since the end of the Second World War, it is somewhat difficult to take a crisis in education as seriously as it deserves. It is tempting indeed to regard it as a local phenomenon, unconnected with the larger issues of the century, to be blamed on certain peculiarities of life in the United States which are not likely to find a counterpart in other + +parts of the world. + +Yet, if this were true, the crisis in our school system would not have become a political issue and the educational authorities would not have been unable to deal with it in time. Certainly more is involved here than the puzzling question of why Johnny can't read. Moreover, there is always a temptation to believe that we are dealing with specific problems confined within historical and national boundaries and of importance only to those immediately affected. It is precisely this belief that in our time has consistently proved false. One can take it as a general rule in this century that whatever is possible in one country may in the foreseeable future be + +equally possible in almost any other. + +Aside from these general reasons that would make it seem advisable for the layman to be concerned with trouble in fields about which, in the specialist's sense, he may know nothing (and this, since I am not a professional educator, is of course my case when I deal with a crisis in education) , there is another even more cogent reason for his concerning himself with a critical situation in which he is not immediately involved. And that is the opportunity, provided by the very fact of crisis-which tears away fa�ades and obliterates prejudices-to explore and inquire into whatever has been laid bare of the essence of the matter, and the essence of education is natality, the fact that human beings are born into the world. The disappearance of prejudices simply means that we have lost the answers on which we ordinarily rely without even realizing they were originally answers to questions. A crisis forces us back to the questions themselves and requires from us either new or old answers, but in any case direct judgments. A crisis becomes a disaster only when we respond to it with preformed judgments, that is, with prejudices. Such an attitude not only sharpens the + +portunity for reflection it provides. + +However clearly a general problem may present itself in a crisis, it is nevertheless impossible ever to isolate completely the universal element from the concrete and specific circumstances in which it makes its appearance. Though the crisis in education may affect the whole world, it is characteristic that we find its most extreme form in America, the reason being that perhaps only in America could a crisis in education actually become a factor in politics. In America, as a matter of fact, education plays a different and, politically, incomparably more important role than in other countries. Technically, of course, the explanation lies in the fact that America has always been a land of immigrants; it is obvious that the enormously difficult melting together of the most diverse ethnic groups-never fully successful but continuously succeeding beyond expectation--can only be accomplished through the schooling, education, and Americanization of the immigrants' children. Since for most of these children English is not their mother tongue but has to be learned in school, schools must obviously assume functions which in a nation-state would be performed as a + +matter of course in the home. + +More decisive, however, for our considerations is the role that continuous immigration plays in the country's political consciousness and frame of mind. America is not simply a colonial country in need of immigrants to populate the land, though independent of them in its political structure. For America the determining factor has always been the motto printed on every dollar bill : Novus Ordo Seclorum, A New Order of the World. The immigrants, the newcomers, are a guarantee to the country that it represents the new crder. The meaning of this new order, this founding of a new world against the old, was and is the doing away with poverty and oppression. But at the same time its magnificence consists in the fact that from the beginning this new order did not shut itself off from the outside world-as has elsewhere been the custom in the founding of utopias-in order to confront it with a perfect model, nor was its purpose to enforce imperial claims or to be preached as an evangel + +to others. Rather its relation to the outside world has been characterized from the start by the fact that this republic, which planned to abolish poverty and slavery, welcomed all the poor and enslaved of the earth. In the words spoken by John Adams in 1765-that is, before the Declaration of Independence-"! always consider the settlement of America as the opening of a grand scheme and design in Providence for the illumination and emancipation of the slavish part of mankind all over the earth." This is the basic intent or the basic law in accordance with which America began her + +historical and political existence. + +The extraordinary enthusiasm for what is new, which is shown in almost every aspect of American daily life, and the concomitant trust in an "indefinite perfectibility"-which Tocqueville noted as the credo of the common "uninstructed man" and which as such antedates by almost a hundred years the development in other countries of the West-would presumably have resulted in any case in greater attention paid and greater significance ascribed to the newcomers by birth, that is, the children, whom, when they had outgrown their childhood and were about to enter the community of adults as young people, the Greeks simply called oi viot, the new ones. There is the additional fact, however, a fact that has become decisive for the meaning of education, that this pathos of the new, though it is considerably older than the eighteenth century, only developed conceptually and politically in that century. From this source there was derived at the start an educational ideal, tinged with Rousseauism and in fact directly influenced by Rousseau, in which education became an instrument of politics, and political + +activity itself was conceived of as a form of education. + +The role played by education in all political utopias from ancient times onward shows how natural it seems to start a new world with those who are by birth and nature new. So far as politics is concerned, this involves of course a serious misconception: instead of joining with one's equals in assuming the effort of persuasion and running the risk of failure, there is dictatorial intervention, based upon the absolute superiority of the adult, and the attempt to produce the new as a fait accompli, that is, as though the new already + +existed. For this reason, in Europe, the belief that one must begin with the children if one wishes to produce new conditions has remained principally the monopoly of revolutionary movements of tyrannical cast which, when they carne to power, took the children away from their parents and simply indoctrinated them. Education can play no part in politics, because in politics we always have to deal with those who are already educated. Whoever wants to educate adults really wants to act as their guardian and prevent them from political activity. Since one cannot educate adults, the word "education" has an evil sound in politics; there is a pretense of education, when the real purpose is coercion without the use of force. He who seriously wants to create a new political order through education, that is, neither through force and constraint nor through persuasion, must draw the dreadful Platonic conclusion : the banishment of all older people from the state that is to be founded. But even the children one wishes to educate to be citizens of a utopian morrow are actually denied their own future role in the body politic, for, from the standpoint of the new ones, whatever new the adult world may propose is necessarily older than they themselves. It is in the very nature of the human condition that each new generation grows into an old world, so that to prepare a new generation for a new world can only mean that one wishes to strike from + +the newcomers' hands their own chance at the new. + +All this is by no means the case in America, and it is exactly this fact that makes it so hard to judge these questions correctly here. The political role that education actually plays in a land of immigrants, the fact that the schools not only serve to Americanize the children but affect their parents as well, that here in fact one helps to shed an old world and to enter into a new one, encourages the illusion that a new world is being built through the education of the children. Of course the true situation is not this at all. The world into which children are introduced, even in America, is an old world, that is, a pre-existing world, constructed by the living and the dead, and it is new o:1ly for those who have newly entered it by immigration. But here illusion is stronger than reality because it springs directly from a basic American experience, the experience + +that a new order can be founded, and what is more, founded with full consciousness of a historical continuum, for the phrase "New World" gains its meaning from the Old World, which, however admirable on other scores, was rejected because it could find no + +solution for poverty and oppression. + +Now in respect to education itself the illusion arising from the pathos of the new has produced its most serious consequences only in our own century. It has first of all made it possible for that complex of modern educational theories which originated in Middle Europe and consists of an astounding hodgepodge of sense and nonsense to accomplish, under the banner of progressive education, a most radical revolution in the whole system of education. What in Europe has remained an experiment, tested out here and there in single schools and isolated educational institutions and then gradually extending its influences in certain quarters, in America about twenty-five years ago completely overthrew, as though from one day to the next, all traditions and all the established methods of teaching and learning. I shall not go into details, and I leave out of account private schools and especially the Roman Catholic parochial school system. The significant fact is that for the sake of certain theories, good or bad, all the rules of sound human reason were thrust aside. Such a procedure is always of great and pernicious significance, especially in a country that relies so extensively on common sense in its political life. Whenever in political questions sound human reason fails or gives up the attempt to supply answers we are faced by a crisis; for this kind of reason is really that common sense by virtue of which we and our five individual senses are fitted into a single world common to us all and by the aid of which we move about in it. The disappearance of common sense in the present day is the surest sign of the presentday crisis. In every crisis a piece of the world, something common to us all, is destroyed. The failure of common sense, like a divining + +In any case the answer to the question of why Johnny can't read or to the more general question of why the scholastic standards of the average American school lag so very far behind the average + +standards in actually all the countries of Europe is not, unfortunately, simply that this country is young and has not yet caught up with the standards of the Old World but, on the contrary, that this country in this particular field is the most "advanced" and most modern in the world. And this is true in a double sense : nowhere have the education problems of a mass society become so acute, and nowhere else have the most modern theories in the realm of pedagogy been so uncritically and slavishly accepted. Thus the crisis in American education, on the one hand, announces the bankruptcy of progressive education and, on the other, presents a problem of immense difficulty because it has arisen under the con- + +ditions and in response to the demands of a mass society. + +In this connection we must bear in mind another more general factor which did not, to be sure, cause the crisis but which has aggravated it to a remarkable degree, and this is the unique role the concept of equality plays and always has played in American life. Much more is involved in this than equality before the law, more too than the leveling of class distinctions, more even than what is expressed in the phrase "equality of opportunity," though that has a greater significance in this connection because in the American view a right to education is one of the inalienable civic rights. This last has been decisive for the structure of the publicschool system in that secondary schools in the European sense exist only as exceptions. Since compulsory school attendance extends to the age of sixteen, every child must enter high school, and the high school therefore is basically a kind of continuation of primary school. As a result of this lack of a secondary school the preparation for the college course has to be supplied by the colleges themselves, whose curricula therefore suffer from a chronic overload, + +which in turn affects the quality of the work done there. + +At first glance one might perhaps think that this anomaly lies in the very nature of a mass society in which education is no longer a privilege of the wealthy classes. A glance at England, where, as everyone knows, secondary education has also been made available in recent years to all classes of the population, will show that this is not the case. For there at the end of primary school, with students + +at the age of eleven, has been instituted the dreaded examination that weeds out all but some ten per cent of the scholars suited for higher education. The rigor of this selection was not accepted even in England without protest; in America it would have been simply impossible . What is aimed at in England is "meritocracy," which is clearly once more the establishment of an oligarchy, this time not of wealth or of birth but of talent. But this means, even though people in England may not be altogether clear about it, that the country even under a socialist government will continue to be governed as it has been from time out of mind, that is, neither as a monarchy nor as a democracy but as an oligarchy or aristocracy-the latter in case one takes the view that the most gifted are also the best, which is by no means a certainty. In America such an almost physical division of the children into gifted and ungifted would be considered intolerable. Meritocracy contradicts the principle of equality, of an equalitarian democracy, no less than any other oligarchy. Thus what makes the educational crisis in American so especially acute is the political temper of the country, which of itself struggles to equalize or to erase as far as possible the difference between young and old, between the gifted and the ungifted, finally between children and adults, particularly between pupils and teachers. It is obvious that such an equalization can actually be accomplished only at the cost of the teacher's authority and at the expense of the gifted among the students. However, it is equally obvious, at least to anyone who has ever come in contact with the American educational system, that this difficulty, rooted in the political attitude of the country, also has great advantages, not simply of a human kind but educationally speaking as well; in any case these general factors cannot explain the crisis in which we presently find ourselves nor justify the measures through which that crisis has been precipitated. + +These ruinous measures can be schematically traced back to three basic assumptions, all of which are only too familiar. The + +first is that there exist a child's world and a society formed among children that are autonomous and must insofar as possible be left to them to govern. Adults are only there to help with this government. The authority that tells the individual child what to do and what not to do rests with the child group itself-and this produces, among other consequences, a situation in which the adult stands helpless before the individual child and out of contact with him. He can only tell him to do what he likes and then prevent the worst from happening. The real and normal relations between children and adults, arising from the fact that people of all ages are always simultaneously together in the world, are thus broken off. And so it is of the essence of this first basic assumption that it takes into ac- + +count only the group and not the individual child. + +As for the child in the group, he is of course rather worse off than before. For the authority of a group, even a child group, is always considerably stronger and more tyrannical than the severest authority of an individual person can ever be. If one looks at it from the standpoint of the individual child, his chances to rebel or to do anything on his own hook are practically nil; he no longer finds himself in a very unequal contest with a person who has, to be sure, absolute superiority over him but in contest with whom he can nevertheless count on the solidarity of other children, that is, of his own kind; rather he is in the position, hopeless by definition, of a minority of one confronted by the absolute majority of all the others. There are very few grown people who can endure such a situation, even when it is not supported by external means of com- + +pulsion; children are simply and utterly incapable of it. + +Therefore by being emancipated from the authority of adults the child has not been freed but has been subjected to a much more terrifying and truly tyrannical authority, the tyranny of the majorny. In any case the result is that the children have been so to speak banished from the world of grown-ups. They are either thrown back upon themselves or handed over to the tyranny of their own group, against which, because of its numerical superiority, they cannot rebel, with which, because they are children, they cannot reason, and out of which they cannot flee to any other world because + +the world of adults is barred to them. The reaction of the children to this pressure tends to be either conformism or juvenile delin- + +quency, and is frequently a mixture of both. + +The second basic assumption which has come into question in the present crisis has to do with teaching. Under the influence of modern psychology and the tenets of pragmatism, pedagogy bas developed into a science of teaching in general in such a way as to be wholly emancipated from the actual material to be taught. A teacher, so it was thought, is a man who can simply teach anything; his training is in teaching, not in the mastery of any particular subject. This attitude, as we shall presently see, is naturally very closely connected with a basic assumption about learning. Moreover, it has resulted in recent decades in a most serious neglect of the training of teachers in their own subjects, especially in the public high schools. Since the teacher does not need to know his own subject, it not infrequently happens that he is just one hour ahead of his class in knowledge. This in turn means not only that the students are actually left to their own resources but that the most legitimate source of the teacher's authority as the person who, turn it whatever way one will, still knows more and can do more than oneself is no longer effective. Thus the non-authoritarian teacher, who would like to abstain from all methods of compulsion because he is + +able to rely on his own authority, can no longer exist. + +But this pernicious role that pedagogy and the teachers' colleges are playing in the present crisis was only possible because of a modern theory about learning. This was, quite simply, the logical application of the third basic assumption in our context, an assumption which the modern world has held for centuries and which found its systematic conceptual expression in pragmatism. This basic assumption is that you can know and understand only what you have done yourself, and its application to education is as primitive as it is obvious: to substitute, insofar as possible, doing for learning. The reason that no importance was attached to the teacher's mastering his own subject was the wish to compel him to the exercise of the continuous activity of learning so that he would not, as they said, pass on "dead knowledge" but, instead, would + +constantly demonstrate how it is produced. The conscious intention was not to teach knowledge but to inculcate a skill, and the result was a kind of transformation of institutes for learning into vocational institutions which have been as successful in teaching how to drive a car or how to use a typewriter or, even more important for the "art" of living, how to get along with other people and to be popular, as they have been unable to make the children acquire the + +normal prerequisites of a standard curriculum. + +However, this description is at fault, not only because it obviously exaggerates in order to drive home a point, but because it fails to take into account how in this process special importance was attached to obliterating as far as possible the distinction between play and work-in favor of the former. Play was looked upon as the liveliest and most appropriate way for the child to behave in the world, as the only form of activity that evolves spontaneously from his existence as a child. Only what can be learned through play does justice to this liveliness. The child's characteristic activity, so it was thought, lies in play; learning in the old sense, by forcing a child into an attitude of passivity, compelled him to give up his + +own playful initiative. + +The close connection between these two things-the substitution of doing for learning and of playing for working-is directly illustrated by the teaching of languages: the child is to learn by speaking, that is by doing, not by studying grammar and syntax; in other words he is to learn a foreign language in the same way that as an infant he learned his own language : as though at play and in the uninterrupted continuity of simple existence. Quite apart from the question of whether this is possible or not-it is possible, to a limited degree, only when one can keep the child all day long in the foreign-speaking environment-it is perfectly clear that this procedure consciously attempts to keep the older child as far as possible at the infant level. The very thing that should prepare the child for the world of adults, the gradually acquired habit of work and of not-playing, is done away with in favor of the autonomy of + +whatever the validity of the pragmatic formula, its application to education, that is, to the way the child learns, tends to make absolute the world of childhood in just the same way that we noted in the case of the first basic assumption. Here, too, under the pretext of respecting the child's independence, he is debarred from the world of grown-ups and artificially kept in his own, so far as that can be called a world. This holding back of the child is artificial because it breaks off the natural relationship between grown-ups and children, which consists among other things in teaching and learning, and because at the same time it belies the fact that the child is a developing human being, that childhood is a temporary + +stage, a preparation for adulthood. + +The present crisis in America results from the recognition of the destructiveness of these basic assumptions and a desperate attempt to reform the entire educational system, that is, to transform it completely. In doing this what is actually being attempted-except for the plans for an immense increase in the facilities for training in the physical sciences and in technology-is nothing but restoration: teaching will once more be conducted with authority; play is to stop in school hours, and serious work is once more to be done; emphasis will shift from extracurricular skills to knowledge prescribed by the curriculum; finally there is even talk of transforming the present curricula for teachers so that the teachers themselves will have to learn something before being turned loose on the + +children. + +These proposed reforms, which arc still in the discussion stage and are of purely American interest, need not concern us here. Nor can I discuss the more technical, yet in the long run perhaps even more important question of how to reform the curricula of elementary and secondary schools in all countries so as to bring them up to the entirely new requirements of the present world. What is of importance to our argument is a twofold question. Which aspects of the modern world and its crisis have actually revealed themselves in the educational crisis, that is, what are the true reasons that for decades things could be said and done in such glaring contradiction to common sense? And, second, what can we learn from this crisis + +for the essence of education-not in the sense that one can always learn from mistakes what ought not to be done, but rather by reflecting on the role that education plays in every civilization, that is on the obligation that the existence of children entails for every + +human society. We shall begin with the second question. + +Ill + +A crisis in education would at any time give rise to serious concern even if it did not reflect, as in the present instance it does, a more general crisis and instability in modern society. For education belongs among the most elementary and necessary activities of human society, which never remains as it is but continuously renews itself through birth, through the arrival of new human beings. These newcomers, moreover, are not finished but in a state of becoming. Thus the child, the subject of education, has for the educator a double aspect: he is new in a world that is strange to him and he is in process of becoming, he is a new human being and he is a becoming human being. This double aspect is by no means self-evident and it does not apply to the animal forms of life; it corresponds to a double relationship, the relationship to the world on the one hand and to life on the other. The child shares the state of becoming with all living things; in respect to life and its development, the child is a human being in process of becoming, just as a kitten is a cat in process of becoming. But the child is new only in relation to a world that was there before him, that will continue after his death, and in which he is to spend his life. If the child were not a newcomer in this human world but simply a not yet finished living creature, education would be just a function of life and would need to consist in nothing save that concern for the sustenance of life and that training and practice in living that all animals assume in + +Human parents, however, have not only summoned their children into life through conception and birth, they have simultaneously introduced them into a world. In education they assume + +responsibility for both, for the life and development of the child and for the continuance of the world. These two responsibilities do not by any means coincide; they may indeed come into conflict with each other. The responsibility for the development of the child turns in a certain sense against the world : the child requires special prntection and care so that nothing destructive may happen to him from the world. But the world, too, needs protection to keep it from being overrun and destroyed by the onslaught of the + +new that bursts upon it with each new generation. + +Because the child must be protected against the world, his traditional place is in the family, whose adult members daily return back from the outside world and withdraw into the security of private life within four walls. These four walls, within which people's private family life is lived, constitute a shield against the world and specifically against the public aspect of the world. They enclose a secure place, without which no living thing can thrive. This holds good not only for the life of childhood but for human life in general. Wherever the latter is consistently exposed to the world with-Dut the protection of privacy and security its vital quality is destroyed. In the public world, common to all, persons count, and so does work, that is, the work of our hands that each of us contributes to our common world; but life qua life does not matter there. The world cannot be regardful of it, and it has to be hidden + +and protected from the world. + +Everything that lives, not vegetative life alone, emerges from darkness and, however strong its natural tendency to thrust itself into the light, it nevertheless needs the security of darkness to grow at all. This may indeed be the reason that children of famous parents so often turn out badly. Fame penetrates the four walls, invades their private space, bringing with it, especially in presentday conditions, the merciless glare of the public realm, which floods everything in the private lives of those concerned, so that the children no longer have a place of security where they can grow. But exactly the same destruction of the real living space occurs wherever the attempt is made to turn the children themselves into a kind of world. Among these peer groups then arises public life of a sort and, + +quite apart from the fact that it is not a real one and that the whole attempt is a sort of fraud, the damaging fact remains that children -that is, human beings in process of becoming but not yet complete-are thereby forced to expose themselves to the light of a + +public existence. + +That modern education, insofar as it attempts to establish a world of children, destroys the necessary conditions for vital development and growth seems obvious. But that such harm to the developing child should be the result of modern education strikes one as strauge indeed, for this education maintained that its exclusive aim was to serve the child and rebelled against the methods of the past because these had not sufficiently taken into account the child's inner nature and his needs. "The Century of the Child," as we may recall, was going to emancipate the child and free him from the standards derived from the adult world. Then how could it happen that the most elementary conditions of life necessary for the growth and development of the child were overlooked or simply not recognized? How could it happen that the child was exposed to what more than anything else characterized the adult world, its public aspect, after the decision had just been reached that the mistake in all past education had been to see the child as nothing + +but an undersized grown-up? + +The reason for this strange state of affairs has nothing directly to do with education; it is rather to be found in the judgments and prejudices about the nature of private life and public world and their relation to each other which have been characteristic of modern society since the beginning of modern times and which educators, when they finally began, relatively late, to modernize education, accepted as self-evident assumptions without being aware of the consequences they must necessarily have for the life of the child. It is the peculiarity of modern society, and by no means a matter of course, that it regards life, that is, the earthly life of the individual as well as the family, as the highest good; and for this reason, in contrast to all previous centuries, emancipated this life and all the activities that have to do with its preservation and enrichment from the concealment of privacy and exposed them tC' + +the light of the public world. This is the real meaning of the emancipation of workers and women, not as persons, to be sure, but insofar as they fulfill a necessary function in the life-process of + +society. + +The last to be affected by this process of emancipation were the children, and the very thing that had meant a true liberation for the workers and the women-because they were not only workers and women but persons as well, who therefore had a claim on the public world, that is, a right to see and be seen in it, to speak and be heard-was an abandonment and betrayal in the case of the children, who are still at the stage where the simple fact of life and growth outweighs the factor of personality. The more completely modern society discards the distinction between what is private and what is public, between what can thrive only in concealment and what needs to be shown to all in the full light of the public world, the more, that is, it introduces between the private and the public a social sphere in which the private is made public and vice versa, the harder it makes things for its children, who by nature require + +the security of concealment in order to mature undisturbed. + +However serious these infringements of the conditions for vital growth may be, it is certain that they were entirely unintentional; the central aim of all modern education efforts has been the welfare of the child, a fact that is, of course, no less true even if the efforts made have not always succeeded in promoting the child's welfare in the way that was hoped. The situation is entirely different in the sphere of educational tasks directed no longer toward the child but toward the young person, the newcomer and stranger, who has been born into an already existing world which he does not know. These tasks are primarily, but not exclusively, the responsibility of the schools; they have to do with teaching and learning; the failure in this field is the most urgent problem in America today. What lies + +at the bottom of it? + +Normally the child is first introduced to the world in school. Now school is by no means the world and must not pretend to be ; it is rather the institution that we interpose between the private domain of home and the world in order to make the transition from the + +family to the world possible at all. Attendance there is required not by the family but by the state, that is by the public world, and so, in relation to the child, school in a sense represents the world, although it is not yet actually the world. At this stage of education adults, to be sure, once more assume a responsibility for the child, but by now it is not so much responsibility for the vital welfare of a growing thing as for what we generally call the free development of characteristic qualities and talents. This, from the general and essential point of view, is the uniqueness that distinguishes every human being from every other, the quality by virtue of which he is not only a stranger in the world but something that has never been here + +before. + +Insofar as the child is not yet acquainted with the world, he must be gradually introduced to it; insofar as he is new, care must be taken that this new thing comes to fruition in relation to the world as it is. In any case, however, the educators here stand in relation to the young as representatives of a world for which they must assume responsibility although they themselves did not make it, and even though they may, secretly or openly, wish it were other than it is. This responsibility is not arbitrarily imposed upon educators; it is implicit in the fact that the young are introduced by adults into a continuously changing world. Anyone who refuses to assume joint responsibility for the world should not have children + +and must not be allowed to take part in educating them. + +In education this responsibility for the world takes the form of authority. The authority of the educator and the qualifications of the teacher are not the same thing. Although a measure of qualification is indispensable for authority, the highest possible qualification can never by itself beget authority. The teacher's qualification consists in knowing the world and being able to instruct others about it, but his authority rests on his assumption of responsibility for that world. Vis-a-vis the child it is as though he were a representative of all adult inhabitants, pointing out the details and saying to + +Now we all know how things stand today in respect to authority. Whatever one's attitude toward this problem may be, it is obvious + +that in public and political life authority either plays no role at all -for the violence and terror exercised by the totalitarian countries have, of course, nothing to do with authority--or at most plays a highly contested role. This, however, simply means, in essence, that people do not wish to require of anyone or to entrust to anyone the assumption of responsibility for everything else, for wherever true authority existed it was joined with responsibility for the course of things in the world. If we remove authority from political and public life, it may mean that from now on an equal responsibility for the course of the world is to be required of everyone. But it may also mean that the claims of the world and the requirements of order in it are being consciously or unconsciously repudiated; all responsibility for the world is being rejected, the responsibility for giving orders no less than for obeying them. There is no doubt that in the modern loss of authority both intentions play a part and have often been simultaneously and inextrica- + +bly at work together. + +In education, on the contrary, there can be no such ambiguity in regard to the present-day loss of authority. Children cannot throw off educational authority, as though they were in a position of oppression by an adult majority-though even this absurdity of treating children as an oppressed minority in need of liberation has actually been tried out in modern educational practice. Authority has been discarded by the adults, and this can mean only one thing: that the adults refuse to assume responsibility for the world + +into which they have brought the children. + +There is of course a connection between the loss of authority in public and political life and in the private pre-political realms of the family and the school. The more radical the distrust of authority becomes in the public sphere, the greater the probability naturally becomes that the private sphere will not remain inviolate. There is this additional fact, and it is very likely the decisive one, that from time out of mind we have been accustomed in our tradition of political thought to regard the authority of parents over children, of teachers over pupils, as the model by which to understand political authority. It is just this model, which can be found as early as + +Plato and Aristotle, that makes the concept of authority in politics so extraordinarily ambiguous. It is based, first of all, on an absolute superiority such as can never exist among adults and which, from the point of view of human dignity, must never exist. In the second place, following the model of the nursery, it is based on a purely temporary superiority and therefore becomes self-contradictory if it is applied to relations that are not temporary by nature -such as the relations of the rulers and the ruled. Thus it lies in the nature of the matter-that is, both in the nature of the present crisis in authority and in the nature of our traditional political thought-that the loss of authority which began in the political sphere should end in the private one; and it is naturally no accident that the place where political authority was first undermined, that is, in America, should be the place where the modern crisis in educa- + +tion makes itself most strongly felt. + +The general loss of authority could, in fact, hardly find more radical expression than by its intrusion into the pre-political sphere, where authority seemed dictated by nature itself and independent of all historical changes and political conditions. On the other hand, modern man could find no clearer expression for his dissatisfaction with the world, for his disgust with things as they are, than by his refusal to assume, in respect to his children, responsibility for all this. It is as though parents daily said: "In this world even we are not very securely at horne; how to move about in it, what to know, what skills to master, are mysteries to us too. You must try to make out as best you can; in any case you are not entitled to call + +us to account. We are innocent, we wash our hands of you." + +This attitude has, of course, nothing to do with that revolutionary desire for a new order in the world-Novus Ordo Seclorumwhich once animated America; it is rather a symptom of that modern estrangement from the world which can be seen everywhere but which presents itself in especially radical and desperate form under the conditions of a mass society. It is true that modern educational experiments, not in America alone, have struck very revolutionary poses, and this has, to a certain degree, increased the difficulty of clearly recognizing the situation and caused a certain + +degree of confusion in the discussion of the problem; for in contradiction to all such behavior stands the unquestionable fact that so long as America was really animated by that spirit she never dreamed of initiating the new order with education but, on the con- + +trary, remained conservative in educational matters. + +To avoid misunderstanding: it seems to me that conservatism, in the sense of conservation, is of the essence of the educational activity, whose task is always to cherish and protect somethingthe child against the world, the world against the child, the new against the old, the old against the new. Even the comprehensive responsibility for the world that is thereby assumed implies, of course, a conservative attitude. But this holds good only for the realm of education, or rather for the relations between grown-ups and children, and not for the realm of politics, where we act among and with adults and equals. In politics this conservative attitudewhich accepts the world as it is, striving only to preserve the status quo--can only lead to destruction, because the world, in gross and in detail, is irrevocably delivered up to the ruin of time unless human beings are determined to intervene, to alter, to create what is new. Hamlet's words, "The time is out of joint. 0 cursed spite that ever I was born to set it right," are more or less true for every new generation, although since the beginning of our century they have perhaps acquired a more persuasive validity than before. Basically we are always educating for a world that is or is becoming out of joint, for this is the basic human situation, in which the world is created by mortal hands to serve mortals for a limited time as home. Because the world is made by mortals it wears out; and because it continuously changes its inhabitants it runs the risk of becoming as mortal as they. To preserve the world against the mortality of its creators and inhabitants it must be constantly set right anew. The problem is simply to educate in such a way that a setting-right remains actually possible, even though it can, of course, never be assured. Our hope always hangs on the new which every generation brings; but precisely because we can base our hope only on this, we destroy everything if we so try to control the new that we, the old, can dictate how it will look. Exactly for + +the sake of what is new and revolutionary in every child, education must be conservative; it must preserve this newness and introduce it as a new thing into an old world, which, however revolutionary its actions may be, is always, from the standpoint of the next genera- + +tion, superannuated and close to destruction. + +IV + +The real difficulty in modern education lies in the fact that, despite all the fashionable talk about a new conservatism, even that minimum of conservation and the conserving attitude without which education is simply not possible is in our time extraordinarily hard to achieve. There are very good reasons for this. The crisis of authority in education is most closely connected with the crisis of tradition, that is with the crisis in our attitude toward the realm of the past. This aspect of the modern crisis is especially hard for the educator to bear, because it is his task to mediate between the old and the new, so that his very profession requires of him an extraordinary respect for the past. Through long centuries, i.e., throughout the combined period of Roman-Christian civilization, there was no need for him to become aware of this special quality in himself because reverence for the past was an essential part of the Roman frame of mind, and this was not altered or ended by Christianity, + +but simply shifted onto different foundations. + +It was of the essence of the Roman attitude (though this was by no means true of every civilization or even of the Western tradition taken as a whole) to consider the past qua past as a model, ancestors, in every instance, as guiding examples for their descendants; to believe that all greatness lies in what has been, and therefore that the most fitting human age is old age, the man grown old, who, because he is already almost an ancestor, may serve as a model for the living. All this stands in contradiction not only to our world and to the modern age from the Renaissance on, but, for example, to the Greek attitude toward life as well. When Goethe said that growing old is "the gradual withdrawal from the wcrld + +of appearances," his was a comment made in the spirit of the Greeks, for whom being and appearing coincide. The Roman attitude would have been that precisely in growing old and slowly disappearing from the community of mortals man reaches his most characteristic form of being, even though, in respect to the world of appearances, he is in the process of disappearing; for only now can he approach the existence in which he will be an authority for + +others. + +With the undisturbed background of such a tradition, in which education has a political function (and this was a unique case), it is in fact comparatively easy to do the right thing in matters of education without even pausing to consider what one is really doing, so completely is the specific ethos of the educational principle in accord with the basic ethical and moral convictions of society at large. To educate, in the words of Polybius, was simply "to let you see that you are altogether worthy of your ancestors," and in this business the educator could be a "fellow-contestant" and a "fellowworkman" because he too, though on a different level, went through life with his eyes glued to the past. Fellowship and authority were in this case indeed but the two sides of the same matter, and the teacher's authority was firmly grounded in the encompassing authority of the past as such. Today, however, we are no longer in that position; and it makes little sense to act as though we still were and had only, as it were, accidentally strayed from the right path and were free at any moment to find our way back to it. This means that wherever the crisis has occurred in the modern world, one cannot simply go on nor yet simply turn back. Such a reversal will never bring us anywhere except to the same situation out of which the crisis has just arisen. The return would simply be a repeat performance-though perhaps different in form, since there are no limits to the possibilities of nonsense and capricious notions that can be decked out as the last word in science. On the other hand, simple, unreflective perseverance, whether it be pressing forward in the crisis or adhering to the routine that blandly believes the crisis will not engulf its particular sphere of life, can only, because it surrenders to the course of time, lead to ruin; it can only, to be + +more precise, increase that estrangement from the world by which we are already threatened on all sides. Consideration of the principles of education must take into account this process of estrangement from the world; it can even admit that we are here presumably confronted by an automatic process, provided only that it does not forget that it lies within the power of human thought and action to + +interrupt and arrest such processes. + +The problem of education in the modern world lies in the fact that by its very nature it cannot forgo either authority or tradition, and yet must proceed in a world that is neither structured by authority nor held together by tradition. That means, however, that not just teachers and educators, but all of us, insofar as we live in one world together with our children and with young people, must take toward them an attitude radically different from the one we take toward one another. We must decisively divorce the realm of education from the others, most of all from the realm of public, political life, in order to apply to it alone a concept of authority and an attitude toward the past which are appropriate to it but have no general validity and must not claim a general validity in + +the world of grown-ups. + +In practice the first consequence of this would be a clear understanding that the function of the school is to teach children what the world is like and not to instruct them in the art of living. Since the world is old, always older than they themselves, learning inevitably turns toward the past, no matter how much living will spend itself in the present. Second, the line drawn between children and adults should signify that one can neither educate adults nor treat children as though they were grown up; but this line should never be permitted to grow into a wall separating children from the adult community as though they were not living in the same world and as though childhood were an autonomous human state, capable of living by its own laws. Where the line between childhood and adulthood falls in each instance cannot be determined by a general rule; it changes often, in respect to age, from country to country, from one civilization to another, and also from individual to individual. But education, as distinguished from learning, must + +have a predictable end. In our civilization this end probably coincides with graduation from college rather than with graduation from high school, for the professional training in universities or technical schools, though it always has something to do with education, is nevertheless in itself a kind of specialization. It no longer aims to introduce the young person to the world as a whole, but rather to a particular, limited segment of it. One cannot educate without at the same time teaching; an education without learning is empty and therefore degenerates with great ease into moralemotional rhetoric. But one can quite easily teach without educating, and one can go on learning to the end of one's days without for that reason becoming educated. All these are particulars, however, that must really be left to the experts and the pedagogues. What concerns us all and cannot therefore be turned over to the special science of pedagogy is the relation between grown-ups and children in general or, putting it in even more general and exact terms, our attitude toward the fact of natality: the fact that we have all come into the world by being born and that this world is constantly renewed through birth. Education is the point at which we decide whether we love the world enough to assume responsibility for it and by the same token save it from that ruin which, except for renewal, except for the corning of the new and young, would be inevitable. And education, too, is where we decide whether we love our children enough not to expel them from our world and leave them to their own devices, nor to strike from their hands their chance of undertaking something new, something unforeseen by us, but to prepan. them in advance for the task of renewing a common + +world. + +THE CRISIS IN CULTURE: + +Its Social and Its Political Significance + +I + +F + +OR more than ten years now, we have witnessed a still growing concern among intellectuals with the relatively new phenomenon of mass culture. The term itself clearly derives from the not much older term "mass society"; the tacit assumption, underlying all discussions of the matter, is that mass culture, logically and inevitably, is the culture of mass society. The most significant fact about the short history of both terms is that, while even a few years ago they were still used with a strong sense of reprobation-implying that mass society was a depraved form of society and mass culture a contradiction in terms-they now have become respectable, the subject of innumerable studies and research projects whose chief effect, as Harold Rosenberg pointed out, is "to add to kitsch an intellectual dimension." This "intellectualization of kitsch" is justified on the grounds that mass society, whether we like it or not, is going to stay with us into the foreseeable future ; hence its "culture," "popular culture [cannot] be left to the populace." 1 However, the + +question is whether what is true for mass society is true for mass culture also, or, to put it another way, whether the relationship between mass society and culture will be, mutatis mutandis, the same + +as the relation of society toward culture which preceded it. + +The question of mass culture raises first of all another and more fundamental problem, namely, the highly problematic relationship of society and culture. One needs only to recall to what an extent the entire movement of modern art started with a vehement rebellion of the artist against society as such (and not against a still unknown mass society) in order to become aware how much this earlier relationship must have left to be desired and thus to beware of the facile yearning of so many critics of mass culture for a Golden Age of good and genteel society. This yearning is much more widespread today in America than it is in Europe for the simple reason that America, though only too well acquainted with the barbarian philistinism of the nouveaux-riches, has only a nodding acquaintance with the equally annoying cultural and educated philistinism of European society, wh�re culture has acquired snob-value, where it has become a matter of status to be educated enough to appreciate culture; this lack of experience may even explain why American literature and painting has suddenly come to play such a decisive role in the development of modern art and why it can make its influence felt in countries whose intellectual and artistic vanguard has adopted outspoken anti-American attitudes. It has, however, the unfortunate consequence that the profound malaise which the very word "culture" is likely to evoke precisely among those who are its foremost representatives may go unnoticed or not be under- + +stood in its symptomatic significance. + +Yet whether or not any particular country has actually passed through all stages in which society developed since the rise of the modern age, mass society clearly comes about when "the mass of the population has become incorporated into society." :! And since society in the sense of "good society" comprehended those parts of the population which disposed not only of wealth but of leisure time, that is, of time to be devoted to "culture," mass society does indeed indicate a new state of affairs in which the mass of the popu- + +lation has been so far liberated from the burden of physically exhaustmg labor that it too disposes of enough leisure for "culture." Hence, mass society and mass culture seem to be interrelated phenomena, but their common denominator is not the mass but rather the society into which the masses too have been incorporated. Historically as well as conceptually, mass society was preceded by society, and society is no more a generic term than mass society; it too can be dated and described historically; it is older, to be sure, than mass society, but not older than the modern age. In fact, all the traits that crowd psychology has meanwhile discovered in mass man : his loneliness-and loneliness is neither isolation nor solitude-regardless of his adaptability; his excitability and lack of standards; his capacity for consumption, accompanied by inability to judge, or even to distinguish; above all, his egocentricity and that fateful alienation from the world which since Rousseau is mistaken for self-alienation-all these traits first appeared in good society, where there was no question of masses, numerically speaking. + +Good society, as we know it from the eighteenth and nineteenth centuries, probably had its origin in the European courts of the age of absolutism, especially the court society of Louis XIV, who knew so well how to reduce French nobility to political insignificance by the simple means of gathering them at Versailles, transforming them into courtiers, and making them entertain one another through the intrigues, cabals, and endless gossip which this perpetual party inevitably engendered. Thus the true forerunner of the novel, this entirely modern art form, is not so much the picaresque romance of adventurers and knights as the Memoires of Saint-Simon, while the novel itself clearly anticipated the rise of the social sciences as well as of psychology, both of which are still centered around conflicts between society and the "individual." The true forerunner of modern mass man is this individual, who was defined and indeed discovered by those who, like Rousseau in the eighteenth century or John Stuart Mill in the nineteenth century, found themselves in open rebellion against society. Since then, the story of a conflict between society and its individuals has repeated itself time and again in reality no less than in fiction; the modem, + +and no longer so modern, individual forms part and parcel of the society against which he tries to assert himself and which always + +gets the better of him. + +There is, however, an important difference between the earlier stages of society and mass society with respect to the situation of the individual. As long as society itself was restricted to certain classes of the population, the individual's chances for survival against its pressures were rather good; they lay in the simultaneous presence within the population of other non-society strata into which the individual could escape, and one reason why these individuals so frequently ended by joining revolutionary parties was that they discovered in those who were not admitted to society certain traits of humanity which had become extinct in society. This again found its expression in the novel, in the well-known glorifications of the workers and proletarians, but also, more subtly, in the role assigned to homosexuals (for instance in Proust) or to Jews, that is, to groups which society had never quite absorbed. The fact thzt the revolutionary elan throughout the nineteenth and twentieth centuries was so much more violently directed against society than against states and governments is not only due to the predominance of the social question in the sense of the twofold predicament of misery and exploitation. We need only to read the record of the French Revolution, and to recall to what an e-xtent the very concept of /e peuple received its connotations from an outrage of the "heart"-as Rousseau and even Robespierre would have said-against the corruption and hypocrisy of the salons, to realize what the true role of society was throughout the nineteenth century. A good part of the despair of individuals under the conditions of mass society is due to the fact that these avenues of escape are now closed because society has incorporated all strata of' the + +population. + +Here we are not concerned with the conflict between the individual and society, however, although it is of some importance w note that the last individual left in a mass society seems to be the artist. Our concern is with culture, or rather with what happens to culture under the different conditions of society and of mass society, + +and our interest in the artist, therefore, does not so much concern his subjective individualism as the fact that he is, after all, the authentic producer of those objects which every civilization leaves behind as the quintessence and the lasting testimony of the spirit which animated it. That precisely the producers of the highest cultural objects, namely works of art, should turn against society, that the whole development of modern art-which together with the scientific development will probably remain the greatest achievement of our age-should have started from and remained committed to this hostility against society demonstrates an existing antagonism between society and culture prior to the rise of mass + +society. + +The charge the artist, as distinguished from the political revolutionary, has laid to society was summed up quite early, at the turn of the eighteenth century, in the one word which has since been repeated and reinterpreted by one generation after the other. The word is "philistinism." Its origin, slightly older than its specific use, is of no great significance; it was first used in German student slang to distinguish between town and gown, whereby, however, the Biblical association indicated already an enemy superior in numbers into whose hands one may fall. When first used as a term -1 think by the German writer Clemens von Brentano, who wrote a satire on the philistine bevor, in und naclz der Gesclziclzte-it designated a mentality which judged everything in terms of immediate usefulness and "material values" and hence had no regard for such useless objects and occupations as are implied in culture and art. All this sounds fairly familiar even today, and it is not without interest to note that even such current slang terms as "square" can already be found in Brentano's early pamphlet. + +If matters had rested there, if the chief reproach leveled against society had remained its lack of culture and of interest in art, the phenomenon with which we deal here would be considerably less complicated than it actually is; by the same token, it would be all but incomprehensible why modern art rebelled against "culture" instead of fighting simply and openly for its own "cultural" interests. The poin� of the matter is that this sort of philistinism, which + +simply consisted in being "uncultured" and commonplace, was very quickly succeeded by another development in which, on the contrary, society began to be only too interested in all these so-called cultural values. Society began to monopolize "culture" for its own purposes, such as social position and status. This had much to do with the socially inferior position of Europe's middle classes, which found themselves-as soon as they acquired the necessary wealth and leisure-in an uphill fight against the aristocracy and its contempt for the vulgarity of sheer moneymaking. In this fight for social position, culture began to play an enormous role as one of the weapons, if not the best-suited one, to advance oneself socially, and to "educate oneself" out of the lower regions, where supposedly reality was located, up into the higher, non-real regions, where beauty and the spirit supposedly were at home. This escape from reality by means of art and culture is important, not only because it gave the physiognomy of the cultural or educated philistine its most distinctive marks, but also because it probably was the decisive factor in the rebellion of the artists against their newly found patrons; they smelled the danger of being expelled from reality into a sphere of refined talk where what they did would lose all meaning. It was a rather dubious compliment to be recognized by a society which had grown so "polite" that, for instance, during the Irish potato famine, it would not debase itself or risk being associated with so unpleasant a reality by normal usage of the word, but would henceforth refer to that much eaten vegetable by saying "that root." This anecdote contains as in a nutshell the definition of + +the cultured philistine.3 + +No doubt what is at stake here is much more than the psychological state of the artists; it is the objective status of the cultural world, which, insofar as it contains tangible things-books and paintings, statues, buildings, and music--comprehends, and gives testimony to, the entire recorded past of countries, nations, and ultimately mankind. As such, the only nonsocial and authentic criterion for judging these specifically cultural things is their relative permanence and even eventual immortality. Only what will last through the centuries can ultimately claim to be a cultural object. The point + +of the matter is that, as soon as the immortal works of the past became the object of social and individual refinement and the status accorded to it, they lost their most important and elemental quality, which is to grasp and move the reader or the spectator over the centuries. The very word "culture" became suspect precisely because it indicated that "pursuit of perfection" which to Matthew Arnold was identical with the "pursuit of sweetness and light." The great works of art are no less misused when they serve purposes of self-education or self-perfection than when they serve any other purposes; it may be as useful and legitimate to look at a picture in order to perfect one's knowledge of a given period as it is useful and legitimate to use a painting in order to hide a hole in the wall. In both instances the art object has been used for ulterior purposes. All is well as long as one remains aware that these usages, legitimate or not, do not constitute the proper intercourse with art. The trouble with the educated philistine was not that he read the classics but that he did so prompted by the ulterior motive of self-perfection, remaining quite unaware of the fact that Shakespeare or Plato might have to tell him more important things than how to educate himself; the trouble was that he fled into a region of "pure poetry" in order to keep reality out of his life-for instance, such "prosaic" things as a potato famine--or to look at it through a veil + +of "sweetness and light." + +We all know the rather deplorable art products which this attitude inspired and upon which it fed, in short the kitsch of the nineteenth century, whose historically so interesting lack of sense for form and style is closely connected with the severance of the arts from reality. The astounding recovery of the creative arts in our own century, and a perhaps less apparent but no less real recovery of the greatness of the past, began to assert itself when genteel society had lost its monopolizing grip on culture, together with its dominant position in the population as a whole. What had hap �ened before and, to an extent, continued, of course, to happen even after the first appearance of modern art, was actually a disintegration of culture whose "lasting monuments" are the neo-Classic, neo-Gothic, neo-Renaissance structures that are strewn all + +over Europe. In this disintegration, culture, more even than other realities, had become what only then people began to call "value," i.e., a social commodity which could be circulated and cashed in in + +exchange for all kinds of other values, social and individual. + +In other words, cultural objects were first despised as useless by the philistine until the cultural philistine seized upon them as a currency by which he bought a higher position in society or acquired a higher degree of self-esteem-higher, that is, than in his own opinion he deserved either by nature or by birth. In this process, cultural values were treated like any other values, they were what values always have been, exchange values; and in passing from hand to hand they were worn down like old coins. They lost the faculty which is originally peculiar to all cultural things, the faculty of arresting our attention and moving us. When this had come about, people began to talk of the "devaluation of values" and the end of the whole process carne with the "bargain sale of values'' (Ausverkauf der Werte ) during the twenties and thirties in Germany, the forties and fifties in France, when cultural and moral + +"values" were sold out together. + +Since then cultural philistinisrn has been a matter of the past in Europe, and while one may see in the "bargain sale of values" the melancholy end of the great Western tradition, it is still an open question whether it is more difficult to discover the great authors of the past without the help of any tradition than it is to rescue them from the rubbish of educated philistinisrn. And the task of preserving the past without the help of tradition, and often even against traditional standards and interpretations, is the same for the whole of Western civilization. Intellectually, though not socially, America and Europe are in the same situation: the thread of tradition is broken, and we must discover the past for ourselvesthat is, read its authors as though nobody had ever read them before. In this task mass society is much less in our way than good and educated society, and I suspect that this kind of reading was not uncommon in nineteenth-century America precisely because this country was still that "unstoried wilderness" from which so many American writers and artists tried to escape. That American + +�ktion and poetry have so richly come into their own ever since Whitman and Melville may have something to do with this. It would be unfortunate indeed if out of the dilemmas and distractions of mass culture and mass society there should arise an altogether unwarranted and idle yearning for a state of affairs which is not better + +hut only a bit more old-fashioned. + +Perhaps the chief difference between society and mass society is that society wanted culture, evaluated and devaluated cultural things into social commodities, used and abused them for its own selfish purposes, but did not "consume" them. Even in their most worn-out shapes these things remained things and retained a certain objective character; they disintegrated until they looked like a heap of rubble, but they did not disappear. Mass society, on the contrary, wants not culture but entertainment, and the wares offered by the entertainment industry are indeed consumed by society just like any other consumer goods. The products needed for entertainment serve the life process of society, even though they may not be as necessary for this life as bread and meat. They serve, as the phrase is, to while away time, and the vacant time which is whiled away is not leisure time, strictly speaking-time, that is, in which we are free from all cares and activities necessitated by the life process and therefore free for the world and its culture-it is rather left-over time, which still is biological in nature, left over after labor and sleep have received their due. Vacant time which entertainment is supposed to fill is a hiatus in the biologically conditioned cycle of labor-in the "metabolism of man with nature," + +as Marx used to say. + +Under modern conditions, this hiatus is constantly growing; there is more and more time freed that must be filled with entertainment, but this enormous increase in vacant time does not change the nature of the time. Entertainment, like labor and sleep, is irrevocably part of the biological life process. And biological life is always, whether laboring or at rest, whether engaged in consumption or in the passive reception of amusement, a metabolism feeding on things by devouring them. The commodities the entertainment industry offers are not "things," cultural objects, whose ex- + +cellence is measured by their ability to withstand the life process and become permanent appurtenances of the world, and they should not be judged according to these standards; nor are they values which exist to be used and exchanged; they are consumer goods, + +destined to be used up, just like any other consumer goods. + +Panis et circenses truly belong together; both are necessary for life, for its preservation and recuperation, and both vanish in the course of the life process-that is, both must constantly be produced anew and offered anew, lest this process cease entirely. The standards by which both should be judged are freshness and novelty, and the extent to which we use these standards today to judge cultural and artistic objects as well, things which are supposed to remain in the world even after we have left it, indicates clearly the extent to which the need for entertainment has begun to threaten the cultural world. Yet the trouble does not really stem from mass society or the entertainment industry which caters to its needs. On the contrary, mass society, since it does not want culture but only entertainment, is probably less of a threat to culture than the philistinism of good society; despite the often described malaise of artists and intellectuals-partly perhaps due to their inability to penetrate the noisy futility of mass entertainment-it is precisely the arts and sciences, in contradistinction to all political matters, which continue to flourish. At any event, as long as the entertainment industry produces its own consumer goods, we can no more reproach it for the non-durability of its articles than we can reproach a bakery because it produces goods which, if they are not to spoil, must be consumed as soon as they are made. It has always been the mark of educated philistinism to despise entertainment and amusement, because no "value" could be derived from it. The truth is we all stand in need of entertainment and amusement in some form or other, because we are all subject to life's great cycle, and it is sheer hypocrisy or social snobbery to deny that we can be amused and entertained by exactly the same things which amuse and entertain the masses of our fellow men. As far as the survival of culture is concerned, it certainly is less threatened by those who + +fill vacant time with entertainment than by those who fill it with some haphazard educational gadgets in order to improve their social standing. And as far as artistic productivity is concerned, it should not be more difficult to withstand the massive temptations of mass culture, or to keep from being thrown out of gear by the noise and humbug of mass society, than it was to avoid the more sophisticated temptations and the more insidious noises of the cul- + +tural snobs in refined society. + +Unhappily, the case is not that simple. The entertainment industry is confronted with gargantuan appetites, and since its wares disappear in consumption, it must constantly offer new commodities. In this predicament those who produce for the mass media ransack the entire range of past and present culture in the hope of finding suitable material. This material, moreover, cannot be offered as it is; it must be altered in order to become entertaining, it must + +be prepared to be easily consumed. + +Mass culture comes into being when mass society seizes upon cultural objects, and its danger is that the life process of society (which like all biological processes insatiably draws everything available into the cycle of its metabolism) will literally consume the cultural objects, eat them up and destroy them. Of course, I am not referring to mass distribution. When books or pictures in reproduction are thrown on the market cheaply and attain huge sales, this does not affect the nature of the objects in question. But their nature is affected when these objects themselves are changedrewritten, condensed, dieested, reduced to kitsch in reproduction, or in preparation for the movies. This does not mean that culture spreads to the masses, but that culture is being destroyed in order to yield entertainment. The result of this is not disintegration but decay, and those who actively promote it are not the Tin Pan Alley composers but a special kind of intellectuals, often well read and well informed, whose sole function is to organize, disseminate, and change cultural objects in order to persuade the masses that Hamlet can be as entertaining as My Fair Lady, and perhaps educational as well. There are many great authors of the past who have sur- + +vived centuries of oblivion and neglect, but it is still an open question whether they will be able to survive an entertaining version of + +what they have to say. + +Culture relates to objects and is a phenomenon of the world; entertainment relates to people and is a phenomenon of life. An object is cultural to the extent that it can endure; its durability is the very opposite of functionality, which is the quality which makes it disappear again from the phenomenal world by being used and used up. The great user and consumer of objects is life itself, the life of the individual and the life of society as a whole. Life is indifferent to the thingness of an object; it insists that every thing must be functional, fulfill some needs. Culture is being threatened when all worldly objects and things, produced by the present or the past, are treated as mere functions for the life process of society, as though they are there only to fulfill some need, and for this functionalization it is almost irrelevant whether the needs in question are of a high or a low order. That the aJ"ts must be functional, that cathedrals fulfill a religious need of society, that a picture is born from the need for self-expression in the individual painter and that it is looked at because of a desire for self-perfection in the spectator, all these notions are so unconnected with art and historically so new that one is tempted simply to dismiss them as modern prejudices. The cathedrals were built ad maiorem gloriam Dei; while they as buildings certainly served the needs of the community, their elaborate beauty can never be explained by these needs, which could have been served quite as well by any nondescript building. Their beauty transcended all needs and made them last through the centuries; but while beauty, the beauty of a cathedral like the beauty of any secular building, transcends needs and functions, it never transcends the world, even if the content of the work happens to be religious. On the contrary, it is the very beauty of religious art which transforms religious and other-worldly contents and concerns into tangible worldly realities; in this sense all art is secular, and the distinction of religious art is merely that it "secularizes"-reifies and transforms into an "objective," tangible, worldly presence-what had existed before outside the world, + +whereby it is irrelevant whether we follow traditional religion and localize this "outside" in the beyond of a hereafter, or follow modern explanations and localize it in the innermost recesses of + +the human heart. + +Every thing, whether it is a use object, a consumer good, or a work of art, possesses a shape through which it appears, and only to the extent that something has a shape can we say that it is a thing at all. Among the things which do not occur in nature but only in the man-made world, we distinguish between use objects and art works, both of which possess a certain permanence ranging from ordinary durability to potential immortality in the case of works of art. As such, they are distinguished from consumer goods on one hand, whose duration in the world scarcely exceeds the time necessary to prepare them, and, on the other hand, from the products of action, such as events, deeds, and words, all of which are in themselves so transitory that they would hardly survive the hour or day they appeared in the world, if they were not preserved first by man's memory, which weaves them into stories, and then through his fabricating abilities. From the viewpoint of sheer durability, art works clearly are superior to all other things; since they stay longer in the world than anything else, they are the worldliest of all things. Moreover, they are the only things without any function in the life process of society; strictly speaking, they are fabricated not for men, but for the world which is meant to outlast the life-span of mortals, the coming and going of the generations. Not only are they not consumed like consumer goods and not used up like use objects; they are deliberately removed from the processes of consumption and usage and isolated against the sphere of human life necessities. This removal can be achieved in a great variety of ways; and only where it is done does culture, in the specific sense, come + +into being. + +The question here is not whether worldliness, the capacity to fabricate and create a world, is part and parcel of human "nature." We know of the existence of worldless people as we know unworldly men; human life as such requires a world only insofar as it needs a horne on earth for the duration of its stay here. Certainly + +every arrangement men make to provide shelter and put a roof .wer their heads-even the tents of nomadic tribes--can serve as a home on earth for those who happen to be alive at the time; but this by no means implies that such arrangements beget a world, let alone a culture. This earthly home becomes a world in the proper sense of the word only when the totality of fabricated things is so organized that it can resist the consuming life process of the people dwelling in it, and thus outlast them. Only where such survival is assured do we speak of culture, and only where we are confronted with things which exist independently of all utilitarian and functional references, and whose quality remains always the same, + +do we speak of works of art. + +For these reasons any discussion of culture must somehow take as its starting point the phenomenon of art. While the thingness of all things by which we surround ourselves lies in their having a shape through which they appear, only works of art are made for the sole purpose of appearance. The proper criterion by which to judge appearances is beauty; if we wanted to judge objects, even ordinary use-objects, by their use-value alone and not also by their appearance-that is, by whether they are beautiful or ugly or something in between-we would have to pluck out our eyes. But in order to become aware of appearances we first must be free to establish a certain distance between ourselves and the object, and the more important the sheer appearance of a thing is, the more distance it requires for its proper appreciation. This distance cannot arise unless we are in a position to forget ourselves, the cares and interests and urges of our lives, so that we will not seize what we admire but let it be as it is, in its appearance. This attitude of disinterested joy (to use the Kantian term, uninteressiertes W ohlgefallen) can be experienced only after the needs of the living organism have been provided for, so that, released from life's neces- + +sity, men may be free for the world. + +The trouble with society in its earlier stages was that its members, even when they had acquired release from life's necessity, could not free themselves from concerns which had much to ao with themselves, their status and position in society and the re + +flection of this upon their individual selves, but bore no relation whatsoever to the world of objects and objectivity they moved in. The relatively new trouble with mass society is perhaps even more serious, but not because of the masses themselves, but because this society is essentially a consumers' society where leisure time is used no longer for self-perfection or acquisition of more social status, but for more and more consumption and more and more entertainment. And since there are not enough consumer goods around to satisfy the growing appetites of a life process whose vital energy, no longer spent in the toil and trouble of a laboring body, must be used up by consumption, it is as though life itself reached out and helped itself to things which were never meant for it. The result is, of course, not mass culture which, strictly speaking, does not exist, but mass entertainment, feeding on the cultural objects of the world. To believe that such a society will become more "cultured" as time goes on and education has done its work, is, I think, a fatal mistake. The point is that a consumers' society cannot possibly know how to take care of a world and the things which belong exclusively to the space of worldly appearances, because its central attitude toward all objects, the attitude of consumption, spells ruin + +to everything it touches. + +II + +I said before that a discussion of culture is bound to take the phenomenon of art as its starting point because art works are cultural objects par excellence. Yet while culture and art are closely interrelated, they are by no means the same. The distinction between them is of no great importance for the question of what happens to culture under the conditions of society and mass society; it is relevant, however, for the problem of what culture is and in + +Culture, word and concept, is Roman in origin. The word "culture" derives from co/ere-to cultivate, to dwell, to take care, to tend and preserve-and it relates primarily to the intercourse of + +man with nature in the sense of cultivating and tending nature until it becomes fit for human habitation. As such, it indicates an attitude of loving care and stands in sharp contrast to all efforts to subject nature to the domination of rnan.4 Hence it docs not only apply to tilling the soil but can also designate the "cult" of the gods, the taking care of what properly belongs to them. It seems it was Cicero who first used the word for matters of spirit and mind. He speaks of excolere animum, of cultivating the mind, and of cultura animi in the same sense in which we speak even today of a cultured mind, only that we are no longer aware of the full metaphorical content of this usage.5 For as far as Roman usage is concerned, the chief point always was the connection of culture with nature; culture originally meant agriculture, which was held· in very high regard in Rome in opposition to the poetic and fabricating arts. Even Cicero's cultura animi, the result of training in philosophy and therefore perhaps coined, as has been suggested, to translate the Greek 7rato€ia, 6 meant tl1e very opposite of being a fabricator or creator of art works. It was in the midst of a primarily agricultural people that the concept of culture first appeared, and the artistic connotations which might have been connected with this culture concerned the incomparably close relationship of the Latin people to nature, the creation of the famous Italian landscape. According to the Romans, art was supposed to rise as naturally as the countryside; it ought to be tended nature; and the spring of all poetry was seen in "the song which the leaves sing to themselves in the green solitude of the woods." 7 But though this may be an eminently poetic thought, it is not likely that great art would ever have sprung from it. It is hardly the mentality of gardeners which pro- + +duces art. + +The great Roman art and poetry carne into being under the impact of the Greek heritage, which the Romans, but never the Greeks, knew how to take care of and how to preserve. The reason why there is no Greek equivalent to the Roman concept of culture lies in the predominance of the fabricating arts in Greek civilization. While the Romans tended to regard even art as a kind of agriculture. of cultivating nature, the Greeks tended to consider even + +agriculture as part and parcel of fabrication, as belonging to the cunning, skillful, "technical" devices with which man, more aweinspiring than all that is, tames and rules nature. What we, still under the spell of the Roman heritage, consider to be the most natural and the most peaceful of man's activities, the tilling of the soil, the Greeks understood as a daring, violent enterprise in which, year in year out, the earth, inexhaustible and indefatigable, is disturbed and violated.8 The Greeks did not know what culture is because they did not cultivate nature but rather tore from the womb of the earth the fruits which the gods had hidden from men (Hesiod); and closely connected with this was that the great Roman reverence for the testimony of the past as such, to which we owe not merely the preservation of the Greek heritage but the very continuity of our tradition, was quite alien to them. Both together, culture in the sense of developing nature into a dwelling place for a people as well as in the sense of taking care of the monuments of the past, determine even today the content and the meaning we + +have in mind when we speak of culture. + +Yet the meaning of the word "culture" is hardly exhausted by these strictly Roman elements. Even Cicero's cultura animi is suggestive of something like taste and, generally, sensitivity to beauty, not in those who fabricate beautiful things, that is, in the artists themselves, but in the spectators, in those who move among them. And this love for beauty the Greeks possessed, of course, to an extraordinary degree. In this sense we understand by culture the attitude toward, or, better, the mode of intercourse prescribed by civilizations with respect to the least useful and most worldly of things, the works of artists, poets, musicians, philosophers, and so forth. If we mean by culture the mode of intercourse of man with the things of the world, then we may try to understand Greek culture (as distinguished from Greek art) by recalling a much quoted saying, reported by Thucydides and attributed to Pericles, which reads as follows: q,tA.oKaA.ovp.Ev yap p.ET' ElinA.da> Kat q,tA.ouoq,ovp.Ev avEv p.aAaKLa<;.9 The sentence, utterly simple, almost defies translation. What we understand as states or qualities, such as love of beauty or love of wisdom (called philosophy) is described here as + +an activity, as though to "love beautiful things" is no less an activity than to make them. Our translation of the qualifying words, furthermore, "accuracy of aim" and "effeminacy," fails to convey that both terms were strictly political, effeminacy being a barbarian vice and accuracy of aim the virtue of the man who knows how to act. Pericles therefore is saying something like this: "We love beauty within the limits of political judgment, and we philoso- + +phize without the barbarian vice of effeminacy." + +Once the meaning of these words, which are so difficult to liberate from their hackneyed translation, begins to dawn upon us, there is much to be surprised at. First, we are told distinctly that it is the polis, the realm of politics, which sets limits to the love of wisdom and of beauty, and since we know that the Greeks thought it was the polis and "politics" (and by no means superior artistic achievements) which distinguished them from the barbarians, we must conclude that this difference was a "cultural" difference as well, a difference in their mode of intercourse with "cultural" things, a different attitude toward beauty and wisdom, which could be loved only within the limits set by the institution of the polis. In other words, it was a kind of over-refinement, an indiscriminate sensitivity which did not know how to choose that was deemed to be barbarian-and neither any primitive lack of culture as we understand it nor any specific quality in the cultural things themselves. Even more surprising perhaps is that the lack of virility, the vice of effeminacy, which we would associate with too great a love of beauty or aestheticism, is mentioned here as the specific danger of philosophy; and the knowledge of how to aim or, as we said, of how to judge, which we would have expected to be a qualification of philosophy, which must know how to aim at truth, is considered + +here to be necessary for the intercourse with the beautiful. + +Could it be that philosophy i.n the Greek sense-which begins with "wonder," with OavfLaCnv, and ends (at least in Plato and Aristotle ) in the speechless beholding of some unveiled truth-is more likely to lead into inactivity than love of beauty? Could it be, on the other hand, that love of beauty remains barbarous unless it is accompanied by dJT£A£ta, by the faculty to take aim in judgment, + +discernment, and discrimination, in brief, by that curious and illdefined capacity we commonly call taste? And finally, could it be that this right love of beauty, the proper kind of intercourse with beautiful things-the cultura animi which makes man fit to take care of the things of the world and which Cicero, in contradistinction to the Greeks, ascribed to philosophy-has something to do with politics? Could it be that taste belongs among the political + +faculties? + +To understand the problems which these questions raise it is important to keep in mind that culture and art are not the same. One way to remain aware of the difference between them is to recall that the same men who praised love of the beautiful and the culture of the mind shared the deep ancient distrust of those artists and artisans who actually fabricated the things which then were displayed and admired. The Greeks, though not the Romans, had a word for philistinism, and this word, curiously enough, derives from a word for artists and artisans, {3avauuo-;; to be a philistine, a man of banausic spirit, indicated, then as today, an exclusively utilitarian mentality, an inability to think and to judge a thing apart from its function or utility. But the artist himself, being a f3avavuo-;, was by no means excluded from the reproach of philistinism; on the contrary, philistinism was considered to be a vice most likely to occur in those who had mastered a TixvTJ, in fabricators and artists. To Greek understanding, there was no contradiction between praise of cfnA.oKaA€iv, the love of the beautiful, and contempt for those who actually produced the beautiful. The mistrust and actual contempt of the artists arose from political considerations: fabrication of things, including the production of art, is not within the range of political activities; it even stands in opposition to them. The chief reason of the distrust of fabrication in all forms is that it is utilitarian by its very nature. Fabrication, but not action or speech, always involves means and ends; in fact, the category of means and ends derives its legitimacy from the sphere of making and fabricating where a clearly recognizable end, the final product, determines and organizes everything that plays a part in the process-the material, the tools, the activity itself, and even the persons partici- + +pating in it; they all become mere means toward the end and they are justified as such. Fabricators cannot help regarding all things as means to their ends or, as the case may be, judging all things by their specific utility. The moment this point of view is generalized and extended to other realms than that of fabrication it will produce the banausic mentality. And the Greeks rightly suspected that this philistinism threatens not only the political realm, as it obviously does because it will judge action by the same standards of utility which are valid for fabrication, demand that action obtain a predetermined end and that it be permitted to seize on all means likely to further this end; it also threatens the cultural realm itself because it leads to a devaluation of things as things which, if the mentality that brought them into being is permitted to prevail, will again be judged according to the standard of utility and thereby lose their intrinsic, independent worth, and finally degenerate into mere means. In other words, the greatest threat to the existence of the finished work arises precisely from the mentality which brought it into being. From which it follows that the standards and rules which must necessarily prevail in erecting and building and decorating the world of things in which we move, lose their validity and become positively dangerous when they are applied to the finished world + +itself. + +This, to be sure, does not tell the whole story of the relation between politics and art. Rome in her early period was so convinced that artists and poets pursued a childish game which did not accord with the gravitas, the seriousness and dignity, proper to a Roman citizen, that she simply suppressed whatever artistic talents might have flourished in the republic prior to Greek influence. Athens, on the contrary, never settled the conflict between politics and art unequivocally in favor of one or the other-which incidentally may be one of the reasons for the extraordinary display of artistic genius in classical Greece-and she kept the conflict alive and did not level it out to indifference of the two realms with regard to each other. The Greeks, so to speak, could say in one and the same breath : "He who has not seen the Zeus of Phidias at Olympia has lived in vain" and: "People like Phidias, namely sculptors, are un- + +fit for citizenship." And Pericles, in the same oration in which he praises the right cfn/..ouocp£iv and cptAoKaA£iv, the active intercourse with wisdom and beauty, boasts that Athens will know how to put "Homer and his ilk" in their place, that the glory of her deeds will be so great that the city will be able to dispense with the professional fabricators of glory, the poets and artists who reify the living word and the living deed, transforming and converting them into things permanent enough to carry greatness into the immortality of fame. We today are more likely to suspect that the realm of politics and active participation in public business give rise to philistinism and prevent the development of a cultivated mind which can regard things in their true worth without reflection upon their function and utility. One of the reasons for this shift of emphasis is, of course, that-for reasons outside these considerations-the mentality of fabrication has invaded the political realm to such an extent that we take it for granted that action, even more than fabrication, is determined by the category of means and ends. This situation, however, has the advantage that the fabricators and artists have been able to give vent to their own view of these matters and to articulate their hostility against the men of action. There is more behind this hostility than competition for the public eye. The trouble is that Homo faber does not stand in the same relationship to the public realm and its publicity as the things he makes, with their appearance, configuration, and form. In order to be in a position to add constantly new things to the already existing world, he himself must be isolated from the public, must be sheltered and concealed from it. Truly political activities, on the other hand, acting and speaking, cannot be performed at all without the presence of others, without the public, without a space constituted by the many. The activity of the artist and of the craftsman is therefore subject to conditions very different from those surrounding political activities, and it is quite understandable that the artist, as soon as he begins to speak his mind on things political, should feel the same distrust for the specifically political realm and its publicity as did the polis for the mentality and conditions of fabrication. This is the true malaise of the artist, not in society but + +in politics, and his scruples and distrust of political activity are no less legitimate than the mistrust of men of action against the mentality of Homo faber. At this point the conflict between art and politics arises, and this conflict cannot and must not be solved. However, the point of the matter is that the conflict, dividing the statesman and the artist in their respective activities, no longer applies when we turn our attention from the making of art to its products, to the things themselves which must find their place in the world. These things obviously share with political "products," words and deeds, the quality that they are in need of some public space where they can appear and be seen; they can fulfill their own being, which is appearance, only in a world which is common to all; in the concealment of private life and private possession, art objects cannot attain their own inherent validity, they must, on the contrary, be protected against the possessiveness of individualswhereby it does not matter whether this protection takes the form of their being set up in holy places, in temples and churches, or placed in the care of museums and the keepers of monuments, although the place where we put them is characteristic of our "culture," that is, of the mode of our intercourse with them. Generally speaking, culture indicates that the public realm, which is rendered politically secure by men of action, offers its space of display to those things whose essence it is to appear and to be beautiful. In other words, culture indicates that art and politics, their conflicts and tensions notwithstanding, are interrelated and even mutually dependent. Seen against the background of political experiences and of activities which, if left to themselves, come and go without leaving any trace in the world, beauty is the very manifestation of imperishability. The fleeting greatness of word and deed can endure in the world to the extent that beauty is bestowed upon it. Without the beauty, that is, the radiant glory in which potential immortality �s made manifest in the human world, all human life would be + +The common element connecting art and politics is that they both are phenomena of the public world. What mediates the conflict between the artist and the man of action is the cultura animi, + +that is, a mind so trained and cultivated that it can be trusted to tend and take care of a world of appearances whose criterion is beauty. The reason Cicero ascribed this culture to a training in philosophy was that to him only philosophers, the lovers of wisdom, approached things as mere "spectators" without any wish to acquire something for themselves, so that he could liken the philosophers to those who, coming to the great games and festivals, sought neither ''to win the glorious distinction of a crown" nor to make "gain by buying or selling" but were attracted by the "spectacle and closely watched what was done and how it was done." They were, as we would say today, completely disinterested and for this very reason those best qualified to judge, but also those who were most fascinated by the spectacle itself. Cicero calls them maxime ingenuum, the most noble group of the free-born men, for what they were doing: to look for the sake of seeing only was the freest, + +liberalissimum, of all pursuits.10 + +For lack of a better word that would indicate the discriminating, discerning, judging elements of an active love of beauty-that cpV..oKaA£iv JL£T' dJT£>..£{a<; of which Pericles speaks-I used the word "taste," and in order to justify this usage and, at the same time, to point out the one activity in which, I think, culture as such expresses itself, I should like to draw upon the first part of Kant's Critique of Judgment, which, as "Critique of Esthetic Judgment," contains perhaps the greatest and most original aspect of Kant's political philosophy. At any rate, it contains an analytic of the beautiful primarily from the viewpoint of the judging spectator, as even the title indicates, and it takes its starting point from the phenomenon of taste, understood as an active relationship to what + +is beautiful. + +In order to see the faculty of judgment in its proper perspective and to understand that it implies a political rather than a merely theoretical activity, we must shortly recall what is usually considered to be Kant's political philosophy, namely, the Critiqt!e of Practical Reason, which deals with the lawgiving faculty of reason. The principle of lawgiving, as laid down in the "categorical imperative"-"always act in such a manner that the principle of your + +action can become a general law''-is based upon the necessity for rational thought to agree with itself. The thief, for instance, is actually contradicting himself, for he cannot wish that the principle of his action, stealing other people's property, should become a general law; such a law would immediately deprive him of his own acquisition. This principle of agreement with oneself is very old; it was actually discovered by Socrates, whose central tenet, as formulated by Plato, is contained in the sentence : "Since I am one, it is better for me to disagree with the whole world than to be in disagreement with myself." 11 From this sentence both Occidental ethics, with its stress upon being in agreement with one's own conscience, and Occidental logic, with its emphasis upon the axiom + +of contradiction, took their starting point. + +In the Critique of Judgement, however, Kant insisted upon a different way of thinking, for which it would not be enough to be in agreement with or.e's own self, but which consisted of being able to "think in the place of everybody else" and which he therefore called an "enlarged mentality" (eine erweiterte Denkungsart) . 1 2The power of judgment rests on a potential agreement with others, and the thinking process which is active in judging something is not, like the thought process of pure reasoning, a dialogue between me and myself, but finds itself always and primarily, even if I am quite alone in making up my mind, in an anticipated communication with others with whom I know I must finally come to some agreement. From this potential agreement judgment derives its specific validity. This means, on the one hand, that such judgment must liberate itself from the "subjective private conditions," that is, from the idiosyncrasies which naturally determine the outlook of each individual in his privacy and are legitimate as long as they are only privately held opinions, but which are not fit to enter the market place, and lack all validity in the public realm. And this enlarged way of thinking, which as judgment knows how to transcend its own individual limitations, on the other hand, cannot function in strict isolation or solitude ; it needs the presence of others "in whose place" it must think, whose perspectives it must take into consideration, and without whom it never has the opportunity to + +operate at all. As logic, to be sound, depends on the presence of the self, so judgment, to be valid, depends on the presence of others. Hence judgment is endowed with a certain specific validity but is never universally valid. Its claims to validity can never extend further than the others in whose place the judging person has put himself for his considerations. Judgment, Kant says, is valid "for every single judging person," 13 but the emphasis in the sentence is on "judging"; it is not valid for those who do not judge or for those who are not members of the public realm where the objects + +of judgment appear. + +That the capacity to judge is a specifically political ability in exactly the sense denoted by Kant, namely, the ability to see things not only from one's own point of view but in the perspective of all those who happen to be present; even that judgment may be one of the fundamental abilities of man as a political being insofar as it enables him to orient himself in the public realm, in the common world-these are insights that are virtually as old as articulated political experience. The Greeks called this ability ¢piw'lut>, or insight, and they considered it the principal virtue or excellence of the statesman in distinction from the wisdom of the philosopher. 14 The difference between this judging insight and speculative thought lies in that the former has its roots in what we usually call common sense, which the latter constantly transcends. Common sensewhich the French so suggestively call the "good sense," le bon sens --discloses to us the nature of the world insofar as it is a common world; we owe to it the fact that our strictly private and "subjective" five senses and their sensory data can adjust themselves to a nonsubjective and "objective" world which we have in common and share with others. Judging is one, if not the most, important activity in which this sharing-the-world-with-others comes to pass. What, however, is quite new and even startlingly new in Kant's propositions in the Critique of Judgment is that he discovered this phenomenon in all its grandeur precisely when he was examining the phenomenon of taste and hence the only kind of judgments which, since they concern merely aesthetic matters, have always been supposed to lie outside the political realm as well as the domain of + +reason. Kant was disturbed by the alleged arbitrarincs� and sulr jectivity of de gustibus non disputandum est (which, no doubt, is entirely true for private idiosyncrasies) , for this arbitrariness offended his political and not his aesthetic sense. Kant, who certainly was not oversensitive to beautiful things, was highly conscious of the public quality of beauty; and it was because of their public relevance that he insisted, in opposition to the commonplace adage, that taste judgments are open to discussion because "we hope that the same pleasure is shared by others," that taste can be subject to dispute, because it "expects agreement from everyone else." 1" Therefore taste, insofar as it, like any other judgment, appeals to common sense, is the very opposite of "private feelings." In aesthetic no less than in political judgments, a decision is made, and although this decision is always determined by a certain subjectivity, by the simple fact that each person occupies a place of his own from which he looks upon and judges the world, it also derives from the fact that the world itself is an objective datum, something common to all its inhabitants. The activity of taste decides how this world, independent of its utility and our vital interests in it, is to look and sound, what men will see and what they will hear in it. Taste judges the world in its appearance and in its worldliness; its interest in the world is purely "disinterested," and that means that neither the life interests of the individual nor the moral interests of the self are involved here. For judgments of taste, the world is the + +primary thing, not man, neither man's life nor his self. + +Taste judgments, furthermore, are currently held to be arbitrary because they do not compel in the sense in which demonstrable facts or truth proved by argument compel agreement. They share with political opinions that they are persuasive ; the judging person -as Kant says quite beautifully--can only "woo the consent of everyone else" in the hope of corning to an agreement with him eventually.16 This "wooing" or persuading corresponds closely to what the Greeks called 1rd8nv, the convincing and persuading speech which they regarded as the typically political form of people talking with one another. Persuasion ruled the intercourse of the citizens of the polis because it excluded physical violence ; but + +the philosophers knew that it was also distinguished from another non-violent form of coercion, the coercion by truth. Persuasion appears in Aristotle as the opposite to 8ta>..ciy�u8at, the philosophical form of speaking, precisely because this type of dialogue was concerned with knowledge and the finding of truth and therefore demanded a process of compelling proof. Culture and politics, then, belong together because it is not knowledge or truth which is at stake, but rather judgment and decision, the judicious exchange of opinion about the sphere of public life and the common world, and the decision what manner of action is to be taken in it, as well as to how it is to look henceforth, what kind of things are to ap- + +pear in it. + +To classify taste, the chief cultural activity, among man's political abilities sounds so strange that I may add another much more familiar but theoretically little-regarded fact to these considerations. We all know very well how quickly people recognize each other, and how unequivocally they can feel that they belong to each other, when they discover a kinship in questions of what pleases and displeases. From the viewpoint of this common experience, it is as though taste decides not only how the world is to look, but also who belongs together in it. If we think of this sense of belonging in political terms, we are tempted to regard taste as an essentially aristocratic principle of organization. But its political significance is perhaps more far-reaching and at the same time more profound. Wherever people judge the things of the world that are common to them, there is more implied in their judgments than these things. By his manner of judging, the person discloses to an extent also himself, what kind of person he is, and this disclosure, which is involuntary, gains in validity to the degree that it has liberated itself from merely individual idiosyncrasies. Now, it is precisely the realm of acting and speaking, that is, the political domain in terms of activities, in which this personal quality comes to the fore in public, in which the "who one is" becomes manifest rather than the qualities and individual talents he may possess. In this respect, the political realm is again opposed to the domain in which the artist and fabricator live and do their work and in which ultimately + +it is always quality that counts, the talents of the maker and the quality of the thing he makes. Taste, however, does not simply judge this quality. On the contrary, quality is beyond dispute, it is no less compellingly evident than truth and stands beyond the decisions of judgment, beyond the need of persuasion and wooing agreement, although there are times of artistic and cultural decay when only few are left who are still receptive to the self-evidence of quality. Taste as the activity of a truly cultivated mind-cultura animi----wmes into play only where quality-consciousness is widely disseminated, the truly beautiful easily recognized; for taste discriminates and decides among qualities. As such, taste and its everalert judgment of things of the world sets its own limits to an indiscriminate, immoderate love of the merely beautiful; into the realm of fabrication and of quality it introduces the personal factor, that is, gives it a humanistic meaning. Taste debarbarizes the world of the beautiful by not being overwhelmed by it; it takes care of the beautiful in its own "personal" way and thus produces a + +"culture." + +Humanism, like culture, is of course of Roman origin; there is again no word in the Greek language corresponding to the Latin humanitasY It will not be inappropriate, therefore, if-to conclude these remarks-! choose a Roman example to illustrate the sense in which taste is the political capacity that truly humanizes the beautiful and creates a culture. There exists an odd statement of Cicero which sounds as though it were deliberately framed to counter the then current Roman commonplace : Amicus Socrates, amicus Plato, sed magis aestimanda veritas. This old adage, whether one agrees with it or not, must have offended the Roman sense of humanitas, of the integrity of the person as person; for human worth and personal rank, together with friendship, are sacrificed here to the primacy of an absolute truth. Nothing, at any rate, could be further from the ideal of absolute, compelling truth than what Cicero has to say: Err are mehercule malo cum Platone . . . quam cum istis (sc. Pythagoraeis) vera sentire-"I prefer before heaven to go astray with Plato rather than hold true views with his opponents." 18 The English translation blurs a certain ambiguity + +of the text; the sentence can mean: I would rather go astray with Platonic rationality than "feel" (sentire ) the truth with Pythagorean irrationality, but this interpretation is unlikely in view of the answer given in the dialogue : "I should not myself be unwilling to go astray with such a man" (Ego enim ipse cum eadem isto non invitus erraverim), where the stress again is on the person with whom one goes astray. Thus, it seems safe to follow the English translation, and then the sentence clearly says : It is a matter of taste to prefer Plato's company and the company of his thoughts even if this should lead us astray from truth. Certainly a very bold, even an outrageously bold statement, especially because it concerns truth; obviously the same could be said and decided with respect to beauty, which for those who have trained their senses as much as most of us have trained our minds is no less compelling than truth. What Cicero in fact says is that for the true humanist neither the verities of the scientist nor the truth of the philosopher nor the beauty of the artist can be absolutes; the humanist, because he is not a specialist, exerts a faculty of judgment and taste which is beyond the coercion which each specialty imposes upon us. This Roman humanitas applied to men who were free in every respect, for whom the question of freedom, of not being coerced, was the decisive one-even in philosophy, even in science, even in the arts. Cicero says: In what concerns my association with men and things, + +I refuse to be coerced even by truth, even by beauty.10 + +This humanism is the result of the cultura animi, of an attitude that knows how to take care and preserve and admire the things of the world. As such, it has the task of arbitrating and mediating between the purely political and the purely fabricating activities, which are opposed to each other in many ways. As humanists, we can rise above these conflicts between the statesman and the artist as we can rise in freedom above the specialties which we all must learn and pursue. We can rise above specialization and philistinism of all sorts to the extent that we learn how to exercise our taste freely. Then we shall know how to reply to those who so frequently tell us that Plato or some other great author of the past has been '>Uperseded; we shall be able to understand that even if all criticism + +of Plato is right, Plato may still be better company than his critics. At any rate, we may remember what the Romans-the first people that took culture seriously the way we do--thought a cultivated person ought to be : one who knows how to choose his company among men, among things, among thoughts, in the present as well + +as in the past. + +TR UTH AND PO LI TICS\* + +I + +T + +HE subject of these reflections is a commonplace. No one has ever doubted that truth and politics are on rather bad terms with each other, and no one, as far as I know, has ever counted truthfulness among the political virtues. Lies have always been regarded as necessary and justifiable tools not only of the politician's or the demagogue's but also of the statesman's trade. Why is that so? And what does it mean for the nature and the dignity of the political realm, on one side, and for the nature and the dignity of + +\* This essay was caused by the so-called controversy after the publication of Eichmann in Jerusalem. Its aim is to clarify two different, though interconnected, issues of which I had not been aware before and whose importance seemed to transcend the occasion. The first concerns the question of whether it is always legitimate to tell the truth-did I believe without qualification in "Fiat veritas, et pereat mundus"? The second arose through the amazing amount of lies used in the "controversy"-lies about what I had written, on one hand, and about the facts I had reported, on the other. The following reflections try to come to grips with both issues. They may also serve as an example of what happens to a highly topical subject when it is drawn into that gap between past and future which is perhaps the proper habitat of all reflections. The reader will find a brief and preliminary con- + +truth and truthfulness, on the other? Is it of the very essence of truth to be impotent and of the very essence of power to be deceitful? And what kind of reality does truth possess if it is powerless in the public realm, which more than any other sphere of human life guarantees reality of existence to natal and mortal men-that is, to beings who know they have appeared out of non-being and will, after a short while, again disappear into it? Finally, is not impotent truth just as despicable as power that gives no heed to truth? These are uncomfortable questions, but they arise necessarily out + +of our current convictions in this matter. + +What lends this commonplace its high plausibility can still be summed up in the old Latin adage "Fiat iustitia, et pereat mundus" ("Let justice be done though the world may perish" ). Apart from its probable author in the sixteenth century (Ferdinand I, successor to Charles V), no one has used it except as a rhetorical question : Should justice be done if the world's survival is at stake? And the only great thinker who dared to go against the grain of the question was Immanuel Kant, who boldly explained that the "proverbial saying ... means in simple language : 'Justice shall prevail, even though all the rascals in the world should perish as a result.' " Since men would not find it worth while to live in a world utterly deprived of justice, this "human right must be held sacred, regardless of how much sacrifice is required of the powers that be . . . regardless of what might be the physical consequences thereof." 1 But isn't this answer absurd? Doesn't the care for existence clearly precede everything else--every virtue and every principle? Is it not obvious that they become mere chimeras if the world, where alone they can be manifested, is in jeopardy? Wasn't the seventeenth century right when it almost unanimously declared that every commonwealth was duty bound to recognize, in Spinoza's words, "no higher law than the safety of [its] own realm"? 2 For surely every principle that transcends sheer existence can be put in the place of justice, and if we put truth in its place-"Fiat veritas, et pereat mundus"-the old saying sounds even more plausible. If we understand political action in terms of the means-end category, we may + +even come to the only seemingly paradoxical conclusion that lying can very well serve to establish or safeguard the conditions for the search after truth-as Hobbes, whose relentless logic never fails to carry arguments to those extremes where their absurdity becomes obvious, pointed out long ago. 3 And lies, since they are often used as substitutes for more violent means, are apt to be considered + +relatively harmless tools in the arsenal of political action. + +Reconsidering the old Latin saying, it will therefore come a� something of a surprise that the sacrifice of truth for the survival of the world would be more futile than the sacrifice of any other principle or virtue. For while we may refuse even to ask ourselves whether life would still be worth living in a world deprived of such notions as justice and freedom, the same, curiously, is not possible with respect to the seemingly so much less political idea of truth. What is at stake is survival, the perseverance in existence (in suo esse perseverare ), and no human world destined to outlast the short life span of mortals within it will ever be able to survive without men willing to do what Herodotus was the first to undertake consciously-namely, AE')'ttv ra Ebvra, to say what is. No permanence, no perseverance in existence, can even be conceived of without men willing to testify to what is and appears to them be- + +cause it is. + +The story of the conflict between truth and politics is an old and complicated one, and nothing would be gained by simplification or moral denunciation. Throughout history, the truth-seekers and truthtellers have been aware of the risks of their business; as long as they did not interfere with the course of the world, they were covered with ridicule, but he who forced his fellow-citizens to take him seriously by trying to set them free from falsehood and illusion was in danger of his life : "If they could lay hands on [such a] man . . . they would kill him," Plato says in the last sentence of the cave allegory. The Platonic conflict between truthteller and citizens cannot be explained by the Latin adage, or any of the later theories that, implicitly or explicitly, justify lying, among other transgressions, if the survival of the city is at stake. No enemy is mentioned + +in Plato's story; the many live peacefully in their cave among themselves, mere spectators of images, involved in no action and hence threatened by nobody. The members of this community have no reason whatever to regard truth and truthtellers as their worst enemies, and Plato offers no explanation of their perverse love of deception and falsehood. If we could confront him with one of his later colleagues in political philosophy-namely, with Hobbes, who held that only "such truth, as opposeth no man's profit, nor pleasure, is to all men welcome" (an obvious statement, which, however, he thought important enough to end his Leviathan with)-he might agree about profit and pleasure but not with the assertion that there existed any kind of truth welcome to all men. Hobbes, but not Plato, consoled himself with the existence of indifferent truth, with "subjects" about which "men care not"-e.g., with mathematical truth, "the doctrine of lines and figures" that "crosses no man's ambition, profit or lust." For, Hobbes wrote, "I doubt not, but if it had been a thing contrary to any man's right of dominion, or to the interest of men that have dominion, that the three angles of a triangle should be equal to two angles of a square; that doctrine should have been, if not disputed, yet by the burning of all books of geometry, suppressed, as far as he whom it concerned was + +able." 4 + +No doubt, there is a decisive difference between Hobbes' mathematical axiom and the true standard for human conduct that Plato's philosopher is supposed to bring back from his journey into the sky of ideas, although Plato, who believed that mathematical truth opened the eyes of the mind to all truths, was not aware of it. Hobbes' example strikes us as relatively harmless; we are inclined to assume that the human mind will always be able to reproduce such axiomatic statements as "the three angles of a triangle should be equal to two angles of a square," and we conclude that "the burning of all books of geometry" would not be radically effective. The danger would be considerably greater with respect to scientific statements; had history taken a different tum, the whole modern scientific development from Galileo to Einstein might not have come to pass. And certainly the most vulnerable + +truth of thls kind would be those highly differentiated and always unique thought trains-of which Plato's doctrine of ideas is an eminent example-whereby men, since time immemorial, have tried to think rationally beyond the limits of human knowledge. The modern age, which believes that truth is neither given to nor disclosed to but produced by the human mind, has assigned, since Leibniz, mathematical, scientific, and philosophical truths to the common species of rational truth as distinguished from factual truth. I shall use this distinction for the sake of convenience without discussing its intrinsic legitimacy. Wanting to find out what injury political power is capable of inflicting upon truth, we look into these matters for political rather than philosophical reasons, and hence can afford to disregard the question of what truth is, and be content to take the word in the sense in which men commonly understand it. And if we now think of factual truths--of such modest verities as the role during the Russian Revolution of a man by the name of Trotsky, who appears in none of the Soviet Russian history books-we at once become aware of how much more vulnerable they are than all the kinds of rational truth taken together. Moreover, since facts and events-the invariable outcome of men living and acting together-constitute the very texture of the political realm, it is, of course, factual truth that we are most concerned with here. Dominion (to speak Hobbes' language ) when it attacks rational truth oversteps, as it were, its domain, while it gives battle on its own ground when it falsifies or lies away facts. The chances of factual truth surviving the onslaught of power are very slim indeed; it is always in danger of being maneuvered out of the world not only for a time but, potentially, forever. Facts and events are infinitely more fragile things than axioms, discoveries, theories-even the most wildly speculative ones-produced by the human mind; they occur in the field of the ever-changing affairs of men, in whose flux there is nothing more permanent than the admittedly relative permanence of the human mind's structure. Once they are lost, no rational effort will ever bring them back. Perhaps the chances that Euclidean mathematics or Einstein's theory of relativity-let alone Plato's philosophy-would have been + +reproduced in time if their authors had been prevented from handing them down to posterity are not very good either, yet they are Infinitely better than the chances that a fact of importance, forgotten or, more likely, lied away, will one day be rediscovered. + +II + +Although the politically most relevant truths are factual, the conflict between truth and politics was first discovered and articulated with respect to rational truth. The opposite of a rationally true statement is either error and ignorance, as in the sciences, or illusion and opinion, as in philosophy. Deliberate falsehood, the plain lie, plays its role only in the domain of factual statements, and it seems significant, and rather odd, that in the long debate about this antagonism of truth and politics, from Plato to Hobbes, no one, apparently, ever believed that organized lying, as we know it today, could be an adequate weapon against truth. In Plato, the truthteller is in danger of his life, and in Hobbes, where he has become an author, he is threatened with the burning of his books; mere mendacity is not an issue. It is the sophist and the ignoramus rather than the liar who occupy Plato's thought, and where he distinguishes between error and lie-that is, between "involuntary and voluntary 1/tfvoos "-he is, characteristically, much harsher on people 'wallowing in swinish ignorance" than on liars. 5 Is this because organized lying, dominating the public realm, as distinguished from the private liar who tries his luck on his own hook, was still unknown? Or has this something to do with the striking fact that, except for Zoroastrianism, none of the major religions included lying as such, as distinguished from "bearing false witness," in their catalogues of grave sins? Only with the rise of Puritan morality, coinciding with the rise of organized science, whose progress had to be assured on the firm ground of the absolute veracity and reliability of every scientist, were lies considered serious offenses. + +However that may be, historically the conflict between truth and politics arose out of two diametrically opposed ways of life-thP. + +life of the philosopher, as interpreted first by Parmenides and then by Plato, and the way of life of the citizen. To the citizens' everchanging opinions about human affairs, which themselves were in a state of constant flux, the philosopher opposed the truth about those things which in their very nature were everlasting and from which, therefore, principles could be derived to stabilize human affairs. Hence the opposite to truth was mere opinion, which was equated with illusion, and it was this degrading of opinion that gave the conflict its political poignancy; for opinion, and not truth, belongs among the indispensable prerequisites of all power. "All governments rest on opinion," James Madison said, and not even the most autocratic ruler or tyrant could ever rise to power, let alone keep it, without the support of those who are like-minded. By the same token, every claim in the sphere of human affairs to an absolute truth, whose validity needs no support from the side of opinion, strikes at the very roots of all politics and all governments. This antagonism between truth and opinion was further elaborated by Plato (especially in the Gorgias) as the antagonism between communicating in the form of "dialogue," which is the adequate speech for philosophical truth, and in the form of "rhetoric," by which the demagogue, as we would say today, persuades the mul- + +titude. + +Traces of this original conflict can still be found in the earlier stages of the modern age, though hardly in the world we live in. In Hobbes, for instance, we still read of an opposition of two "contrary faculties" : "solid reasoning" and "powerful eloquence," the former being "grounded upon principles of truth, the other upon opinions . . . and the passions and interests of men, which are different and mutable." 6 More than a century later, in the Age of Enlightenment, these traces have aln:ost but not quite disappeared, and where the ancient antagonism still survives, the emphasis has �hifted. In terms of pre-modern philosophy, Lessing's magnificent "Sage jeder, was ihm W ahrheit diinkt, und die Wahrheit selbst sei Gott empfohlen" ("Let each man say what he deems truth, and let truth itself be commended unto God" ) would have plainly si.I?Ilified, Man is not capable of truth, all his truths, alas, are + +oo�at, mere opinions, whereas for Lessing it meant, on the contrary, Let us thank God that we don't know the truth. Even where the note of jubilation-the insight that for men, living in company, the inexhaustible richness of human discourse is infinitely more significant and meaningful than any One Truth could ever be-is absent, the awareness of the frailty of human reason has prevailed since the eighteenth century without giving rise to complaint or lamentation. We can find it in Kant's grandiose Critique of Pure Reason, in which reason is led to recognize its own limitations, as we hear it in the words of Madison, who more than once stressed that "the reason of man, like man himself, is timid and cautious when left alone, and acquires firmness and confidence in proportion to the number with which it is associated." 7 Considerations of this kind, much more than notions about the individual's right to self-expression, played a decisive part in the finally more or less successful struggle to obtain freedom of thought for the spoken and + +the printed word. + +Thus Spinoza, who still believed in the infallibility of human reason and is often wrongly praised as a champion of free thought and speech, held that "every man is by indefeasible natural right the master of his own thoughts," that "every man's understanding is his own, and that brains are as diverse as palates," from which he concluded that "it is best to grant what cannot be abolished" and that laws prohibiting free thought can only result in "men thinking one thing and saying another," hence in "the corruption of good faith" and "the fostering of ... perfidy." However, Spinoza nowhere demands freedom of speech, and the argument that human reason needs communication with others and therefore publicity for its own sake is conspicuous by its absence. He even counts man's need for communication, his inability to hide his thoughts and keep silent, among the "common failings" that the philosopher does not share. 8 Kant, on the contrary, stated that "the external power that deprives man of the freedom to communicate his thoughts pubiicly, deprives him at the same time of his freedom to think" (italics added ), and that the only guarantee for "the correctness" of our thinking lies in that "we think, as it were, in com- + +munity with others to whom we communicate our thoughts as they communicate theirs to us." Man's reason, being fallible, can function only if he can make "public use" of it, and this is equally true for those who, still in a state of "tutelage," are unable to use their minds "without the guidance of somebody else" and for the "scholar," who needs "the entire reading public" to examine and + +control his results.9 + +In this context, the question of numbers, mentioned by Madison, is of special importance. The shift from rational truth to opinion implies a shift from man in the singular to men in the plural, and this means a shift from a domain where, Madison says, nothing counts except the "solid reasoning" of one mind to a realm where "strength of opinion" is determined by the individual's reliance upon "the number which he supposes to have entertained the same opinions"-a number, incidentally, that is not necessarily limited to one's contemporaries. Madison still distinguishes this life in the plural, which is the life of the citizen, from the life of the philosopher, by whom such considerations "ought to be disregarded," but this distinction has no practical consequence, for "a nation of philosophers is as little to be expected as the philosophical race of kings wished for by Plato." 10 We may note in passing that the very notion of "a nation of philosophers" would have been a contradiction in terms for Plato, whose whole political philosophy, including its outspoken tyrannical traits, rests on the conviction that truth + +can be neither gained nor communicated among the many. + +In the world we live in, the last traces of this ancient antagonism between the philosopher's truth and the opinions in the market place have disappeared. Neither the truth of revealed religion, which the political thinkers of the seventeenth century still treated as a major nuisance, nor the truth of the philosopher, disclosed to man in solitude, interferes any longer with the affairs of the world. In respect to the former, the separation of church and state has given us peace, and as to the latter, it ceased long ago to claim dominion-unless one takes the modem ideologies seriously as philosophies, which is difficult indeed since their adherents openly proclaim them to be political weapons and consider the whole + +question of truth and truthfulness irrelevant. Thinking in tenns of the tradition, one may feel entitled to conclude from this state of affairs that the old conflict has finally been settled, and especially that its original cause, the clash of rational truth and opinion, has + +disappeared. + +Strangely, however, this is not the case, for the clash of factual truth and politics, which we witness today on such a large scale, has-in some respects, at least-very similar traits. While probably no former time tolerated so many diverse opinions on religious or philosophical matters, factual truth, if it happens to oppose a given group's profit or pleasure, is greeted today with greater hostility than ever before. To be sure, state secrets have always existed; every government must classify certain information, withhold it from public notice, and he who reveals authentic secrets has always been treated as a traitor. With this I am not concerned here. The facts I have in mind are publicly known, and yet the same public that knows them can successfully, and often spontaneously, taboo their public discussion and treat them as though they were what they are not-namely, secrets. That their assertion then should prove as dangerous as, for instance, preaching atheism or some other heresy proved in former times seems a curious phenomenon, and its significance is enhanced when we find it also in countries that are ruled tyrannically by an ideological government. (Even in Hitler's Germany and Stalin's Russia it was more dangerous to talk about concentration and extermination camps, whose existence was no secret, than to hold and to utter "heretical" views on anti-Semitism, racism, and Communism.) What seems even more disturbing is that to the extent to which unwelcome factual truths are tolerated in free countries they are often, consciously or unconsciously, transformed into opinions-as though the fact of Germany's support of Hitler or of France's collapse before the German armies in 1940 or of Vatican policies during the Second World War were not a matter of historical record but a matter of opinion. Since such factual truths concern issues of immediate political relevance, there is more at stake here than the perhaps inevitable tension between two ways of life within the framework of a common and commonly + +recognized reality. What is at stake here is this common and factual reality itself, and this is indeed a political problem of the first order. And since factual truth, though it is so much less open to argument than philosophical truth, and so obviously within the grasp of everybody, seems often to suffer a similar fate when it is exposed in the market place-namely, to be countered not by lies and deliberate falsehoods but by opinion-it may be worth while to reopen the old + +and apparently obsolete question of truth versus opinion. + +For, seen from the viewpoint of the truthteller, the tendency to transform fact into opinion, to blur the dividing line between them, is no less perplexing than the truthteller's older predicament, so vividly expressed in the cave allegory, in which the philosopher, upon his return from his solitary journey to the sky of everlasting ideas, tries to communicate his truth to the multitude, with the result that it disappears in the diversity of views, which to him are illusions, and is brought down to the uncertain level of opinion, so that now, back in the cave, truth itself appears in the guise of the 00Kli J.LOL ("it SeemS tO me" )-the Very OO�aL he had hoped tO leaVe behind once and for all. However, the reporter of factual truth is even worse off. He does not return from any journey into regions beyond the realm of human affairs, and he cannot console himself with the thought that he has become a stranger in this world. Similarly, we have no right to console ourselves with the notion that his truth, if truth it should be, is not of this world. If his simple factual statements are not accepted-truths seen and witnessed with the eyes of the body, and not the eyes of the mind-the suspicion arises that it may be in the nature of the political realm to deny or pervert truth of every kind, as though men were unable to come to terms with its unyielding, blatant, unpersuasive stubbornness. If this should be the case, things would look even more desperate than Plato assumed, for Plato's truth, found and actualized in solitude, transcends, by definition, the realm of the many, the world of human affairs. (One can understand that the philosopher, in his isolation, yields to the temptation to use his truth as a standard to be imposed upon human affairs; that is, to equate the transcendence inherent in philosophical truth with the altogether different kind + +of "transcendence" by which yardsticks and other standards of measurement are separated from the multitude of objects they arc to measure, and one can equally well understand that the multitude will resist this standard, since it is actually derived from a sphere that is foreign to the realm of human affairs and whose connection with it can be justified only by a confusion.) Philosophical truth. when it enters the market place, changes its nature and becomes opinion, because a veritable fLmif3aut<; ££ .. a>..>..o yivo<;, a shifting not merely from one kind of reasoning to another but from one way of + +human existence to another, has taken place. + +Factual truth, on the contrary, is always related to other people : it concerns events and circumstances in which many are involved; it is established by witnesses and depends upon testimony; it exists only to the extent that it is spoken about, even if it occurs in the domain of privacy. It is political by nature. Facts and opinions, though they r.1ust be kept apart, are not antagonistic to each other; they belong to the same realm. Facts inform opinions, and opinions, inspired by different interests and passions, can differ widely and still be legitimate as long as they respect factual truth. Freedom of opinion is a farce unless factual information is guaranteed and the facts themselves are not in dispute. In other words, factual truth informs political thought just as rational truth informs + +philosophical speculation. + +But do facts, independent of opinion and interpretation, exist at all? Have not generations of historians and philosophers of history demonstrated the impossibility of ascertaining facts without interpretation, since they must first be picked out of a chaos of sheer happenings (and the principles of choice are surely not factual data) and then be fitted into a story that can be told only in a certain perspective, which has nothing to do with the original occurrence? No doubt these and a great many more perplexities inherent in the historical sciences are real, but they are no argument against the existence of factual matter, nor can they serve as a justification for blurring the dividing lines between fact, opinion, and interpretation, or as an excuse for the historian to manipulate facts as he pleases. Even if we admit that every generation has the right + +to write its own history, we admit no more than that it has the right to rearrange the facts in accordance with its own perspective; we don't admit the right to touch the factual matter itself. To illustrate this point, and as an excuse for not pursuing this issue any further: During the twenties, so a story goes, Clemenceau, shortly before his death, found himself engaged in a friendly talk with a representative of the Weimar Republic on the question of guilt for the outbreak of the First World War. "What, in your opinion," Clemenceau was asked, "will future historians think of this troublesome and controversial issue?" He replied, "This I don't know. But I know for certain that they will not say Belgium invaded Germany." We are concerned here with brutally elementary data of this kind, whose indestructibility has been taken for granted even by the most + +extreme and most sophisticated believers in historicism. + +It is true, considerably more than the whims of historians would be needed to eliminate from the record the fact that on the night of August 4, 1914, German troops crossed the frontier of Belgium; it would require no less than a power monopoly over the entire civilized world. But such a power monopoly is far from being inconceivable, and it is not difficult to imagine what the fate of factual truth would be if power interests, national or social, had the last say in these matters. Which brings us back to our suspicion that it may be in the nature of the political realm to be at war with truth in all its forms, and hence to the question of why a commitment even to factual truth is felt to be an anti-political attitude. + +Ill + +When I said that factual, as opposed to rational, truth is not antagonistic to opinion, I stated a half-truth. All truths-not only the various kinds of rational truth but also factual truth-are opposed to opinion in their mode of asserting validity. Truth carries within itself an element of coercion, and the frequently tyrannical tendencies so deplorably obvious among professional truthtellers may be caused less by a failing of character than by the strain of habitually + +living under a kind of compulsion. Statements such as "The three angles of a triangle are equal to two angles of a square," "The earth moves around the sun," "It is better to suffer wrong than to do wrong," "In August 1914 Germany invaded Belgium" are very different in the way they are arrived at, but, once perceived as true and pronounced to be so, they have in common that they are beyond agreement, dispute, opinion, or consent. For those who accept them, they are not changed by the numbers or lack of numbers who entertain the same proposition; persuasion or dissuasion is useless, for the content of the statement is not of a persuasive nature but of a coercive one. (Thus Plato, in the Timaeus, draws a line between men capable of perceiving the truth and those who happen to hold right opinions. In the former, the organ for the perception of truth [ vovs ] is awakened through instruction, which of course implies inequality and can be said to be a mild form of coercion, wherea� the latter had merely been persuaded. The views of the former, says Plato, are immovable, while the latter can always be persuaded to change their minds.11) What Mercier de la Riviere once remarked about mathematical truth applies to all kinds of truth : "Euclide est un veritable despote; et les verites geometriques qu'il nous a transmises, sont des lois veritablement despotiques." In much the same vein, Grotius, about a hundred years earlier, had insisted-when he wished to limit the power of the absolute prince-that "even God cannot cause two times two not to make four." He was invoking the compelling force of truth against political power; he was not interested in the implied limitation of divine omnipotence. These two remarks illustrate how truth looks in the purely political perspective, from the viewpoint of power, and the question is whether power could and should be checked not only by a constitution, a bill of rights, and by a multiplicity of powers, as in the system of checks and balances, in which, in Montesquieu's words, "le pouvoir arrete le pouvoir" that is, by factors that arise out of and belong to the political realm proper-but by something that arises from without, has its source outside the political realm, and is as independent of the wishes and + +Seen from the viewpoint of politics, truth has a despotic character. It is therefore hated by tyrants, who rightly fear the competition of a coercive force they cannot monopolize, and it enjoys a rather precarious status in the eyes of governments that rest on consent and abhor coercion. Facts are beyond agreement and consent, and all talk about them-all exchanges of opinion based on correct information-will contribute nothing to their establishment. Unwelcome opinion can be argued with, rejected, or compromised upon, but unwelcome facts possess an infuriating stubbornness that nothing can move except plain lies. The trouble is that factual truth, like all other truth, peremptorily claims to be acknowledged and precludes debate, and debate constitutes the very essence of political life. The modes of thought and communication that deal with truth, if seen from the political perspective, are necessarily domineering; they don't take into account other people's opinions, and taking these into account is the hallmark of all strictly political + +thinking. + +Political thought is representative. I form an opinion by considering a given issue from different viewpoints, by making present to my mind the standpoints of those who are absent; that is, I represent them. This process of representation does not blindly adopt the actual views of those who stand somewhere else, and hence look upon the world from a different perspective; this is a question neither of empathy, as though I tried to be or to feel like somebody else, nor of counting noses and joining a majority but of being and thinking in my own identity where actually I am not. The more people's standpoints I have present in my mind while I am pondering a given issue, and the better I can imagine how I would feel and think if I were in their place, the stronger will be my capacity for representative thinking and the more valid my final conclusions, my opinion. (It is this capacity for an "enlarged mentality" that enables men to judge; as such, it was discovered by Kant in the first part of his Critique of Judgment, though h� did not recognize the political and moral implications of his discovery.) The very process of opinion formation is determined by those in whose places somebody thinks and uses his own mind, and the + +only condition for this exertion of the imagination is disinterestedness, the liberation from one's own private interests. Hence, even if I shun all company or am completely isolated while forming an opinion, I am not simply together only with myself in the solitude of philosophical thought; I remain in this world of universal interdependence, where I can make myself the representative of everybody else. Of course, I can refuse to do this and form an opinion that takes only my own interests, or the interests of the group to which I belong, into account; nothing, indeed, is more common, even among highly sophisticated people, than the blind obstinacy that becomes manifest in lack of imagination and failure to judge. But the very quality of an opinion, as of a judgment, depends upon + +the degree of its impartiality. + +No opinion is self-evident. In matters of opinion, but not in matters of truth, our thinking is truly discursive, running, as it were, from place to place, from one part of the world to another, through all kinds of conflicting views, until it finally ascends from these particularities to some impartial generality. Compared to this process, in which a particular issue is forced into the open that it may show itself from all sides, in every possible perspective, until it is flooded and made transparent by the full light of human comprehension, a statement of truth possesses a peculiar opaqueness. Rational truth enlightens human understanding, and factual truth must inform opinions, but these truths, though they are never obscure, are not transparent either, and it is in their very nature to withstand further elucidation, as it is in the nature of light to with- + +stand enlightenment. + +Nowhere, moreover, is this opacity more patent and more irritating than where we are confronted with facts and factual truth, for facts have no conclusive reason whatever for being what they are ; they could always have been otherwise, and this annoying contingency is literally unlimited. It is because of the haphazardness of facts that pre-modern philosophy refused to take seriously the realm of human affairs, which is permeated by factuality, or to believe that any meaningful truth could ever be discovered in the "melancholy haphazardness" (Kant) of a sequence of event� + +which constitutes the course of this world. Nor has any modem philosophy of history been able to make its peace with the intractable, unreasonable stubbornness of sheer factuality; modem philosophers have conjured up all kinds of necessity, from the dialectical necessity of a world spirit or of material conditions to the necessities of an allegedly unchangeable and known human nature, in order to c!eanse the last vestiges of that apparently arbitrary "it might have been otherwise" (which is the price of freedom) from the only realm where men are truly free. It is true that in retrospect-that is, in historical perspective-every sequence of events looks as though it could not have happened otherwise, but this is an optical, or, rather, an existential, illusion : nothing could ever happen if reality did not kill, by definition, all the other potential- + +ities originally inherent in any given situation. + +In other words, factual truth is no more self-evident than opinion, and this may be among the reasons that opinion-holders find it relatively easy to discredit factual truth as just another opinion. Factual evidence, moreover, is established through testimony by eyewitnesses-notoriously unreliable-and by records, documents, and monuments, all of which can be suspected as forgeries. In the event of a dispute, only other witnesses but no third and higher instance can be invoked, and settlement is usually arrived at by way of a majority; that is, in the same way as the settlement of opinion disputes-a wholly unsatisfactory procedure, since there is nothing to prevent a majority of witnesses from being false witnesses. On the contrary, under certain circumstances the feeling of belonging to a majority may even encourage false testimony. In other words, to the extent that factual truth is exposed to the hostility of opinion-holders, it is at least as vulnerable as rational phil- + +osophical truth. + +I observed before that in some respects the teller of factual truth is worse off than Plato's philosopher-that his truth has no transcendent origin and possesses not even the relatively transcendent qualities of such political principles as freedom, justice, honor, and courage, all of which may inspire, and then become manifest in, human action. We shall now see that this disadvantage has more + +serious consequences than we had thought; namely, consequences that concern not only the person of the truthteller but-more important-the chances for his truth to survive. Inspiration of and manifestation in human action may not be able to compete with the compelling evidence of truth, but they can compete, as we shall see, with the persuasiveness inherent in opinion. I took the Socratic proposition "It is better to suffer wrong than to do wrong" as an example of a philosophical statement that concerns human conduct, and hence has political implications. My reason was partly that this sentence has become the beginning of Western ethical thought, and partly that, as far as I know, it has remained the only ethical proposition that can be derived directly from the specifically philosophical experience. (Kant's categorical imperative, the only competitor in the field, could be stripped of its Judaeo-Christian ingredients, which account for its formulation as an imperative instead of a simple proposition. Its underlying principle is the axiom of non-contradiction-the thief contradicts himself because he wants to keep the stolen goods as his property-and this axiom owes its validity to the conditions of thought that Socrates was the + +first to discover.) + +The Platonic dialogues tell us time and again how paradoxical the Socratic statement (a proposition, and not an imperative) sounded, how easily it stood refuted in the market place where opinion stands against opinion, and how incapable Socrates was of proving and demonstrating it to the satisfaction not of his adversaries alone but also of his friends and disciples. (The most dramatic of these passages can be found in the beginning of the Republic.12 Socrates, having tried in vain to convince his adversary Thrasymachus that justice is better than injustice, is told by his disciples, Glaukon and Adeimantus, that his proof was far from convincing. Socrates admires their speeches: "There must indeed be some divine quality in your nature, if you can plead the cause of injustice so eloquently and still not be convinced yourselves that it is better than justice." In other words, they were convinced belore the argument started, and all that was said to uphold the truth of the proposition not onlv failed to persuade the non- + +convinced but had not even the force to confirm their convictions.) Everything that can be said in its defense we find in the various Platonic dialogues. The chief argument states that for man, being one, it is better to be at odds with the whole world than to be at odds with and contradicted by himself 13-an argument that is compelling indeed for the philosopher, whose thinking is characterized by Plato as a silent dialogue with himself, and whose existence therefore depends upon a constantly articulated intercourse with himself, a splitting-into-two of the one he nevertheless is; for a basic contradiction between the two partners who carry on the thinking dialogue would destroy the very conditions of philosophizing.14 In other words, since man contains within himself a partner from whom he can never win release, he will be better off not to live in company with a murderer or a liar. Or, since thought is the silent dialogue carried on between me and myself, I must be careful to keep the integrity of this partner intact; for otherwise I shall + +surely lose the capacity for thought altogether. + +To the philosopher-or, rather, to man insofar as he is a thinking being-this ethical proposition about doing and suffering wrong is no less compelling than mathematical truth. But to man insofar as he is a citizen, an acting being concerned with the world and the pub!ic welfare rather than with his own well-being-including, for instance, his "immortal soul" whose "health" should have precedence over the needs of a perishable body-the Socratic statement is not true at all. The disastrous consequences for any community that began in all earnest to follow ethical precepts derived from man in the singular-be they Socratic or Platonic or Christianhave been frequently pointed out. Long before Machiavelli recommended protecting the political realm against the undiluted principles of the Christian faith (those who refuse to resist evil permit the wicked "to do as much evil as they please" ), Aristotle warned against giving philosophers any say in political matters. (Men who for professional reasons must be so unconcerned with "what is good for themselves" cannot very well be trusted with what is good for others, and least of all with the "common good," the down-to-earth + +Since philosophical truth concerns man m his singularity, it is unpolitical by nature. If the philosopher nevertheless wishes his truth to prevail over the opinions of the multitude, he will suffer defeat, and he is likely to conclude from this defeat that truth is impotent-a truism that is just as meaningful as if the mathematician, unable to square the circle, should deplore the fact that a circle is not a square. He may then be tempted, like Plato, to win the ear of some philosophically inclined tyrant, and in the fortunately highly unlikely case of success he might erect one of those tyrannies of "truth" which we know chiefly from the various political utopias, and which, of course, politically speaking, are as tyrannical as other forms of despotism. In the slightly less unlikely event that his truth should prevail without the help of violence, simply because men happen to concur in it, he would have won a Pyrrhic victory. For truth would then owe its prevalence not to its own compelling quality but to the agreement of the many, who might change their minds tomorrow and agree on something else; what had been philosophical truth would have become mere opinion. Since, however, philosophical truth carries within itself an element of coercion, it may tempt the statesman under certain conditions, no less than the power of opinion may tempt the philosopher. Thus, in the Declaration of Independence, Jefferson declared certain "truths to be self-evident," because he wished to put the basic consent among the men of the Revolution beyond dispute and argument; like mathematical axioms, they should express "beliefs of men" that "depend not on their own will, but follow involuntarily the evidence proposed to their minds." 16 Yet by saying "We hold these truths to be self-evident," he conceded, albeit without becoming aware of it, that the statement "All men are created equal, + +. + +is not self-evident but stands in need of agreement and consentthat equality, if it is to be politically relevant, is a matter of opinion, and not "the truth." There exist, on the other hand, philosophical or religious statements that correspond to this opinionsuch as that all men are equal before God, or before death, or insofar as they all belong to the same species of animal rationalebut none of them was ever of any political or practical conse- + +quence, because the equalizer, whether God, or death, or nature, transcended and remained outside the realm in which human intercourse takes place. Such "truths" are not between men but above them, and nothing of the sort lies behind the modern or the ancient -especially the Greek--<:onsent to equality. That all men are created equal is not self-evident nor can it be proved. We hold this opinion because freedom is possible only among equals, and we believe that the joys and gratifications of free company are to be preferred to the doubtful pleasures of holding dominion. Such preferences are politically of the greatest importance, and there are few things by which men are so profoundly distinguished from each other as by these. Their human quality, one is tempted to say, and certainly the quality of every kind of intercourse with them, depends upon such choices. Still, these are matters of opinion and not of truth-as Jefferson, much against his will, admitted. Their validity depends upon free agreement and consent; they are arrived at by discursive, representative thinking; and they are communicated by + +means of persuasion and dissuasion. + +The Socratic proposition "It is better to suffer wrong than to do wrong" is not an opinion but claims to be truth, and though one may doubt that it ever had a direct political consequence, its impact upon practical conduct as an ethical precept is undeniable ; only religious commandments, which are absolutely binding for the community of believers, can claim greater recognition. Does this fact not stand in clear contradiction to the generally accepted impotence of philosophical truth? And since we know from the Platonic dialogues how unpersuasive Socrates' statement remained for friend and foe alike whenever he tried to prove it, we must ask ourselves how it could ever have obtained its high degree of validity. Obviously, this has been due to a rather unusual kind of persuasion; Socrates decided to stake his life on this truth-to set an example, not when he appeared before the Athenian tribunal but when he refused to escape the death sentence. And this teaching by example is, indeed, the only form of "persuasion" that philosophical truth is capable of without perversion or distortion;17 by the same token, philosophical truth can become "practical" and inspire action + +without violating the rules of the political realm only when it manages to become manifest in the guise of an example. This is the only chance for an ethical principle to be verified as well as validated. Thus, to verify, for instance, the notion of courage we may recall the example of Achilles, and to verify the notion of goodness we are inclined to think of Jesus of Nazareth or of St. Francis; these examples teach or persuade by inspiration, so that whenever we try to perform a deed of courage or of goodness it is as though we imitated someone else-the imitatio Christi, or whatever the case may be. It has often been remarked that, as Jefferson said, "a lively and lasting sense of filial duty is more effectually impressed on the mind of a son or daughter by reading King Lear than by all the dry volumes of ethics and divinity that ever were written," 18 and that, as Kant said, "general precepts learned at the feet either of priests or philosophers, or even drawn from one's own resources, are never so efficacious as an example of virtue or holiness." 19 The reason, as Kant explains, is that we always need "intuitions . . . to verify the reality of our concepts." "If they are pure concepts of the understanding," such as the concept of the triangle, "the intuitions go by the name of schemata," such as the ideal triangle, perceived only by the eyes of the mind and yet indispensable to the recognition of all real triangles; if, however, the concepts are practical, relating to conduct, "the intuitions are called examples." 20 And, unlike the schemata, which our mind produces of its own accord by means of the imagination, these examples derive from history and poetry, through which, as Jefferson pointed out, an altogether different "field of imagination + +is laid open to our use." + +This transformation of a theoretical or speculative statement into exemplary truth-a transformation of which only moral philosophy is capable-is a borderline experience for the philosopher: by setting an example and "persuading" the multitude in the only way open to him, he has begun to act. Today, when hardly any philosophical statement, no matter how daring, will be taken seriously enough to endanger the philosopher's life, even this rare chance of having a philosophical truth politically validated has disappeared. + +In our context, however, it is important to notice that such a possibility does exist for the teller of rational truth; for it does not exist under any circumstances for the teller of factual truth, who in this respect, as in other respects, is worse off. Not only do factual statements contain no principles upon which men might act and which thus could become manifest in the world; their very content defies this kind of verification. A teller of factual truth, in the unlikely event that he wished to stake his life on a particular fact, would achieve a kind of miscarriage. What would become manifest in his act would be his courage or, perhaps, his stubbornness but neither the truth of what he had to say nor even his own truthfulness. For why shouldn't a liar stick to his lies with great courage, especially in politics, where he might be motivated by patriotism or some + +other kind of legitimate group partiality? + +IV + +The hallmark of factual truth is that its opposite is neither error nor illusion nor opinion, no one of which reflects upon personal truthfulness, but the deliberate falsehood, or lie. Error, of course, is possible, and even common, with respect to factual truth, in which case 'this kind of truth is in no way different from scientific or rational truth. But the point is that with respect to facts there exists another alternative, and this alternative, the deliberate falsehood, does not beloilg to the same species as propositions that, whether right or mistaken, intend no more than to say what is, or how something that is appears to me. A factual statement-Germany invaded Belgium in August 1914-acquires political implications only by being put in an interpretative context. But the opposite proposition, which Clemenceau, still unacquainted with the art of rewriting history, thought absurd, needs no context to be of political significance. It is clearly an attempt to change the record, and as such, it is a form of action. The same is true when the liar, lacking the power to make his falsehood stick, does not insist on the gospel truth of his statement but pretends that this is his "opinion," + +to which he claims his constitutional right. This is frequently done by subversive groups, and in a politically immature public the resulting confusion can be considerable. The blurring of the dividing line between factual truth and opinion belongs among the many forms that lying can assume, all of which are forms of action. + +While the liar is a man of action, the truthteller, whether he tells rational or factual truth, most emphatically is not. If the teller of factual truth wants to play a political role, and therefore to be persuasive, he will, more often than not, go to considerable lengths to explain why his particular truth serves the best interests of some group. And, just as the philosopher wins a Pyrrhic victory when his truth becomes a dominant opinion among opinion-holders, the teller of factual truth, when he enters the political realm and identifies himself wit!l some partial interest and power formation, compromises on the only quality that could have made his truth appear plausible, namely, his personal truthfulness, guaranteed by jmpartiality, integrity, independence. There is hardly a political figure more likely to arouse justified suspicion than the professional truthteller who has discovered some happy coincidence between truth and interest. The liar, on the contrary, needs no such doubtful accommodation to appear on the political scene; he has the great advantage that he always is, so to speak, already in the midst of it. He is an actor by nature; he says what is not so because he wants things to be different from what they are-that is, he wants to change the world. He takes advantage of the undeniable affinity of our capacity for action, for changing reality, with this mysterious faculty of ours that enables us to say, "The sun is shining," when it is raining cats and dogs. If we were as thoroughly conditioned in our behavior as some philosophies have wished us to be, we would never be able to accomplish this little miracle. In other words, our ability to lie-but not necessarily our ability to tell the truth-belongs among the few obvious, demonstrable data that confirm human freedom. That we can change the circumstances under which we live at all is because we are relatively free from them, and it is this freedom that is abused and perverted through mendacity. If it is the well-nigh irresistible temptation of the profes- + +sional historian to fall into the trap of necessity and implicitly deny freedom of action, it is the almost equally irresistible temptation of the professional politician to overestimate the possibilities of this freedom and implicitly condone the lying denial, or distortion of + +facts. + +To be sure, as far as action is concerned, organized lying is a marginal phenomenon, but the trouble is that its opposite, the mere telling of facts, leads to no action whatever; it even tends, under normal circumstances, toward the acceptance of things as they are. (This, of course, is not to deny that the disclosure of facts may be legitimately used by political organizations or that, under certain circumstances, factual matters brought to public attention will considerably encourage and strengthen the claims of ethnic and social groups.) Truthfulness has never been counted among the political virtues, because it has little indeed to contribute to that change of the world and of circumstances which is among the most legitimate political activities. Only where a community has embarked upon organized lying on principle, and not only with respect to particulars, can truthfulness as such, unsupported by the distorting forces of power and interest, become a political factor of the first order. Where everybody lies about everything of importance, the truthteller, whether he knows it or not, has begun to act; he, too, has engaged himself in political business, for, in the unlikely event that he survives, he has made a start + +toward changing the world. + +In this situation, however, he will again soon find himself at an annoying disadvantage. I mentioned earlier the contingent character of facts, which could always have been otherwise, and which therefore possess by themselves no trace of self-evidence or plausibility for the human mind. Since the liar is free to fashion his "facts" to fit the profit and pleasure, or even the mere expectations, of his audience, the chances are that he will be more persuasive than the truthteller. Indeed, he will usually have plausibility on his side; his exposition will sound more logical, as it were, since the element of unexpectedness-one of the outstanding characteristics of all events-has mercifully disappeared. It is not only ra- + +tional truth that, in the Hegelian phrase, stands common sense on its head; reality quite frequently offends the soundness of common- + +sense reasoning no less than it offends profit and pleasure. + +We must now turn our attention to the relatively recent phenomenon of mass manipulation of fact and opinion as it has become evident in the rewriting of history, in image-making, and in actual government policy. The traditional political lie, so prominent in the history of diplomacy and statecraft, used to concern either true secrets-data that had never been made public-or intentions, which anyhow do not possess the same degree of reliability as accomplished facts; like everything that goes on merely inside ourselves, intentions are only potentialities, and what was intended to be a lie can always turn out to be true in the end. In contrast, the modern political lies deal efficiently with things that are not secrets at all but are known to practically everybody. This is obvious in the case of rewriting contemporary history under the eyes of those who witnessed it, but it is equally true in image-making of all sorts, in which, again, every known and established fact can be denied or neglected if it is likely to hurt the image; for an image, unlike an old-fashioned portrait, is supposed not to flatter reality but to offer a full-fledged substitute for it. And this substitute, because o0f modern techniques and the mass media, is, of course, much more in the public eye than the original ever was. We are finally confronted with highly respected statesmen who, like de Gaulle and Adenauer, have been able to build their basic policies on such evident non-facts as that France belongs among the victors of the last war and hence is one of the great powers, and "that the barbarism of National Socialism had affected only a relatively small percentage of the country." 21 All these lies, whether their authors know it or not, harbor an element of violence ; organized lying always tends to destroy whatever it has decided to negate, although only totalitarian governments have consciously adopted lying as the first step to murder. When Trotsky learned that he had never played a role in the Russian Revolution, he must have known that his death warrant had been signed. Clearly, it is easier to eliminate a public figure from the record of history if at the same time he + +can be eliminated from the world of the living. In other words, the difference between the traditional lie and the modern lie will more often than not amount to the difference between hiding and de- + +stroying. + +Moreover, the traditional lie concerned only particulars and was never meant to deceive literally everybody; it was directed at the enemy and was meant to deceive only him. These two limitations restricted the injury inflicted upon truth to such an extent that to us, in retrospect, it may appear almost harmless. Since facts always occur in a context, a particular lie-that is, a falsehood that makes no attempt to change the whole context-tears, as it were, a hole in the fabric of factuality. As every historian knows, one can spot a lie by noticing incongruities, holes, or the junctures of patched-up places. As long as the texture as a whole is kept intact, the lie will eventually show up as if of its own accord. The second limitation concerns those who are engaged in the business of deception. They used to belong to the restricted circle of statesmen and diplomats. who among themselves still knew and could preserve the truth. They were not likely to fall victims to their own falsehoods; they could deceive others without deceiving themselves. Both of these mitigating circumstances of the old art of lying are noticeably ab- + +sent from the manipulation of facts that confronts us today. + +What, then, is the significance of these limitations, and why are we justified in calling them mitigating circumstances? Why has selfdeception become an indispensable tool in the trade of imagemaking, and why should it be worse, for the world as well as for the liar himself, if he is deceived by his own lies than if he merely deceives others? What better moral excuse could a liar offer than that his aversion to lying was so great that he had to convince himself before he could lie to others, that, like Antonio in The Tempest, he had to make "a sinner of his memory, To credit his own lie"? And, finally, and perhaps most disturbingly, if the modem political lies are so big that they require a complete rearrangement of the whole factual texture-the making of another reality, as it were, into which they will fit without seam, crack, or fissure, exactly as the facts fitted into their own original context-what + +an adequate substitute for reality and factuality? + +A medieval anecdote illustrates how difficult it can be to lie to others without lying to oneself. Jt is a story about what happened one night in a town on whose watchtower a sentry was on duty day and night to warn the people of the approach of the enemy. The sentry was a man given to practical jokes, and that night he sounded the alarm just in order to give the townsfolk a little scare. His success was overwhelming: everybody rushed to the walls and the last to rush was the sentry himself. The tale suggests to what extent our apprehension of reality is dependent upon our sharing the world with our fellow-men, and what strength of character is required to stick to anything, truth or lie, that is unshared. In other words, the more successful a liar is, the more likely it is that be will fall prey to his own fabrications. Furthermore, the selfdeceived joker who proves to be in the same boat as his victims will appear vastly superior in trustworthiness to the cold-blooded liar who permits himself to enjoy his prank from without. Only self-deception is likely to create a semblance of truthfulness, and in a debate about facts the only persuasive factor that sometimes has a chance to prevail against pleasure, fear, and profit is personal + +appearance. + +Current moral prejudice tends to be rather harsh in respect to cold-blooded lying, whereas the often highly developed art of selfdeception is usually regarded with great tolerance and permissiveness. Among the few examples in literature that can be quoted against this current evaluation is the famous scene in the monastery at the beginning of The Brothers Karamazov. The father, an inveterate liar, asks the Staretz, "And what must I do to gain salvation?" and the Staretz replies, "Above all, never lie to yourself!" Dostoevski adds no explanation or elaboration. Arguments in support of the statement "It is better to lie to others than to deceive yourself' would have to point out that the cold-blooded liar remains aware of the distinction betwen truth and falsehood, so the truth he is hiding from others has not yet been maneuvered out of the world altogether; it has found its last refuge in him. The injury + +done to reality is neither complete nor final, and, by the same token, the injury done to the liar himself is not complete or final either. He lied, but he is not yet a liar. Both he and the world he deceived are not beyond "salvation"-to put it in the language of the Staretz. Such completeness and potential finality, which were unknown to former times, are the dangers that arise out of the modern manipulation of facts. Even in the free world, where the government has not monopolized the power to decide and tell what factually is or is not, gigantic interest organizations have generalized a kind of raison d'etat frame of mind such as was formerly restricted to the handling of foreign affairs and, in its worst excesses, to situations of clear and present danger. And national propaganda on the government level has learned more than a few tricks from business practices and Madison Avenue methods. Images made for domestic consumption, as distinguished from lies directed at a foreign adversary, can become a reality for everybody and first of all for the image-makers themselves, who while still in the act of preparing their "products" are overwhelmed by the mere thought of their victims' potential numbers. No doubt, the originators of the lying image who "inspire" the hidden persuaders still know that they want to deceive an enemy on the social or the national level, but the result is that a whole group of people, and even whole nations, may take their bearings from a web of deceptions to which + +their leaders wished to subject their opponents. + +What then happens follows almost automatically. The main effort of both the deceived group and the deceivers themselves is likely to be directed toward keeping the propaganda image intact, and this image is threatened less by the enemy and by real hostile interests than by those inside the group itself who have managed to escape its spell and insist on talking about facts or events that do not fit the image. Contemporary history is full of instances in which tellers of factual truth were felt to be more dangerous, and even more hostile, than the real opponents. These arguments against self-deception must not be confused with the protests of "idealists," whatever their merit, against lying as bad in principle and against the age-old art of deceiving the enemy. Politically, the point is + +that the modern art of self-deception is likely to transform an outside matter into an inside issue, so that an international or intergroup conflict boomerangs onto the scene of domestic politics. The self-deceptions practiced on both sides in the period of the Cold War are too many to enumerate, but obviously they are a case in point. Conservative critics of mass democracy have frequently outlined the dangers that this form of government brings to international affairs-without, however, mentioning the dangers peculiar to monarchies or oligarchies. The strength of their arguments lies in the undeniable fact that under fully democratic conditions de- + +ception without self-deception is well-nigh impossible. + +Under our present system of world-wide communication, covering a large number of independent nations, no existing power is anywhere near great enough to make its "image" foolproof. Therefore, images have a relatively short life expectancy; they are likely to explode not only when the chips are down and reality makes its reappearance in public but even before this, for fragments of facts constantly disturb and throw out of gear the propaganda war between conflicting images. However, this is not the only way, or even the most significant way, in which reality takes its revenge on those who dare defy it. The life expectancy of images could hardly be significantly increased even under a world government or some other modern version of the Pax Romana. This is best illustrated by the relatively closed systems of totalitarian governments and one-party dictatorships, which are, of course, by far the most effective agencies in shielding ideologies and images from the impact of reality and truth. (And such correction of the record is never smooth sailing. We read in a memorandum of 1935 found in the Smolensk Archive about the countless difficulties besetting this kind of enterprise. What, for instance, "should be done with speeches by Zinoviev, Kamenev, Rykov, Bukharin, et al., at Party Congresses, plenums of the Central Committee, in the Comintern, the Congress of Soviets, etc.? What of anthologies on Marxism ... written or edited jointly by Lenin, Zinoviev, ... and others? What of Lenin's writings edited by Kamenev? .. . What should be done in cases where Trotsky . . . had written an article + +in an issue of the Communist International? Should the whole number be confiscated?" 22 Puzzling questions indeed, to which the Archive contains no replies. ) Their trouble is that they must constantly change the falsehoods they offer as a substitute for the real story; changing circumstances require the substitution of one history book for another, the replacement of pages in the encyclopedias and reference books, the disappearance of certain names in favor of others unknown or little known before. And though this continuing instability gives no indication of what the truth might be, it is itself an indication, and powerful one, of the lying character of all public utterances concerning the factual world. It has frequently been noticed that the surest long-term result of brainwashing is a peculiar kind of cynicism-an absolute refusal to believe in the truth of anything, no matter how well this truth may be established. In other words, the result of a consistent and total substitution of lies for factual truth is not that the lies will now be accepted as truth, and the truth be defamed as lies, but that the sense by which we take our bearings in the real world-and the category of truth vs. falsehood is among the mental means to this end-is being + +destroyed. + +And for this trouble there is no remedy. It is but the other side of the disturbing contingency of all factual reality. Since everything that has actually happened in the realm of human affairs could just as well have been otherwise, the possibilities for lying are boundless, and this boundlessness makes for self -defeat. Only the occasional liar will find it possible to stick to a particular falsehood with unwavering consistency; those who adjust images and stories to ever-changing circumstances will find themselves floating on the wide-open horizon of potentiality, drifting from one possibility to the next, unable to hold on to any one of their own fabrications. Far from achieving an adequate substitute for reality and factuality, they have transformed facts and events back into the potentiality out of which they originally appeared. And the surest sign of the factuality of facts and events is precisely this stubborn thereness, whose inherent contingency ultimately defies all attempts at conclusive explanation. The image:;, on the contrary, can always be + +explained and made plausible-this gives them their momentary advantage over factual truth-but they can never compete in stability with that which simply is because it happens to be thus and not otherwise. This is the reason that consistent lying, metaphorically speaking, pulls the ground from under our feet and provides no other ground on which to stand. (In the words of Montaigne, "If falsehood, like truth, had but one face, we should know better where we are, for we should then take for certain the opposite of what the liar tells us. But the reverse of truth has a thousand shapes and a boundless field.") The experience of a trembling wobbling motion of everything we rely on for our sense of direction and reality is among the most common and most vivid experiences of + +men under totalitarian rule. + +Hence, the undeniable affinity of lying with action, with changing the world-in short, with politics-is limited by the very nature of the things that are open to man's faculty for action. The convinced image-maker is in error when he believes that he can anticipate changes by lying about factual matters that everybody wishes to eliminate anyhow. The erection of Potemkin's villages, so dear to the politicians and propagandists of underdeveloped countries, never leads to the establishment of the real thing but only to a proliferation and perfection of make-believe. Not the past-and all factual truth, of course, concerns the past-or the present, insofar as it is the outcome of the past, but the future is open to action. If the past and present are treated as parts of the future-that is, changed back into their former state of potentiality-the political realm is deprived not only of its main stabilizing force but of the starting point from which to change, to begin something new. What then begins is the constant shifting and shuffling in utter sterility which are characteristic of many new nations that had the bad + +luck to be born in an age of propaganda. + +That facts are not secure in the hands of power is obvious, but the point here is that power, by its very nature, can never produce a substitute for the secure stability of factual reality, which, because it is past, has grown into a dimension beyond our reach. Facts assert themselves by being stubborn, and their fragility is + +oddly combined with great resiliency-the same irreversibility that is the hallmark of all human action. In their stubbornness, facts are superior to power; they are less transitory than power formations, which arise when men get together for a purpose but disappear as soon as the purpose is either achieved or lost. This transitory character makes power a highly unreliable instrument for achieving permanence of any kind, and, therefore, not only truth and facts are insecure in its hands but untruth and non-facts as well. The political attitude toward facts must, indeed, tread the very narrow path between the danger of taking them as the results of some necessary development which men could not prevent and about which they can therefore do nothing and the danger of denying them, of trying to manipulate them out of the world. + +v + +In conclusion, I return to the questions I raised at the beginning of these reflections. Truth, though powerless and always defeated in a head-on clash with the powers that be, possesses a strength of its own: whatever those in power may contrive, they are unable to discover or invent a viable substitute for it. Persuasion and violence can destroy truth, but they cannot replace it. And this applies to rational or religious truth just as it applies, more obviously, to factual truth. To look upon politics from the perspective of truth, as I have done here, means to take one's stand outside the political realm. This standpoint is the standpoint of the truthteller, who forfeits his position-and, with it, the validity of what he has to sayif he tries to interfere directly in human affairs and to speak the language of persuasion or of violence. It is to this position and its significance for the political realm that we must now turn our at- + +tention. + +The standpoint outside the political realm-outside the community to which we belong and the company of our peers-is clearly characterized as one of the various modes of being alone. Outstanding among the existential modes of truthtelling are the solitude + +only their integrity but their very existence depends upon the good will of the government anyway. Very unwelcome truths have emerged from the universities, and very unwelcome judgments have been handed down from the bench time and again ; and these institutions, like other refuges of truth, have remained exposed to all the dangers arising from social and political power. Yet the chances for truth to prevail in public are, of course, greatly improved by the mere existence of such places and by the organization of independent, supposedly disinterested scholars associated with them. And it can hardly be denied that, at least in constitutionally ruled countries, the political realm has recognized, even in the event of conflict, that it has a stake in the existence of men + +and institutions over which it has no power. + +This authentically political significance of the Academe is today easily overlooked because of the prominence of its professional schools and the evolution of its natural-science divisions, where, unexpectedly, pure research has yielded so many decisive results that have proved vital to the country at large. No one can possibly gainsay the social and technical usefulness of the universities, but this importance is not political. The historical sciences and the humanities, which are supposed to find out, stand guard over, and interpret factual truth and human documents, are politically of greater relevance. The telling of factual truth comprehends much more than the daily information supplied by journalists, though without them we should never find our bearings in an ever-changing world and, in the most literal sense, would never know where we are. This is, of course, of the most immediate political importance; but if the press should ever really become the "fourth branch of government," it would have to be protected against government power and social pressure even more carefully than the judiciary is. For this very important political function of supplying information is exercised from outside the political realm, strictly speaking; + +Reality is different from, and more than, the totality of facts and events, which, anyhow, is unascertainable. Who says what is-AE/'H ra Mvr a-always tells a story, and in this story the particular + +facts lose their contingency and acquire some humanly comprehensible meaning. It is perfectly true that "all sorrows can be borne if you put them into a story or tell a story about them," in the words of Isak Dinesen, who not only was one of the great storytellers of our time but also-and she was almost unique in this respect-knew what she was doing. She could have added that joy and bliss, too, become bearable and meaningful for men only when they can talk about them and tell them as a story. To the extent that the teller of factual truth is also a storyteller, he brings about that "reconciliation with reality" which Hegel, the philosopher of history par excellence, understood as the ultimate goal of all philosophical thought, and which, indeed, has been the secret motor of all historiography that transcends mere learnedness. The transformation of the given raw material of sheer happenings which the historian, like the fiction writer (a good novel is by no means a simple concoction or a figment of pure fantasy), must effect is closely akin to the poet's transfiguration of moods or movements of the heart-the transfiguration of grief into lamentations or of jubilation into praise. We may see, with Aristotle, in the poet's political function the operation of a catharsis, a cleansing or purging of all emotions that could prevent men from acting. The political function of the storyteller-historian or novelist-is to teach acceptance of things as they are. Out of this acceptance, which can also be called truthfulness, arises the faculty of judgment-that, again in Isak Dinesen's words, "at the end we shall be privileged to view, and review, it-and that is what is named the + +day of judgment." + +There is no doubt that all these politically relevant functions are performed from outside the political realm. They require non-commitment and impartiality, freedom from self-interest in thought and judgment. The disinterested pursuit of truth has a long history; its origin, characteristically, precedes all our theoretical and scientific traditions. including our tradition of philosophical and political thought. I think it can be traced to the moment when Homer chose to sing the deeds of the Trojans no less than those of the Achaeans, and to praise the glory of Hector, the foe and the defeated man. + +no less than the glory of Achilles, the hero of his kinfolk. This had happened nowhere before ; no other civilization, however splendid, had been able to look with equal eyes upon friend and foe, upon success and defeat-which since Homer have not been recognized as ultimate standards of men's judgment, even though they are ultimates for the destinies of men's lives. Homeric impartiality echoes throughout Greek history, and it inspired the first great teller of factual truth, who became the father of history: Herodotus tells us in the very first sentences of his stories that he set out to prevent "the great and wondrous deeds of the Greeks and the barbarians from losing their due meed of glory." This is the root of all so-called objectivity-this curious passion, unknown outside Western civilization, for intellectual integrity at any price. Without it no science + +would ever have come into being. + +Since I have dealt here with politics from the perspective of truth, and hence from a viewpoint outside the political realm, I have failed to mention even in passing the greatness and the dignity of what goes on inside it. I have spoken as though the political realm were no more than a battlefield of partial, conflicting interests, where nothing counted but pleasure and profit, partisanship, and the lust for dominion. In short, I have dealt with politics as though I, too, believed that all public affairs were ruled by interest and power, that there would be no political realm at all if we were not bound to take care of life's necessities. The reason for this deformation is that factual truth clashes with the political only on this lowest level of human affairs, just as Plato's philosophical truth clashed with the political on the considerably higher level of opinion and agreement. From this perspective, we remain unaware of the actual content of political life--of the joy and the gratification that arise out of being in company with our peers, out of acting together and appearing in public, out of inserting ourselves into the world by word and deed, thus acquiring and sustaining our personal identity and beginning something entirely new. However, what I meant to show here is that this whole sphere, its greatness notwithstanding, is limited-that it does not encompass the whole of man's and the world's exister..ce. It is limited by those things + +which men cannot change at will. And it is only by respecting its own borders that this realm, where we are free to act and to change, can remain intact, preserving its integrity and keeping its promises. Conceptually, we may call truth what we cannot change; metaphorically, it is the ground on which we stand and the sky + +that stretches above us. + +THE CONQUEST OF SPACE + +AND THE STATURE + +OF MAN + +' 'HAS man's conquest of space increased or diminished his stat- + +ure?" 1 The question raised is addressed to the layman, not + +the scientist, and it is inspired by the humanist's concern with man, as distinguished from the physicist's concern with the reality of the physical world. To understand physical reality seems to demand not only the renunciation of an anthropocentric or geocentric world view, but also a radical elimination of all anthropomorphic elements and principles, as they arise either from the world given to the five human senses or from the categories inherent in the human mind. The question assumes that man is the highest being we know of, an assumption which we have inherited from the Romans, whose humanitas was so alien to the Greeks' frame of mind that they had not even a word for it. (The reason for the absence of the word humanitas from Greek language and thought was that the Greeks, in contrast to the Romans, never thought that man is the highest being there is. Aristotle calls this belief atopos, "absurd.")2 + +This view of man is even more alien to the scientist, to whom man is no more than a special case of organic life and to whom man's habitat-the earth, together with earthbound laws-is no more than a special borderline case of absolute, universal laws, that is, laws that rule the immensity of the universe. Surely the scientist cannot permit himself to ask : What consequences will the result of my investigations have for the stature (or, for that matter, for the future ) of man? It has been the glory of modern science that it has been able to emancipate itself completely from all such + +anthropocentric, that is, truly humanistic, concerns. + +The question propounded here, insofar as it is addressed to the layman, must be answered in terms of common sense and in everyday language (if it can be answered at all). The answer is not likely to convince the scientist, because he has been forced, under the compulsion of facts and experiments, to renounce sense perception and hence common sense, by which we coordinate the perception of our five senses into the total awareness of reality. He has also been forced to renounce normal language, which even in its most sophisticated conceptual refinements remains inextricably bound to the world of the senses and to our common sense. For the scientist, man is no more than an observer of the universe in its manifold manifestations. The progress of modem science has demonstrated very forcefully to what an extent this observed universe, the infinitely small no less than the infinitely large, escapes not only the coarseness of human sense perception but even the enormously ingenious instruments that have been built for its refinement. The data with which modern physical research is concerned turn up like "mysterious messenger[s] from the real world." 3 They are not phenomena, appearances, strictly speaking, for we meet them nowhere, neither in our everyday world nor in the laboratory; we know of their presence only because they affect our measuring instruments in certain ways. And this effect, in the telling image of Eddington, may "have as much resemblance" to what they are "as a telephone number has to a subscriber." 4 The point of the matter is that Eddington, without the slightest hesitation, assumes that these physical data emerge from + +a "real world," more real by implication than the world we live in; the trouble is that something physical is present but never + +appears. + +The goal of modem science, which eventually and quite literally has led us to the moon, is no longer "to augment and order" human experiences (as Niels Bohr,5 still tied to a vocabulary that his own work has helped to make obsolete, described it) ; it is much rather to discover what lies behind natural phenomena as they reveal themselves to the senses and the mind of man. Had the scientist reflected upon the nature of the human sensory and mental apparatus, had he raised questions such as What is the nature of man and what should be his stature? What is the goal of science and why does man pursue knowledge? or even What is life and what distinguishes human from animal life?, he would never have arrived where modem science stands today. The answers to these questions would have acted as definitions and hence as limitations of his efforts. In the words of Niels Bohr, "Only by renouncing an explanation of life in the ordinary sense do we gain a possibility of + +taking into account its characteristics." 6 + +That the question proposed here makes no sense to the scientist qua scientist is no argument against it. The question challenges the layman and the humanist to judge what the scientist is doing because it concerns all men, and this debate must of course be joined by the scientists themselves insofar as they are fellow citizens. But all answers given in this debate, whether they come from laymen or philosophers or scientists, are nonscientific (although not antiscientific); they can never be demonstrably true or false. Their truth resembles rather the validity of agreements than the compelling validity of scientific statements. Even when the answers are given by philosophers whose way of life is solitude, they are arrived at by an exchange of opinions among many men, most of whom may no longer be among the living. Such truth can never command general agreement, but it frequently outlasts the compellingly and demonstrably true statements of the sciences which, especially in recent times, have the uncomfortable inclination never + +to stay put, although at any given moment they are, and must be, valid for all. In other words, notions such as life, or man, or science, or knowledge are prescientific by definition, and the question is whether or not the actual development of science which has led to the conquest of terrestrial space and to the invasion of the space of the universe has changed these notions to such an extent that they no longer make sense. For the point of the matter is, of course, that modern science-no matter what its origins and original goals-has changed and reconstructed the world we live in so radically that it could be argued that the layman and the humanist, still trusting their common sense and communicating in everyday language, are out of touch with reality; that they understand only what appears but not what is behind appearances (as though trying to understand a tree without taking the roots into account); and that their questions and anxieties are simply caused by ignorance and therefore are irrelevant. How can anyone doubt that a science enabling man to conquer space and to + +go to the moon has increased his stature? + +This sort of bypassing the question would be very tempting indeed if it were true that we have come to live in a world that only the scientists "understand." They would then be in a position of the "few" whose superior knowledge entitles them to rule the "many," namely, all non-scientists, laymen from the scientist's point of view-be they humanists, scholars, or philosophers-all those, in short, who raise pre-scientific questions because of igno- + +rance. + +This division between the scientist and the layman, however, is very far from the truth. The fact is not merely that the scientist spends more than half of his life in the same world of sense perception, of common sense, and of everyday language as his fellowcitizens, but that he has come in his own privileged field of activity to a point where the naive questions and anxieties of the layman have made themselves felt very forcefully, albeit in a different manner. The scientist has not only left behind the layman with his limited understanding; he has left behind a part of himself and his own power of understanding, which is still human understanding, + +when he goes to work in the laboratory and begins to communicate in mathematical language. Max Planck was right, and the miracle of modern science is indeed that this science could be purged "of all anthropomorphic elements" because the purging was done by men.7 The theoretical perplexities that have confronted the new non-anthropocentric and non-geocentric (or heliocentric) science because its data refuse to be ordered by any of the natural mental categories of the human brain are well enough known. In the words of Erwin Schroedinger, the new universe that we try to "conquer" is not only "practically inaccessible, but not even thinkable," for "however we think it, it is wrong; not perhaps quite as meaningless as a 'triangular circle,' but much more so than a + +'winged lion.' " 8 + +There are other difficulties of a less theoretical nature. Electronic brains share with all other machines the capacity to do man's work better and faster than man. The fact that they supplant and enlarge human brain power rather than labor power causes no perplexity to those who know how to distinguish between the "intellect" necessary to play good checkers or chess and the human mind.9 This, indeed, proves no more than that labor power and brain power belong in the same category, and that what we call intelligence and can measure in terms of IQs has hardly any more to do with the quality of the human mind than being its indispensable conditio sine qua non. There are, however, scientists who state that computers can do "what a human brain cannot comprehend," 10 and this is an altogether different and alarming proposition; for comprehension is actually a function of the mind and never the automatic result of brain power. If it should be trueand not simply a case of a scientist's self-misunderstanding-that we are surrounded by machines whose doings we cannot comprehend although we have devised and constructed them, it would mean that the theoretical perplexities of the natural sciences on the highest level have invaded our everyday world. But even if we remain in the strictly theoretical framework, the paradoxes that have begun to worry the great scientists themselves are �ufficiently serious to alarm the layman. Whereas the often mentioned "lag" + +of the social sciences with respect to the natural sciences or of man's political development with respect to his technical and scientific know-how is no more than a red herring drawn into this debate; it can only divert attention from the main problem, which is that man can do, and successfully do, what he cannot compre- + +hend and cannot express in everyday human language. + +It may be noteworthy that among the scientists it was primarily the older generation, men like Einstein and Planck, Niels Bohr and Schroedinger, who were most acutely worried about this state of affairs which their own work had chiefly brought about. They were still firmly rooted in a tradition that demanded that scientific theories fulfill certain definitely humanistic requirements such as simplicity, beauty and harmony. A theory was still supposed to be "satisfactory," namely, satisfactory to human reason in that it served to "save the phenomena," to explain all observed facts. Even today, we still hear that "modem physicists are inclined to believe in the validity of general relativity for aesthetic reasons, because it is mathematically so elegant and philosophically so satisfying." 11 Einstein's extreme reluctance to sacrifice the principle of causality as Planck's Quantum Theory demanded is well known; his main objection was, of course, that with it all lawfulness was about to depart from the universe, that it was as though God ruled the world by "playing dice." And since his own discoveries, according to Niels Bohr, had come about through a "remolding and generalizing [of] the whole edifice of classical physics . . . lending to our world picture a unity surpassing all previous expectations," it seems only natural that Einstein tried to come to terms with the new theories of his colleagues and his successors through "the search for a more complete conception," through a new and surpassing generalization.12 Thus Max Planck could call the Theory of Relativity "the completion and culmination of the structure of classical physics," its very "crowning point." But Planck himself, although fully aware that the Quantum Theory, in contrast to the Theory of Relativity, signified a complete break with classical physical theory, held it to be "essential for the healthy develop- + +rnent of physics that among the postulates of this science we reckon, not merely the existence of law in general, but also the strictly + +·causal character of this law." 13 + +Niels Bohr, however, went one step further. For him, causality, ·determinism, and necessity of laws belonged to the categories of "our necessarily prejudiced conceptual frame," and he was no longer frightened when he met "in atomic phenomena regularities ·Of quite a new kind, defying deterministic pictorial description." 14 The trouble is that what defies description in terms of the "prejudices" of the human mind defies description in every conceivable way of human language ; it can no longer be described at all, and it is being expressed, but not described, in mathematical processes. Bohr still hoped that, since "no experience is definable without a logical frame," these new experiences would in due time fall into place through "an appropriate widening of the conceptual framework" which would also remove all present paradoxes and "apparent disharmonies." 15 But this hope, I am afraid, will be disappointed. The categories and ideas of human reason have their ultimate source in human sense experience, and all terms describing .our mental abilities as well as a good deal of our conceptual language derive from the world of the senses and are used metaphorically. Moreover, the human brain which supposedly does our thinking is as terrestrial, earthbound, as any other part of the human .body. It was precisely by abstracting from these terrestrial conditions, by appealing to a power of imagination and abstraction that would, as it were, lift the human mind out of the gravitational field .of the earth and look down upon it from some point in the universe, that modern science reached its most glorious and, at the same + +time, most baffling achievements. + +In 1929, shortly before the arrival of the Atomic Revolution, marked by the splitting of the atom and the hope for the conquest -of universal space, Planck demanded that the results obtained by mathematical processes "must be translated back into the language of the world of our senses if they are to be of any use to us." In the three decades that have passed since these words were written, such + +translation has become even less possible while the loss of contact between the physical world view and the sense world has become even more conspicuous. But-and in our context this is even more alarming-this has by no means meant that results of this new science are of no practical use, or that the new world view, as Planck had predicted in case the translation back into ordinary language should fail, "would be no better than a bubble ready to burst at the first puff of wind." 16 On the contrary, one is tempted to say that it is much more likely that the planet we inhabit will go up in smoke as a consequence of theories that are entirely unrelated to the world of the senses, and defy all description in human language, than that even a hurricane will cause the theories to burst + +like a bubble. + +It is, I think, safe to say that nothing was more alien to the minds of the scientists, who brought about the most radical and the most rapid revolutionary process the world has ever seen, than any will to power. Nothing was more remote than any wish to "conquer space" and to go to the moon. Nor were they prompted by an unseemly curiosity in the sense of a temptatio oculorum. It was indeed their search for "true reality" that led them to lose confidence in appearances, in the phenomena as they reveal themselves of their own accord to human sense and reason. They were inspired by an extraordinary love of harmony and lawfulness which taught them that they would have to step outside any merely given sequence or series of occurrences if they wanted to discover the overall beauty and order of the whole, that is, the universe. This may explain why they seem to have been less distressed by the fact their discoveries served the invention of the most murderous gadgets than disturbed by the shattering of all their most cherished ideals of necessity and lawfulness. These ideals were lost when the scientists discovered that there is nothing indivisible in matter, no o:-tomos, that we live in an expanding, non-limited universe, and that chance seems to rule supreme wherever this "true reality," the physical world, has receded entirely from the range of human senses and from the range of all instruments by which their coarseness was refined. From this, it seems to follow that causality, + +necessity, and lawfulness are categories inherent in the human brain and applicable only to the common-sense experiences of earthbound creatures. Everything that such creatures "reasonably" demand seems to fail them as soon as they step outside the range of + +their terrestrial habitat. + +The modern scientific enterprise began with thoughts never thought before (Copernicus imagined he was "standing in the sun ... overlooking the planets" )17 and with things never seen before (Galileo's telescope pierced the distance between earth and sky and delivered the secrets of the stars to human cognition "with all the certainty of sense evidence" ) .18 It reached its classic expression with Newton's law of gravitation, in which the same equation covers the movements of the heavenly bodies and the motion of terrestrial things on earth. Einstein indeed only generalized this science of the modern age when he introduced an "observer who is poised freely in space" and not just at one definite point like the sun, and he proved that not only Copernicus but also Newton still required "that the universe should have a kind of center," although this center, of course, was no longer the earthY' It is, in fact, quite obvious that the scientists' strongest intellectual motivation was Einstein's "striving after generalization," and that if they appealed to power at all, it was the interconnected formidable power of abstraction and imagination. Even today, when billions of dollars are spent year in and year out for highly "useful" projects that are the immediate results of the development of pure, theoretical science, and when the actual power of countries and governments depends upon the periormance of many thousands of researchers, the physicist is still likely to look down upon all these space scien- + +tists as mere "plumbers." 20 + +The sad truth of the matter, however, is that the lost contact between the world of the senses and appearances and the physical world view has been re-established not by the pure scientist but by the "plumber." The technicians, who account today for the overwhelming majority of all "researchers," have brought the results of the scientists down to earth. And even though the scientist is still beset by paradoxes and the most bewildering perplexities, the very + +fact that a whole technology could develop out of his results demonstrates the "soundness" of his theories and hypotheses more convincingly than any merely scientific observation or experiment ever could. It is perfectly true that the scientist himself does not want to go to the moon; he knows that for his purposes unmanned spaceships carrying the best instruments human ingenuity can invent will do the job of exploring the moon's surface much better than dozens of astronauts. And yet, an actual change of the human world, the conquest of space or whatever we may wish to call it, is achieved only when manned space carriers are shot into the universe, so that man himself can go where up to now only human imagination and its power of abstraction, or human ingenuity and its power of fabrication, could reach. To be sure, all we plan to do now is to explore our own immediate surroundings in the universe, the infinitely small place that the human race could reach even if it were to travel with the velocity of light. In view of man's life span-the only absolute limitation left at the present moment-it is quite unlikely that he will ever go much farther. But even for this limited job, we have to leave the world of our senses and of + +our bodies not only in imagination but in reality. + +It is as though Einstein's imagined "observer poised in free space"-surely the creation of the human mind and its power of abstraction-is being followed by a bodily observer who must behave as though he were a mere child of abstraction and imagination. It is at this point that all the theoretical perplexities of the new physical world view intrude as realities upon man's everyday world and throw out of gear his "natural," that is, earthbound, common sense. He would, for instance, be confronted in reality with Einstein's famous "twin paradox," which hypothetically assumes that "a twin brother who takes off on a space journey in which he travels at a sizable fraction of the speed of light would return to find his earthbound twin either older than he or little more than a dim recollection in the memory of his descendants." 2 1 For although many physicists had found this paradox difficult to swallow, the "clock paradox," on which it is based, seems to have + +been verified experimentally, so that the only alternative to it would be the assumption that earthbound life under all circumstances remains bound to a time concept that demonstrably does not belong among "true realities," but among mere appearances. We have reached the stage where the Cartesian radical doubt of reality as such, the first philosophical answer to the discoveries of science in the modern age, may become subject to physical experiments that would make short shrift of Descartes' famous consolation, I doubt, therefore I am, and of his conviction that, whatever the state of reality and of truth as they are given to the senses and to reason, you cannot "doubt of your doubt and remain uncertain whether + +you doubt or not." 22 + +The magnitude of the space enterprise seems to me beyond dispute, and all objections raised against it on the purely utilitarian level-that it is too expensive, that the money were better spent on education and the improvement of the citizens, on the fight against poverty and disease, or whatever other worthy purposes may come to mind-sound to me slightly absurd, out of tune with the things that are at stake and whose consequences today appear still quite unpredictable. There is, moreover, another reason why I think these arguments are beside the point. They are singularly inapplicable because the enterprise itself could come about only through an amazing development of man's scientific capabilities. The very integrity of science demands that not only utilitarian considerations but the reflection upon the stature of man as well be left in abeyance. Has not each of the advances of science, since the time of Copernicus, almost automatically resulted in a decrease in his stature? And is the often repeated argument that it was man who achieved his own debasement in his search for truth, thus proving anew his superiority and even increasing his stature, more than a sophism? Perhaps it will turn out that way. At any event, man, insofar as he is a scientist, does not care about his own stature in the universe or about his position on the evolutionary ladder of animal life; this "carelessness" is his pride and his glory. The + +simple fact that physicists split the atom without any hesitations the very moment they knew how to do it, although they realized full well the enormous destructive potentialities of their operation, demonstrates that the scientist qua scientist does not even care about the survival of the human race on earth or, for that matter, about the survival of the planet itself. All associations for "Atoms for Peace," all warnings not to use the new power unwisely, and even the pangs of conscience many scientists felt when the first bombs fell on Hiroshima and Nagasaki cannot obscure this simple, elementary fact. For in all these efforts the scientists acted not as scientists but as citizens, and if their voices have more authority than the voices of laymen, they do so only because the scientists are in possession of more precise information. Valid and plausible arguments against the "conquest of space" could be raised only if they were to show that the whole enterprise might be self-defeating + +in its own terms. + +There are a few indications that such might indeed be the case. If we leave out of account the human life span, which under no circumstances (even if biology should succeed in extending it significantly and man were able to travel with the speed of light) will permit man to explore more than his immediate surroundings in the immensity of the universe, the most significant indication that it might be self-defeating consists in Heisenberg's discovery of the uncertainty principle. Heisenberg .showed conclusively that there is a definite and final limit to the accuracy of all measurements obtainable by man-devised instruments for those "mysterious messengers from the real world." The uncertainty principle "asserts that there are certain pairs of quantities, like the position and velocity of a particle, that are related in such a way that determining one of them with increased precision necessarily entails determining the other one with reduced precision." 23 Heisenberg concludes from this fact that "we decide, by our selection of the type of observation employed, which aspects of nature are to be determined and which are to be blurred." 24 He holds that "the most important new result of nuclear physics was the recognition of the possibility of applying + +quite different types of natural laws, without contradiction, to one and the same physical event. This is due to the fact that within a system of laws which are based on certain fundamental ideas only certain quite definite ways of asking questions make sense, and thus, that such a system is separated from others which allow different questions to be put." 25 From this he concluded that the modern search for "true reality" behind mere appearances, which has brought about the world we live in and resulted in the Atomic Revolution, has led into a situation in the sciences themselves in which man has lost the very objectivity of the natural world, so that man in his hunt for "objective reality" suddenly discovered that he + +always "confronts himself alone." 26 + +The remarks of Heisenberg seem to me to transcend by far the field of strictly scientific endeavor and to gain in poignancy if they are applied to the technology that has grown out of modern science. Every progress in science in the last decades, from the moment it was absorbed into technology and thus introduced into the factual world where we live our everyday lives, has brought with it a veritable avalanche of fabulous instruments and ever more ingenious machinery. All of this makes it more unlikely every day that man will encounter anything in the world around him that is not manmade and hence is not, in the last analysis, he himself in a different disguise. The astronaut, shot into outer space and imprisoned in his instrument-ridden capsule where each actual physical encounter with his surroundings would spell immediate death, might well be taken as the symbolic incarnation of Heisenberg's man-the man who will be the less likely ever to meet anything but himself and man-made things the more ardently he wishes to eliminate all anthropocentric considerations from his encounter with the non- + +human world around him. + +It is at this point, it seems to me, that the humanist's concern with man and the stature of man has caught up with the scientist. (t is as though the sciences had done what the humanities never ;ould have achieved, namely, to prove demonstrably the validitJ of this concern. The situation, as it presents itself today, oddly re + +scmbles an elaborate verification of a remark by Franz Kafka, written at the very beginning of this development : Man, he said, "found the Archimedean point, but he used it against himself; it seems that he was permitted to find it only under this condition." For the conquest of space, the search for a point outside the earth from which it would be possible to move, to unhinge, as it were. the planet itself, is no accidental result of the modern age's science. This was from its very beginnings not a "natural" but a universal science, it was not a physics but an astrophysics which looked upon the earth from a point in the universe. In terms of this development, the attempt to conquer space means that man hopes he will be able to journey to the Archimedean point which he anticipated by sheer force of abstraction and imagination. However, in doing so, he will necessarily lose his advantage. All he can find is the Archimedean point with respect to the earth, but once arrived there and having acquired this absolute power over his earthly habitat, he would need a new Archimedean point, and so ad infinitum. In other words, man can only get lost in the immensity of the universe, for the only true Archimedean point would be the abso- + +lute void behind the universe. + +Yet even if man recognizes that there might be absolute limits to his search for knowledge and that it might be wise to suspect such limitations whenever it turns out that the scientist can do more than he is capable of comprehending, and even if he realizes that he cannot "conquer space," but at best make a few discoveries in our solar system, the journey into space and to the Archimedean point with respect to the earth is far from being a harmless or unequivocally triumphant enterprise. It could add to the stature of man inasmuch as man, in distinction from other living things, desires to be at home in a "territory" as large as possible. In that case, he would only take possession of what is his own, although it took him a long time to discover it. These new possessions, like all property, would have to be limited, and once the limit is reached and tii.e limitations established, the new world view that may conceivably grow out of it is likely to be once more geocentric and + +anthropomorphic, although not in the old sense of the earth being the center of the universe and of man being the highest being there is. It would be geocentric in the sense that the earth, and not the universe, is the center and the home of mortal men, and it would be anthropomorphic in the sense that man would count his own factual mortality among the elementary conditions under which his + +scientific efforts are possible at all. + +At this moment, the prospects for such an entirely beneficial development and solution of the present predicaments of modern science and technology do not look particularly good. We have come to our present capacity to "conquer space" through our new ability to handle nature from a point in the universe outside the earth. For this is what we actually do when we release energy processes that ordinarily go on only in the sun, or attempt to initiate in a test tube the processes of cosmic evolution, or build machines for the production and control of energies unknown in the household of earthly nature. Without as yet actually occupying the point where Archimedes had wished to stand, we have found a way to act on the earth as though we disposed of terrestrial nature from outside, from the point of Einstein's "observer freely poised in space." If we look down from this point upon what is going on on earth and upon the various activities of men, that is, if we apply the Archimedean point to ourselves, then these activities will indeed appear to ourselves as no more than "overt behavior," which we cetn study with the same methods we use to study the behavior of rats. Seen from a sufficient distance, the cars in which we travel and which we know we built ourselves will look as though they were, as Heisenberg once put it, "as inescapable a part of ourselves as the snail's shell is to its occupant." All our pride in what we can do will disappear into some kind of mutation of the human race; the whole of technology, seen from this point, in fact no longer appears "as the result of a conscious human effort to extend man's material powers, but rather as a large-scale biological process." 27 Under these circumstances, speech and everyday language would indeed be no longer a meaningful utter- + +ance that transcends behavior even if it only expresses it, and it would much better be replaced by the extreme and in itself mean- + +ingless formalism of mathematical signs. + +The conquest of space and the science that made it possible have come perilously close to this point. If they ever should reach it in earnest, the stature of man would not simply be lowered by all + +standards we know of, but have been destroyed. + +NO TES + +INDEX OF NAMES + +NOTES + +Preface + +1. For this quotation and the following, see Rene Char, Feuillel\$ d'Hypnos, Paris, 1946. Written during the last year of the Resistance, 1943 to 1944, and published in the Collection Espoir, edited by Albert Camus, these aphorisms, together with later pieces, appeared in English under the title Hypnos Waking; Poems and Prose, New York, 1956. 2. The quotation is from the last chapter of Democracy in A merica, New York, 1945, vol. II, p. 331. It reads in full: "Although the revolution that is taking place in the social condition, the laws, the opinions, and the feelings of men is still very far from being terminated, yet its results already admit of no comparison with anything that the world has ever before witnessed. I go back from age to age up to the remotest antiquity, but I find no parallel to what is occurring before my eyes; as the past has ceased to throw its light upon the future, the mind of man wanders in obscurity." These lines of Tocqueville anticipate not only the aphorisms of Rene Char; curiously enough, if one reads them textually, they also anticipate Kafka's insight (see the following) that it is the future that sends man's mind back into the past "up to the remotest + +antiquity." + +3. The story is the last of a series of "Notes from the year 1920," under the title "HE." Translated from the German by Willa and Edwin Muir, they appeared in this country in The Great Wall of China, New York, 1946. I followed the English translation except in a few places where a more literal translation was needed for my purposes. The German original-in vol. 5 of the Gesammelte Schriften, New York, 1946 + +Er hat zwei Gegner: Der erste bedriingt ihn von hinten, vom Urspm11,r:; her. Der zweite verwehrt ihm den Weg nach vorn. Er kampft mit heiden. Eigentlich unterstiitzt ihn der erste im Kampf mit dem Zweiten, denn er will ihn nach vorn drlingen und ebenso unterstiitzt ihn der zweite im Kampf mit dem Ersten; denn er treibt ihn doch zuriick. So ist es aber nur theoretisch. Denn es sind ja nicht nur die zwei Gegner da, sondern auch noch er selbst, und wer kennt eigentlich seine A bsichten? Immerhin ist es sein Traum, dass er einmal in einem unbewachten A ugenblick-dazu gehort allerdings eine Nacht, so finster wie noch keine war-aus der Kampflinie ausspringt und wegen seiner Kampfeserfahrung zum Richter uber seine miteinander klimpfenden Gegner erhoben wird. + +1. Tradition and the Modern Age + +1. Laws 775. + +2. For Engels, see his Anti-Diihring, ZUrich, 1934, p. 275. For Nietzsche, see Morgenrote, Werke, Miinchen, 1954, vol. I, aph. 179. 3. The statement occurs in Engels' essay on "The Part played by Labour in the Transition from Ape to Man," in Marx and Engels, Selected Works, London, 1950, vol. II, p. 74. For similar formulations by Marx himself, see especially "Die heilige Familie" and "Nationaloko- + +nomie und Philosophie" in Jugendschriften, Stuttgart, 1953. + +4. Quoted here from Capital, Modern Library Edition, p. 824. 5. See Gotzendammerung, ed. K. Schlechta, MUnchen, vol. II, + +p. 963. + +6. In Das Kapital, ZUrich, 1933, vol. III, p. 870. + +7. I refer here to Heidegger's discovery that the Greek word for + +truth means literally "disclosure"-ci-A�Bna. 8. Op. cit., ZUrich, p. 689. 9. Ibid., pp. 697-698. + +10. That "the Cave is comparable with Hades" is also suggested by F. M. Cornford in his annotated translation of The Republic, New + +York, 1956, p. 230. + +11 . See Jugendschriften, p. 274. + +1. Cicero, De legibus I, 5; De oratore II, 55. Herodotus, the first historian, did not yet have at his disposal a word for history. He usP.d the + +word 1uTop£iv, but not in the sense of "historical narrative." Like d8lJ•at, to know, the word 1crTopta is derived from iB-, to see, and icrTwp means originally "eyewitness," then the one who examines witnesses and obtains truth through inquiry. Hence, icrTOp£"iv has a double meaning: to testify and to inquire. (S) but cannot do this with respect to the individual. In our context, it is irrelevant that the treatise is not by Aristotle but by one of his pupils, for we find the same thought in the treatise On Generation and Corruption in the concept of Becoming, which moves in a cycley€v£crt> £� ci.\A�Aow KvKA!fl, 3 31 a8. The same thought of an "immortal + +human species" occurs in Plato, Laws, 721. See note 9. + +4. Nietzsche, Wille zur Macht, Nr. 617, Edition Kroner, 1930. 5. Rilke, A us dem Nachlass des Grafen C. W., first series, poem X. Although the poetry is untranslatable, the content of these verses might be expressed as follows: "Mountains rest beneath a splendor of stars, but even in them time flickers. Ah, unsheltered in my wild, darkling heart + +20. De Civitate Dei, XII, 13. + +21. See Theodor Mornmsen, "St. Augustine and the Christian Idea of Progress," in Journal of the History of Ideas, June 1951. A close reading shows a striking discrepancy between the content of this excellent article and the thesis expressed in its title. The best defense of the Christian origin of the concept of history is found in C. N. Cochrane, op. cit. , p. 474. He holds that ancient historiography carne to an end because it had failed to establish "a principle of historical intelligibility" and that Augustine solved this problem by substituting "the logos of + +Christ for that of classicism as a principle of understanding." + +22. Especially interesting is Oscar Cullman, Christ and Time, London, 1951. Also Erich Frank, "The Role of History in Christian Thought" in Knowledge, Will and Belief, Collected Essays, Ziirich, + +1955. + +23. In Die Entstehung des Historismus, Miinchen and Berlin, + +1936, p. 394. + +24 . .lohn Baillie, The Belief in Progress, London, 1950. + +25. De Re Publica, 1.7. + +26. The word seems to have been rarely used even in Greek. It occurs in Herodotus (book IV, 93 and 94) in the active sense and applies to the rites performed by a tribe that does not believe in death. The point is that the word does not mean "to believe in immortality," but "to act in a certain way in order to assure the escape from dying." In the passive sense (O.OavaTl{£u8at, "to be rendered immortal") the word also occurs in Polybius (book VI, 54, 2); it is used in the description of Roman funeral rites and applies to the funeral orations, which render immortal through "constantly making new the fame of good men." The Latin equivalent, aeternare, again applies to immortal fame. (Hor- + +ace, Carmines, book IV, c. 14, 5.) + +Clearly, Aristotle was the first and perhaps the last to use this word for the specifically philosophic "activity" of contemplation. The text reads as follows: o{J XP� St KaTa TOV'> 7rapatvOVVTa'> av8pw7r!Va cppov£iv, av8pW7rOV OVTa o{JSt OVTJTa TOV (JVTJTOV, a.U.' €¢' ouov €vS£;)(£Tal O.OavaT[{uv. . . . (Nichomachean Ethics, 11 77b31). "One should not think as do those who recommend human things for those who are mortals, but immortalize as far as possible .... " The medieval Latin translation (Eth. X, Lectio XI) does not use the old Latin word aeternare but translates "immortalize" through immortalem facere-to make immortal, presumably one's self. (Oportet autem non secundum suadentes humana hominem entem, neque mortalia mortalem; sed inquantum contingit immortalem facere . .. . ) Modern standard translations fall + +into the same error (see for instance the translation by W. D. Ross, who translates: "we must ... make ourselves immortal" ). In the Greek text, the word a8avaTl,ELv, like the word pov£iv, is an intransitive verb, it has no direct object. (I owe the Greek and Latin references to the kind help of Professors John Herman Randall, Jr., and Paul Oscar Kristeller of Columbia University. Needless to say, they are not responsible for + +translation and interpretation.) + +27. It is rather interesting to note that Nietzsche, who once used the term "eternize"-probably because he remembered the passage in Aristotle-applied it to the spheres of art and religion. In Vom Nutzen und Nachteil der Historie fur das Leben, he speaks of the "aeternisieren- + +den Miichten der Kunst und Religion." 28. Thucydides II, 41. + +29. How the poet, and especially Homer, bestowed immortality upon mortal men and futile deeds, we can still read in Pindar's Odesnow rendered into English by Richmond Lattimore, Chicago, 1955. See, for instance, "Isthmia" IV : 60 ff.; "Nemea" IV: 10, and VI: 5o-55. + +30. De Civitate Dei, XIX, 5. + +31. Johannes Gustav Droysen, Historik (1882) , Miinchen and B\_erlin, 1937, para. 82: "Was den Tieren, den Pflanzen ihr GattungsbegrifJ-denn die Gattung ist, iva TOV ad Kat TOV 8£tOV f.L£Tfxwuw--das ist den Menschen die Geschiclzte." Droysen does not mention author or + +source of the quotation. It sounds Aristotelian. + +32. Leviathan, book I, ch. 3. + +33. Democracy in America, 2nd part, last chapter, and 1st part, + +"Author's Introduction," respectively. + +34. The first to see Kant as the theorist of the French Revolution was Friedrich Gentz in his "Nachtrag zu dem Rasonnement des Herrn Prof. Kant iiber das Verhaltnis zwischen Theorie und Praxis" in Ber- + +liner Monatsschrift, December 1793. + +35. Idee zu einer allgemeinen Geschichte in weltburger/icher + +Absicht, Introduction. + +36. Op. cit., Third Thesis. + +37. Hegel in The Philosophy of History, London, 1905, p. 21. + +38. Nietzsche, Wille zur Macht, no. 29 1. + +39. Martin Heidegger once pointed to this weird fact in a public discussion in Zurich (published under the title: "Aussprache mit Martin Heidegger am 6. November 1951 ," Photodruck Jurisverlag, Zurich, 1952) : " ... der Satz: man kann a/les beweisen [ist] nicht ein Freibrief, sondern ein Hinweis auf die Moglichkeit, tlass dort, wo man beweist im Sinne der Deduktion aus Axiomen, dies jederzeit in gewissem Sinne moglich ist. Das ist das unheimlich Riitselhafte, dessen Gelzeimnis ich + +ally a hindrance to his work; that, however, it was necessary [for a good king] to listen to the true philosopher and to be agreeable to their advice." See Kurt von Fritz, The Constitution of Athens, and Related Texts, 1950. In Aristotelian terms, both Plato's philosopher-king and the Greek tyrant rule for the sake of their own interest, and this was for Aristotle, though not for Plato, an outstanding characteristic of tyrants. Plato was not aware of the resemblance, because for him, as for Greek current opinion, the principal characteristic of the tyrant was that he deprived the citizen of access to a public realm, to a "market place" where he could show himself, see and be seen, hear and be heard, that he prohibited the ayoprunv and 7TOAtT£V£u8at, confined the citizens to the privacy of their households, and demanded to be the only one in charge of public affairs. He would not have ceased to be a tyrant if he had used his power solely in the interests of his subjectsas indeed some of the tyrants undoubtedly did. According to the Greeks, to be banished to the privacy of household life was tantamount to being deprived of the specifically human potentialities of life. In other words, the very features which so convincingly demonstrate to us the tyrannical character of Plato's republic-the almost complete elimination of privacy and the omnipresence of political organs and institutions-presumably prevented Plato from recognizing its tyrannical character. To him, it would have been a contradiction in terms to brand as tyranny a constitution which not only did not relegate the citizen to his household but, on the contrary, did not leave him a shred of private life whatsoever. Moreover, by calling the rule of law "despotic," Plato stresses its non-tyrannical character. For the tyrant was always supposed to rule over men who had known the freedom of a polis and, being deprived of it, were likely to rebel, whereas the despot was assumed to rule over people who had never known freedom and were by nature incapable of it. It is as though Plato said : My laws, your new despots, will not deprive you of anything you rightfully enjoyed before; they are adequate to the very nature of human affairs and you have no more right to rebel against their rule than the slave has a right to rebel + +against his master. + +9. "Eternal Peace," The Philosophy of Kant, ed. and trans. C. J. + +Friedrich, Modern Library Edition, 1949, p. 456. + +10. Von Fritz, op. cit., p. 54, rightly insists on Plato's aversion to violence, "also revealed by the fact that, wherever he did make an attempt to bring about a change of political institutions in the direction of his political ideals, he addressed himself to men already in power." 11. Werner Jaeger's statement in Paideia, New York, 1943, vol. II, p. 416n; "The idea that there is a supreme art of measurement and + +that the philosopher's knowledge of values (phronesis) is the ability to measure, runs through all Plato's work right down to the end" is true only for Plato's political philosophy. The very word cppov7JUL<> characterizes in Plato and Aristotle the insight of the statesman rather than toe + +"wisdom" of the philosopher. + +12. The Republic, book VII, 516-5 17. + +13. See especially Timaeus, 31, where the divine Demiurge makes the universe in accordance with a model, a 7rapa8ny(UL, and The Repub- + +lic, 596 ff. + +14. In Protrepticus, quoted from von Fritz, op. cit. + +15. Laws, 710-71 1. + +16. This presentation is indebted to Martin Heidegger's great interpretation of the cave parable in Platons Lehre von der Wahrheit, Bern, 1947. Heidegger demonstrates how Plato transformed the concept of truth (uA�Ona) until it became identical with correct statements (op0oT7J<;) . Correctness indeed, and not truth, would be required if the philosopher's knowledge is the ability to measure. Although he explicitly mentions the risks the philosopher runs when he is forced to return to the cave, Heidegger is not aware of the political context in which the parable appears. According to him, the transformation comes to pass because the subjective act of vision (the i8ti:v and the iS£a in the mind of the philosopher) takes precedence over objective truth (aA�Ona) , which, according to Heidegger, signifies Unverborgenheit. + +17. Symposion, 21 1-212. + +18. Phaedrus, 248 : cpLAoaocpo<; � cptAoKaAo<>, and 250. + +19. In The Republic, 518, the good, too, is called cpavoTaTov, the most shining one. Obviously it is precisely this quality which indicates the precedence which the beautiful originally had over the good in + +Plato's thought. + +20. The Republic, 475-476. In the tradition of philosophy, the result of this Platonic repudiation of the beautiful has been that it was omitted from the so-called transcendentals or universals, that is, those qualities possessed by everything that is, and which were enumerated in medieval philosophy as unum, alter, ens, and bonum. Jacques Mar� itain, in his wonderful book, Creative Intuition in Art and Poetry, Bollingen Series XXXV, I, 1953, is aware of this omission and insists that beauty be included in the realm of transcendentals, for "Beauty is + +the radiance of all transcendentals united" (p. 162) . + +21. In the dialogue Politicus: "for the most exact measure of all things is the good" (quoted from von Fritz, op. cit.). The notion must have been that only through the concept of the good do things become + +22. Politics, 1332b 12 and 1332b36. The distinction between the younger and older ones goes back to Plato; see Republic, 412, and + +Laws, 690 and 714. The appeal to nature is Aristotelian. + +23. Politics, 1328b35. 24. Economics, 1343a1-4. 25. Jaeger, op. cit., vol. I, p. 111. + +26. Economics, 1343b24. + +27. The derivation of religio from religare occurs in Cicero. Since we deal here only with the political self-interpretation of the Romans, the question whether this derivation is etymologically corr.ect is irrel- + +evant. + +28. See Cicero, De Re Publica, III, 23. For the Roman belief in the eternity of their city, see Viktor Poeschl, Romischer Staat und + +griechisches Staatsdenken bei Cicero, Berlin, 1936. + +29. Annals, book 43, ch. 13. 30. De Re Publica, 1, 7. + +31. Cicero, De Legibus, 3, 12, 38. 32. Esprit des Lois, book XI, ch. 6. + +33. Professor Carl J. Friedrich drew my attention to the important discussion of authority in Mommsen's Romisches Staatsrecht; see + +pp. 1034, 1038-1039. + +34. This interpretation is further supported by the idiomatic Latin + +use of alicui auctorem esse for "giving advice to somebody." + +35. See Mommsen, op cit., 2nd edition, vol. I, pp. 73 ff. The Latin word numen, which is nearly untranslatable, meaning "divine command" as well as the divine modes of acting, derives from nuere, to nod in affirmation. Thus the commands of the gods and all their interference in human affairs are restricted to approval or disapproval of + +human actions. + +36. Mommsen, ibid., p. 87. + +37. See also the various Latin idioms such as auctores habere for having predecessors or examples; auctoritas maiorum, signifying the authoritative example of the ancestors; usus et auctoritas as used in Roman law for property rights which come from usage. An excellent presentation of this Roman spirit as well as a very useful collection of the more important source materials are to be found in Viktor Poeschl, + +op. cit., especially pp. 101 ff. + +38. R. H. Barrow, The Romans, 1949, p. 194. + +39. A similar amalgamation of Roman imperial political sentiment with Christianity is discussed by Erik Peterson, Der Monotheismus als politisches Problem, Leipzig, 1935, in connection with Orosius, who related the Roman Emperor Augustus to Christ. "Dabei ist deutlich, + +dass Augustus auf diese Weise christianisiert und Christus zum civis + +roman us wird, romanisiert worden ist'' ( p. 92). + +40. Duo quippe sunt . . . quibus principaliter mundus hie regitur, : auctoritas sacra pontificum et regalis potestas. In Migne, PL, + +vol. 59, p. 42a. + +41. Eric Voegelin, A New Science of Politics, Chicago, 1952, + +p. 78. + +42. See Phaedo 80 for the affinity of the invisible soul with the traditional place of invisibility, namely, Hades, which Plato construes + +etymologically as "the invisible." 43. Ibid., 64-66. + +44. With the exception of the Laws, it is characteristic of Plato's political dialogues that a break occurs somewhere and the strictly argumentative procedure has to be abandoned. In The Republic, Socrates eludes his questioners several times; the batHing question is whether justice is still possible if a deed is hidden from men and gods. The discussion of what justice is breaks down at 372a and is taken up again in 427d, where, however, not justice but wisdom and E�{3ovA{a are defined. Socrates comes back to the main question in 403d, but discusses uwcpporn!117J instead of justice. He then starts again in 433b and comes almost immediately to a discussion of the forms of government, 445d ff., until the se-venth book with the cave story puts the whole argument on an entirely different, nonpolitical level. Here it becomes clear why Glaukon could not receive a satisfactory answer: justice is an idea and + +must be perceived; there is no other possible demonstration. + +The Er-myth, on the other hand, is introduced by a reversion of the whole argument. The task had been to find justice as such, even if hidden from the eyes of gods and men. Now (612) Socrates wishes to take back his initial admission to Glaukon that, at least for the sake of the argument, one would have to assume that "the just man may appear unjust and the unjust just" so that no one, neither god nor man, could definitely know who is truly just. And in its stead, he puts the assumption that "the nature both of the just and the unjust is truly known to the gods." Again, the whole argument is put on an entirely different level-this time on the level of the multitude and outside the range of + +argument altogether. + +The case of Gorgias is quite similar. Once more, Socrates is incapable of persuading his opponent. The discussion turns about the Socratic conviction that it is better to suffer wrong than to do wrong. When Kallikles clearly cannot be persuaded by argument, Plato proceeds to tell his myth of a hereafter as a kind of ultima ratio, and, in distinction to The Republic, he tells it with great diffidence, clearly + +indicating that the teller of the story, Socrates, does not take it seriously. 45. Imitation of Plato seems to be beyond doubt in the frequent cases where the motif of apparent death recurs, as in Cicero and Plutarch. For an excellent discussion of Cicero's Somnium Scipionis, the myth which concludes his De Re Publica, see Richard Harder, "Ueber Ciceros Somnium Sci pion is" (Kleine Schriften, Miinchen, 1960) , who also shows convincingly that neither Plato nor Cicero followed Pythag- + +orean doctrines. + +46. This is especially stressed by Marcus Dods, Forerunners of + +Dante, Edinburgh, 1903. 47. See Gorgias, 524. + +48. See Gorgias, 522/3 and Phaedo, 110. In The Republic, 614, + +Plato even alludes to a tale told by Ulysses to Alcinous. + +49. The Republic, 379a. + +50. As Werner Jaeger once called the Platonic god in Theology of + +the Early Greek Philosophers, Oxford, 1947, p. 194n. + +51. The Republic, 615a. + +52. See especially the Seventh Letter for Plato's conviction that + +truth is beyond speech and argument. + +53. Thus John Adams in Discourses on Davila, in Works, Boston, + +185 1, vol. VI, p. 280. + +54. From the draft Preamble to the Constitution of Massachusetts, + +Works, vol. IV, 221. + +55. John Stuart Mill, On Liberty, ch. 2. + +56. The Prince, ch. 15. 57. The Prince, ch. 8. + +58. See especially the Discourses, book III, ch. 1. + +59. It is curious to see how seldom Cicero's name occurs in Machiavelli's writings and how carefully he avoided him in his interpre- + +tations of Roman history. + +60. De Re Publica, VI, 12. + +61. Laws, 711a. + +62. These assumptions, of course, could be justified only by a de- + +tailed analysis of the American Revolution. + +63. The Prince, ch. 6. + +4. What Is Freedom? + +1. I follow Max Planck, "Causation and Free Will" (in The New Science, New York, 1959) because the two essays, written from the + +ing simplicity and clarity. + +2. Ibid. + +3. John Stuart Mill, On Liberty. + +4. See "On Freedom" in Dissertationes, book IV, 1, § 1. + +5. 1310a25 ff. 6. Op. cit., § 75. 7. Ibid., § 11 8 8. §§ 81 and 83. + +9. See Esprit des Lois, XII, 2: "La /iberte philosophique consiste dans l'exercice de Ia volonte .... La liberte politique consiste dans Ia + +surete." + +10. lntellectus apprehendit agibile antequam voluntas illud velit; sed non apprehendit determinate hoc esse agendum quod apprehendere + +dicitur dictare. Oxon. IV, d. 46, qu. 1, no. 10. + +11. John Stuart Mill, op. cit. + +12. Leibniz only sums up and articulates the Christian tradition when he writes: "Die Frage, ob unserem Willen Freiheit ;,ukommt, bedeutet eigentlich nichts anderes, als ob ihm Willen zukommt. Die Ausdrucke '/rei' und 'willensgemiiss' besagen dasselbe." (Schriften zur Metaphysik I, "Bemerkungen zu den cartesischen Prinzipien." Zu + +Artikel 39.) + +13. Augustine, Confessions, book VIII, ch. 8. + +14. We find this conflict frequently in Euripides. Thus Medea, before murdering her children, says: "and I know which evils I am about to commit, but 6vp.o> is stronger than my deliberations" ( 1078 ff.) ; and Phaedra (Hippolytus, 376 ff.) speaks in a similar vein. The point of the matter is always that reason, knowledge, insight, etc., are too weak to withstand the onslaught of desire, and it may not be accidental that the conflict breaks out in the soul of women, who are less under + +the influence of reasoning than men. + +15. "Insofar as the mind commands, the mind wills, and insofar as the thing commanded is not done, it wills not," as Augustine put it, in the famous ch. 9 of book VIII of the Confessions, which deals with the will and its power. To Augustine, it was a matter of course that + +••to will" and "to command" are the same. + +16. Augustine, ibid. + +17. Pythian Ode IV, 287-289 : + +lKTO<; tX€LV 1ro0a. 18. Esprit des Lois, XII, 2 and XI, 3. + +20. Ibid. + +21. See the first four chapters of the second book of The Social Contract. Among modern political theorists, Carl Schmitt is the most able defender of the notion of sovereignty. He recognizes clearly that the root of sovereignty is the will: Sovereign is who wills and commands. See especially his Verfassungslehre, Miinchen, 1928, pp. 7 ff., + +146. + +22. Book XII, ch. 20. + +6. The Crisis in Culture + +1. Harold Rosenberg in a brilliantly witty essay, "Pop Culture: + +Kitsch Criticism," in The Tradition of the New, New York, 1959. + +2. See Edward Shils, "Mass Society and Its Culture" in Daedalus, Spring 1960; the whole issue is devoted to "Mass Culture and Mass + +Media." + +3. I owe the story to G. M. Young, Victorian England. Portrait of + +an Age, New York, 1954. + +4. For etymological origin and usage of the word in Latin, see, in addition to the Thesaurus linguae latinae, A. Walde, Lateinisches Etymologisches W orterbuch, 1938, and A. Ernout & A. Meillet, Dictionnaire Etymologique de Ia Langue Latine. Histoire des Mots, Paris, 1932. For the history of word and concept since antiquity, see Joseph Niedermann, Kultur-Werden und Wandlungen des Begriffes und seiner Ersatzbegri/Je von Cicero bis Herder, in Biblioteca dell' Archi- + +vum Romanum, Firenze, 1 94 1 , vol. 28. + +5. Cicero, in his Tusculan Disputations, I, 13, says explicitly that the mind is like a field which cannot be productive without proper cultivation-and then declares: Cultura autem animi philosophia est. 6. By Werner Jaeger in Antike, Berlin, 1928, vol. IV. 7. See Mommsen, Romische Geschichte, book I, ch. 14. + +8. See the famous chorus in Antigone, 332 ff. + +9. Thucydides, II, 40. 10. Cicero, op. cit., V, 9. 11. Plato, Gorgias, 482. + +12. Critique of Judgment, § 40. 13. Ibid., introduction, VII. + +14. Aristotle, who (Nicomachean Ethics, book 6) deliberately set ilie insight of the statesman against the wisdom of the philosopher, + +the public opinion of the Athenian polis. 15. Critique of Judgment, §§ 6, 7, 8. + +Hi. Ibid. § 19. + +17. For the history of word and concept, see Niedermann, op. cit., Rudolf Pfeiffer, Humanitas Erasmiana, Studien der Bibliothek Warburg, no. 22, 1931, and "Nachtragliches zu Humanitas" in Richard Harder's Kleine Schriften, Miinchen, 1960. The word was used to translate the Greek cfnXavOpw1rta, a word originally used of gods and rulers and therefore with altogether different connotations. Humanitas, as Cicero understood it, was closely connected with the old Roman virtue of dementia and as such stood in a certain opposition to Roman gravitas. It certainly was the sign of the educated man but, and this is important in our context, it was the study of art and literature rather than of philosophy which was supposed to result in + +"humanity." + +18. Cicero, op. cit., I, 39-40. I follow the translation by J. E. + +King in Loeb's Classical Library. + +19. Cicero speaks in a similar vein in De Legibus, 3, 1: He praises Atticus cuius et vita et oratio consecuta mihi videtur difficillimam illam societatem gravitatis cum humanitate-"whose life and speech seem to me to have achieved this most difficult combination of gravity with humanity"-whereby, as Harder (op. cit.), points out, Atticus's gravity consists in his adhering with dignity to Epicurus's philosophy, whereas his humanity is shown by his reverence for Plato, + +which proves his inner freedom. + +7. Truth and Politics + +1. Eternal Peace, Appendix I. + +2. I quote from Spinoza's Political Treatise because it is noteworthy that even Spinoza, for whom the libertas philosophandi was the true end of government, should have taken so radical a position. + +3. In the Leviathan (ch. 46) Hobbes explains that "disobedience may lawfully be punished in them, that against the Jaws teach even true philosophy." For is not "leisure the mother of philosophy; and Commonwealth the mother of peace and leisure"? And does it not follow that the Commonwealth will act in the interest of philosophy when it suppresses a truth which undermines peace? Hence the truth- + +teller, in order to cooperate in an enterprise which is so necessary for his own peace of body and soul, decides to write what he knows "to be false philosophy." Of this Hobbes suspected Aristotle of all people, who according to him "writ it as a thing consonant to, and corroborative of [the Greeks'] religion; fearing the fate of Socrates.'' It never occurred to Hobbes that all search for truth would be self-defeating if its conditions could be guaranteed only by deliberate falsehoods. Then, indeed, everybody may turn out to be a liar like Hobbes' Aristotle. Unlike this figment of Hobbes' logical fantasy, the real Aristotle was of course sensible enough to leave Athens when he came to fear the fate of Socrates; he was not wicked enough to write what he knew to be false, nor was he stupid enough to solve his problem of survival by + +destroying everything he stood for. 4. Ibid., ch. 11. + +5. I hope no one will tell me any more that Plato was the inventor of the "noble lie." This belief rested on a misreading of a crucial passage (414C) in The Republic, where Plato speaks of one of his mythsa "Phoenician tale"-as a welioos . Since the same Greek word signifies "fiction," "error," and "lie" according to context-when Plato wants to distinguish between error and lie, the Greek language forces him to speak of "involuntary" and "voluntary" 1/to.Doos -the text can be rendered with Cornford as "bold flight of invention" or be read with Eric Voegelin (Order and History: Plato and Aristotle, Louisiana State University, 1957, vol. 3, p. 106) as satirical in intention; under no circumstances can it be understood as a recommendation of lying as we understand it. Plato, of course, was permissive about occasional lies to deceive the enemy or insane people-The Republic, 382; they are "useful ... in the way of medicine ... to be handled by no one but a physician," and the physician of the polis is the ruler ( 3 88 ). But, contrary to the cave allegory, no principle is involved in these passages. + +6. Leviathan, Conclusion. 7. The Federalist, no. 49. + +8. Theologico-Political Treatise, ch. 20. + +9. See "What Is Enlightenment?" and "Was heisst sich 1m + +Denken orientieren?" + +10. The Federalist, no. 49. 11. Timaeus, 510-52. + +12. See The Republic 367. Compare also Crito 49 D: "For I know that only a few men hold, or ever will hold, this opinion. Between those who do and those who don't there can be no common deliberation; they will necessarily look upon each other with contempt + +13. See Gm·gias 482, where Socrates tells Callicles, his opponent. that he will "not be in agreement with himself but that throughour his life. he will contradict himself." He then adds: "I would much rather th�t the whole world be not in agreement with me and talk against me than that I, who am one, should be in discord with myself + +and talk in self-contradiction." + +14. For a definition of thought as the silent dialogue between me and myself, see especially Theaetetus 189-1 90, and Sophist 263-264. It is quite in keeping with this tradition that Aristotle calls the friend, with whom you speak in the form of dialogue an auros CiAXos, another + +self. + +15. Nicomachean Ethics, book 6, especially 1140b9 and 1141b4. 16. See Jefferson's "Draft Preamble to the Virginia Bill Establish- + +ing Religious Freedom." + +17. This is the reason for Nietzsche's remark in "Schopenhauer als Erzieher" : "lch mache mir a us einem Philosoph en gerade so vie!, + +als er imstande ist, ein Beispiel zu geben." + +18. In a letter to W. Smith, November 13, 1787. + +19. Critique of Judgment, Paragraph 32. + +20. Ibid., Paragraph 59. + +21 . For France, see the excellent article "De Gaulle: Pose and Policy," in Foreign Affairs, July 1965. The Adenauer quotation is from his Memoirs 1945-1953, Chicago, 1966, p. 89, where, however, he puts this notion into the minds of the occupation authorities. But he has + +repeated the gist of it many times during his chancellorship. + +22. Parts of the archive were published in Merle Fainsod, + +Smolensk Under Soviet Rule, Cambridge, Mass., 1958. See p. 374. + +8. The Conquest of Space and the Stature of Man + +1. This question was asked for a "Symposium on Space" by the editors of Great Ideas Today ( 1963 ) with special emphasis on what "the exploration of space is doing to man's view of himself and to man's condition. The question does not concern man as a scientist, nor + +man as a producer or consumer, but rather man as human." 2. Nicomachean Ethics, book VI, ch. 7, 1141 a20 ff. + +York, 1958, p. 88. + +6. Ibid., p. 76. + +7. Planck, op. cit. p. 503. + +8. See Planck's Science and Humanism, London, 1951, pp. + +25-26. + +9. John Gilmore, in a sharply critical letter when this article first appeared in 1963, puts the matter very nicely: "During the last several years we have in fact succeeded in writing computer programs that enable these machines to exhibit behavior that anyone not familiar with the makeup of the programs would unhesitatingly describe as intelligent, even highly intelligent. Alex Bernstein, for example, has devised a program that enables a machine to play spectacular good checkers. In particular, it can play better checkers than Bernstein. This is an impressive achievement; but it is Bernstein's and not the machine's." I had been misled by a remark of George Gamow-see + +note 10-and have changed my text. + +10. George Gamow, "Physical Sciences and Technology," in + +Great Ideas Today, 1962, p. 207. Italics added. + +11. Sergio de Benedetti, as quoted by Walter Sullivan, "Physical + +Sciences and Technology," in Great Ideas Today, 1961, p. 198. + +12. Bohr, op. cit., pp.70 and 61 respectively. + +13. Planck, op. cit., pp. 493, 517, and 514 respectively. + +14. Bohr, op. cit., pp. 31 and 71 respectively. + +15. Ibid., p. 82. + +16. Planck, op. cit., pp. 509 and 505 respectively. + +17. See J. Bronowski, Science and Human Values, New York, + +1956, p. 22. + +18. See The Starry Messenger, translation quoted from Discoveries + +and Opinions of Galileo, New York, 1957, p. 28. + +19. See Einstein's Relativity, The Special and General Theory (1905 & 1916), quoted in Great Ideas Today, 1961, pp. 452 and 465 + +respectively. + +20. Walter Sullivan, op. cit. , p. 189. + +21. Ibid., p. 202. + +22. I quote from Descartes' dialogue "The Search after Truth by the Light of Nature," where his central position in this matter of doubting is more in evidence than in the Principles. See E. S. Haldane and G. R. T. Ross edition of his Philosophical Works, London, 1931, + +23. I owe this definition to John Gilmore's letter, mentioned in note 9. Mr. Gilmore, however, does not believe that this imposes + +limitations on the knowledge of the practicing physicist. I think that Heisenberg's own "popular" statements bear me out on this point. But this is by no means the end of this controversy. Mr. Gilmore as well as Mr. Denver Lindley believes that the great scientists may very well be wrong when it comes to evaluating philosophically their own work. Mr. Gilmore and Mr. Lindley accuse me of using the scientists' statements uncritically, as though they could speak about the implications of their work with the same authority as they talk about their subjects properly speaking. ("Your confidence in the great figures in the scientific community is touching," says Mr. Gilmore.) This argument, I think, is valid; no scientist, no matter how eminent, can ever claim the same soundness for "philosophical implications" he or somebody else discovers in his work or in his utterances about it as he could claim for the discoveries themselves. Philosophic truth, whatever it may be, is certainly not scientific truth. Still, it is difficult to believe that Planck and Einstein, Niels Bohr, Schrodinger and Heisenberg, all of whom were puzzled and greatly worried about the consequences and general implications of their work as practicing physicists, should all + +have been subject to the delusions of self-misunderstanding. + +24. In Philosophic Problems of Nuclear Science, New York, + +1952, p. 73. + +25. Ibid., p. 24. + +26. In The Physicist's Conception of Nature, New York, 1958, + +p 24. + +27. Ibid., pp. 18-19. + +IN DEX OF NAMES + +Achilles, 46, 248, 263 + +Adam, 66, 73 + +Adams, John, 134, 176, 294 + +Adeimantus, 244 + +Adenauer, Konrad, 252, 299 + +Alcinous, 294 + +Anastasius I, Emperor, 126 Aquinas, Thomas, 133 Archimedes, 279 + +Aristotle, 17-20, 22, 42, 45-47, 63, 71, 76, 104-107, 110, 11 3, 11 6-20, 130, 147, 191, 223, 245, 265, 285, 286, 287, 288, + +289, 290, 298, 299 Arnold, Matthew, 203 + +Augustine, 65-66, 72-73, 126, 131, 146, 147, 157, 159, 161, + +162, 167, 287, 295 Augustus, 106, 292 + +Baillie, John, 287 Barrow, R. H., 292 Bernstein, Alex, 300 + +Bohr, Niels, 267, 270, 271, 300, + +301 + +Bonaparte, Napoleon, 81 Brentano, Clemens von, 201 Bronowski, Jacob, 300 Bukharin, Nikolai, 256 Burckhardt, Jacob, 18, 45 + +Caligula, Gaius, 106 Camus, Albert, 283 + +Char, Ren�. 3, 4, 7, 8, 9, 283 Charles I (King of England) , 150 Charles V (Holy Roman em- + +peror ), 228 + +Christ, Jesus, 65-67, 126, 129, + +133, 167, 248, 292 Churchill, Winston, 156 + +Cicero, Marcus Tullius, 41, 71. 121, 139, 212, 213, 215, 219, 224-25, 284, 292, 294, 296, + +Clemenceau, Georges, 239, 249 Clement of Alexandria, 131 Cochrane, C. N., 285, 287 Constantine the Great, 125 Copernicus, Nicolaus, 56, 273 , + +275 + +Cornford, F. M., 284, 298 Cullman, Oscar, 287 + +De Gaulle, Charles, 252, 299 Descartes, Rene, 29, 30, 38, 54- + +56, 70, 275, 300 Dinesen, Isak, 262 Dionysus, Exiguus, 67 Dods, Marcus, 294 + +Dostoevski, Feodor M., 30, 254 Droysen, Johannes G., 49, 53, 75, + +288 + +Duns Scotus, John, 152 + +Eddington, Sir Arthur S., 266 Einstein, Albert, 230, 270, 273, + +274, 279, 301 + +Engels, Friedrich, 19, 21, 284 + +Ennius, Quintus, 122 + +Ephesus, 46 + +Epictetus, 147, 148, 162 + +Epicurus, 297 Ernout, A., 296 + +Fainsod, Merle, 299 Faulkner, William, 10 + +Ferdinand I (Holy Roman em- + +peror ), 228 Francis, St. 248 + +Friedrich, C. J., 290, 292 Fritz, Kurt von, 290 + +Galileo, 49, 56, 230, 273 Gamow, George, 300 Gassendi, Pierre, 56 Gelasius, Pope, 126 Gentz, Friedrich, 288 Gilmore, John, 300, 301 Glaukon, 244, 293 + +God, 77, 87, 97, 127, 133, 135 Goethe, Johann W. von, 82, 193 + +Gorgias, 293 + +Gregory of Nyssa, 128 Gregory the Great, 134 Grotius, Hugo, 70 + +Haldane, E. S., 300 Hamlet, 192, 207 Harder, Richard, 297 Hector, 51-52, 262 + +Hegel, Georg W., 8, 11, 18, 23, 26, 28-30, 35, 37-39, 45, 67- 69, 75-77, 80, 83, 85, 262, 288 + +Heidegger, Martin, 288, 29 1 Heine, Heinrich, 134 + +Heisenberg, Werner K., 86, 276, 277, 279, 286, 289, 301 + +Heraclitus, 46, 229 + +Herder, Johann C. von, 69, 82 Herodotus, 41, 44-45, 48, 51, 64, 166, 263, 284, 285, 287 + +Hesiod, 46, 213 Hitler, Adolf, 133, 236 + +Hobbes, Thomas, 22, 56, 70, 73, 76, 98, 128, 150, 160, 230, 23 1, + +233, 297-98 + +Homer, 36-37, 48, 51, 72, 124, + +262-63, 288 Hook, Sidney, 35 + +Jefferson, Thomas, 246-48, 299 Jesus of Nazareth, see Christ + +Kafka, Franz, 7, 9-1 3, 14, 277, + +283 Kallikles, 293 Kamenev, Lev, 256 + +Kant, Immanuel, 40, 56, 82-84, 107, 11 0, 144, 219, 220-22, 228, 234, 241, 242, 244, 248, + +288 + +Kepler, Johann, 56 + +Kierkegaard, Soren, 25, 26, 28- + +32, 35, 38-39, 94 Koyre, Alexandre, 286 Kristeller, Paul 0., 288 + +Lafayette, Marie Joseph, Marquis + +de, 163 + +Lattimore, Richmond, 288 Leibniz, Gottfried, 23 1, 29 5 Lenin, Nikolai, 19-20, 141, 256 Lessing, Gotthold E., 80, 233-34 Lindley, Denver, 285, 301 + +Livy, 121 + +Louis XIV (King of France), 199 + +Luther, Martin, 56 + +Machiavelli, Niccolo, 22, 136-39, 140, 141, 153, 245, 294 Madison, James, 233, 234, 235 + +Malraux, Andre, 8 Maritain, Jacques, 29 1 + +Marx, Karl, 17-26, 28-35, 38-40, 70, 77-81, 83, 139, 205, 284 + +Meinecke, Friedrich, 68, 286 Melville, Herman, 205 + +Mercier de Ia Riviere, Paul, 240 + +Mersenne, Marin, 56 + +Mill, John S., 199, 294, 295 + +Minerva, 121 Mnemosyne, 43 + +Mommsen, Theodor, 123, 287. + +289, 292, 296 + +Montesquieu, Charles L., 122, 150, 152, 160-61, 163, 240 Muir, Willa and Edwin, 283 Murray, Gilbert, 285 + +Napoleon, 81 + +Newton, Isaac, 82, 273 + +Niedermann, Joseph, 296, 297 Nietzsche, Friedrich, 19, 25, 26, 28-32, 34-35, 37-39, 55, 83, + +284, 288, 299 + +Origen, 128, 131 Orosius, 66, 292 Otto, W. F., 286 + +Paine, Thomas, 163 + +Parmenides, 46, 124, 157, 233 + +Pascal, Blaise, 94 + +Paul, 146, 157, 158, 161, 167 Pericles, 72, 213-1 4, 217, 219 + +Peterson, Erik, 292 Pfeiffer, Rudolf, 297 Phaedra, 295 + +Plato, 17-1 9, 23, 25, 26, 28, 30, 35-40, 46-47, 68, 78, 93, 99, 104-1 5, 11 8, 120, 124-27, 129-35, 137, 139, 157-59, 191, 203, 214, 220, 224, 225- 226, 229-33, 235, 237, 240, 246, 260, 263, 285, 286, 289- + +29 1, 296, 297, 298 + +Pliny, 122 Plotinus, 145 Plutarch, 123, 294 Poeschl, Viktor, 292 Polybius, 194, 287 Potemkin, Grigori, 258 Proust, Marcel, 200 Pythagorean, 225, 294 + +Randall, John H., Jr., 288 Ranke, Leopold von, 49 Reinhardt, Karl, 283 Rilke, Rainer Maria, 44 + +Robespierre, Maximilien, 134, + +139, 141, 200 Romulus, 123 + +Rosenberg, Harold, 197, 296 + +Ross, G. R. T., 300 Ross, W. D., 288 + +Rousseau, Jean-Jacques, 82, 163- + +164, 176, 199, 200 Rykou, Aleksei, 256 + +Saint-Simon, Louis, Due de, 199 + +Sartre, Jean-Paul, 9 Satan, 128, 129 + +Schroedinger, Erwin, 269, 270, + +286, 301 Scipio, Publius, 139 + +Smith, W., 299 + +Socrates. 46, 72, 107, 11 4, 11 6, + +129, 157 + +' 159, 220, 224, 244, + +247, 293, 294, 298 + +Sophocles, 42 + +Spinoza, Baruch, 150, 234, 297 + +Stalin, Joseph, 88, 236 + +Tertullian, 131, 13 3 Thrasymachus, 244 + +Thucydides, 48, 51-52, 166, 213, + +288, 296 Tiberius, 106 + +Tocqueville, Alexis de, 7, 77, 17 6, + +283 + +Trotsky, Leon, 23 1, 252, 256 + +Ulysses, 45, 294 + +Vico, Giovanni B., 50, 57-58, 77, + +82, 84 Virgil, 121 + +Voegelin, Eric, 293 , 298 + +Walde, A., 296 Wallon, H., 289 + +Whitehead, Alfred N., 62 Whitman, Walt, 205 Wilson, Edmund, 24 Wind, Edgar, 286 + +Young, G. 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+VOLUME 1 + +Theory of Practical Ensembles + +JEAN-PAUL SARTRE + +Translated by Alan Sheridan-Smith Edited by Jonathan Ree Foreword by Fredric Jameson + +> VERSO London • New York + +This translation ftrst published by New Left Books 1976 + +© Editions Gallimard 1960 Translation © New Left Books 1976 + +Corrected edition ftrst published by Verso in 1991based on the revised French edition of 1985© Editions Gallimard 1960, 1985 + +This edition ftrst published by Verso 2004 + +© Verso 2004 + +l"oreword © Fredric Jameson 2004 + +All rights reserved + +The moral rights of the authors, editor and translator have been asserted + +1357910 8642 + +Verso + +UK: 6Meard Street, London W1F OEG + +US: 180 Varick Street , New York, NY 10014-46 06 + +www.versobooks.com + +Verso is the imprint of New Left Books + +ISBN 1-85984-485-5 + +British Library Cataloging in Publication Data + +t\ catalogue record for this book is available from the British Library + +Library of Congress Cataloging-in-Publishing Data + +A catalog record for this book is available from the Library of Congress + +Typeset in Fournier + +Printed in the UK by Biddies, King's Lynn + +Contents + +EDITOR' + +S NOTE Xl + +FOREWORD by Fredricjameson Xlll + +INTRODUCTION 13 + +I THE DOGMATIC DIALECTIC + +AND THE CRITICAL DIALECTIC 15 + +Dialectical Monism IS + +2 Scientific and Dialectical Reason 18 + +3 Hegelian Dogmatism 21 4 The Dialectic in Marx 23 + +5 Thought, Being and Truth in Marxism 24 6 The External Dialectic in Modern Marxism 26 + +7The Dialectic of Nature 27 + +8 Critique of the External Dialectic 29 9 The Domain of Dialectical Reason 32 + +II CRITIQUE OF CRITICAL INVESTIGATION 42 + +I The Basis of Critical Investigation 42 2 Dialectical Reason as Intelligibility 43 + +3 Totality and Totalisation 45 + +4 Critical Investigation and Totalisation 47 + +5Critical Investigation and Action 49 + +6 The Problem of Stalinism 51 7 The Problem of the Individual 53 + +8 Totalisation and History 57 + +9Primary and Secondary Intelligibility 57 + +10The plan of this Work 64 II The Individual and History 70 12Intellection and Comprehension 74 + +BOOK I FROM INDIVIDUAL PRAXIS + +TO THE PRACTICO-INERT 77 + +IINDIVIDUAL PRAXIS AS TOTALISATION 79 + +Need 79 + +2The Negation of the Negation 83 + +3 Labour 89 + +II HUMAN RELATIONS AS A MEDIATION + +BETWEEN DIFFERENT SECTORS OF MATERIALITY 95 + +IIsolated Individuals 95 + +2Duality and the Third Party 100 + +3 Reciprocity, Exploitation and Repression 109 + +III MATTER AS TOTALISED TOTALITY: + +A FIRST ENCOUNTER WITH NECESSITY 122 + +Scarcity and Mode of production 122 + +(i) Scarcity and History 125 (ii) Scarcity and Marxism 140 + +2Worked Matter as the Alienated Objectification of Individual and Collective Praxis 153 + +(i) Matter as Inverted Praxis 16 1 + +(ii) Interest 197 + +3 Necessity as a New Structure of Dialectical + +Investigation 220 + +4 Social Being as Materiality: Class Being 228 + +IV COLLECTIVES 256 + +I Series: the Queue 256 + +Indirect Gatherings: the Radio Broadcast 270 Impotence as a Bond: the Free Market 277 Series and Opinion: the Great Fear 293 Series and Class: the French Proletariat 306 + +6 Collective Praxis 318 + +BOOK II FROM GROUPS TO HISTORY 343 + +I THE FUSED GROUP 345 The Genesis of Groups 345 2 The Storming of the Bastille 351 3 The Third Party and the Group 363 4 The Mediation of Reciprocity: the + +Transcendence-Immanence Tension 374 5 The Intelligibility of the Fused Group 382 + +II THE STATUTORY GROUP 405 + +The Surviving Group: Differentiation 405 + +2 The Pledge 417 + +III THE ORGANISATION 445 + +Organised Praxis and Function 445 2 Reciprocity and Active Passivity 463 3 Structures: the Work of Levi-Strauss 479 (i) Structure and Function 484 (ii) Structure and System 491 + +(iii) Structure and the Group's Idea of Itself 499 + +IV THE CONSTITUTED DIALECTIC 505 + +Individual and Common Praxis: + +the Manhunt 505 + +2 Spontaneity and Command 519 + +3Disagreements in Organisational Sub-groups 524 + +4 Praxis as Process 539 + +5 Taylorism 559 + +V THE UNITY OF THE GROUP AS OTHER: + +THE MILITANT 564 + +VI THE INSTITUTION 576 + +1 Mediated Reciprocity in the Group 576 + +2 Purges and Terror 583 + +3 Institutionalisation and Inertia 599 4 Institutionalisation and Sovereignty 607 + +5 States and Societies 635 6 Other-direction: the Top Ten, + +VII THE PLACE OF HISTORY 664 + +The Reciprocity of Groups and Collectives 664 2 The Circularity of Dialectical Investigation 671 + +3 The Working Class as Institution, Fused + +Group and Series 678 + +4 Economism, Materialism and Dialectics 710 + +5 Racism and Colonialism as Praxis and Process 716 + +VIII CLASS STRUGGLE AND DIALECTICAL REASON 735 + +1 Scarcity, Violence and Bourgeois Humanism 735 + +2Malthusianism as the Praxis-Process of the Bourgeoisie 754 + +(i) June 1848 754 + +(ii) Bourgeois 'Respectability' in the Late Nineteenth Century 770 + +(iii) Class Struggle in the Twentieth Century 781 + +3Class Struggle as a Conflict of Rationalities 794 4 The Intelligibility of History: Totalisation without + +a Totaliser 805 + +ANNEXE 821 + +GLOSSARY 827 + +INDEX 831 + +Editor's Note + +The text translated here was originally published in 1960 in a volume entitled Critique de la Raison Dialectique, precede de Questions de Methode, Tome I, Thiorie des Ensembles Pratiques. Questions de Methode was originally published as a separate essay, and is available in English (entitled either The Problem of Method or Search for a Method). I t is therefore not translated here. N one of the material translated here + +has appeared in English before except in small fragments. + +Sartre's text was written hastily, and is not easy to translate. The glossary explains how various neologisms and technical terms have normally been translated; but it must be admitted that in many cases, including such crucial terms as 'experience' and 'depassement' (which we have translated by 'investigation' and 'transcendence' respectively), no + +completely satisfactory English equivalent has been found. + +Many of Sartre's longer sentences and paragraphs have been divided, as have his chapters. Most of the divisions into chapters, sections and subsections, along with their titles, are our own. So too are most of the footnotes. In these and other matters, the German translation by + +Traugott Konig (Rowohlt 1967) has been very useful to us. + +jonathan Ree + +1976 + +Foreword + +Fredric Jameson + +There are many reasons why Sartre's Critique has not had the attention it deserved, and its unfinished character is the least of those (especially since, except for the plays, he never really finished anything). For one thing, it came at a moment in the early 1960s when the intellectual hegemony of existentialism - virtually universal in the immediate postwar years - was giving way to that new intellectual passion called structuralism. Claude Levi-Strauss's rather summary attack on Sartre's 'myth' of the French Revolution (and no doubt provoked by Sartre's reassimilation of nascent structuralism in the lectures in which the Critique was first presented) anticipated Frans:ois Furet's version of the topic by twenty years without the anti-communism. (Sartre's view of 'structure' as the objectification of praxis, its exoskeletal trace, will be revived and powerfully augmented by Pierre Bourdieu's Esquisse d'une theorie de fa pratique of 1972, which itself in turn in many ways marked the end of the structuralist period.) But Levi-Strauss's authority in the early 1960s was powerful enough to legitimate a wholesale reaction against, and withdrawal from, phenomenological positions in general: yet those still very much motivated the insistence of the Critique on the necessity for a continuity between individual and group experience. Meanwhile, now that structuralism has followed existentialism into intellectual history, it is the notorious stylistic difficulty of the Critique that offers the more fundamental reason why all those who ought to be most immediately concerned by it - they include political philosophers, sociologists, militants interested in the Laclau-Mouffe dynamics of action, as well as whatever Sartreans may have survived the deluge (Bernard-Henri Levi's enthusiastic new book suggests that there may be a whole generation of new converts waiting in the wings) + +- have given it a wide berth. + +This very linguistic difficulty reinforces the idea that philosophers have no business reflecting on sociological issues that ought to be left to experts. The professionalization of the social sciences thus reinforces empiricist and anti-theoretical prejudices already alerted by Sartre's radical political positions and in particular his rather strident adherence to Marxism (and to the 'orthodox Marxism' of the early I960s at thatl). How can he write on the French Revolution? He's no historian, he o nly uses secondary sources! How can he write on the history of French unions and anarcho-sy ndicalism? He's no labor historian! How can he write on French Malthusianism and France's peculiar economic development? He's not an economic historian! And as for Chinese deforestation and the gold and silver of the Spanish New World - it's obvious that a philosopher has no expertise on any of these subjects. Perhaps, as he is a 'culture worker', he might at best be granted some authority in speaking, as he does, about French 'distinction' and bourgeois manners (another theme in which he is followed, far more famously, by Bourdieu later on). So the idea, from Kant to Deleuze, that the philosopher's job is to look over the shoulder of the various scientists and experts and check their thinking and their use of abstract categories - this notion of the philosopher's + +vocation is no longer very current among us. + +I + +Do we need, in other words, to philosophize history ? In a nominalistic age, indeed, 'philosophies of history ' (famously rebaptized by Jean-Fran�ois Lyotard as 'grand narratives') are greeted with universal suspicion, even though the most tenacious of them - the story of moder nization -continues to have a powerful grip on political thinking in East and West alike. Capitalism itself lives in a perpetual present; the human past seems to be a senseless accumulation of unsuccessful human efforts and intentions; yet the future of technology inspires blind and unshakeable faith. Sartre here offers to reorganize this doxa into what may at least be considered as negative meanings, in the categories of counter-finality and the practico-inert: a proposal which would, as we shall see, restore a certain philosophical meaning to historical events, at the same time as it risks projecting some new cyclical + +'vision of history ' + +As for the undoubted difficulty and occasional unreadability of this text, so thoroughly devoid of the fireworks that make up Sartre's other discursive writing, the complaint betrays something of a misapprehension as to the internal dy namics of this philosophical prose. It is meant to be a study in the status of two kinds of thinking, analy tic + +reason and dialectical reason. But unlike so much of Sartre's philosophy, it does not have as its primary function the invention of new philosophical concepts (although new terms- and concepts do emerge from it). Rather, it is an operation in matching an already existing dialectical language or code against a series of individual and collective experiences. The Critique is thus from this standpoint to be seen as an austere and formalistic exercise, without any instrumental coloration, like late Bach; and it invites us to judge whether the rewriting of this or that type of historical content in the terminology, for example, of the negation of the negation (or of subject and object, passive and active, multiplicity and unification, transcendent and immanent, exteriority and interiority) is successful: that is, whether the new formulations have a new and heightened kind of intelligibility in their own right. This can be an exasperating process, particularly when Sartre tries out various different versions of this matching in succession. But the reader's interest will be fully stimulated only if this unique and peculiar linguistic operation is the center of the focus. The problem can be rephrased as a testing of the validity of Engels' dialectical categories (for it is he, rather than Marx himself, who originally formulated them, in the Anti-DilAring) for the illumination - which is to say, the rewriting - of history, and not least of contemporary twentieth-century history (up to 1960). This means that Sartre here takes on himself a preexisting alien language: that of Engels' three laws of the dialectic - the transformation of quantity into quality (and vice versa); the interpenetration of opposites; and the negation of the negation. He will now attempt to rewrite the problems of a philosophy of history at a level of philosophical intensity and abstraction quite different from that of the orthodox Marxist version of this philosophy to be found in Stalin's dialectical materialism - a 'philosophy ' still very much alive at the moment in which Sartre is writing and is attempting to work out his own practical and theoretical relationship to the existing Communist Parties as well as to the other revolutionary traditions. Much is thus at stake in this seemingly formalistic exercize; I therefore recommend a preliminary approach through the form and its problems, before we hazard a judgment on the resultant content, not to speak of the success of the enterprise as a whole. Yet for the reader, in order to read and understand the work in the first place, as with most original philosophies, we are here required to learn what amounts to a new language, as Sartre constructs one out of his matching and rewriting enterprise, a new artificial language he not only devised but taught himself to + +speak with occasionally maddening fluency. The Critique is thus a 'language experiment', and the reader is to be reassured that with a + +little practice its rhythms fall into place. + +This approach can be further strengthened by an awareness of the continuities between Sartre's earlier existential system (embodied in Being and Nothingness) and this new project which so many people have wrongly assumed to mark a break with existentialism and a philosophical as well as a political turn towards Marxism - the implication being that Sartre will now stage a wholesale replacement of his older concepts and terms. The argument for this rather different kind of matching operation, however, depends on establishing a fundamental continuity between the two moments, something Perry Anderson has succinctly evoked as a 'conduit from many of the concepts of Being and Nothingness to those of the Critique of Dialectical Reason: among others, the notion of "facticity" leading to that of "scarcity", "inauthendeity" to "serality", the instability of the "for-itself-in-itself" to that of the "fused group" , Yet the rewriting process is far from being a static translation of the older system, in which the bleak pessimism of the existential period is replaced by the ferocious world of competition and violence in the dialectical one. I want to go further and to claim that the revisions of the Critique make possible a genuine philosophical solution to the dilemma that remained open in Being and Nothingness, namely that of 'concrete relations with the other': we will return to + +this below. + +At any rate, it seems best to skip over the methodological reflexions with which the text begins (and even the questions of structure and the frustrating perspective according to which the first volume merely lays in place the philosophical instruments - seriality, group-in-fusion, etc. - which are to be concretely deployed in the second one) and to note a few basic initial presuppositions. Thus, if we are to continue the translational operation sketched out above, we will have to say that what is here called praxis is more or less the same as what Being and Nothingness called the project: The new language betokens an extension of the original concept rather than its replacement, for now what will be argued is that the freely chosen project describes not only individual action but collective acts as well; or better still, that understanding collective action is not different in nature than the understanding of the individual (existential) act. Here, in other words, we find the same fundamental existential and phenomenological bias mentioned above, but which now confronts us with the fundamental dilemma of the + +Critique, namely whether collective or historical events can be thought to have the same transparency for understanding as do individual ones. This is not at all evident, and Sartre's task is clearly a difficult one, which a mere change in terminology is unlikely to make any easier. As if all this were not enough, the very status of Volume I of the Critique makes for some additional complications. For it is in effect a preparatory volume, and never arrives at what will presumably be the central concern of this philosophical enterprise, namely the meaning of history. What are being laid in place in this volume (the only completed one) are merely the basic sociological and even metaphysical concepts, the static instruments, required before we set 'history' in motion. The division of the projected work into two general types of discourse - that of methodology and basic concepts, and the more properly philosophical argument about history's putative unity, direction and meaning - would seem however to be a rather undialectical one: in both Hegel and Marx the Darstellung of the basic concepts turned into a whole dialectical exposition in its own right (in Hegel, the Logic, or perhaps even the Encyclopedia as a whole), in Marx, the first and simplest approach to capital (Volume I), which was to have been redeveloped dialectically in the far more complex spirals of Volumes II and III (along with the projected unwritten ones), which retrace the earlier simple or 'basic' steps in more concrete trajectories (many capitals, capital as a whole). Nothing of the sort is here in Sartre, whose defense might take the following form: Marxism and the tradition now already exists, so that it is not a question of expounding utterly new conceptualities but rather critically and di alectically reexamining those in place to restore to them a dialectical spirit which has long since evaporated in the hands of the various orthodoxies. And this is a task that probably has to proceed, a la Hobbes, in a more or + +less analytical fashion. + +The other explanation is a reflex of Sartre's unique strengths rather than of any formal or conceptual weakness: it is simply his irrepressibly narrative spirit, which tends to convert any simple expository task into a storytelling form, something evidently related to the historical subject-matter, for which 'concrete' always means 'event' Thus even economics - the question of inflation in imperial Spain - or sociology - the exposition of what class interest might mean - let alone the long illustrative sections drawn either from the French Revolution or from the Soviet Revolution down to Stalinism -all of these illustrations tend to overpower the surface text and to acquire a dynamism of their own. + +But this means that the reader is tempted to mistake these narrative illustrations for so many positive philosophical propositions about concrete history: something which results in the fundamental error so many readers (including myself, in an earlier effort) have made about Volume I, namely the notion that it sets in place a cyclical view of history in which groups incessantly form and then dissolve back into seriality, leaving an essentially dictatorial structure in place behind + +them. We will come back to this issue. + +Let me now enumerate the key moments, which is to say the key operative concepts, of Volume 1. I have already suggested that the first of these concepts, the very starting point, that of scarcity, allows Sartre to preserve the much disputed dialectical category of the negation of the negation: scarcity is seen as an initial structure of the world, or of being, which is negated and transcended by human need - the experience of lack and desire, of hunger and thirst, is then the initial way in which we organize the en-soi (being-in-itself) into a situation, turning a combination of chemical elements into a desert or a lush landscape. The human organism, as a meaningless fact, thereby makes itself over into a project, into a praxis that can henceforth have a meaning (to call it a human meaning is simply to multiply these terms unnecessarily), and thus an outcome, whether of failure or success. But to begin with scarcity is also to short-circuit and disqualify the whole false problem of human nature (something the fundamental existential tenet - existence precedes essence - sought to do on a more abstract level). Now it becomes possible to share the realist pessimism of Hobbes or Machiavelli - that human beings are necessarily evil -without any metaphysical premises about nature itself. Indeed the simple fact of inhabiting a world of scarcity (a world we still inhabit even if or when our own society happens to become rich and prosperous) explains the fact of violence and aggressivity in a situational rather than a naturalistic way: 'When, in the course of a migration, members of a tribal group come across a strange tribe, they suddenly discover man as an alien species, that is, as a fierce carnivorous beast who can lay ambushes and make tools' (107).\* This is not some belated form of social darwinism nor even a proposition out of socio-biology, it is the expression of human freedom, as well as of that of reciprocity: 'In pure reciprocity, that which is Other than me is also the same. But in reciprocity as modified by scarcity, the same appears to us as anti-human in so far as this same man appears as + +radically Other - that is to say, as threatening us with death' (131-2). Scarcity is thus a contingent feature of our world (we can imagine SF alien creatures from a world without scarcity, but then they would not be human in the ways we experience that condition). Meanwhile, generosity, cooperation and the like are not false or fictional, but they are not features of human nature either (there is no such thing as human nature). They are, rather, other forms in which our freedom negates that + +initial fact of being. + +Once this initial ontological (or even metaphysical) premise is given, we are in a position to name and to appreciate its transformations. Once again, these are given in the order of their emergence: that is to say, a Hegelian or evolutionary presentation is adopted which can very easily lend itself to the narrative misconceptions I have already warned about. In other words, this sequence of concepts, categories or forms can very easily be mistaken for something like a 'philosophy of history' (a misconception, to be sure, only strengthened by the decision to publish this enormous definitional section as a whole book or separate volume in its own right). Let's go even further than this, on the grounds that authors are always complicitous in the misunderstandings of their own works: this sequence then may well in reality betray something like an alternate 'philosophy of history' within the larger (and never completed) text; it betrays a cyclical pattern virtual in Sartre's thinking and no doubt in contradiction with the official analysis of historical direction + +he meant to offer us. + +At any rate, the first move in this 'emergence' will follow the logical order of Being and Nothingness, where pure being (being-in-itself) is then initially shaped and organized by the negativity of human beings (or by being-for-itself). Here the being of scarcity is transformed into a situation of need by way of the negativity of human lack (or: inorganic being is transformed by organic being or life), and there results a first simple and fundamental form of the project, the negation of the negation: the form in other words of human action itself. In the translational scheme with which Sartreans must become familiar in order to read the Critique, the key term 'project' is here rendered as + +praxIs. + +I t would be tempting indeed to pause for a lexical digression on this momentous word, recoined and placed back in philosophical circulation by Count Cieslowski in 1839, and then almost at once appropriated by Marx in the Theses on Feuerbach (1845-1846), where it is defined as sinnlich-menschliche Tiitigkeit or 'sensuous human + +activity', that is to say a material, or materialist, action involving change. What does the new borrowing add to the plainer language of acts themselves? Well, to be sure, even the choice of the word act adds something to our narrative understanding of events, since it implies a unified process which leaves real traces (as opposed, in one of Sartre's favorite dualisms, to the mere gesture, on the one hand, or the immaterial thought or wish on the other - that 'mere interpretation' of which Marx accused the philosophers). Praxis then suggests that we need to open up even the conventional conception (or better still category) of the act, to include two more dimensions: one of ontology + +and one of history. + +Praxis thus implies and designates the deep structure of the act, as that combines being and negativity; and it also asks us to consider the humblest act in what Hegel would have called a world-historical light, or what Sartre himself terms the incarnation of the meaning of History itself: in this sense, then, the opening of a can of peas stages my whole relationship to being itself at the same time that it inflects the historical modalities of the world of capitalist industrial production (in this case, as we shall see, what Sartre calls 'exigency'). 'Praxis' does not impose those two dimensions of meaning on an act in advance, but rather opens the act up to an interrogation in terms of both or either one. But as if that were not enough (now closing our parenthesis), the word praxis itself in the Critique is quickly doubled and outpaced by another one, a true neologism this, whose technical meaning has latterly been utterly transformed and travestied by its increasingly central role in ideological debate. This is of course the word 'totalization', which Sartre coined specifically in order to differentiate himself from Lukacs and the latter's key word 'totality' Unfortunately, the ideological connotation with which the Sartrean term has been more recently endowed pointedly conflates these two terms, and makes Sartre over into yet another philosopher of 'totality', that is to say, not merely of universals and of Marxism, but, above all in the context of identity politics, a philosopher representative of identity itself and the hegemony of the white male Western intellectual (and no doubt characterizing the left intellectual, as opposed to the various right-wing ideologies). 'Totalizing' has thus become a slogan which identifies a claim to speak from above and for all of society, as opposed to the minoritarian and differential positions of this or that Foucauldian 'specific intellectual' There is thus, in the deployment of this epithet in discursive struggle, a movement out from the condemnation of the various Communist + +Parties and their claims to truth and to hegemonic leadership towards the indictment of political intellectuals generally as those espouse this or that 'total' systemic change of capitalism as a whole, as opposed to + +this or that specific minority group agenda within capitalism. + +Nor did Lukacs himself really mean anything so offensive, even though the 'standpoint of totality' will be evoked as a criterion of truth, where it means grasping the system as a whole, and characterizes a dialectic for which thinking starts not with Descartes' smallest parts or units and working upwards but with the most complex final form and working downwards. But Lukacs identified this standpoint and this perspective with a class position; and he evoked the proletariat's 'aspiration to totality' rather than their empirical possession of such a universal view, which the party itself was supposed to mediate, by way + +no doubt of all kinds of bad 'totalizations' + +However one evaluates Lukacs's so -called standpoint theory, which has been very suggestively revived and adopted by theoreticians of gender and of race, it has nothing whatsoever to do with Sartre's usage. Sartrean totalization was meant, indeed, to exclude any implication that multiples like the 'group in fusion' have the ontological status of a totality or an organism (of a 'hyperorganism' as Sartre's text will constantly warn us). For Sartre, then, a totality is precisely a static concept, a concept of being rather than of process, and one governed by analytic + +rather than by dialectical reason. + +But these lofty philosophical issues are scarcely raised by Sartre's use of the word totalization, which simply means praxis itself, organized activity with a view towards an end; and, whatever its possible extension to collective and historical movements and events, its relevancy begins with the behavior of individuals, and indeed with acts as insignificant as that opening of a can, I have already singled out. + +It is curious that Sartre should have chosen a relatively spatial word, redolent of exteriority, to characterize even the initial forms of human activity; indeed we will find it associated with unification as well, which compounds our sense of the incongruity of the choice of such terms to characterize interiority and human action. Yet they evoke the multiple and the dispersed, separation and heterogeneity, in order to dramatize what the human project most immediately confronts and what it must most immediately overcome. Indeed, I feel that the importance of the notion and the experience of multiplicity for Sartre has scarcely yet been evaluated, for it arguably governs everything from the inert things and beings of the outside world all the way to + +demography itself, in its twin form of philosophical otherness and of + +colonial subjugation. + +At any rate, in this first context of the simplest acts of individuals, totalization and unification underscore what negativity, the project, human praxis, first does to the world of being that confronts us, which is to organize its scattered bits and pieces, its 'blooming buzzing confusion', into a unified situation: for it is only with the situationthis great leitmotif of the dynamism of Sartre's earlier work - that praxis can begin, as the intervention into and the transformation - Sartre say s, the dipassement, the transcendence - of that situation it has itself initially brought into being (a dimension of the nascent act reminiscent of Heidegger's VorgrifJ). And with this 'first' human act, + +then, we are thrown into history itself. + +For what totalization or praxis produces is one form or another of 'worked matter', what Hegel would have called my objectification in the outside world, and as it were an inert and alienated trace of my completed act. And with this, the dialectic itself begins, and the funda. mental dualism of all of Sartre's philosophy rears its head, namely the radical differentiation between people and things, between my consciousness, my alienation in matter, and my alienation by other people. This, which was the tripartite organizing principle of Being and Nothingness, must not be confused with that dualism of subject and object, of the pour-soi and the en-soi, to which Merleau-Ponty objected, in his own effort to restore a phenomenological monism by way of the corps propre. (Yet Merleau-Ponty was himself guilty of this particular dualism common to all phenomenology, and the central target, not only of Heidegger's Kehre, but of so-called poststructuralism in general.) No, this particular dualism is scandalous precisely because it is itself the recognition of the scandal of the existence of other people, surely Sartre's central philosophical motif and the most original and durable element of his various systems. Nor is it subject to the usual critiques of dualism as such, since it is a dualism which functions as a moment in the reestablisment of monism proper. In this respect, the remarks about Marxism, which Sartre considers to be 'in fact both + +monist and dualist', are significant: + +It is dualist because it is monist. Marx's ontological monism consisted in affirming the irreducibility of Being to thought, and, at the same time, in reintegrating thoughts with the real as a particular form of human activity .... (25) The dialectic is precisely a form of monism, + +in that oppositions appear to it as moments which are posited for + +themselves for an instant before bursting. (\80) + +But these methodological considerations do not yet specify the concrete and fundamental dualism at work in the Critique, which can be understood as constituting a commentary on Marx's famous remark: 'Men make their own history, but not under conditions of their own choosing: On Sartre's reading, however, what will be underscored is the peculiarity of just those 'situations not of their own choosing', which, however, as historical situations, were in fact the result of human action in the past, even though they may now be considered as materiality. The point here is that, although such 'conditions' are material ones, they are certainly not natural, in the sense of absolute contingency unmodified by human action. (Or, to be even more precise about it, even 'contingency' is the result of human reality, insofar as it has already been produced as contingency by human need + +and human desire.) + +At any rate, Sartre will now reformulate the maxim in a new and circular way: 'the crucial discovery of dialectical investigation is that man is "mediated" by things to the same extent as things are "mediated" by man' (79). 'Matter', he observes elsewhere, is 'a mediation between individuals' (113). At this point, we approach one of the great original ideas of the Critique, which goes well beyond the alienation theory of the early Marx. Just as theology needs to account for evil and suffering in a world otherwise attributed to God, so any conceptually satisfying 'philosophy of history' needs to account for violence and failure in some meaningful way, rather than as a series of accidents that fall outside of meaning. The Communist Manifesto does so by underscoring the dialectical nature of capitalism, its immensely destructive power, which is at one with its immensely productive power. Sartre's dialectic will go further than this by theorizing an antidialectic intertwined with the dialectic of human praxis, a counterfinality inextricably conjoined with the finalities of human action and production. Indeed, this new force has a bonus for us in the invention of a new concept and a new and durable philosophical term, the socalled practico-inert, as a more precise way of designating objects which are not mere things and agencies which are not exactly people either. But this will not be a Manichaean vision of history: that type of evil is, as we have seen, already profoundly human: it is the immeasurable brutality people visit on other people within the world of scarcity. This + +new kind of negative force is to be understood in a different way, and to theorize it properly would, as Sartre observes, explain how praxis can logically' be an experience both of necessity and of freedom' (79). Indeed, 'what has never been attempted is a study of the type of passive action which materiality as such exerts on man and his History in returning a stolen praxis to man in the form of a counterfinality' (124), We have here to do, therefore, with a type of 'unintended consequence' quite different also from the reversals of human action in history, as Marx writes their comic epic in The Eighteenth Brumaire of Louis Bonaparte. (Indeed this new anti-dialectic offers one more dramatization of the banality and inadequacy of current fashionable attempts to rewrite the dialectic precisely in such everyday or 'common-language' + +terms as that precisely of an 'unintended consequence'.) + +Counterfinality is thus a negative version of Hegel's 'ruse of history' (or 'ruse of reason'), which he himself derived from Adam Smith's hidden hand and Mandeville's Fable of the Bees, with the qualification that what was unexpectedly positive in them becomes, characteristically enough, implacably negative in Sartre. The premise, however, remains that of the efficacy of praxis: what is negative in counterfinality is not the result of a matter as such, but rather of the human productivity or praxis invested in it, and returning in unrecognizable form upon the human beings who invested their labor in it in the first place. Sartre will also call the bearer of this new, and active, malign power 'worked matter' (matiere ouyree), and it can be distinguished from human 'totalization in course' as being very precisely an already 'totalized totality' This is thus the place of the various historical forms Marx calls modes of production, and it is the concomitant of a specific form of human sociality Sartre will call 'the collective' (among which is included the Marxian phenomenon of social class). We can better understand this important notion by observing that it can be said to have two distinct + +sources. + +On the one hand, we may find it anticipated in the relatively phenomenological rehearsal of the oppositions between activity and passivity, and interiority and exteriority, in which (as in the other oppositions we have already enumerated) a human realm is opposed to a non-human one. For, as Sartre never ceases to remind us, in this following Heidegger as well as many of the descriptions of Being and Nothingness, the human agency works on exteriority by making itself exterior, and works on passivity by making itself passive . Not only is this the meaning of the tool as such, but it is also the disposition of the hand that wields the tool. + +But this work on the self and on my own body, which lends my body efficacity in the passive and external realm of bodies as such, also in some reciprocal yet seemingly magic fashion endows the matter on + +which I work with some of my human characteristics. + +At which point we may take up what strikes me as Sartre's other source, namely Marx's own notion of 'stored labor', and in particular the consequences of the labor process for machinery and machineproduced goods. The non-human world must for Marx be distinguished from a material invested by labor: such material objects become 'masses of crystallized labor-time', their raw material 'soaked in labor' Machinery now dialectically transforms this process of investment on a higher level, adding value to its product which is distinct from but compounded with the immediate human labor also involved. This is because the machine stores up the labor which has gone into its own production and then reinvests it in its new product: 'Only in large-scale industry has man succeeded in making the product of his past labor, labor which has already been objectified, perform + +gratuitous service on a large scale, like a force of nature' + +It is this peculiar temporal deferal-the possibility of storing up an initial quantity of expended labor in order to reinvest it in smaller amounts later on in a secondary product - which seems to me the most suggestive antecedent for grasping what Sartre will now describe as a more 'metaphysical' process. Nor should the fundamental opposition of multiplicity and unity be left out: for counterfinality reflects a 'material unity of human actions And passive unity, as the synthetic appearance of pure dispersal and as the exteriorization of the bond of interiority, is for praxis its unity as Other and in the domain of the other' (163). (This first passive activity of worked matter will find its echo in that much later objectification which is the social + +institution, characterized as an 'active passivity' .) + +Two famous examples or set-pieces will be called upon to illustrate the baleful effects of this 'praxis without an author' (166): the deforestation of China and the monetary crisis which strikes the Spanish empire at the height of its power in the New World. But it is important to remember that it is this global unity of counterfinality which also defines social class, as that shared situation which makes an agglomeration of individuals over into a class (and a collective in the larger sense): so that Sartre's excursus on class interest here (197-219) can be seen as a doctrinal obligation and a more specific contribution to Marxian class theory, and one which is in addition meant to distinguish + +this particular social structure from other features generally lumped + +together under an omnibus concept of ideology. + +In Marx, the structure of labor and the structure of the commodity are two faces of the same phenomenon, two distinct languages, as it were, which characterize the same fundamental originality of capitalism like the alternating figuration of waves and that of particles in quantum theory. So it is that at this point in the Critique the dialectic, or antidialectic, of worked matter turns over into an examination of the type of social relations inseparable from it. We must here remember the paradox of the we-subject as it was described in Being and Nothingness: it is a form of subjectivity in which my ( purely psychological) identification with other people is mediated by the 'directions' on the world of things, the instructions on the box, the proper method for opening a can. But it is through such requirements (exigences, here translated exigencies) that worked matter directs our activity in general. The subjectivity which accompanies this purely ideal or imaginary community with other people, other users and consumers, but other + +workers as well, will now be called seriality. + +With this, we are at the very heart of this first, definitional volume of the Critique and are in a position to evaluate its central conceptual antithesis between two fundamental forms of collective existence, between the side-by-side indifference and anony mity of the serial agglomeration and the tightly-knit interrelationship of the group-infusion. This is an antithesis that is not merely a classificatory one, for as a principle of social dynamics and an empirical fact of social history, the group-in-fusion emerges from seriality as a reaction against it, its subsequent development and fate governed by the danger of its + +dissolution back into seriality again. + +Nor is this a particularly original distinction, although Sartre's account of the internal structure of each form is remarkable and probably without precedent. Yet formally the antithesis has something of the same spirit as that traditionally attributed to the distinction between anthropology and sociology, given its now classical (modern) form by Tonnies in his famous opposition between Gemeinschafi and Gesellschafi, the former designating small clan-based or tribal, pre-modern or 'traditional' societies, the latter the great urban agglomerations of modern industrial ones. In the Critique, however, no particular social or political form is attributed to the two terms; indeed, they are scarcely symmetrical at all in that sense, since seriality is a social condition that must extend through all kinds of societies and populations, while the group-in-fusion is hardly + +a social form at all, but rather an emergence and an event, the formation of a guerilla unit, the sudden cry stallization of an 'in-group' of any kind. (As we shall see, the formation of the group has a motivation and real historical content; but that content is quite irrelevant for the present structural description, and might range from stamp collecting to assas- + +sination conspiracies or political parties.) + +The more fundamental question about the antithesis is an ethical one, for it is clear from the language of these descriptions that a judgment is implicit in them, and that the serial state, however comfortable or content its members might consider themselves to be, is one of mediocrity if not of alienation, while the group-in-fusion incarnates active human praxis in a uniquely heightened fashion - a kind of praxis all the more distinctive in that it constitutes the production, not of things, but of + +other people and the self, of a new kind of sociality. + +Our question must then turn on the affinity between this judgment on social relations (which might in a pinch be foreshortened into a distinction between the private and the political) and the existential legacy of the concepts of authenticity and inauthenticity, which clearly spring to the tip of the tongue with any evocation of seriality and group existence. For this is an ambiguous legacy indeed, and in its first modern form, in Heidegger's work of the 1920S, is overwhelmingly conservative in tenor: authentic is the individual's being-unto-death, and the call of a duty or mission, which if it is not overtly couched in group terms certainly evokes the soldier and the military unit. What is unmistakably inauthentic on the other hand is the anonymous state of what the 1920S characterized as 'mass man', the faceless crowds of the big city, the 'man' or 'on' (German and French versions of the anybody or the impersonal 'you'). Sartrean seriality is not far behind these early accounts, even though already in Being and Nothingness the class character of these collective actors is reversed, and it is the bourgeois we-subject which is inauthentic, while the we-object, the alienated and reified small group, is described in terms of underclass marginality and already anticipates + +the account of the group-in-fusion. + +At a time when the very notions of authenticity and in authenticity have come to seem suspiciously humanist and psychologizing, if not individualist, Sartre's celebration of the group may well incur the diagnosis of anarchism, or even left infantilism: the Right may well indict it for the excesses of the 1960s and their aftermath; the Left sense in it some surviving trace of left adventurism and romanticism; while Americans are likely to conjecture uncomfortable affinities with conspir- + +atorial terrorist organizations. It would be more difficult, however, to take the other alternative offered by Sartre's antithesis and to come out + +with a full-throated defense and endorsement of seriality. + +It is easiest to deal with the two states together, as they are in fact defined in deliberately antithetical terms. Thus in seriality, as in the now famous example of the waiting line for a city bus, 'everyone is the same as the Others in so far as he is Other than himself' (260). And this otherness is as spatial as it is psychological: I am not in the center of my world, which is elsewhere, in other people (all of whom feel the same way as I do). In the group, on the contrary, each member is the center, the center is everywhere; otherness has been converted into identity. Nor, inasmuch as group-formation is first and foremost an attempt to overcome the serial situation, is it surprising to find that in the g roup, everyone is the same as the other, and otherness has momentarily become a kind of collective identity. But it will also be clear that this second structure is necessarily far more complex than the first one, of seriality, in which people stand in a simple exteriority + +to one another. + +Certainly seriality also knows its paradoxes: it is indeed no accident that Sartre's principal extended illustrations are those of radio broadcasts and of the free market. In fact, I believe, the notion of seriality developed here is the only philosophically satisfactory theory of public opinion, the only genuine philosophy of the media, that anyone has proposed to date: something that can be judged by its evasion of the conceptual traps of collective consciousness on the one hand, and of behaviorism or manipulation on the other. If this were all Sartre had managed to do in the Critique, it would already mark a considerable achievement (neglect of which may reflect the turn of current media theory towards a problematic of the image as much as anything else). When it comes to the group-in-fusion, however, things are by no means so simple: we must reckon with what is no longer a dualism, a simple reciprocity or indifference of one person to another, but rather with a triadic form, in which (as in the group-object theory of Being and Nothingness) formerly serial individuals are united by the threat (or the Look) of an external third, which the emergent group must then interiorize in order to retain its coherence and its dynamic . Thus each member becomes a third to all the others, thereby grounding that omnipresent centrality of each member that was far too simply evoked + +The individual, as a thi rd party, is connected, in the unity of a single praxis (and therefore of a single perceptual vista) with the unity of individuals as inseparable moments of a nontotalised totalisation, and with each of them as a third party, that is to say, through the mediation of the group. In terms of perception, I perceive the group as my common unity, and, simultaneously, as a mediation between me and every other thi rd party the members of the group are third parties, which means that each of them totalises the reciprocity of others. (374) + +Just as this seemingly Ptolemaic sy stem of turning thirds (tiers) proves to be something familia r that we know already from our daily experience, so the reader will find tha t, with a little pra ctice, this rather + +startling prose quickly becomes readable enough. + +We leave the reader to navigate it, but with an important proviso: we have here only designated the emergence of the group - famously illustrated by Sartre in the taking of the Bastille. What is not yet clear, indeed what is supremely problematic, is how it can possibly remain in being, as a group, when the threat of the external third party (the King's troops) has been withdrawn. One simple and obvious answer overshoots the mark: and that is that the group cannot remain in being; indeed it never was in being to begin with, in the ontological sense. It never had, nor can it ever acquire, any durable ontological status; it cannot therefore accede to any new form of collective being which might be expected to supercede that of the individual 'being-for-itself' and thereby to cancel the famous peroration of Being and Nothingness. Here as there, then, 'man' remains a 'useless passion': yet at the same time Sartre's inveterate pessimism can here be grasped far more clearly as a critical instrument, and not merely an inheritance of the out- ofdate Cartesian and phenomenological traditions of a 'philosophy of the subject ' centered on a purely individual consciousness. Rather, as alway s in Sartre, ontological failure and anxiety are energizing and the + +stimulus to further praxis and subsequent group formation: + +The group has not, and cannot have, the ontological nature which it claims in its praxis; conversely, each and all are produced and defined in terms of this non-existent totality. There is a sort of internal vacuum, an unbridgeable and indeterminate distance, a sort of malaise in every community, large or small; and this uneasiness occasions a strengthening of the practices of integration, and increases with the integration of the + +I t remains to indicate briefly how, in this situation and seemingly doomed to failure, the group does finally manage to become something structurally other than a mere punctual interruption of seriality. + +We have already hinted at the crucial mechanism by which a few straggling 'others ' momentarily brought together by an external threat (from the external Other or third) solidify this momentary solidarity: it is by interiorizing the tiers itself (the 'third party') in such a way that each member of the initial group becomes a third to all the others. Each is now both part and whole of this strange new structure, both individual member and also that now internalized exteriority which grasps all of the members ('as though from the outside') as a group. We must not say that at this stage there is no leader: on the contrary, at this stage everyone is the leader, whose task, like the tribal chieftain of Pierre Clastres's anthropology, is not to impose a line of action but merely to speak its possibility aloud, to be the mouthpiece of the + +situation itself before the group . + +It is a Utopian state (Malraux's 'lyric apocalypse ' ) which cannot last. Everything now turns on the problem of the future, and of the future of the group: it will be clear in a moment how this problem sets vibrating the deepest existenti al concerns of Being and Nothingness at the same time that it generates its most dramatic language, its most + +eloquent pathos: my project is ' + +atemporal form where I await myself + +in the future, where I make an appointment with myself on the other side of that hour, of that day, of that month. Anxiety is the fear of not finding myself at that appointment, of no longer even wishing to be there in the first place' But where the group is concerned, this appointment is the pledge, and the paradigm of the French Revolution reveals that its fundamental structure is the Terror and the threat of death. The Tennis-Court Oath is the moment in which this paradigm becomes fixed: the very beginning of the Revolution itself - the revolutionary ' Revolution, as opposed to the counterrevolution of the nobles against the King that preceded and triggered it. For in the Tennis - Court Oath, the bourgeoisie and its hegemonic bloc, reassembled in an unused space in the palace, collectively swear, under pain of dea th, not to separate until the Constitution shall have been established 'sur des fondements so/ides ' ( June 20, 1789). The crucial clause, 'under pain of death', is not merely Sartre's interpretation or extrapolation: it is the implied reading deduced after the fact by Robespierre's Terror, as the la tter's justifica tion. It is also the (desperate and impossible) attempt to solve the problem of future + +commitment already raised in Being and Nothingness: for this consent to my own death and execution (by all the members of the group) is not only my effort to compel the fidelity of all the others, it is also and first and foremost my attempt to protect myself against myself, to compel the fidelity of my future self against the present one (422). It is, finally, also the production of treason as such, since seriality cannot know the latter, which can only exist as the violation of this very oath of allegiance. This is the moment to remember the profound resonance of this theme of treason and the traitor throughout all of Sartre: as the 'objective treason' of the intellectual, never fully or ontologically committed to any cause; as the jouissance of treason in the rebel (particularly in Genet), or of the homme de ressentiment (particularly in the collaborators); the great test of my authenticity as well (will I stand up under torture?), and the eternal self-doubt of the bourgeois renegade against his own class, variously elaborated in Lucifer and the Lord and in Words, if not in the interminable Family Idiot itself. + +The pledge is now the positive side of all that, the great moment of affirmation in all of Sartre; indeed it is the very 'origin of humanity' + +(436): + +we are the same because we emerged from the clay at the same date and through all the others; and so we are, as it were, an individual species, which has emerged at a particular moment through a sudden mutation; but our specific nature unites us in so far as it is freedom thi s fraternity is not based, as is sometimes stupidly supposed, on physical resemblance expressing some deep identity of nature. If it were, why should not a pea in a can be described as the brother of another pea in the same can? We are brothers in so far as, following the creative act of the pledge, we are our own sons, our common creation. (437) + +The pledge is thus the climactic moment of constituent power: its articulation as a date and an event is what gives the French Revolution its paradigmatic quality over all those other revolutions in which it is necessarily present but only implicit as an act and as the very expression of the multitude. Its theorization places Sartre squarely in the great tradition that runs from Rousseau to Antonio Negri and + +passes through the Paris Commune itself. + +The more sombre concluding pages of the Critique will then observe and bear witness to the inevitable decline from this apotheosis. They chronicle the slow ossification of the group under the pressure of some + +surrounding universal seriality. Indeed, they permit us to reaffirm the transformation (or sublation) of the older question of authenticity into this newer political and collective dilemma. For (as in Heidegger), authenticity is never, for Sartre, a state which one can somehow achieve and in which one can then dwell and persevere: it is a precarious space conquered from the swamp of inauthenticity itself, into which it then fatally lapses. If one can speak, indeed, of anything like a human nature, then one must say that that nature is first and foremost inauthentic, in which moments of authenticity are but fitful and evanescent episodes (it is a doctrine already anticipated in a distorted form by Christian images of sin and grace). But this raises serious questions about the implications for a philosophy of history of such a view of group authenticity. + +At any rate, it would seem that Sartre foresees at least three ways in which the group can dissolve: it can of course simply disperse back into seriality, like a crowd which dissolves and goes back to its ordinary business. But this is to grasp the group-in-fusion before the defining moment of the pledge. After that, what lies in store for it is institutionalization, with its dual forms of bureaucracy and dictatorship, forms which Sartre's account - with its accounts of schism and factionality, of the passive activity of the institutional practico-inert, of hierarchy, of the externalization of authority and the emergence of the sovereign and of a henceforth serial obedience - seems to conflate and to identify together. But this is because the underlying paradigm has changed; and from now on, and throughout Volume II of the Critique, it will be the fate of the Soviet Revolution after Lenin's death which is the reference. (Thus the entire Critique may also be read as an elaborate historical commentary, in the spirit of Machiavelli or Gramsci, on these two supreme events which are the French and the Soviet Revolutions.) But it should not thereby be concluded that the Critique replicates the standard bourgeois dogma according to which revolution (here, group formation) inevitably leads to totalitarianism (or in other words, Stalinism). Nor, on the other hand, do we here discover in advance the Deleuze-Guattari vision of innumerable nomadic and guerrilla warmachines forever flinging themselves against the inevitable State. In Sartre, the State itself is a reified group-in-fusion which has established itself within a milieu of seriality (perhaps on the distant analogy of + +those former nomads who become the imperial ruling class). + +The point is, however, as has already been warned, that this first volume of the Critique is not intended to offer a vision of History; but only to lay in place the concepts and the categories with which such a + +vision might be constructed. If history is already present here, this is merely in the formal sense in which all histo ry offers an endless spectacle of the interaction of seriality and group formation, like a great current, on which white water, ripples and swells, appear and disappear ceaselessly. Yet the river's source and its drainage, its ultimate return into the sea, are issues distinct from this steady stream into + +which one always steps. + +Those issues, intimated at the end of this volume and then sporadically developed in what was to have been the second one, turn on the rather different matter of historical unification, and of Sartre's fundamental maxim that the many histories of the past have gradually become unified into one history. Any 'philosophy of history' today must begin with this qualification that History, in that unified and universal sense, has not yet existed, but is only now coming into being. There were once many distinct and unrelated histories, many distinct modes of production, as innumerable, if not as grains of sand, then at least as the languages of the New World and of Australasia, so many separate and unrelated tribes and groups of hunters and gatherers, who only gradually over many millennia come to be unified, that is to say, to share the common destiny which a wo rld capitalism gradually imposes on them. In the brief decades between Sartre's composition of the Critique and the visible emergence of what we now call globalization, this principle has become inescapable, and with it the very + +possibility of a universal history reemerges in a new way. + +2004 + +The Dogmatic Dialectic + +and the Critical Dialectic + +z Dialectical Monism + +Everything we established in The Problem of Method! follows from our fundamental agreement with historical materialism. But as long as we present this agreement merely as one option among others we shall have achieved nothing, and our conclusions will remain conjectural. I have proposed certain methodological rules; but they cannot be valid, in fact they cannot even be discussed, unless the materialist dialectic can be assumed to be true. It must be proved that a negation of a negation can be an affirmation, that conflicts - within a person or a group - are the motive force of History, that each moment of a series is comprehensible on the basis of the initial moment, though irreducible to it, that History continually effects totalisations of totalisations, and so on, before the details of an analytico-synthetic and regressive- + +progressive method can be grasped. + +But these principles cannot be taken for granted; indeed most anthropologists (anthropologistes) would reject them. Of course, the determinism of the positivists is necessarily a form of materialism: whatever its subject matter, it endows it with the characteristics of mechanical materiality, namely inertia and exterior causation. But it normally rejects the reinteriorisation of the different moments in a synthetic progression. Where we see the developmental unity of a single process, the positivists will attempt to show several independent, exterior factors of which the event under consideration is the resultant. What the positivists reject is a monism of interpretation. Take, + +I. Though a separate essay, this is printed at the beginning of the French edition of Critique. It is available in English as The Problem of Method, trans. Hazel E. Barnes (London, Methuen, 1964). The American edition is published + +under the title Search for a Method. [Ed.] + +for example, the excellent historian Georges Lefebvre. He CritiCises Jaures2 for claiming to see the unity of a process in the events of 1789. 'As presented by Jaures, 1789 was one simple event. The cause of the Revolution was the ripening of the power of the bourgeoisie, and its result was the legalisation of that power. But it is now well known that the Revolution of 1789 as a specific event required a truly abnormal and unpredictable set of immediate causes: a financial crisis aggravated by the war in America; unemployment, caused by the commercial treaty of 1786 and by the war in the Far East; and, finally, high prices and shortages brought about by the poor harvest of 1788 and by the + +edict of 1787 which had emptied the granaries.'3 + +As for underlying causes, Lefebvre stresses the fact that without the abortive aristocratic revolution, which began in 1787, the bourgeois revolution would have been impossible. He concludes: 'The rise of a revolutionary class is not necessarily the only cause of its victory; nor is its victory inevitable; nor need it lead to violence. In this instance, the Revolution was begun by those whom it was to annihilate rather than by those who profited from it, and ... there is no reason to suppose that great kings could not have checked the progress of the + +aristocracy in the eighteenth century.'4 + +I do not wish to analyse this text, at least at present. Certainly, Lefebvre may be right to say that Jaures' interpretation is simplistic, that the uni ty of a historical process is more ambiguous, more 'polyvalent' than he says - at least in its origins. One might try to find the unity of the disparate causes in a broader synthesis, to show that the incompetence of the eighteenth century kings was effect as much as cause, etc., to rediscover circularities, and to show how chance is integrated into those 'feed-back' devices which are the events of History; and that it is instantly incorporated by the whole so that it appears to everyone as a manifestation of providence, etc. But this misses the point. It is not a matter even of showing that such syntheses are possible, but of proving that they are necessary: not any particular one, but in general that the scientist must adopt, in every case and at + +every level, a totalising attitude towards his subject matter. + +Let us not forget that anthropologists never reject the dialectical method absolutely. Even Lefebvre does not formulate a general criti- + +cism of every attempt at totalisation. On the contrary, in his celebrated lectures on the French Revolution he approached the relations between the Assembly, the Commune and various groups of citizens, from IO August to the September Massacres, as a dialectician; he gave the 'First Terror' the unity of a developing totalisation. But Lefebvre refused to adopt the totalising attitude consistently. In response to our questions, he would no doubt say that History is not a unity, that it obeys diverse laws, that an event may be produced by the pure accidental coincidence of independent factors, and that it may, in turn, develop according to totalising schemata which are peculiar to it. In short, Lefebvre would simply say that he rejects monism, not because + +it is monism, but because it seems to him a priori. + +The same attitude has been formulated in other branches of knowledge. The sociologist Georges Gurvitch has described it very accurately as dialectical hyper-empiricism.5 This is a neo-positivism which rejects every a priori; neither the exclusive appeal to analytical Reason, nor the unconditional choice of dialectical Reason can be justified rationally. We must accept the object as it is and let it develop freely before our eyes, without prejudging what types of rationality we will encounter in our investigations. The object itself dictates the method , the manner of approach. Gurvitch calls his hyper-empiricism 'dialectical', but this hardly matters since all he means is that his object (social facts) presents itself to investigation as dialectical. His dialecticism is thus itself an empirical conclusion. This means that the attempt to establish totalising movements, reciprocities of conditioning - or, as Gurvitch quite correctly puts it, reciprocities of 'perspectives' - etc., is based on past investigations and is confirmed by present ones. Generalising this attitude, one might, I think, speak of a neo-positivism which discovers in a given region of anthropology now a dialectical field, now a field of analytical determinism, and now, if occasion demands, other + +types of rationality. 6 + +;. Georges Gurvitch, 'Hyper-Empirisme dialectique', Cahiers Internationaux + +de Sociologie XV, 1953. [Ed.] + +6. Theoretical psychoanalysis simultaneously employs determinism, the dialectic, and 'paradox' in the Kierkegaardian sense of the term. Ambivalence, for example, cannot now be regarded as a contradiction or exactly as a Kierkegaardian ambiguity. Given the way the concept is used, one is tempted to think of a real contradiction with interpenetrating terms, or in other words, of a contradiction without opposition. In my opinion, what psychoanalysts lack is opposition, at least in certain respects (for there is dialectical conflict between the id, the super- + +Within the limits of an empirical anthropology this distrust of the apriori is perfectly justified. I have shown in The Prohlem of Method that this is necessary if a living Marxism is to incorporate into itself the disciplines which have hitherto remained external to it. However, whatever else one may say about it, this incorporation must consist in revealing beneath the classical determinism of particular 'fields', their dialectical connection with the whole or, where we are dealing with processes whose dialectical character is already recognised, in revealing this regional dialectic as the expression of a deeper totalising movement. In the end, this means that we are confronted once again with the need to establish the dialectic as the universal method and universal law of anthropology. And this amounts to requiring Marxists to establish their method a priori: whatever relations are investigated, there will never be enough of them to establish a dialectical materialism. Such an extrapolation - that is, an infinitely infinite extrapolation + +- is radically different from scientific induction. + +2Scientific and Dialectical Reason + +The attempt to ground the Marxist dialectic on anything other than its content, that is to say, the knowledge which it provides, might be de- + +ego and the ego). They have nonetheless constructed a rationality and what might be called a logic of ambiguity - which would scandalise poor Kierkegaard. This logic is non-Aristotelian (because it expresses the connection between facts and attitudes which transcend one another, meet again, and struggle against each other and because, in the last analysis, it is applicable to neuroses, that is to say, to circular heings); but this logic is not entirely Hegelian either, since it is concerned with reciprocity of conditioning rather than with totalisation. However, to the extent that, for such a logic, a particular action is an expression of the circularity of the conditions and of the individual history, the analysed subject appears as a true whole. The truth is, however, that his being is passivity, at least in 'classical' psychoanalysis. The fact that Freudian analysts have been led to attribute greater and greater importance to the functions of the ego scarcely affects this. The simple fact that Anna Freud (following so many others) can refer to these functions as 'defence mechanisms' imprints upon the work of the ego an a priori inertia. In the same way physics speaks of 'forces' and of 'work' without ever abandoning the + +terrain of exteriority. + +. + +nounced as idealism. In the first place, it might be said that Diogenes demonstrated motion by walking; but what ifhe had been momentarily paralysed? There is a crisis in Marxist culture; there are many signs today that this crisis is temporary, but its very existence prohibits us + +from justifying the principles by their results. + +The supreme paradox of historical materialism is that it is, at one and the same time, the only truth of History and a total indetermination of the Truth. The totalising thought of historical materialism has established everything except its own existence. Or, to put it another way, contaminated by the historical relativism which it has always opposed, it has not exhibited the truth of History as it defines itself, or shown how this determines its nature and validity in the historical process, in the dialectical development of praxis and of human experience. In other words, we do not know what it means for a Marxist historian to speak the truth. Not that his statements are false - far from it; but he does not have the concept of Truth at his disposal. In this way, Marxism presents itself to us, as ideologists,7 as an unveiling of being, and at the same time as an unanswered question as to the validity + +of this unveiling. + +In response to this, it may be claimed that physicists are not concerned with the ground of their inductions. This is true. But there is a general, formal principle; that there are strict relations between facts. This means: the real is rational. But is this really a principle, in the ordinary sense of the term? Let us say, rather, that it is the condition and fundamental structure of scientific praxis. Through experimentation, as through any other form of activity, human action posits and imposes its own possibility. Praxis does not, even dogmatically, affirm the absolute rationality of the real, if this means that reality obeys adefinite system of a priori principles and laws, or, in other words, that it complies with a kind of constituted reason. Whatever the object of his research, whatever its orientation, the scientist, in his activity, assumes that reality will always manifest itself in such a way that a provisional and fluid rationality can be constituted in and through it. This amounts to saying that the human mind will accept everything presented to it by investigation and will subordinate its conception of + +7. 'Ideologues'. Sartre defines this word in The Pro[,[em of Method: 'Those intellectuals who come after the great flowering and who undertake to set the systems in order ... should not be called philosophers .... These relatiYe men I propose to call "ideologists" ' . The Pro61em of Method, trans. Hazel E. Barnes, + +p. 8. [Ed.] + +logic and of intelligibility to the actual data revealed by its investigations. Bache1ard has shown clearly how modern physics is in itself a neW rationalism: the only presupposition of the praxis of the natural sciences is an assertion of unity conceived as the perpetual unification of an increasingly real diversity. But this unity depends on human activity rather than on the diversity of phenomena. Moreover, it is neither a knowledge, nor a postulate, nor a Kantian a priori. It is action asserting itself within the undertaking, in the explanation of the field and the unification of the means by the end (or of the sum of experi- + +mental results by the aim of the experiment). + +This is why any comparison between the scientific principle of + +rationality and the dialectic is absolutely unacceptable. + +Scientific research can in fact be unaware of its own principal features. Dialectical knowledge, in contrast, is knowledge of the dialectic. For science, there is not any formal structure, nor any implicit assertion about the rationality of the universe: Reason is developing, and the mind prejudges nothing. In complete contrast, the dialectic is both a method and a movement in the object. For the dialectician, it is grounded on a fundamental claim both about the structure of the real and about that of our praxis. We assert simultaneously that the process of knowledge is dialectical, that the movement of the object (whatever it may be) is itself dialectical, and that these two dialectics are one and the same. Taken together, these propositions have a material content; they themselves are a form of organised knowledge, or, to put it + +differently, they define a rationality of the world. + +The modern scientist sees Reason as independent of any particular rational system. For him, Reason is the mind as an empty unifier. The dialectician, on the other hand, locates himself within a system: he defines a Reason, and he rejects a priori the purely analytical Reason of the seventeenth century, or rather, he treats it as the first moment of a synthetic, progressive Reason. It is impossible to see this as a kind of practical assertion of our detachment; and equally impossible to make of it a postulate, or a working hypothesis. Dialectical Reason transcends the level of methodology; it states what a sector of the universe, or, perhaps, the whole universe is. It does not merely direct research, or even pre-judge the mode of appearance of objects. Dialectical Reason legislates, it defines what the world (human or total) must be like for dialectical knowledge to be possible; it simultaneously elucidates the movement of the real and that of our thoughts, and it elucidates the one by the other. This particular rational system, however, is + +supposed to transcend and to integrate all models of rationality. Dialectical Reason is neither constituent nor constituted reason; it is Reason constituting itself in and through the world, dissolving in itself all constituted Reasons in order to constitute new ones which it transcends and dissolves in turn. It is, therefore, both a type of rationality and the transcendence of all types of rationality. The certainty of always being able to transcend replaces the empty detachment of formal rationality: the ever present possibility of unifying becomes the permanent necessity for man of totalising and being totalised, and for the world of being an ever broader, developing totalisation. But knowledge of such scope would be a mere philosophical dream if it did not have all the marks of apodictic certainty. This means that practical successes are not enough; even if the assertions of the dialectician were infinitely confirmed by research, this permanent confirmation would + +not get us beyond empirical contingency. + +So we must take up the whole problem once again, and explore the limits, the validity and the extent of dialectical Reason. We cannot deny that a Critique (in the Kantian sense of the term) of dialectical Reason can be made only by dialectical Reason itself; and indeed it must be allowed to ground itself and to develop itself as a free critique of itself, at the same time as being the movement of History and of knowledge. This is precisely what has not been done until now: + +dialectical Reason has been walled up in dogmatism. + +JHegelian Dogmatism + +The source of this dogmatism lies in the basic problem of 'dialectical materialism' . In setting the dialectic back on its feet Marx revealed the true contradictions of realism. These contradictions were to be the very substance of knowledge, but they have been concealed. \Ve must + +therefore take them as our starting-point. + +The superiority of Hegelian dogmatism, for those who believe in it, lies precisely in that part of it which we now reject - its idealism. For Hegel, the dialectic had no need to prove itself. In the first place Hegel took himself to be at the beginning of the end of History, that is to say, at that moment of Truth which is death. The time had come + +to judge, because in future the philosopher and his judgement would never be required again. Historical evolution required this Last Judgement; it culminated in its philosopher. Thus the totalisation was complete: all that remained was to bring down the curtain. Besides, and most important, the movement of Being and the process of Knowledge are inseparable. This implies, as Hyppolite rightly says, that Knowledge of the Other (object, world, nature) is self-Knowledge, and conversely. Thus Hegel could write: 'Scientific knowledge, however, demands precisely that we surrender to the life of the object, or, which means the same thing, that one hold present and express the internal necessity of this object.'8 Absolute empiricism becomes identical with absolute necessity: the object is taken as given, at its moment in the history of the World and of Spirit. But this means that consciousness returns to the beginning of its Knowledge and allows this Knowledge freely to reconstitute itself within consciousness it reconstitutes knowledge for itself; it means, in other words, that consciousness can see the strict necessity of the sequence and of the moments which gradually constitute the world as a concrete totality, because it is consciousness itself which constitutes itself for itself as absolute Knowledge, in the absolute freedom of its strict necessity. The reason why Kant could preserve the dualism of noumena and phenomena is that, for him, the unification of sense experience was effected by formal and non-temporal principles : the content of Knowledge could not change the mode of knowing. But if form and knowledge were modified together, and by each other, if necessity no longer belonged to a pure conceptual activity, but to a perpetual, and perpetually total, transformation, then it would have to be suffered in the realm of Being in order to be recognised in the development of Knowledge; and it would have to be lived in the movement of knowledge in order to be attributed to the development of the object. In Hegel's time, this seemed to imply the identity of Knowledge and its object. Consciousness was consciousness of the Other, and the Other was the being-other of + +consciousness. + +8. G. W. F. Hegel, Phenomenology of Spirit, (Preface) trans. Kaufman in Walter Kaufman, Hegel, London, Weidenfeld 'Ind Nichplson? 1966, p. 434. + +[Ed.] + +4 The Dialectic in Marx + +Marx's originality lies in the fact that, in Opposltlon to Hegel, he demonstrated that History is in development, that Being is irreducible to Knowledge, and, also, that he preserved the dialectical movement both in Being and in Knowledge. He was correct, practically. But having failed to re-think the dialectic, Marxists have played the Positivist game. Positivists often ask Marxists how they can claim, given that Marx had the good sense to realise that 'pre-history' had not yet come to an end, to detect the 'ruses' of History, the 'secret' of the proletariat, and the direction of historical development. For Positivists, prediction is possible only to the extent that the current order of succession reenacts a previous order of succession; and so the future repeats the past. Hegel could have answered them by saying that he had only predicted the past, in that his history was finished and complete and that, as a matter of fact, the moment which posits itself for itself in the process of living History can only guess the future, as the truth of its + +own incompleteness, unknowable + +for it. The Marxist future, however, + +is a genuine future: it is completely new, and irreducible to the present. Nevertheless, Marx does make predictions, and long term rather than short term ones. But in fact, according to Positivist Rationalism, Marx had disqualified himself from doing this, and given that he himself was pre-historical and within pre-history, his judgements can have only a relative and historical significance - even when they concern the past. Thus Marxism as dialectic must reject the relativism of the positivists. And it must be understood that relativism rejects not only vast historical syntheses, but also the most modest assertions of dialectical Reason: whatever we may sayar know, however close we may be to the present or past event which we attempt to reconstitute in its totalising movement, Positivism will always deny us the right. It does not regard the synthesis of all knowledge as completely impossible (though it envisages it as an inventory rather than as an organisation of Knowledge): but it considers such a synthesis impossible now. It is therefore necessary to demonstrate, in opposition to Positivism, how, at this very moment, dialectical Reason can assert certain totalising + +truths - if not the whole Truth. + +5Thought, Being and Truth in Marxism + +But that is not all. For Hegel, as we have seen, the apodicticity of dialectical knowledge implied the identity of being, action and knowledge. Marx, howevcl, began by positing that material existence was irreducible to knowledge, that praxis outstrips Knowledge in its real efficacy. Needless to say, this is my own position. However, this position gives rise to new difficulties : how can we establish that one and the same movement animates these different processes? In particular, thought is both Being and knowledge of Being. It is the praxis of an individual or a group, in particular conditions, at a definite moment of History. As such, thought is subject to the dialectic as its law, just like the historical process, considered either as a whole or in its particular details. But it is also knowledge of the dialectic as Reason, that is, as the law of Being. But this presupposes an explanatory + +separation from dialectical objects, al + +lowing us to unvei + +l their move- + +ment. Is there not an inevitable contradiction between the knowledge of Being and the being of knowledge? The demonstration that thought, as Being, is carried along in the same movement as the whole of History, does not dissolve all contradictions. In fact it is precisely to this extent that thought is incapable of grasping itself in the necessity + +of its own dialectical development. + +In the Phenomenology of Spirit, consciousness apprehends its own necessity in the Other and, at the same time, it apprehends in itself the necessity of the Other. But, once again, the totalising operation is carried out in the past - according to Hegel , Christianity and scepticism provide the means for understanding the previous moment, Stoicism - and, in general, Being is Knowledge, and thought itself is simultaneously both constituent and constituted. In one and the same movement it is subject to its law in so far as it is constituted, and it knows this law in so far as it is constituent. But if thought were no longer the whole, it would see its own development as if it were an empirical succession of moments, and this lived experience (Ie vecu) would appear as contingency and not as necessity. If thought were to understand itself as a dialectical process, it could not formulate its discovery except as a simple fact. Still less could thought pretend to settle the question whether the movement of its object is + +modelled on the movement of thought, or whether the movement of thought is modelled on that of its object. If material being, praxis and knowledge are indeed irreducible realities, do we not have to appeal to a pre-established harmony in order to relate their developments? In other words, if the search for Truth is to be dialectical in its methods, how can it be shown without idealism that it corresponds to the movement of Being? And on the other hand, if Knowledge is to allow Being to develop itself according to its own laws, how can we prevent whatever processes are involved from appearing as empirical? Moreover, in the latter case, the question arises how passive, and therefore non-dialectical, thought can evaluate the dialectic; o r in ontological terms, how it can be that the only reality which lies beyond the laws of synthetic Reason is that which decrees them. Let no one think that he can get out of these dilemmas by means of some pseudo-dialectical answer such as: Thought is dialectical by virtue of its object, it is simply the dialectic as the movement of the real. For, even if it is true that History becomes intelligible when considered dialectically, the example of the Positivists shows that this can be regarded as mere determinism. For this reason, one must al ready be situatedwithin constituent dialectical Reason in order to see History as constituted dialectical Reason. But if dialectical Reason creates itself (rather than suffering itself), how can one prove that it corresponds to the dialectic of Being, without relapsing into idealism? This old problem recurs whenever traditional dogmatic dualism is revived. No doubt it will seem surprising that I refer to Marxist monism as a dualism; it is, in fact, both + +monist and dualist. + +It is dualist because it is monist. Marx's ontological monism consisted in affirming the irreducibility of Being to thought, and, at the same time, in reintegrating t/!Oughts with the real as a particular form of human activity. This monistic claim, however, appears as a dogmatic Truth. But we must distinguish it from conservative ideologies which are mere products of the universal dialectic: in this way thought as the vehicle of truth can recover what it has lost ontologically since th( + +collapse of idealism, and become a Norm of Knowledge. + +Of course dialectical materialism has a practical advantage over contemporary ideologies in that it is the ideology of the rising class. But if it were merely the inert expression of this rise, or even of revolutionary praxis, if it did not direct its attention back upon this rise so as to explain it, to reveal it to itself, how could we speak of a progress of consciousness? How could the dialectic be regarded as the real movement of History unfolding itself? Like philosophical liberalism today, + +it would be no more than a mythical reflection. Besides, for the dialectician, even ideologies, however mystifying, contain an element of truth, as Marx often emphasised. But how is this partial truth to be established ? Materialist monism, in short, has successfully eliminated the dualism of thought and Being in favour of total Being, which is thereby grasped in its materiality. But the effect of this has only been to re-establish, as an antinomy - at least an apparent one - the dualism + +of Being and Truth. + +6 The External Dialectic in Modern Marxism + +This difficulty has appeared insurmountable to modern Marxists. They have seen only one solution: to refuse to acknowledge thought itself as a dialectical activity, to dissolve it into the universal dialectic, and to eliminate man by dispersing him into the universe. This enables them to substitute Being for Truth. There is no longer knowledge in the strict sense of the term; Being no longer manifests itselfin any way whatsoever: it merely evolves according to its own laws. The dialectic of Nature is Nature without men. There is therefore no more need for certainty, for criteria; even the attempt to criticise and establish knowledge becomes useless. Knowledge of whatever form is a relation between man and the world around him, and if man no longer + +exists this relation disappears. + +The source of this unfortunate approach is well known: as Whitehead said, a law begins by being a hypothesis and ends by becoming a fact. When we say that the earth revolves, we no longer feel that we are stating a theory, or that we are relying on a system of knowledge; we feel that we are in the presence of the fact itself, which immediately eliminates us as knowing subjects in order to restore to us our 'nature' as objects of gravitation. For anyone with a realist view of the world, knowledge therefore destroys itself in order to hecome the world, and this is true not only of philosophy but also of all scientific Knowledge. When dialectical materialism claims to establish a dialectic of Nature it does not present itself as an attempt at an extremely general synthesis of human knowledge, but rather as a mere ordering of the facts. And its claim to be concerned with facts is not unjustified: when Engels speaks of the expansion of bodies or of electric current, he is indeed + +referring to the facts themselves - although these facts may undergo essential changes with the progress of science. This gigantic - and, as we shall see, abortive - attempt to allow the world to unfold itself by itself and to no one, we shall call external, or transcendental, dialectical materialism (Ie materialisme dialectique du dehors ou transcendental). + +JThe Dialectic of Nature + +It is cleat that this kind of materialism is not Marxist, but still it is defined by Marx: 'The materialist outlook on nature means nothing more than the conception of nature just as it is, without alien addition.'9 On this conception, man returns to the very heart of Nature as one of its objects and develops before our eyes in accordance with the laws of Nature, that is, as pure materiality governed by the universal laws of the dialectic. The object of thought is Nature as it is, and the study of History is only a particular form of it: we must trace the movement that produces life out of matter, man out of primitive forms of life, and social history out of the first human communities. The advantage of this conception is that it avoids the problem: it presents the dialectic, a priori and without justification, as the fundamental law of Nature. This external materialism lays down the dialectic as exteriority: the Nature of man lies outside him in an a priori law, in an extra-human nature, in a history that begins with the nebulae. For this universal dialectic, partial totalisations do not have even provisional value; they do not exist. Everything must always be referred to the totality of natural history of which human history is only a particular form. Thus all real thought, as it actually forms itself in the concrete movement of History, is held to be a complete distortion of its object. It becomes a truth again only if it is reduced to a dead object, to a result; and thus a position outside man, and on the side of things, is adopted so that the idea can be seen as a thing signified by things rather than as a signifying + +9. This sentence appears to be by Engels and not by Marx. It is part of an unused section of a draft of Engels, Ludwig Feuerhach and the Outcome of Classical German Philosophy. The text of this unused section appears as a section of Dialectics of Nature, trans. C. P. Dutt, Moscow, Progress Publishers, 1934, pp. 19 5-9. Sartre refers to the same remark in The Problem of Method, p. 32, n. 9, and + +also below, p. 181 [Ed.] + +act. In this way, that 'alien addition' which is man - concrete, living man with his human relations, his true or false thoughts, his actions, his real purposes - is removed from the world. An absolute object is put in his place: 'What we call a sUbject is only an object considered as the centre of particular reactions.' lO The notion of truth is replaced by those of success or normality as applied to performances in tests : 'As the centre of more or less delayed reactions, the body performs movements which organise themselves as behaviour. This produces actions. (Thinking is an action. Suffering is an action.) These actions can be regarded as "tests" .. ,?S trials.'ll Thus we get back to the disguised scepticism of 'reflection'. But when everything has apparently culminated in sceptical objectivism, we suddenly realise that it has been imposed on us dogmatically, that it is the Truth of Being as it appears to universal consciousness. Spirit sees dialectic as the law of the world. + +Consequently we fall back into complete dogmatic idealism. + +Scientific laws are experimental hypotheses verified by facts; but at present, the absolute principle that 'Nature is dialectical' is not open to verification at all. You may claim that some set of laws established by scientists represents a certain dialectical movement in the Objects of these laws, but you cannot prove it.l2 Neither the laws nor the 'great theories' will change, however you view them. Your problem is not whether light transmits energy particles to the bodies it illuminates, but whether quantum theory can be integrated into a dialectical totalisation of the universe. You need not question the kinetic theory of gases; you need only see whether it weakens the totalisation. You are reflecting on Knowledge. And since the law discovered by the scientist, taken in isolation, is neither dialectical nor anti-dialectical (it is only a quantitative determination of a functional relation), the consideration of scientific facts (that is to say, of established laws) cannot furnish, or even suggest, a proof of the dialectic. Dialectical Reason can only be captured elsewhere, so that it can be forcibly imposed on + +10. Pierre Naville, Introduction generale a 'La Dialectique de fa Nature' de + +Frederic Engels, Paris, Librairie Marcel Riviere, 1950, p. 59. + +Ihid. + +12 . These remarks apply, of course, only to the dialectic conceived as an abstract and universal law of Nature. However, when the dialectic is applied to human history, it loses none of its lzeuristic value. Concealed, it directs the collection of facts; then it reveals itself by making them comprehensible, by totalising them. This comprehension reveals a new dimension of History, and finally, its + +truth, its intelligibility. + +the data of physics and chemistry. It is well known, in fact, that the notion of dialectic emerged in History along quite different paths, and that both Hegel and Marx explained and defined it in terms of the relations of man to matter, and of men to each other. The attempt to find the movement of human history within natural history was made only later, out of a wish for unification. Thus the claim that there is a dialectic of Nature refers to the totality of material facts - past, present, future - or, to put it another way, it involves a totalisation of temporality. 13 I t has a curious similarity to those Ideas of Reason which, according to Kant, were regulative and incapable of being corroborated by any + +particular experience. + +8Critique of the External Dialectic + +Thus a system of ideas is contemplated by a pure consciousness which has pre-constituted their law for them,14 though utterly incapable of justifying this ukase. But in order to grasp materiality as such, it is not sufficient to discuss the word 'matter'. Language is ambiguous in that words sometimes designate objects and sometimes concepts; and this is why materialism as such is not opposed to idealism. In fact, there is a materialist idealism which, in the last analysis, is merely a discourse on the idea of matter; the real opposite of this is realist materialism - the thought of an individual who is situated in the world, penetrated by every cosmic force, and treating the material universe as something which gradually reveals itself through a 'situated' praxis. In the present case, we are evidently confronted with an idealism which has appropriated the vocabulary of science in order to express ideas of such poverty that one can see straight through them. But the important point is this: if you are hunting for the Truth (as a human undertaking) of the Universe, you will find it, in the very words you use, as the object of an absolute and constituting consciousness. This means that it is impossible to get away from the problem of Truth. Naville deprives his + +'centres of delayed reactions' of the ability to distinguish between True and False; he imposes the dialectic on them without allowing them knowledge of it; but what he says thereby becomes an absolute truth + +without foundation. + +How can we accept this doubling of personality? How can a man who is lost in the world, permeated by an absolute movement coming from everything, also be this consciousness sure both of itself and of the Truth? It is true that Naville observes that 'these centres of reaction elaborate their behaviour according to possibilities which, at the level both of the individual and of the species, are subject to an unalterable and strictly determined devel opment .', and that 'experimentally established reflex determinations and integrations enable one to appreciate the narrowing margin within which organic behaviour can be said to be autonomous'. We obviously agree with this; but the important thing is Naville's application of these observations, which inevitably leads to the theory of reflection, to endowing man with constituted reason; that is, to making thought into a form of behaviour strictly conditioned by the world (which of course it is), while neglecting to say that it is also knowledge of the world. How could 'empirical' man think? Confronted with his own history, he is as uncertain as when he is confronted by Nature, for the law does not automatically produce knowledge of itself - indeed, if it is passively suffered, it transforms its object into passivity, and thus deprives it of any possibility of collecting its atomised experiences into a synthetic unity. Meanwhile, at the level of generality where he is situated, transcendental man, contemplating laws, cannot grasp individuals. Thus, in spite of ourselves, we are offered two thoughts, neither of which is able to think us, or, for that matter, itse((: the thought which is passive, given, and discontinuous, claims to be knowledge but is really only the delayed effect of external causes, while the thought which is active, synthetic and desituated, knows nothing of itself and, completely immobile, contemplates a world without thought. Our doctrinaires have mistaken for a real recognition of Necessity what is actually only a particular form of alienation, which makes their own lived thinking appear as an object for a universal Consciousness, and which reflects on it as though it were the + +Thought of the Other. + +We must stress this crucial fact: Reason is neither a bone15 nor an + +accident. In other words, if dialectical Reason is to be rationality, it must provide Reason with its own reasons. From this point of view, analytical rationalism demons trates itself, because, as we have seen, it is the pure affirmation - at a quite superficial level - of the bond of exteriority as permanent possibility. But let us see what Engels says about 'the most general laws' of 'the history of nature and human + +society'. It is this: + +they can be reduced in the main to three: + +The law of the transformation of quantity into quality, and vice + +versa; + +The law of the interpenetration of opposites; The law of the negation of the negation. + +All three are developed by Hegel in his idealist fashion as mere laws of thought ... • The mistake lies in the fact that these laws are foisted on nature and history as laws of thought, and not deduced from them.'15a Engels' uncertainty is revealed by his words, for abstraction is not the same as deduction. And how can universal laws be deduced from a set of particular laws? If you want a name, it can only be called induction. And as we have seen, the only dialectic one will find in Nature is a dialectic that one has put there oneself. But let us suppose for a moment that universal laws can actually be induced, that is to say, that they provide both a means of ordering scientific Knowledge and a heuristic procedure. For all that, they will remain only probabilities. Let us suppose, also, that their probability is very high and that, consequently, we are obliged to accept them as true. Where will this get us? To a discovery of the laws of Reason in the universe, like Newton's discovery of the principle of gravitation. When Newton said 'Hypotheses non jingo', he meant that while calculation and investigation permitted him to prove the de facto existence of gravitation, he would not try to establish it de jure, to explain it, to reduce it to some more general principle. Thus, to his contemporaries, rationality seemed to come to a halt with demonstrations and proofs; the fact in tself remained inexplicable and contingent. Science does not have to account for the facts that it discovers; it firmly establishes their existence and their relations with other facts. Later, the movement of scientific thought itself was to lift this mortgage, for in contemporary physics gravitation is treated quite differently; without ceasing to be a + +fact, it is no longer the un transcend able final fact; it is part of a new conception of the universe and we know now that every contingent fact, however untranscendable it may appear, will be transcended in its + +turn, by other facts. + +But what are we to make of a doctrine which presents the laws of Reason in the same way as Newton presented those of gravitation? If someone had asked Engels: Why are there three laws rather than ten, or just one?; Why are the laws of thought these and not others?; Where do they come from?; Is there some more general principle from which they might be deduced, instead of appearing as having the contingency of a fact?; Is there some way of uniting them in an organised synthesis, and putting them in some order?; etc., he would probably have shrugged his shoulders and replied, like Newton, 'Hypotheses non jingo'. The upshot of this is paradoxical : Engels criticises Hegel for imposing the laws of thought on matter, but he does precisely the same himself, in that he expects the sciences to verify a dialectical reason which he discovered in the social world. But, in the historical and social world, as we shall see, there really is a dialectical reason; by transferring it into the 'natural' world, and forcibly inscribing it there, Engels stripped it of its rationality: there was no longer a dialectic which man produced by producing himself, and which, in turn, produced man; there was only a contingent law, of which nothing could be said except it is so and not otherwise. In short, Reason once more becomes a bone, since it is merely a fact and has no knowable necessity. It so happens that opposites interpenetrate. Rationality is merely a final and universal law; and tllerefore it is irrationality pure and simple. However one looks at it, transcendental materialism leads to the irrational, either by ignoring the thought of empirical man, or by creating a noumenal consciousness which imposes its law as a whim, or again, by discovering in Nature 'without alien addition' the laws of dialectical + +Reason in the form of contingent facts. + +9The Domain of Dialectical Reason + +Must we then deny the existence of dialectical connections in inanimate Nature? By no means. Indeed, in the present state of our knowledge, + +I do not see that we are in a position to affirm or deny it. Every one is free either to helieve that physico-chemical laws express a dialectical reason, or not to helieve it. In any case, in the domain of the facts of inorganic Nature, the claim must be extra-scientific. We merely ask for the restoration of the order of certainties and discoveries: for if there is such a thing as a dialectical reason, it is revealed and established in and through human praxis, to men in a given society at a particular moment of its development. On the basis of this discovery, the limits and scope of dialectical certainty have to be established. The dialectic will be an effective method as long as it remains necessary as the law of intelligibility and as the rational structure of Being. A materialist dialectic will be meaningless if it cannot establish, within human history, the primacy of material conditions as they are discovered by the praxis of particular men and as they impose themselves on it. In short, if there is to be any such thing as dialectical materialism, it must be a historical materialism, that is to say, a materialism from within; it must be one and the same thing to produce it and to have it imposed on one, to live it and to know it. Consequently, this materialism, if it exists, can be true only within the limits of our social universe. It is at the heart of a society which is organised and stratified - and which is also rent by strife - that the appearance of a new machine will bring profound changes which will reverberate from the infrastructures to the superstructures; it is within a society which possesses tools and institutions that the material facts - the poverty or richness of the subsoil, the climate, etc. - which condition it and in relation to which + +it is itself defined, will be discovered. + +As for the dialectic of Nature, it cannot be anything more than the object of a metaphysical hypothesis. The procedure of discovering dialectical rationality in praxis, and then projecting it, as an unconditional law, on to the inorganic world, and then returning to the study of societies and claiming that this opaquely irrational law of nature conditions them, seems to us to be a complete aberration. A human relation, which can be recognised only because we are ourselves human, is encountered, hypostasised, stripped of every human characteristic and, finally, this irrational fabrication is substituted for the genuine relation which was encountered in the first place. Thus in the name of monism the practical rationality of man making History is replaced by the ancient notion of a blind Necessity, the clear by the obscure, the evident by the conjectural, Truth by Science Fiction. If there is a dialectic now. and if we are to establish it, we shall have to seek it + +where it is. We shall accept the idea that man is a material being among other material beings and, as such, does not have a privileged statute; we shall even refuse to reject a priori the possibility that a concrete dialectic of Nature will one day be discovered, which would mean that the dialectical method would become a heuristic in the natural sciences and would be used by scientists themselves and under experimental control. All I say is that dialectical Reason must be turned over once again, that it must be recognised where it is there to be seen, instead of being dreamed of in areas where we cannot yet grasp it. There is such athing as historical materialism, and the law of this materialism is the dialectic . But if, as some writers imply, dialectical materialism is to be understood as a monism which is supposed to control human history from outside, then we are compelled to say that there is no such thing as + +dialectical materialism, at least for the time being.l6 + +This long discussion has not been useless: it has enabled us to formulate our problem; it has revealed the conditions under which a dialectic can be established. No doubt these conditions are contradictory, but it is their moving contradictions which will throw us into the dialectical movement. Engels' mistake, in the text we quoted above, was to think that he could extract his dialectical laws from Nature by non-dialectical procedures comparison, analogy, abstraction and induction. In fact, dialectical Reason is a whole and must ground itself + +by itself, or dialectically. + +(I) The failure of dialectical dogmatism has shown us that the + +16. It may be said that the metaphysical hypothesis of a dialectic of Nature becomes more interesting when it is used to explain the passage from inorganic matter to organic bodies, and the evolution of life on earth. This is true. But it should be noted that this formal interpretation of life and evolution will never be more than a pious dream as long as scientists have no way of using the notions of 'totality' and 'totalisation' as a guiding hypothesis. Nothing is gained by proclaiming that the evolution of the species or the appearance of life are moments of the 'dialectic of Nature' as long as we are ignorant of flOW life appeared and how species are transformed. For the present, biology, in its actual research, remains positivistic and analytical. It is possible that a deeper knowledge of its object, through its contradictions, will force biology to consider the organism in its totality, that is to say, dialectically, and to consider all biological facts in their relation of interiority. This is possible, but it is not certain. In any event, it is curious that Marxists, as dialecticians of nature, denounce as idealists those who, like Goldstein, attempt (rightly or wrongly) to consider organic beings as totalities although this only involves showing (or trying to show) the dialectical irreducibility of the 'state of matter' which is life, to another state - inorganic + +matter - which nevertheless generated it. + +dialectic as rationality must be open to direct, everyday investigation, both as the objective connection between facts and as the method for knowing and fixing this connection. But at the same time. the provisional character of dialectical hyper-empiricism forces us to the conclusion that dialectical universality must be imposed a priori as a necessity. The 'a priori', here, has nothing to do with any sort of constitutive principles which are prior to experience. It relates to a universality and necessity which are contained in every experience but which transcend any particular experience. But since, as Kant showed, experience provides facts but not necessity, and since we reject all idealist soiutions, there is obviously a contradiction here. Husserl could speak of apodictic certainty without much difficulty, but this was because he remained on the level of pure, formal consciousness apprehending itself in its formality; but, for us, it is necessary to find our apodictic + +experience in the concrete world of History. + +(2 ) We have noticed the aporias of being and knowledge in Marx. It is clear that the former is irreducible to the latter. On the other hand, the 'dialectic of Nature' has shown us that knowledge vanishes when reduced to one modality of being among others. Nevertheless, this dualism, which threatens to lead us into some form of disguised spiritualism, must be rejected. The possibility that a dialectic exists is itself dialectical; or, to put it another way, the only possible unity of the dialectic as law of historical development and the dialectic as knowledge-in-movement of this development is the unity of a dialectical movement. Being is the negation of knowledge, and knowledge + +draws its being from the negation of being. + +(3) 'Men make their own History ... but under circumstances ... given and transmitted from the past.'17 If this statement is true, then both determinism and analytical reason must be categorically rejected as the method and law of human history. Dialectical rationality, the whole of which is contained in this sentence, must be seen as the permanent and dialectical unity of freedom and necessity. In other words, as we have seen, the universe becomes a dream if the dialectic controls man from outside, as his unconditioned law. But if we imagine that every one simply follows his inclinations and that these molecular collisions produce large scale effects, we will discover average or statistical results, but not a historical development. So, in a sense, man + +submits to the dialectic as to an enemy power; in another sense, he creates it; and if dialectical Reason is the Reason of History, this contradiction must itself be lived dialectically, which means that man must be controlled by the dialectic in so far as he creates it, and create it in so far as he is controlled by it. Furthermore, it must be understood that there is no such thing as mall; there are people, wholly defined by their society and by the historical movement which carries them along; if we do not wish the dialectic to become a divine law again, a metaphysical fate, it must proceed from individuals and not from some kind of supra-individual ensemble. Thus we encounter '\ new contradiction: the dialectic is the law of totalisation which creates several collectivities, several societies, and one history - realities, that is, which impose themselves on individuals; but at the same time it must be woven out of millions of individual actions. We must show how it is possible for it to be both a resultant, though not a passive average, and a totalising force, though not a transcendent fate, and how it can continually bring + +about the unity of dispersive profusion and integration. + +(4) We are dealing with a materialist dialectic; and by this I mean from a strictly epistemological point of view - that thought must discover its own necessity in its material object, at the same time as discovering in itself, in so far as it is itself a material heing, the necessity of its object. This could be done within Hegelian idealism, and either the dialectic is a dream or it can be done in the real material world of Marxism. This inevitably refers us from thought to action. Indeed, the former is only a moment of the latter. We must therefore inquire whether, in the unity of an apodictic experience, every praxis is constituted, in and through the material universe, as the transcendence of its object-being (etre-ohjet) by the Other, while revealing the praxis of the Other as an object. But, at the same time, a relation must be established, by and through the Other, between each praxis and the universe of things, in such a way that, in the course of a perpetual totalisation, the thing becomes human and man realises himself as a thing. It must be shown, in concrete reality, that the dialectical method is indistinguishable from the dialectical movement; indistinguishable, that is to say, both from the relations which each person has with everyone through inorganic materiality, and from those which he has with his materiality and with his own organic material existence, through his relations with others. We must show, therefore, that the dialectic is based on this, everyone's permanent experience: in the universe of exteriority, one's relation of exteriority to the material + +leads to several reflections. In the first place, no one can discover the dialectic while keeping the point of view of analytical Reason; which means, among other things, that no one can discover the dialectic while remaining external to the object under consideration. Indeed, for anyone considering a given system in exteriority, no specific investigation can show whether the movement of the system is a continuous unfolding or a succession of discrete instants. The stance of the desituated experimenter, however, tends to perpetuate analytical Reason as the model of intelligibility; the scientist's passivity in relation to the system will tend to reveal to him a passivity of the system in relation to himself. The dialectic reveals itself only to an observer situated in interiority, that is to say, to an investigator who lives his investigation both as a possible contribution to the ideology of the entire epoch and as the particular praxis of an individual defined by his historical and personal career within the wider history which conditions it. In short, in order to preserve the Hegelian idea (that Consciousness knows itself in the Other and knows the Other in itself), while completely discarding its idealism, I must be able to say that the praxis of everyone, as a dialectical movement, must reveal itself to the individual as the necessity of his own praxis and, conversely, that the freedom, for everyone, of his individual praxis must re-emerge in everyone so as to reveal to the individual a dialectic which produces itself and produces him in so far as it is produced. The dialectic as the living logic of action is invisible to a contemplative reason: it appears in the course of praxis as a necessary moment of it; in other words, it is created anew in each action (though actions arise only on the basis of a world entirely constituted by the dialectical praxis of the past) and becomes a theoretical and practical method when action in the course of development begins to give an explanation of itself. In the course of this action, the dialectic appears to the individual as rational transparency in so far as he produces it, and as absolute necessity in so far as it escapes him, that is to say, quite simply, in so far as it is produced by others. Finally, to the extent that the individual becomes acquainted with himself in the transcendence (depassement) of his needs, he becomes acquainted with the law which others impose on him in transcending their own (he becomes acquainted with it: this does not mean that he submits to it), and becomes acquainted with his own autonomy (in so far as it can be, and constantly is, exploited by the other - shamming, manoeuvring, etc.) as an alien power and the autonomy of the others as the inexorable law which enables him to coerce them. But, through the very + +reciprocity of coercions and autonomies, the law ends up by escaping everyone, and in the revolving movement of totalisation it appears as dialectical Reason, that is to say, external to all because internal to each; and a developing totalisation, though without a totaliser, of all + +the totalised totalisations and of all the de-totalised totalities. + +If dialectical Reason is to be possible as the career of all and the freedom of each, as experience and as necessity, if we are to display botlt its total translucidity (it is no more than ourself) and its untranscendable severity (it is the unity of everything that conditions us), if we are to ground it as the rationality of praxis, of totalisation, and of society's future, if we are then to criticise it as analytical Reason has been criticised, that is to say, if we are to determine its significance, then we must realise the situated experience of its apodicticity through ourselves. But let it not be imagined that this experience is comparable to the 'intuitions' of the empiricists, or even to the kind of scientific experiments whose planning is long and laborious, but whose result can be observed instantaneously. The experience of the dialectic is itself dialectical : this means that it develops and organises itself on all levels. At the same time, it is the very experience of living, since to live is to act and be acted on, and since the dialectic is the rationality of praxis. It must be regressive because it will set out from lived experience (Ie vecu) in order gradually to discover all the structures of praxis. However, we must give notice that the investigation we are undertaking, though in itself historical, like any other undertaking, does not attempt to discover the movement of History, the evolution of labour or of the relations of production, or class conflicts. Its goal is simply to reveal and establish dialectical rationality, that is to say, the complex + +play of praxis and totalisation. + +When we have arrived at the most general conditionings, that is to say, at materiality, it will then be time to reconstruct, on the basis of the investigation, the schema of intelligibility proper to the totalisation. This second part, which will be published later,19 will be what one might call a synthetic and progressive definition of 'the rationality of action'. In this connection, we shall see how dialectical Reason extends beyond analytical Reason and includes within itself its own critique and its own transcendence. However, the limited character of the project cannot be emphasised sufficiently. I have said - and I repeat - that the only valid interpretation of human History is historical + +materialism. So I shall not be restating here what others have + +already done a thousand times; besides, it is not my subject. + +If a summary of this introduction is required, however, one could say that in the field of dialectical rationality historical materialism is its own proof, but that it does not provide a foundation for this rationality even, and above all, if it provides the History of its development as constituted Reason. Marxism is History itself becoming conscious of itself, and if it is valid it is by its material content, which is not, and cannot be, at issue here. But precisely because its reality resides in its content, the internal connections which it brings to light, in so far as they are part of its real content, are indeterminate in form. In particular, when a Marxist makes use of the notion of 'necessity' in order to characterise the relation of two events within one and the same process, we remain hesitant, even if the attempted synthesis convinces us completely. This does not mean that we reject necessity in human affairs quite the opposite; but simply that dialectical necessity is by definition different from the necessity of analytical Reason and that Marxism is not concerned - why should it be? - with determining and establishing this new structure of being and of experience. Thus our task cannot in any way be to reconstruct real History in its development, any more than it can consist in a concrete study of forms of production or of the groups studied by the sociologist and the ethnographer. Our problem is critical. Doubtless this problem is itself raised by History. But it is precisely a matter of testing, criticising and establishing, within History and at this particular moment in the development of human societies, the instruments of thought by means of which History thinks itself in so far as they are also the practical instruments by means of which it is made. Of course, we shall be driven from doing to knowing and from knowing to doing in the unity of a process which will itself be dialectical. But our real aim is theoretical. It can be formulated in the following terms: on what conditions is the knowledge of a History possible? To what extent can the connections brought to light be necessary? What is dialectical rationality, and what are its limits and foundation? Our extremely slight dissociation of ourselves from the letter of Marxist doctrine (which I indicated in The Problem of Method) enables us to see the meaning of this question as the disquiet of the genuine experience which refuses to collapse into non-truth. It is to this disquiet that we are attempting to respond. But I am far from believing that the isolated effort of an individual can provide a satisfactory answer - even a partial one - to so vast a question, a question + +which engages with the totality of History. If these initial investigations have done no more than enable me to define the problem, by means of provisional remarks which are there to be challenged and modified, and if they give rise to a discussion and if, as would be best, this discussion is carried on collectively in working groups, then I + +shall be satisfied. + +Critique of + +Cri tical Investigation + +z The Basis of Critical Investigation + +We know the abstract conditions which this investigation must satisfy if it is to be possible. But these conditions leave its individual reality undetermined. In the same way, in the sciences of Nature we can have a general idea of the aim of an experiment (experience) and the conditions for it to be valid, without knowing what physical fact is to be investigated, what instruments it will employ, or what experimental system it will identify and construct. In other words, a scientific hypothesis includes its own experimental requirements; it indicates, in broad outline, the conditions that the proof must satisfy; but this initial schema can be distinguished only formally from the conjecture which is to be tested. This is why the hypothesis has sometimes been called an experimental idea. It is historical circumstances (the history of the instruments, the contemporary state of knowledge) which give the projected experiment its peculiar physiognomy: thus Faraday, Foucault and Maxwell, for example, constructed such and such a system in order to get such and such a result. But our concern is with the problem of a totalising investigation, and this clearly means that it bears only an extremely distant resemblance to the experiments of the exact sciences. Nevertheless, it too must present itself in its technical particularity, detail the instruments of thought it employs, outline the concrete system it will constitute (that is to say, the structural reality which will be exteriorised in its experimental practice). This is what we shall now specify.20 By what particular experimentation can we expect + +20. These moments are in fact for the most part inseparable. But it is appropriate that methodological reflection should at least register an example of the + +to expose and demonstrate the reality of the dialectical process ? What instruments do we heed ? What is their point of application ? What experimental system must we construct? On the basis of what facts ? What type of extrapolation will it justify? What will be the validity of + +its proofs? + +2Dialectical Reason as Intelligibility + +In order to answer these questions we must have some guide-line; and this is provided purely by what the object demands. We must turn, therefore, to this basic demand. But if this demand is reduced to the simple question, 'Are there ontological regions where the law of being and, correlatively, that of knowledge can be said to be dialectical?', there is a serious risk of making it unintelligible and of relapsing either into some form of hyper-empiricism or into the opacity and contingency of the laws formulated by Engels. If we were to discover these regions in the same way as natural regions (for example, an area of the earth, together with its climate, hydrography, orography, flora and fauna, etc.) are discovered, then the discovery would share the opacity of something merely found. If, on the other hand, we were to ground our dialectical categories on the impossibility of experience without them, as Kant did for positivis t Reason, then we would indeed attain necessity, but we would have contaminated it with the opacity of facts. Indeed, to say, 'If there is to be any such thing as experience, the human mind must be able to unify sensuous diversity through synthetic judgements', is, ultimately, to base the whole critical edifice on the unintelligible judgement (a judgement of fact), 'But experience does occur.' And we shall see later that dialectical Reason is itself the intelligibility of positivist Reason; and this is precisely why positivist Reason presents itself at first as the unintelligible law of empirical + +intelligibility. 21 + +21. I am thinking here of the Critique of Pure Reason rather than of Kant's later works. It has been clearly demonstrated that, in the very last part of Kant's life, the requirement of intelligibility led him right up to the threshold of dia- + +If, however, dialectical Reason has to be grasped initially through human relations, then its fundamental characteristics imply that it appears as apodictic experience in its very intelligibility. It is not a matter of simply asserting its existence, but rather of directly experiencing its existence through its intelligibility, independent of any empirical discovery. In other words, if the dialectic is the reason of being and of knowledge, at least in certain regions, it must manifest itself as double intelligibility. Firstly, the dialectic as the law of the world and of knowledge must itself be intelligible; so that, unlike positivist Reason, it must include its own intelligibility within itself. Secondly, if some real fact - a historical process, for example - develops dialectically, the law of its appearing and its becoming must be - from the stand-point of knowledge - the pure ground of its intelligibility. For the present, we are concerned only with original intelligibility. This intelligibility - the translucidity of the dialectic - cannot arise if one merely proclaims dialectical laws, like Engels and Naville, unless each of these laws is presented as a mere sketch, revealing the dialectic as a totality. The rules of positivist Reason appear as separate instructions (unless this Reason is envisaged as a limiting case of dialectical Reason and from its point of view). Each of the so-called 'laws' of dialectical Reason is the whole of the dialectic: otherwise the dialectic would cease to be a dialectical process, and thought, as the praxis of the theoretician, would necessarily be discontinuous. Thus the basic intelligibility of dialectical Reason, if it exists, is that of a totalisation. In other words, in terms of our distinction between being and knowledge, a dialectic exists if, in at least one ontological region, a totalisation is in progress which is immediately accessible to a thought which unceasingly totalises itself in its very comprehension of the totalisation from which it emanates and which makes itself its object. It has often been observed that the laws stated by Hegel and his disciples do not at first seem intelligible; taken in isolation, they may even seem false or gratuitous. Hyppolite has shown convincingly that the negation of the negation - if this schema is envisaged in itself - is not necessarily an affirmation. Similarly, at first glance, the opposition between contradictories does not seem to be necessarily the motive force of the dialectical process. Hamelin, for example, based his whole system on the opposition between contraries. Or, to give another example, it is difficult to see how a new reality, transcending contradictions while preserving them within itself, can be both irreducible to them and intelligible in terms of them. But, these difficulties arise + +only because the dialectical 'principles' are conceived either as mere data or as induced laws; in short, because they are seen from the point of view of positivist Reason in the same way as positivist Reason conceives its own 'categories'. Each of these so called dialectical laws becomes perfectly intelligible when seen from the point of view of totalisation. It is therefore necessary for the critical investigation to ask the fundamental question: is there a region of being where totalisation + +is the very form of existence? + +3 Totality and Totalisation + +From this point of view, and before taking the discussion any further, we must make a clear distinction between the notions of totality and totalisation . A totality is defined as a being which, while radically distinct from the sum of its parts, is present in its entirety, in one form or another, in each of these parts, and which relates to itself either through its relation to one or more of its parts or through its relation to the relations between all or some of them. If this reality is created (a painting or a symphony are examples, if one takes integration to an extreme), it can exist only in the imaginary (l'imaginaire), that is to say, as the correlative of an act of imagination. The ontological status to which it lays claim by its very definition is that of the in-itself, the inert. The synthetic unity which produced its appearance of totality is not an activity, but only the vestige of a past action (just as the unity of a medallion is the passive remnant of its being struck). Through its being-in-exteriority, the inertia of the in-itself gnaws away at this appearance of unity; the passive totality is, in fact, eroded by infinite divisibility. Thus, as the active power of holding together its parts, the totality is only the correlative of an act of imagination: the symphony or the painting, as I have shown elsewhere, are imaginaries projected through the set of dried paints or the linking of sounds which function as their analogon. In the case of practical objects - machines, tools, consumer goods, etc. - our present action makes them seem like totalities by resuscitating, in some way, the praxis which attempted to totalise their inertia. We shall see below that these inert totalities are of crucial importance and that they create the kind of relation between + +men which we will refer to, later, as the practico-inert. These human objects are worthy of attention in the human world, for it is there that they attain their practico-inert statute; that is to say, they lie heavy on our destiny because of the contradiction which opposes praxis (the labour which made them and the labour which utilises them) and inertia, within them. But, as these remarks show, they are products; and the totality, despite what one might think, is only a regulative principle of the totalisation (and all at once disintegrates into the inert + +ensemble of its provisional creations). + +If, indeed, anything is to appear as the synthetic unity of the diverse, it must be a developing unification, that is to say, an activity. The synthetic unification of a habitat is not merely the labour which has produced it, but also the activity of inhabiting it; reduced to itself, it reverts to the multiplicity of inertia. Thus totalisation has the same statute as the totality, for, through the multiplicities, it continues that synthetic labour which makes each part an expression of the whole and which relates the whole to itself through the mediation of its parts. But it is a developing activity, which cannot cease without the multiplicity reverting to its original statute. This act delineates a practical field which, as the undifferentiated correlative of praxis, is the formal unity of the ensembles which are to be integrated; within this practical field, the activity attempts the most rigorous synthesis of the most differentiated multiplicity. Thus, by a double movement, multiplicity is multiplied to infinity, each part is set against all the others and against the whole which is in the process of being formed, while the totalising activity tightens all the bonds, making each differentiated element both its immediate expression and its mediation in relation to the other elements. On this basis, it is easy to establish the intelligibility of dialectical Reason; it is the very movement of totalisation. Thus, to take only one example, it is within the framework of totalisation that the negation of the negation becomes an affirmation. Within the practical field, the correlative of praxis, every determination is a negation, for praxis, in differentiating certain ensembles, excludes them from the group formed by all the others; and the developing unification appears simultaneously in the most differentiated products (indicating the direction of the movement), in those which are less differentiated (indicating continuities, resistances, traditions, a tighter, but more superficial, unity), and in the conflict between the two (which expresses the present state of the developing totalisation). The new negation, which, in determining the less differentiated ensembles, will + +raise them to the level of the others, is bound to eliminate the negation which set the ensembles in antagonism to each other. Thus it is only within a developing unification (which has already defined the limits of its field) that a determination can be said to be a negation and that the negation of a negation is necessarily an affirmation. If dialectical Reason exists, then, from the ontological point of view, it can only be a developing totalisation, occurring where the totalisation occurs, and, from the epistemological point of view, it can only be the accessibility of that totalisation to a knowledge which is itself, in principle, totalising in its procedures. But since totalising knowledge cannot be thought of as attaining ontological totalisation as a new totalisation of it, dialectical knowledge must itself be a moment of the totalisation, or, in other words, totalisation must include within itself its own reflexive retotalisation as an essential structure and as a totalising process within + +the process as a whole. + +4 Critical Investigation and Totalisation + +Thus the dialectic is a totalising activity. Its only laws are the rules produced by the developing totalisation, and these are obviously concerned with the relation between unification and the unified,22 that is + +22. A few examples: the whole is entirely present in the part as its present meaning and as its destiny. In this case, it is opposed to itself as the part is opposed to the whole in its determination (negation of the whole) and, since the parts are opposed to one another (each part is both the negation of the others and the whole, determining itself in its totalising activity and conferring upon the partial structures the determinations required by the total movement), each part is, as such, mediated by the whole in its relations with the other parts: within a totalisation, the multiplicities (as bonds of absolute exteriority - i.e., quantities) do not eliminate, but rather interiorise, one another. For example, the fact oj" being a hundred (as we shall see when we discuss groups) becomes for each of the hundred a synthetic relation of interi ority with the other ninety-nine; his individual reality is affected by the numerical characteristics of heing- tlle-hundredth. Thus quantity can become quality (as Engels said, following Hegel) only within a whole which reinteriorises even relations of exteriority. In this way, the whole (as a totalising act) becomes the relation among the parts. In other words, totalisation is a mediation between the parts (considered in their determinations) + +to say, the modes of effective presence of the totalising process in the totalised parts. And knowledge, itself totalising, is the totalisation itself in so far as it is present in particular partial structures of a definite kind. In other words, totalisation cannot be consciously present to itself if it remains a formal, faceless activity of synthetic unification, but can be so only through the mediation of differentiated realities which it unifies and which effectively embody it to the extent that they totalise themselves by the very movement of the activity of totalising. These remarks enable us to define the first feature of the critical investigation: it takes place inside the totalisation and can be neither a contemplative recognition of the totalising movement, nor a particular, autonomous totalisation of the known totalisation. Rather, it is a real moment of the developing totalisation in so far as this is embodied in all its parts and is realised as synthetic knowledge of itself through the mediation of certain of these parts. In practice, this means that the critical investigation can and must be anyone's reflexive experience. + +as a relation of interiority: within and through a totalisation, each part is mediated by all in its relation to each, and each is a mediation between all; negation (as determination) becomes a synthetic bond linking each part to every other, to all, and to the whole. But, at the same time, the linked system of mutually conditioning parts is opposed to the whole as an act of absolute unification, to precisely the extent that this system in movement does not and cannot exist except as the actual embodiment and present reality (here and now) of the whole as a developing synthesis. Similarly, the synthetic relations that two (or n + I) parts maintain between themselves, precisely because they are the effective embodiment of the whole, oppose them to every other part, to all the other parts as a linked system and, consequently, to the whole in its triple reality as a developing synthesis, as an effective presence in every part, and as a surface organisation. Here we are only giving a few abstract examples; but they are sufficient to illustrate the meaning of the bonds of interiority within a developing totalisation. Obviously these oppositions are not static (as they might be if, as might happen, the totalisation were to result in totality); rather they perpetually transform the interior field to the extent that they translate the developing act into its practical efficacity. It is no less clear that what I call a 'whole' is not a totality, but the unity of the totalising act in so far as it diversifies itself and embodies itself in totalised + +diversities. + +5 Critical Investigation and Action + +But we must both deepen and delimit our terms. For when I say that the investigation must be rif/exive, I mean that, in the particularity of its moments, it cannot be separated from the developing totalisation any more than reflection can be distinguished from human praxis. I have shown elsewhere that reflection must not be conceived as a parasitical, distinct consciousness, but as the distinctive structure of certain 'consciousnesses'. If a totalisation is developing in a given region of reality, it must be a unique process occurring in unique conditions and, from the epistemological point of view, it will produce the universals which explain it and individualise them by interiorising them. (Indeed, all the concepts forged by history, including that of man, are similarly individualised universals and have no meaning apart from this individual process.) The critical investigation can only be a moment of this process, or, in other words, the totalising process produces itself as the critical investigation of itself at a particular moment of its development. And this critical investigation apprehends the individual movement through reflection, which means that it is the particular moment in which the act gives itself a reflexive structure. Thus the universals of the dialectic - principles and laws of intelligibility - are individualised universals; attempts at abstraction and universalisation can only result in schemata which are continually valid for that process. Later, we shall see how far formal extrapolations are conceivable (on the abstract hypothesis that other, as yet unknown, ontological regions are also totalisations); but, at any rate, such extrapolations cannot claim to be knowledge and their only utility, if they are possible, is to throw more light on the particularity of the totalising + +process where the investigation takes place. + +6The Problem of Stalinism + +This makes clear how we are to understand the word 'anyone'. If the totalisation produces a moment of critical consciousness as the necessary + +incarnation of its totalising praxis, then obviously this moment can only appear at particular times and places. In its deep reality as well as in its modes of appearance, it is conditioned by the synthetic rule characteristic of this particular totalisation as well as by prior circumstances which it must transcend and retain within itself according to this rule . To make myself clearer, let me say that - if, as we assume, the region of totalisation is, for us, human history - the critique of dialectical Reason could not appear before historical totalisation had produced that individualised universal which we call the dialectic, that is to say, before it was posited for itself in the philosophies of Hegel and Marx. Nor could it occur before the abuses which have obscured the very notion of dialectical rationality and produced a new divorce between praxis and the knowledge which elucidates it. Indeed, Critique derives its etymological meaning and its origin from the real need to separate the true from the false, to define the limits of totalising activities so as to restore to them their validity. In other words, critical investigation could not occur in our history, before Stalinist idealism had sclerosed both epistemological methods and practices. It could take place only as the intellectual expression of that re-ordering which characterises, in this 'one World' of ours, the post-Stalinist period. Thus, when we claim that anyone can carry out the critical investigation, this does not mean it could happen at any period. It means anyone today. What, then, does 'anyone' mean? We use this term to indicate that, if the historical totalisation is to be able to exist, then any human life is the direct and indirect expression of the whole (the totalising movement) and of all lives to precisely the extent that it is opposed to everything and to everyone. Consequently, in any life (though more or less explicitly, depending on the circumstances) totalisation effects the divorce of blind unprincipled praxis and sclerosed thought, or, in other words, the obscuring of the dialectic which is a moment of the totalising activity of the world. Through this contradiction, lived in discontent and, at times, in agony, the totalisation compels everyone, as part of his individual destiny, to reexamine his intellectual tools; and this represents in fact a new, more detailed, more integrated and richer moment of human development. In fact, we are witnessing today the emergence of numerous attempts all of them interesting and all of them debatable (including, of course, this one) - to interrogate the dialectic about itself. This means not only that the origin of critical investigation is itself dialectical, but also that the appearance of a reflexive and critical consciousness in everyone + +takes the form of individual attempts to grasp the moment of historical totalisation through one's own life, conceived as an expression of the whole. Thus, in its most immediate and most superficial character, the critical investigation of totalisation is the very life of the investigator in so far as it reflexively criticises itself. In abstract terms, this means that only a man who lives within a region of totalisation can apprehend the bonds of interiority which unite him to the totalising movement. + +7The Problem of the Individual + +These remarks coincide with those I made in The Problem of Method about the need to approach social problems by situating oneself in relation to the ensembles under consideration. They also remind us that the epistemological starting point must always be consciousness as apodictic certainty (of) itself and as consciousness of such and such an object. But we are not concerned, at this point, with interrogating consciousness about itself: the object it must give itself is precisely the life, the objective being, of the investigator, in the world of Others, in so far as this being totalises itself from birth and will continue to totalise itself until death. On this basis, the individual disappears from historical categories : alienation, the practico-inert, series, groups, classes, the components of History, labour, individual and communal praxis - the individual has lived, and he still lives, all of these in interiority. But if there is a movement of dialectical Reason, it is this movement which produces this life, this membership of a particular class, of certain milieux and of certain groups; it is the totalisation itself which brought about his successes and his failures, through the vicissitudes of his community, and his personal joys and sorrows. Through his love or family relations, through his friendships and through the 'relations of production' that have marked his life, the dialectical bonds reveal themselves. For this reason, his understanding of his own life must go so far as to deny its distinctiveness so as to seek its dialectical intelligibility within human development as a whole. What I have in mind is not an act of consciousness which would make him grasp the content of his life in terms of concrete history, of the class to which he belongs, its characteristic contradictions and its struggles against other + +classes: we are not trying to reconstruct the real history of the human + +race; we are trying to establish the Truth of History. + +The point is, therefore, that the critical investigation should bear on the nature of bonds of interiority (if they exist), on the basis of the human relations which define the investigator. Ifhe is to be totalised by history, the important thing is that he should re-live his membership of human ensembles with different structures and determine the reality of these ensembles through the bonds which constitute them and the practices which define them. And to precisely the extent that the investigator is in himself (like any other individual) a living mediation between these different kinds of ensembles, his critical investigation must reveal whether this mediating bond is itself an expression of totalisation. In short, if there is such a thing as the unity of History, the experimenter must see his own life as the Whole and the Part, as the bond between the Parts and the Whole, and as the relation between the Parts, in the dialectical movement of Unification; he must be able to leap from his individual life to History simply by the practical negation of the negation which defines his life. From this point of view, the order of the investigation becomes clear: it must be regressive. The critical investigation will move in the opposite direction to the synthetic movement of the dialectic as a method (that is to say, in the opposite direction to Marxist thought, which proceeds from production and the relations of production to the structures of groups, and then to their internal contradictions, to various milieux and, where appropriate, to the individual); it will set out from the immediate, that is to say from the individual fulfillin g himself in his abstract23 praxis, so as to rediscover, through deeper and deeper conditionings, the totality of his practical bonds with others and, thereby, the structures of the various practical multiplicities and, through their contradictions and struggles, the absolute concrete: historical man. This is tantamount to saying that the individual, the investigator under investigation, is both myself and no one. The hond between collectives and groups remains: through the lived interconnection between affiliations, we shall, through this disappearing self, grasp the dynamic relations between the different social structures in so far as they transform + +23. I am using the term 'abstract' here in the sense of incomplete. The individual is not abstract from the point of view of his individual reality (one could say that he is the concrete itself); but only on condition that the ever deeper determinations which constitute him in his very existence as a historical agent and, + +aggregates, and still others which (depending on the state of knowledge) possess bo th characteristics. Equally, cultural regions might be defined on the basis of their internal, dialectical conditioning while their interrelations were supposed to be ones of pure contiguity (or certain + +exterior bonds). + +But if History is a totalisation which temporalises itself, culture is itself a temporalising and temporalised totalisation, despite the 'disparateness' of my knowledge and perhaps of knowledge in general within the objective Culture of this century. This problem must be resolved according to whether dialectical investigation is, or is not, possible. Supposing, for a moment, that it is possible, it is immediately clear that my culture cannot be treated as a subjective accumulation of knowledge and methods 'in my mind'; instead, this culture which I call mine must be conceived as a specific participation in interiority in the objective culture. And instead of me being a particular social atom which itself defines the cultural possibilities, this participation defines me (in a specific way) . As soon as I reflexively grasp this bond of interiority which links me to the cultural totalisation, I disappear as a cultivated individual and emerge as the synthetic bond between everyone and what might be called the cultural field. And this connection will itself appear in all its complexity (relation of the Whole to the Whole for my mediation, opposition of the Whole to the part and to the Whole, opposition between some parts and the part and the Whole, etc.). Moreover - still on the assumption that dialectical investigation is possible - this very bond gives us access to the Culture itself as totalisation and temporalisation. In this way, I find myself dialectically conditioned by the totalised and totalising past of the process of human development : as a 'cultured' man (an expression which applies to every man, whatever his culture, and even if he is an illiterate) I totalise myself on the basis of centuries of history and, in accordance with my culture, I totalise this experience. This means that my life itself is centuries old, since the schemata which permit me to understand, to modify and to totalise my practical undertakings (and the set of determinations which go with them) have entered the present (present in their effects and past in their completed history). In this sense, diachronic evolution is present (as past - and, as we shall see later, as future) in synchronic totalisation; their relations are bonds of interiority and, to the extent that critical investigation is possible, the temporal depth of the totalising process becomes evident as soon as I + +Of course, the individual is here only the methodological point of departure, and his short life soon becomes diluted in the pluridimensional human ensemble which temporalises its totalisation and totalises its temporality. To the extent that its individual universals are perpetually aroused, in my immediate as well as my reflective life, and, from the depths of the past in which they were born, provide the keys and the rules of my actions, we must be able, in our regressive investigation, to make use of the whole of contemporary knowledge (at least in principle) to elucidate a given undertaking or social ensemble, a particular avatar of praxis. In other words, the first use of culture must be in the unreflected content of critical reflexion, to the extent that its first grasp of synchronisms is through the present individual. Far from assuming, as certain philosophers have done, that we know nothing, we ought as far as possible (though it is impossible) to assume that we know everything. At any rate, we use the whole of knowledge in order to decipher the human ensembles which constitute the individual and which the individual totalises by the very style in which he lives them. We use this knowledge because the dream of an absolute ignorance which reveals pre-conceptual reality is a philosophical folly, as dangerous as the dream of the 'noble savage' in the eighteenth century. It is possible to be nostalgic about illiteracy, but this nostalgia is itself a cultural phenomenon, since absolute illiteracy is not aware of itself and, if it is, it sets about eliminating itself. Thus the starting point of 'supposing we know nothing', as a negation of culture, is only culture, at a certain moment of totalising temporalisation, choosing to ignore itselfJor its own sake. It is, one might say, a sort of pre-critical attempt to criticise knowledge, at a time when the dialectic has not reached the + +stage of criticising itself. + +Our critical investigation, on the other hand, will make use of everything that comes to hand because, in an individual life, each praxis uses the whole of culture and becomes both synchronic (in the ensemble of the present) and diachronic (in its human depth); and because our investigation is itself a cultural fact. In the methodical reconstruction of History it is practically forbidden to follow analogies of content, and to interpret, for example, a revolution such as Cromwell's in terms of the French Revolution. On the other hand, if we are trying to grasp formal bonds, (for example, any kind of bonds of interiority) between individuals or groups, to study the different forms of practical multiplicities and the kinds of interrelations which exist within them, the best example is the clearest provided by culture regardless of date. In + +other words, the dialectic is not the culmination of history; it can only exist as the original movement of totalisation. Of course, the dialectic must in the first instance be the immediate, simple lived praxis, and, in so far as it acts upon itself in the course of time so as to totalise itself, it discloses itself and progressively mediates itself through critical reflection. But for this reflection, by definition, the immediate no longer exists in relation to �ither present or past praxis. The former, contemporary with the critical investigation, acquires a reflexive structure at the moment of its constitution; the latter, precisely because it has been preserved (at least vestigially) or reconstituted, is already mediated when it is brought to light: in this case reflexive scissiparity becomes a kind of distantiation. But a reflexive critique forms part of what we shall call reconstituting praxis (that of the historian or the ethnographer); and reconstituting praxis - in so far as it effects reconstitution is indissolubly linked to reconstituted praxis. (It constructs past, that is to say transcended, reality, by rediscovering it in the present transcendence which preserved it; and it is itself constructed by this resuscitated past which transforms it in so far as it restores it.) Furthermore, as a transcended past, the reconstituted praxis necessarily forms part of our present praxis as its diachronic depth. Thus, the reflexive critique becomes critical and quasi-reflexive knowledge when it seeks its examples and its explanations in the objective Culture. And let us not forget that the choice of social memories defines both the present praxis (in so far as it motivates this choice) and social memory in so far as it has produced our praxis along with its characteristic + +choice. + +This being so, reflexive investigation and quasi-reflexive knowiedge are completely homogeneous in bringing to light the synthetic bonds of History. The content of these bonds, in its materiality, can be used only to distinguish and to differentiate: it must be recognised that a friendship in Socrates' time has neither the same meaning nor the same functions as a friendship today. But this differentiation, which completely rules out any belief in 'human nature' , only throws more light on the synthetic bond of reciprocity (which will in any case be described below) - an individualised universal, and the very foundation of all human relations. Bearing in mind these difficulties, we may select the best examples of this fundamental reciprocity from the past which we did not live, but which is nevertheless, through the medium of culture + +, + +completely ours. We are proposing not the rewriting of human history, but the critical investigation of bonds of interiority, or, in other words, + +the discovery, in connection with real, though quite ordinary, undertakings, structures and events, of the answer to this all-important question: in the process of human history, what is the respective role of relations of interiority and exteriority? And if this total investigation which can be summed up as that of my whole life in so far as it is dissolved in the whole of history, and of the whole of history in so far as it is concentrated in an entire life - establishes that the bond ofexteriority (analytical and positivist reason) is itself interiorised by practical multiplicities, and that it acts within them (as a historical force) only to the extent that it becomes an interior negation of interiority,24 we will find ourselves situated, through the investigation itself, at the heart of a + +developing totalisation. + +9 Primary and Secondary Intelligibility + +But our task involves more than establishing the existence of an ontological region of totalisation within which we are situated. For if dialectical reason exists, the totalising movement must, at least in principle, be intelligihle to us everywhere and at all times. (Sometimes our information may not be sufficient to make an event accessible to us; but even if this were usually so, intelligibility in principle would still have to be guaranteed by our investigation.) This is a matter of secondary intelligibility. Primary intelligibility, if it is to be possible, that is to say, if there is such a thing as a totalising temporalisation - must, as we have seen, consist in reducing the laws of the dialectic to moments of the totalisation. Instead of grasping certain principles within ourselves, apriori (that is to say, certain opaque limits of thought), we must grasp the dialectic in the Object and understand it - to the extent that each of us, simultaneously individual and the whole of human history, produces it from this double point of view and is subject to it in producing it as the totalising movement. Secondary intelligibility, however, is not the translucidity of dialectical Reason: it is the intelligibility of partial moments of the totalisation, resulting from the totalisation itself in its + +temporalisation, that is to say, through the critical application of dialectical schemata. We have seen that dialectical Reason, when applied to the sciences of Nature, cannot be 'comtitutive' : in other words, it is no more than the empty idea of totalisation projected beyond the strict and quantitative laws established by positivist Reason. Within the totalisation where we are and which we are, however, dialectical Reason must prove its constant superiority for the under standing of historical facts: it must dissolve the positivist, analytical interpretation from within its own totalising activity; it must reveal certain structures, relations and meanings which necessarily elude all positivism. Moreover, in the limiting case of perfect information, the event itself must become transparent, that is to say, it must reveal itself as accessible only to dialectical Reason. This means that the movement by which totalising agents, in transcending their contradictions, produce new and irreducible moments of the totalisation must present itself to us both as reality and as elucidation. In other words, if there is any such thing as dialectical Reason, it must be defined as the absolute intelligibility of the irreducibly new, in so far as it is irreducibly new. It is the opposite of the positivist analytical enterprise of explaining new facts by reducing them to old ones. And, in a sense, the positivist tradition is so firmly anchored in us, even today, that the requirement of intelligibility may seem paradoxical. The new, in so far as it is new, seems to elude the intellect: the new quality is regarded as a brute fact or, at best, its irreducibility is taken to be temporary, and analysis is expected to reveal old elements in it. But in fact it is man who brings novelty into the world: it is his praxis (at the level of perception: colours, odours) which, through the partial or total reorganisation of the practical field, produces a new instrument in the new unity of its appearance and function; it is the praxis of users which, coordinated with that of producers, will maintain the tool in the human world and, through use, link together its so-called 'elements' in such a way as to preserve its irreducibility, in relation to men. 'Human reality' is a synthesis at the level of techniques, and at the level of that universal technique which is thought. This much is clear. It is also clear - and it will become clearer - that analytical Reason is a synthetic transformation to which thought intentionally subjects itself: this thought must become a thing and control itself in exteriority in order to become the natural milieu in which the object under investigation defines itself in itself, as conditioned in exteriority. In this respect, as we shall see in detail later, thought, when it makes itself + +into directed inertia in order to act on inertia, conforms to the rule of the practical organism at every level. But, while making itself the object of this transformation, thought also controls it and realises it in connection with the inert system it is trying to study. It becomes the law of bodies in motion (at first as an indeterminate schema and in order to become this specific law), or the rule of chemical combination (as the simple, a priori certainty that such combinations cannot be totalisations). Thus analytical Reason, as the pure, universal schema of natural laws, is really only the result of a synthetic transformation or, so to speak, a particular practical moment of dialectical Reason: this latter, like animal-tools, uses its organic powers to make certain regions of itself into a quasi-inorganic residue deciphering the inert by means of its own inertia; scientific thought is synthetic in its internal movement (creation of experiments and hypotheses), and (in the case of the sciences of Nature in their present state) analytical in its noemic projection of itself. Its hypotheses are synthetic in virtue of their unifying function (y=f(x)) and analytical in virtue of the dispersive inertia of their material content. If our experiment is a success, we shall see later that dialectical Reason sustains, controls and constantly recreates positivist Reason as its relation of exteriority with natural exteriority. But this posi tivist Reason, produced like the chitinous carapaces of certain insects, has its foundation and intelligibility only in dialectical Reason. If it is sometimes true and intelligible that an object gets its unity from exterior forces, and if these forces are themselves systematically conditioned by the indefinite exteriority of the universe, this is because man is part of this universe and is strictly conditioned by it; because all praxis, and consequently all knowledge, must unify molecular dispersal (either by constructing a tool, or by unifying social multiplicity within a group by interiorising it). Thus the sciences of Nature are analytical with respect to their content, whereas scientific thought is both analytical in its particular procedures and synthetic by virtue + +of its ultimate aims. + +But if there is such a thing as totalisation, it would be wrong to suppose that the existence of organising and creative thought is the unintelligible fact about the human race, or some kind of unconscious activity revealed only through the use of the methods and the knowledge of the natural sciences. To understand a mathematical or experimental proof is to understand the method and orientation of thought. In other words, it is to grasp both the analytical necessity of the calculations (as a system of equivalences, and so as the reduction of change + +to zero) and the synthetic orientation of these equivalences towards the creation of new knowledge. Indeed, even if a reduction of the new to the old were to be rigorously proved, the emergence of proved knowledge where before there was only a vague hypothesis which at any rate lacked Truth, must be seen as an irreducible novelty in the order of knowledge and its practical applications. And if there could be no complete intelligibility of this irreducibility, there could be neither any consciousness of its aim nor any understanding of the gradual progress of the proof (on the part either of the scientist who invented the experiment or of the student listening to an account of it) . Thus natural science has the same structure as a machine: it is controlled by a totalising thought which enriches it and finds applications for it and, at the same time, the unity of its movement (accumulation) totalises ensembles and systems of a mechanical order for man. Interiority + +exteriorises itself in order to interiorise exteriority. + +The transparence of praxis (let us say, for the moment, of individual praxis) has its source in the indissoluble connection between negation (which totalises in situation what it negates) and a project which defines itself in terms of an abstract and still formal whole which the practical agent projects into the future and which appears as the reorganised unity of the negated situation. In this sense, the very temporalisation of an undertaking is accessible since it can be understood on the basis of the future which conditions it (that is to say of the Whole which praxis conceives as having to be realised). Thus in the very act of negating, negation creates a temporary totality; it totalises hefore becoming partial. Furthermore, when it resolves to negate a particular structure of the rejected situation, it does so on the basis of a provisional totalisation; the particularisation of the negation is not pure analysis, but, on the contrary, a dialectical moment: the secondary structure appears within the provisional whole as expressing the totality and as incapable of changing without the totality itself being modified (or even, as incapable of changing except as a result of the prior modification of the totality). This unification, in fact (and the discovery which is effected in the totalised field) is intelligibility in the first instance, in so far as human praxis, transparent to itself as the unity in act either of a rejection or of a project, defines its own practical understanding as the totalising grasp of a unified diversity (to understand, for a technician, is to see the whole - the entire functioning of a machine to be repaired, for example - and to search for the particular structures which obstruct its functioning on the hasis of this overall function). It + +is a case, in fact, of what we were talking about a moment ago: totalisation diversifies itself and integration grows proportionately stronger. But it is also a movement from the future (for example, the machine in working order) towards the past: repairing something means grasping its integrity both as a temporal abstract and as the future state which is to be reconstituted. On this basis, all the activities of a practical agent are to be understood through the future as a perpetual re-totalisation of the provisional totality. And the ensemble of these moments, themselves re-totalised by the temporalisation, is in fact original intelligibility, for the practical agent is transparent to himself as the unifying unity of himself and his environment. In this sense, the new is immediately intelligible to him in his activity itself (in so far as this activity produces it, no t in so far as it comes from outside), since, for the practical agent, it is nothing but his own practical unity in so far as he constantly produces it outside himself as the mark of an ever deeper diversity. Thus dialectical intelligibility rests on the intelligibility of every new determination of a practical totality, in so far as this determination is nothing other than the preservation and the totalising transcendence of all previous determinations and in so far as this transcendence and preservation are explicable by a totality which has + +to be realised. 25 + +These remarks do not prejudge the outcome of the critical investigation which we are about to undertake. They merely indicate its intention. It is possible that, on some plane, individual praxis is transparent to itself and that, in this transparence, it provides the model and the rules of full intelligibility; but this still has to be proved. It is also conceivable, at least hypothetically, that human thought (in so far as it is itself praxis and a moment of praxis) is fundamentally the understanding of novelty (as a perpetual re-organisation of the given in accordance with acts explicable by their end).26 But it is clear that this + +25. This totality is only a moment of practical totalisation. If the agent regards it as definitive, this can only be for reasons external to the pure diversifying unification, such as its utility. Besides, we shall see that the created totality will elude him to the extent that its very realisation causes it to relapse into original + +inertia and into pure exteriority. + +26. From the point of view of the future totality, each new state of the organised system is in reality a pre-novelty, and it shows its intelligibility only in so far as it is already transcended by the future unity, in so far as it is not new enough. Take the simple example of intuitive (and dialectical) certainty as compared with a geometrical proof. It is quite certain - first and foremost for a child - that a + +is not the important point; it is not just a matter of studying an individual at work. A critique of dialectical Reason must concern itself with the field of application and the limits of this reason. If there is to be any such thing as the Truth of History (rather than several truths, even if they are organised into a system), our investigation must show that the kind of dialectical intelligibility which we have described above applies to the process of human history as a whole, or, in other words, that there is a totalising temporalisation of our practical multiplicity and that it is intelligible, even though this totalisation does not involve a grand totaliser. It is one thing to claim that individuals (possibly 'social atoms') totalise dispersals through their very existence (but individually and each within the private region of his work), and it is quite another to show that they totalise themselves, intelligibly, without + +for the most part showing any concern about it. + +zo The Plan of this Work + +If History is totalisation and if individual practices are the sole ground of totalising temporalisation, it is not enough to reveal the totalisation developing in everyone, and consequently in our critical investigations, through the contradictions which both express and mask it. Our critical investigation must also show us how the practical multiplicity (which may be called 'men' or 'Humanity' according to taste) realises, in its very dispersal, its interiorisation. In addition, we must exhibit + +the perception of a developing praxis in the light of its final term). If this immediate understanding of practical novelty seems, in the example we have just considered, useless and almost childish this is because geometry is concerned not with acts but with their vestiges. It matters little for geometry whether its geometrical figures are abstractions, limiting schemata of real work; geometry is concerned only to reveal relations of radical exteriority beneath the seal of interiority which is stamped on these figures when they are generated. But this means that intelligibility disappears. In effect, practical syntheses are studied in so far as the synthesising action becomes a pure passive designation making way for the establishment of relations of exteriority between the elements which it has brought together. We shall see later how the practico-inert rediscovers this passive exteriorisation of practical interiorisation and how, in tracing this process, + +the dialectical necessity of this totalising process. Indeed, the multiplicity of dialectical agents (that is, of individuals producing a praxis) seems at first sight to involve a second-order atomism, through the multiplicity of totalisations. If this were so, we should return on a new level, to the atomism of analytical Reason. But since our starting point is individual praxis, we must carefully follow up every one of those threads of Ariadne which lead from this praxis, to the various forms of human ensembles; and in each case we shall have to determine the structures of these ensembles, their real mode of formation out of their elements, and finally their totalising action upon the elements which formed them. But it will never be sufficient to show the production of ensembles by individuals or by one another, nor, conversely, to show how individuals are produced by the ensembles which they compose. It will be necessary to show the dialectical intelligibility of these trans- + +formations in every case. + +Of course, this is a matter of formal intelligibility. By this I mean that we must understand the bonds between praxis, as self-conscious, and all the complex multiplicities which are organised through it and in which it loses itself as praxis in order to become praxis-process. However - and I shall have occasion to repeat this still more emphatically - it is no part of my intention to determine the concrete history of these incarnations of praxis. In particular, as we shall see later, the practical individual enters into ensembles of very different kinds, for example, into what are called groups and what I shall call series. It is no part of our project to determine whether series precede groups or vice versa, either originally or in a particular moment of History. On the contrary: as we shall see, groups are born of series and often end up by serialising themselves in their turn. So the only thing which matters to us is to display the transition from series to groups an ... trom groups to series as constant incarnations of our practical multiplicity, and to test the dialectical intelligibility of these reversible processes. In the same way, when we study class and class-being (1' hre de classe) we shall find ourselves drawing examples from the history of the working class. But the purpose will not be to define the particular class which is known as the proletariat: our sole aim will be to seek the constitution of a class in these examples, its totalising (and detotalising) function and its dialectical intelligibility (bonds of interiority and of exteriority, interior structures, relations to other classes, etc.). In short, we are dealing with neither human history, nor sociology, nor ethnography. To parody a title of Kant's, we would claim, rather, to be + +laying the foundations for 'Prolegomena to any future anthropology' If our critical investigation actually yields positive results, we shall have established a priori - and not, as the Marxists think they have done, a posteriori - the heuristic value of the dialectical method when applied to the human sciences, and the necessity, with any fact, provided it is human, of reinserting it within the developing totalisation and understanding it on this basis. Thus the critical investigation will always present itself as a double investigation: iftotalisation exists, the investigation will supply us with, on the one hand (and in the regressive order), all the means brought into play by the totalisation, that is to say the partial totalisations, detotalisations and retotalisations in their functions and abstract structures and, on the other hand, it must enable us to see how these forms dialectically generate one another in the full intelligibility of praxis. Moreover, in so far as our investigation proceeds from the simple to the complex, from the abstract to the concrete, from the constituting to the constituted, we must be able to settle, without reference to concrete history, the incarnations of individual praxis, the formal structural conditions of its alienation27 and the abstract circumstances which encourage the constitution of a common praxis. This leads to the principal divisions of this first volume: the constituent dialectic (as it grasps itself in its abstract translucidity in individual praxis) finds its limit within its own work and is transformed into an anti-dialectic. This anti-dialectic, or dialectic against the dialectic (dialectic ofpassiyity),28 must reveal series to us as + +'27. This means: the dialectical investigation of alienation as an a priori possibility of human praxis on the basis of the real alienations to be found in concrete History. It would indeed be inconceivable that human activity should be alienated or that human relations should be capable of being rei./ied if there were no such thing as alienation and reification in the practical relation of the agent to the object of his act and to other agents. Neither the un-situated freedom of certain idealists, nor the Hegelian relation of consciousness to itself, nor the mechanistic determinism of certain pseudo-Marxists can account for it. It is in the concrete and synthetic relation of the agent to the other through the mediation of the thing, and to the thing through the mediation of the other, that we shall be able to discover the + +foundations of all possible alienation. + +'28. The dialectic of passivity is in no way reducible to analytical reason, which is the a priori construction of the inert (spatio-temporal) framework of exteriority as such, or which, as it were, is the dialectic giving itself exteriority in order to grasp the exterior and manifesting itself implicitly only in the unitary direction of the passive behaviour of exteriorised exteriority. What we call the dialectic of passivity, or anti-dialectic, is the moment of intelligibility corresponding to a praxis turned against itself in so far as it is reinstated as the per- + +a type of human gathering and alienation as a mediated relation to the other and to the objects of labour in the element of seriality and as a serial mode of co-existence. 29 At this level we will discover an equivalence between alienated praxis and worked inertia, and we shall call the domain of this equivalence the practico-inert. And we shall see the group emerge as a second type of dialectical gathering, in opposition both to the practico-inert and to impotence. But I shall distinguish, as will be seen, between the constituted dialectic and the constituent dialectic to the extent that the group has to constitute its common praxis through the individual praxis of the agents of whom it is composed. Therefore, if there is to be any such thing as totalisation, the intelligibility of constituted dialectical Reason (the intelligibility of corrnnon actions and of praxis-process) must be based on constituent dialectical reason (the abstract and individual praxis of man at work). Within the context of our critical investigation, we shall be able at this point to define the limits of dialectical intelligibility and, by the same token, the specific meaning of totalisation. It may then appear that realities such as class, for example, do not have a unique and homogeneous kind of being, but rather that they exist and they create themselves on all levels at once, through a more complex totalisation than we expected (since the anti-dialectic must be integrated and totalised, but not destroyed, by the constituted dialectic which, in turn, can + +totalise only on the basis of a constituent dialectic). + +At this level, it will become evident that the regressive investigation has reached bedrock. In other words, we shall have grasped our individual depth in so far as, through the movement of groups and series, our roots reach down to fundamental materiality. Every moment of the regress will seem more complex and general than the + +manent seal of the inert. At this level we shall have to turn our attention to the way inertia itself becomes dialectical through having this seal placed upon it: not in so far as it is pure inertia, but in so far as we must station ourselves at the point of view of inert exteriority in order to discover passivised praxis (for example, the circulation of currency). On the surface, this pseudo-dialectic or inverted dialectic has the appearance of magic, but in fact it has its own type of rationality + +which we shall have to reveal. + +29. Obviously alienation is a much more complex phenomenon and its conditions, as we shall see, are present at all levels of experiel'lce. Nevertheless we must here indicate its ground. For example, alienation exists as a constant danger within the practical group. But this is intelligible only in so far as the most lively and united group is always in danger of relapsing into the series from which + +it came. + +isolated, superficial moment of our individual praxis, yet from another point of view, it remains completely abstract, that is, it is still no more than a possihility. Indeed, whether we consider the relations between group and series formally, in so far as each of these ensembles may produce the other, or whether we grasp the individual, within our investigation, as the practical ground of an ensemble and the ensemble as producing the individual in his reality as historical agent, this formal procedure will lead us to a dialectical circularity. This circularity exists; it is even (for Engels as much as for Hegel) characteristic of the dialectical order and of its intelligibility. But the fact remains that reversible circularity is in contradiction with the irreversibility of History, as it appears to investigation. Though it is true in the abstract that groups and series can indifferently produce each other, it is "also true that historically a particular group, through its serialisation, produces a given serial ensemble (or conversely) and that, if a new group originated in the serial ensemble, then, whatever it might be, it would be irreducible to the serial ensemble. Moreover, such a regressive investigation, though it brings certain conflicts into play, only reveals our underlying structures and their intelligibility, without revealing the dialectical relations between groups and series, between different + +series or between different groups. + +Thus, dialectical investigation in its regressive moment will reveal to us no more than the static conditions of the possibility of a totalisation, that is to say, of a history. We must therefore proceed to the opposite and complementary investigation: by progressively recomposing the historical process on the basis of the shifting and contradictory relations of the formations in question, we shall experience History; and this dialectical investigation should be able to show us whether the contradictions and social struggles, the communal and individual praxis, labour as producing tools, and tools as producing men and as regulator of human labour and human relations, etc., make up the unity of an intelligible (and thus directed) totalising movement. But above all, though these discoveries have to be made and consolidated in relation to these particular examples, our critical investigation aims to recompose the intelligibility of the historical movement within which the different ensembles are defined by their conflicts. On the basis of synchronic structures and their contradictions, it seeks the diachronic intelligibility of historical transformations, the order of their conditionings and the intelligible reason for the irreversibility of History, that is to say, for its direction. This synthetic progression, + +though merely formal, must fulfil several functions: by recomposing instances in terms of process, it must lead us, if not to the absolute concrete, which can only be individual (this event at this date of this history), at least to the absolute system of conditions for applying the + +determination 'concrete fact' to the fact of one history. + +In this sense it could be said that the aim of the critical investigation is to establish a structural and historical anthropology, that the regressive moment of the investigation is the basis of the intelligibility of sociological Knowledge (without prejudging any of the individual components of this Knowledge), and that the progressive moment must be the basis of the intelligibility of historical Knowledge (without prejudging the real individual unfolding of the totalised facts). Naturally, the progression will deal with the same structures as those brought to light by regressive investigation. Its sole concern will be to rediscover the moments of their inter-relations, the ever vaster and more complex movement which totalises them and, finally, the very direction of the totalisation, that is to say, the 'meaning of History' and its Truth. The multiple, fundamental bonds between the constituent dialectic and the constituted dialectic and vice versa through the constant mediation of the anti-dialectic, will become clear to us in the course of these new investigations. If the results of the investigation are positive, we shall finally be in a position to define dialectical Reason as the constituent and constituted reason of practical multiplicities. We shall then understand the meaning of totalisation without a totaliser, or a de- totalised totalisation, and we shall finally be able to prove the strict equivalence between praxis with its particular articulations and the dialectic as the logic of creative action, that is to say, in the final + +analysis, as the logic of freedom. + +Volume I of the Critique of Dialectical Reason stops as soon as we reach the 'locus of history'; it is solely concerned with finding the intelligible foundations for a structural anthropology - to the extent, of course, that these synthetic structures are the condition of a directed, developing totalisation. Volume II, which will follow shortly,30 will retrace the stages of the critical progression: it will attempt to establish that there is one human history, with one truth and one intelligibility - not by considering the material content of this history, but by demonstrating that a practical multiplicity, whatever it may be, must unceasinglytotalise itselfthrough interiorisingitsmultiplicityat all ievels. + +1 1 The Individual and History + +The link of our critical investigation is none other than the fundamental identity between an individual life and human history (or, from the methodological point of view, the 'reciprocity of their perspectives'). Strictly speaking, the identity of these two totalising processes must itself be proved. But in fact critical investigation proceeds from exactly this hypothesis and each moment of the regression (and, later, of the progression) directly calls it into question. The continuity of the regression would be interrupted at every level if ontological identity and methodological reciprocity did not in fact always appear both as fact and as necessary and intelligible Truth. In reality, the hypothesis which makes the critical investigation feasible is precisely the one which the investigation aims to prove. If there is a dialectic we must submit to it as the unavoidable discipline of the totalisation which totalises us and grasp it, in its free practical spontaneity, as the totalising praxis which we are; at each stage in our investigation we must rediscover, within the intelligible unity of the synthetic movement, the, contradiction and indissoluble connection between necessity and freedom, though, at each moment, this connection appears in different forms. In any case, if my life, as it deepens, becomes History, it must reveal itself, at a deep level of its free development, as the strict necessity of the historical process so as to rediscover itself at an even deeper level, as the freedom of this necessity + +and, finally, as the necessity of freedom. 31 + +The critical investigation will reveal this interplay of aspects in so far as the totaliser is always also the totalised, even if, as we shall see, he is the Prince in person. And, if the investigation is successful, and we reveal the rocky sub-soil of necessity beneath the translucidity of + +31. Though I present the final relation between these realities in this form, I am not halting the enumeration of these contradictory unities on account of the two terms of the comparison: nothing would prevent us from circularly conceiving other dialectical moments in which the succession of the unities mentioned would turn out to take place in the opposite order. If I halt the enumeration here, this is because the very movement of structural and historical totalisation requires, as we shall see, that these unities, and these alone, should mark the moments of our + +investigation. + +free individual praxis, we will be able to hope that we have taken the right track. Then we shall be able to glimpse what these two volumes together will try to prove: that necessity, as the apodictic structure of dialectical investigation, resides neither in the free development of interiority nor in the inert dispersal of exteriority; it asserts itself, as an inevitable and irreducible moment, in the interiorisation of the exterior and in the exteriorisation of the interior. This double movement will be that of our entire regressive investigation: a thorough examination of individual praxis will show us that it interiorises the exterior (in delimiting, through action itself, a practical field); but conversely, we shall grasp in the tool and in objectification through labour an intentional exteriorisation of interiority (of which a seal is both the symbol and the example) ; similarly, the movement by which the practical life of the individual must, in the course of the investigation, dissolve itself into sociological or historical totalisations, does not preserve the translucid interiority of the totalising agent in the new form, which appears as the objective reality of life (series, group, system, process). To put it more vividly if less precisely, it is initially within itself that free subjectivity discovers its objectivity as the intelligible necessity of being a perspective within totalisations which totalise it (which integrate it in synthetic developing forms). Subjectivity then appears, in all its abstraction, as the verdict which compels us to carry out, freely and through ourselves, the sentence that a 'developing' society has pronounced upon us and which defines us a priori in our being. This + +is the level at which we shall encounter the practico-inert. + +However, it must be understood that praxis presupposes a material agent (the organic individual) and the material organisation of an operation on and by matter. Thus we shall never find men who are not mediated by matter at the same time as they mediate different material regions. A practical multiplicity is a certain relation of matter to itself through the mediation of the praxis which transforms the inert into worked matter, just as the collection of objects which surrounds us imposes its mediation on the practical multiplicity which totalises us. Thus, the history of man is an adventure of nature, not only because man is a material organism with material needs, but also because worked matter, as an exteriorisation of interiority, produces man, who produces or uses this worked matter in so far as he is forced to re-interiorise the exteriority of his product, in the totalising movement of the multiplicity which totalises it. The external unification of the inert, whether by the seal or by law, and the introduction of inertia + +at the heart of praxis both result, as we have seen, in producing necessity as a strict determination at the heart of human relations. And the totalisation which controls me, in so far as I discover it within my free lived totalisation, only takes the form of necessity for two fundamental reasons: first, the totalisation which totalises me has to make use of the mediation of inert products of labour; second, a practical multiplicity must always confront its own external inertia, that is to say, its character as a discrete quantity. We shall see that the interiorisation of number is not always possible and that, when it does take place, quantity produces in each member of a group a thick layer of inertia (exteriority within interiority), though it is lived dialectically in interiority. Consequently, the problem of necessity, which is immediately given as a structure of our critical investigation, necessarily leads us to the fundamental problem of anthropology, that is, to the relations of practical organisms to inorganic matter. We must never lose sight of the fact that exteriority, (that is to say, quantity, or, in other words, Nature), is, for every multiplicity of agents, a threat both from without and from within (we shall see its role in the anti-dialectic), and that it is both the permanent means and the profound occasion for totalisation. We shall also see that it is the essence of man in the sense that essence, as transcended past, is inert and becomes the transcended objectification of the practical agent (thus producing within everyone and within every multiplicity the continually resolved and constantly renewed contradiction between man-as-producer and man-as-product).32 In the second volume we will also learn that exteriority is the inert motive force of History in that it is the only possible basis for the novelty which places its seal on it and which it preserves both as an irreducible moment and as a memory of Humanity. Whether as inert motive force or as creative memory, inorganic matter (always organised by us) is never absent from the history of our organic materialities; it is the condition of exteriority, interiorised so as to make history possible, and this fundamental condition is the absolute requirement that there must be a necessity in History at the very heart of intelligibility - and perpetually dissolved in the movement of + +32. The objectification of man places a seal on the inert. Thus, a transcended objectification, in so far as it is the space of the practical man, is, in the last analysis, a robot. In the strange world which we are describing the robot is the essence of man: he freely transcends himself towards the future, but he thinks of himself as arobot as soon as he looks back on his past. He comes to know himself in the inert and is therefore a victim of his reified image, even prior to all alienation. + +practical understanding.33 Thus, our critical investigation must present us with apodicticity as the indissoluble unity - at every totalising and totalised level - of the organic and the inorganic through all the forms that this connection can assume (from the presence of the inorganic within the organism itself and all around it, up to and including the + +33. There is, in fact, a contradiction between intelligibility and necessity. Intelligibility makes the new perfectly clear on the basis of the old; it enables us to witness the transparent practical production of the new on the basis of previously defined factors and in the light of totalisation. However, precisely because this light is shed everywhere, it dissolves that external control which, as we shall see, necessity is and remains, even wi thin processes of thought . For necessity merely eliminates all possibility by simply positing from the exterior the impossibility, giveny and [, that x should not occur (and of course this impossibility also applies to processes of thought). Dialectical understanding, in so far as it offers a full, temporalised intuition of the organising movement whereby y and i' are unified in x simply through their connection of interiority (within the developing totalisation), tends to get absorbed into the very temporalisation of this certainty. Transparency is its own guarantee, and the basic problem is not that of ruling out possibilities, but that of grasping, the full realisation of one possibility, in every one of its moments, and on the basis of a future totality. Certainty tends to avoid apodicticity to the extent that necessity tends to repel certainty. But in so far as historical certainty must always display the bonds of interiority, to the extent that these unite and partially transform an exterior diversity (every element of which is external to the others, external to itself and controlled from the exterior), to the extent, also, that these interior bonds are affected through their very activity with a quasi-exteriority, necessity a:ppears within certainty as the formal inertia of intelligibility; every adjustment tends to dissolve it in the very movement which circumscribes the inert diversity and seems, for a moment, to endow it with an internal and autonomous strength. But necessity reappears at the very end of the partial totalisation as the bony structure, the skeleton of certainty: thus the intelligibility of praxis comes to depend on the result of the praxis, both as it was projected and yet always different, and this result, in so far as it differs (that is to say, in so far as it too is connected to the whole by exteriority) will appear as incapable of being different than it is (and by the same token all totalising processes of thought will appear as having been incapable of being other than they are). It is worth recalling - as an illustration rather than an example - that the reading of novels and plays is a totalisation (as is the life of the reader). On the basis of the double totalisation effected by History, and as his own individual life, the reader approaches the work as a totality to be re-totalised in its own individuality. The understanding of actions or of dialogues must, if the work is to satisfy the mind, be both the translucidity of the unforseen, (one witnesses the intelligible birth of a response, for example, as the partial re-totalisation of the situation and of the conflicts) and, in so far as each moment falls within a past of inertia, the impossibility, to which immediate memory is subjected, that this moment should have + +organisation of the inorganic and the presence of number as pure exteriority within number interiorised by organised practical multiplicity) . It is in this way that we rediscover the schema of the critical investigation. In the regressive moment, we shall find the constituent dialectic, the anti-dialectic and the constituted dialectic. And in the moment of synthetic progression, we shall trace the totalising movement which integrates these three partial movements within a total totalisation. On this basis we shall be able to put the question of possihility in history (and, in general, in praxis), and of historical necessity in its true light. It is thus in this progressive moment that we shall finally understand our original problem: what is Truth as the praxis of synthetic unification, and what is History? Why is there such athing as human history (ethnography having acquainted us with societies with no history) ? And what is the practical meaning of historical totalisation in so far as it can reveal itself today to a (totalising + +and totalised) agent situated within History in development? + +12 Intellection and Comprehension + +The close connection between comprehension (fa comprehension), as I defined it in The Problem of Method, 34 and intellection (I' intellection), as we must be able to define it if there is such a thing as dialectic, will no doubt have been noticed. Comprehension is simply the translucidity of praxis to itself, whether it produces its own elucidation in constituting itself, or recognises itself in the praxis of the other. In either case, the comprehension of the act is effected by the (produced or reproduced) act; and the teleological structure of the activity can only be grasped within a project which defines itself by its goal, that is to say, by its future, and which returns from this future in order to elucidate the present as the negation of the transcended past. From this point of view, every praxis is a partial re-totalisation of the practical field (in so far as this is defined by its negation - the first internal totalisation + +34. 'Comprehension is nothing other than my real life; it is the totalizing movement which gathers together my neighbour, myself, and the environment in the synthetic unity of an objectification in process'. The Prohlem of Method, trans. + +effected by the agent or the practical multiplicity), and it is because my life is a perpetual (horizontal and vertical) re-totalisation that I have access to the other's present on the basis of his future. Now, dialectical intelligibility is, as we have seen, defined by the degree of transparency of the developing totalisation and the practical agent can temporalise an intelligible certainty only in so far as, situated within this totalisation, he is himself both totalising and totalised. It might seem, therefore, that 'intellection' is only another word for comprehension - in which case it would seem to be useless. However, it is usual to oppose intellection (restricted to the processes of analytical Reason) to com- + +prehension (which occurs only in the human sciences). + +This distinction, however commonplace, is quite meaningless. There is no such thing as intelligibility in the sciences of Nature : when praxis puts its seal on a region of the exteriority of inertia, it produces and reveals necessity in the form of the impossibility that the facts in question should be other than they are; and as we have seen, Reason then makes itself into a system of inertia in order to rediscover sequences in exteriority and in order both to produce and to discover necessity as their sale exterior unity. Necessity as succession in exteriority (the moments are exterior to each other and they cannot occur in a different order) is only the mind producing and discovering its own limit, that is to say, producing and discovering the impossibility of thinking in exteriority.35 The discovery of thought as impossibility is the complete opposite of understanding, for understanding can only be the recognition of the accessibility of the real to a rational praxis. Comprehension, on the other hand, which recognises this accessibility within the human sciences, is insufficiently grounded and, unless it is reduced to praxis producing itself along with its elucidation, it is in danger of becoming irrational or mystical intuition (sympathy, etc.). If we are to see comprehension as a moment of praxis, then it goes without saying that it is totalising and that it grasps the temporalising and temporalised certainty of practices, wherever they occur, in so far + +as they are totalisations. + +The opposition between the intelligible and the comprehensible ought really to be rejected. It is not as though there are two fundamentally different kinds of certainty. If we retain the two terms in + +35. When I say 'producing', it is obvious that I am not thinking of Kantian 'categories'. The seal impressed upon exteriority is only a practical operation (such as the construction of a mechanical model or an experimental system). + +spite of this, it is because comprehension is a kind of species of which intellection is the genus. We shall in fact retain the term 'comprehensible' to designate any intentional praxis (whether of an individual or of a group). And of course affectivity itself is practical. Thus we do not mean to confine comprehension to pure straightforward action and labour. Whenever a praxis can be traced to the intention of a practical organism or of a group, even if this intention is implicit or obscure to the agent himself, there is comprehension. However, critical investigation will reveal actions without an agent, productions without a producer, totalisations without a totaliser, counter-finalities and infernal circularities. We shall also discover multiplicities producing totalised thoughts and acts without reference to the individuals composing them, indeed without their even being aware of it. In such cases, and in many others which will turn up in due course, either the Truth of History is not unified, or totalising intellection must be possible. Vagabond and authorless, these free actions, which can overturn a society or its dead institutions, and which have always lost their meaning (and, perhaps, taken on a new meaning), must be totalisable, cannot remain foreign bodies within developing History; consequently, they must be intelligible. Intellection, being more complex, must be able to grasp, on the basis of the developing totalisation, the source of such things, the reasons (within History) for their inhumanity and for their accessibility, as such, to a totalising anthropology: it must see them arise and dissolve themselves in the unity of a dialectical process, that is, in direct connection with praxis itself and as the transitory exteriority of an interiority. For this reason, I shall call any temporalising dialectical certainty, in so far as it is capable of totalising all practical realities intellection, and reserve the term comprehension for the totalising group or any praxis in so far as it is intentionally pro- + +duced by its author or authors. + +Book I + +From Individual Praxis + +to the Practico-Inert + +the plurality of organisations. One need only open one's eyes to see this. Our problem concerns these connections. If there are individuals, + +who, or what, totalises? + +A simple but inadequate answer is that there would not even be the beginnings of partial totalisation if the individual were not totalising through himself. The entire historical dialectic rests on individual praxis in so far as it is already dialectical, that is to say, to the extent that action is itself the negating transcendence of contradiction, the determination of a present totalisation in the name of a future totality, and the real effective working of matter. This much is clear, and is an old lesson of both subjective and objective investigation. Our problem is this: what becomes of the dialectic if there are only particular men each of whom is dialectical? As I have said, the investigation provides its own intelligibility. We must therefore see what is the real rationality of action, at the level of individual praxis (ignoring for the moment the collective constraints which give rise to it, limit it or make it ineffective). Everything is to be explained through need (Ie besoin); need is the first totalising relation between the material being, man, and the material ensemble of which he is part. This relation is univocal, and of interiority. Indeed, it is through need that the first negation of the negation and the first totalisation appear in matter. Need is a negation of the negation in so far as it expresses itself as a lack within the organism; and need is a positivity in so far as the organic totality tends to preserve itself as such through it. The original negation, in fact, is an initial contradiction between the organic and the inorganic, in the double sense that lack is defined in relation to a totality, but that a lacuna, a negativity, has as such a mechanical kind of existence, and that, in the last analysis, what is lacking can be reduced to inorganic or less organised elements or, quite simply, to dead flesh, etc. From this point of view, the negation of this negation is achieved through the transcendence of the organic towards the inorganic: need is a link of univocal immanence with surrounding materiality in so far as the organism tries to sustain itself with it; it is already totalising, and doubly so, for it is nothing other than the living totality, manifesting itself as a totality and revealing the material environment, to infinity, as the + +total field of possibilities of satisfaction. + +On the level which concerns us here, there is nothing mysterious in this transcendence through need since the basic behaviour associated with need for food reproduces the elementary processes of nutrition: chewing, salivation, stomach contractions, etc. Transcendence here + +takes the form of a simple unity of a totalising function working in a vacuum. \Vithout a unity of basic behaviour within the whole, there would be no such thing as hunger; there would only be a scattering of disconnected, frantic actions. Need is a function which posits itself for itself and totalises itself as a function because it is reduced to an empty gesture, functioning for itself and not within the integration of organic life. And this isolation threatens the organism as a whole with disintegration - the danger of death. This initial totalisation is transcendent to the extent that the being of the organism lies outside it, immediately or mediately, in inanimate being; need sets up the initial contradiction because the organism, in its being, depends directly (oxygen) or indirectly (food), on unorganised being and because, conversely, the control of its reactions imposes a biological statute on the inorganic. In fact, this is really a matter of two statutes of the same materiality, since everything points to the fact that living bodies and inanimate objects are made of the the same molecules.1 Yet these statutes contradict one another, since one of them presupposes a bond of interiority between the whole as a unity and molecular relations, whereas the other is purely external. Nevertheless, negativity and contradiction come to the inert through organic totalisation. As soon as need appears, surrounding matter is endowed with a passive unity, in that a developing totalisation is reflected in it as a totality: matter revealed as passive totality by an organic being seeking its being in it - this is Nature in its initial form. Already, it is in terms of the total field that need seeks possibilities of satisfaction in nature, and it is thus totalisation which will reveal in the passive totality its own material being as abundance or + +scarcity. + +But while Nature appears, through the mediation of need, as a false organism, the organism exteriorises itself in Nature as pure materiality. In effect, a biological statute is superimposed, in the organism, on a physico-chemical statute. And while it is true that, in the interiority of nutritive assimilation, molecules are controlled and filtered in close coordination with the permanent totalisation, yet when it is seen from the point of view of exteriority the living body obeys all the exterior laws. In this sense, one could say that the matter outside it subjects the living body to an inorganic statute precisely to the extent that it is itself transformed into a totality. The living body is therefore in danger in the universe, and the universe harbours the possibility of the + +non-being of the organism. Conversely, if it is to find its being within Nature or to protect itself against destruction, the organic totality must transform itself into inert matter, for it is only as a mechanical system that it can modify the material environment. The man of need is an organic totality perpetually making itself into its own tool in the milieu of exteriority. The organic totality acts on inert bodies through the medium of the inert body which it is and which it makes itself. It is inert in as much as it is already subjected to all the physical forces which reveal it to itself as pure passivity; it makes itself inert in its being in so far as it is only externally and through inertia itself that a body can + +act on another body in the milieu of exteriority. + +The action of a living body on the inert can be exercised either directly or through the mediation of another inert body, in which case we call the intermediary a tool. But once the organised body takes its own inertia as mediation between inert matter and its own need, instrumentality, purpose and labour are given together: the totality to be preserved is, in effect, projected as the totalisation of the movement by which the living body uses its inertia to overcome the inertia of things. At this level, the transcendence of exteriority towards interiorisation is characterised both as existence and as praxis. Organic functioning, need and praxis are strictly linked in a dialectical manner; dialectical time came into being, in fact, with the organism; for the living being can survive only by renewing itself. This temporal relation between the future and the past, through the present, is none other than the functional relation of the totality to itself; the totality is its own future lying beyond a present of reintegrated disintegration. In short, a living unity is characterised by the decompression of the temporality of the instant; but the new temporality is an elementary synthesis of change and identity, since the future governs the present in so far as this future strictly identifies itself with the past. The cyclical processwhich characterises both biological time and that of primi tive societies2 - is interrupted externally, by the environment, simply because the contingent and inescapable fact of scarcity disrupts exchanges. This di sruption is lived as negation in the simple sense that the cyclical move- + +2. This is not because these societies are organic, for, as we shall see, organicism has to be absolutely rejected, but because their individual members remain very close to the organic temporality of cyclical repetition, and because the mode of production helps to maintain the process of repetition - at first through itself, and then through the type of mediation and integration which it introduces into + +the institutional relations between men. + +ment or function continues in a vacuum, thus denying the identity of the future and the past and relapsing to the level of a present circular organisation conditioned by the past. This dislocation is necessary if the organism is to become, not the milieu and destiny of the function, + +but its end. + +The only real difference between primitive synthetic temporality and the time of elementary praxis lies in the material environment which, by not containing what the organism seeks, transforms the totality as future reality into possibility. Need, as a negation of the negation, is the organism itself, living itself in the future, through present disorders, as its own possibility and, consequently, as the possibility of its own impossibility; and praxis, in the first instance, is nothing but the relation of the organism, as exterior and future end, to the present organism as a totality under threat; it is function exteriorised. The real difference is not between function as internal assimilation and the construction of tools with an end in view. Many species of animals, in fact, make tools of themselves : that is to say, organised matter produces the inorganic or the pseudo-inert out of itself. I have said that organisms cannot act on the environment without temporarily returning to the level of inertia; but animal-tools make themselves permanently inert in order to protect their lives or, to put it another way, instead of using their own inertia they hide it behind a created inertia. It is at this ambiguous level that the dialectical transition from function to action can be seen. The project, as transcendence, is merely the exteriorisation of immanence; transcendence itself is already present in the functional fact of nutrition and excretion, since what we find here is a relation of univocal interiority between two states of materiality. And, conversely, transcendence contains immanence within itself in that its link with its purpose and with the environment + +remains one of exteriorised interiority. + +2The Negation of the Negation + +Thus although in the first instance the material universe may make man's existence impossible, it is through man that negation comes to man and to matter. It is on this basis that we can understand in its + +original intelligibility the celebrated law of 'the negation of the negation' which Engels erroneously presents as, basically, an irrational 'abstraction' from natural laws. In reality, the dialectic of Nature whether one seeks it in 'changes of state' in general or makes it the external dialectic in human history - is incapable of providing an answer to two essential questions: why should there be any such thing as negation either in the natural world or in human history? And why and in what specific circumstances does the negation of a negation yield to affirmation? Indeed, it is not clear why transformations of energy - even if they are 'vectoral' as M. Naville would have it, even if certain among them are reversible and others irreversible, even if, as in chemical experiments, certain partial reactions occur within an overall reaction and alter it3 - should be regarded as negations, except by men and as a convention for indicating the direction of the process. There is no denying that matter passes from one state to another, and this means that change takes place. But a material change is neither an affirmation nor a negation; it cannot destroy anything, since nothing was constructed; it cannot overcome resistances, since the forces involved simply produced the result they had to. To declare that two opposed forces applied to a membrane negate each other is as absurd as saying that they collaborate to determine a certain tension. The only possible use for the order of negation is to distinguish one direction from an other. + +3. I am thinking, for example, of what has been known, since Sainte-Claire Deville, as chemical equilibrium: when the chemist attempts, by putting two substances, a and b, together in certain experimental conditions to produce two other substances, c and d, the direct reaction, a + b = c + d, is normally accompanied by the inverse reaction, c and d reacting with one another to form a and b. Thus a chemical equilibrium is reached; the transformation stops half-way. Here, we have indeed two forms of reaction and there is nothing to stop the scientist calling one of them positive and the other negative, provided that this is in relation to his human undertaking, whether experimental or industrial. If 'inverse' reactions are regarded as negative, this means that their existence prevents the achievement of a certain result; they are impediments in relation to the directed ensemble. If one is dealing with strictly natural reactions, reactions occurring outside the laboratory and having no connection with any preconceived hypothesis, it is still possible to regard one of them as a positive and the other as a negative quantity, but only as an indication of the order in which they occur. In any case this is a molecular redistribution which, though directed, is not in itself either positive or negative. Moreover, even if the inverse reaction is regarded as the negation of the direct reaction, the definitiveresult is not a synthetic form but an inert equilibrium, a mere coexistence of results - all of them 'positive' too, whether their origins are + +'positive' or 'negative'. + +Resistance and, consequently, negative forces can exist only within a movement which is determined in accordance with the future, that is to say, in accordance with a certain form of integration. If the end to be attained were not fixed from the beginning, how could one even conceive of a restraint? In other words, there is no negation unless the future totalisation is continually present as the de-totalised totality of the ensemble in question. When Spinoza says 'All determination is negation,' he is right,from his point of view, because substance, for him, is an infinite totality. This formula is thus an intellectual tool for describing and comprehending the internal relations of the whole. But if Nature is an immense dispersive decompressio"1, if the relations between natural facts can only be conceived in the mode of exteriority, then the individual couplings of certain particles and the little solar system which temporarily results from them are not particularisations, except in a purely formal, logical and idealist sense. To say that through entering into a given combination, a molecule thereby does not enter another, is merely to reiterate the proposition one wishes to affirm in a negative form -like a logician replacing 'All men are mor- + +tal' by 'All non-mortals are non-men'. + +Determination will be real negation only if it identifies the determined within a totalisation or a totality. Now,praxis, born of need, is a totalisation whose movement towards its own end practically makes the environment into a totality. It is to this double point of view that the movement of the negative owes its intelligibility. On the one hand, the organism engenders the negative as that which destroys its unity: discharge and excretion, as a directed movement of rejection, are just opaque and biological forms of negation. Similarly, lack appears through function, not only as a mere inert lacuna, but also as an opposition of function to itself. Finally, need posits negation by its very existence in that it is itself an initial negation of lack. In short, the intelligibility of the negative as a structure of Being can be made manifest only in connection with a developing process of totalisation; negation is defined on the basis of a primary force, as an opposing force of integration, and in relation to a future totality as the destiny or end of the totalising movement. At a still deeper level, and more obscurely, the organism itself as a transcendence of the multiplicity of exteriority is a univocal primary negation in that it preserves multiplicity within itself and unites itself against this multiplicity, without being able to eliminate it. Multiplicity is its danger, the constant threat to it; and, at the same time, it is its mediation with the material + +universe which surrounds it and which can negate it. Thus negation is determined by unity; indeed it is through unity and in unity that it can manifest itself. In the first instance, negation manifests itself not as a contrary force, but, what amounts to the same thing, as partial determination of the whole in so far as this partial determination is posited + +for itself. + +On this basis, a dialectical logic of negation conceived as the relation of internal structures both to each other and to the whole within a complete totality or within a developing totalisation, could be constructed. It would then become clear that, within the field of existence and tension determined by the whole, every particular exists in the unity of a fundamental contradiction: it is a determination of the whole and, consequently, it is the whole which gives rise to it; in a certain sense, in so far as the being of the whole demands that it be present in all its parts, every particular is the whole itself. But at the same time, as arrest, as turning-back upon themselves, as delimitation, particulars are not the whole, and in fact it is in opposition to the totality (rather than to beings which transcend it) that they particularise themselves. But in the context of this fundamental contradiction, particularisation is precisely the negation of interiority - as particularisation of the whole it is the whole opposing itself through a particular which it governs and which depends on it; and as determination - that is, as limitation - it becomes the nothing which stands in the way of the retotalisation of the whole and which would destroy itself in such a retotalisation. It is the existence of this non-being as a developing relation between the constituted whole and the constituent totalisation, that is to say, between the whole as the future, abstract, hut already present result and the dialectic as a process tending to constitute in its concreteness the totality which defines it as its future and its end; it is the existence of this nothingness, which is both active (totalisation positing its moments) and passive (the whole as the presence of the future), which constitutes the first intelligible dialectical negation. And it is within the totality, as the abstract unity of a field of forces and tension, that the negation of + +a negation becomes an affirmation. + +Thus, however, it manifests itself - whether as the liquidation of a partial moment or as the appearance of other moments in conflict with the first (in short, the differentiation· or even fragmentation of the partial totality into smaller parts) - the new structure is the negation of the first (either directly or by attracting, through its very presence, the relation of the first to the whole). In this way, the whole manifests + +totality even if their sources lie elsewhere, at the furthest corner of the world. Everything which takes place within a totality, even disintegration, is a total event of the totality as such and is intelligible only in terms of the totality. But as soon as the ferment of the totalised plurality produces a few passive syntheses, it shatters the relation of immediate integration between the elements and the whole, within the + +constituted whole. + +The relative autonomy of the part thus formed necessarily acts as a brake on the overall movement; the whirlpool of partial totalisation thus constitutes itself as a negation of the total movement. By the same token, even in the case of a transformation necessary for praxis, its determination becomes its negation: the relation of the integrated elements to the partial whole is more precise, less 'indeterminate' than its relation to the overall totalisation, but poorer and less comprehensive. As a result of its new bond of exteriorised interiority, the element loses the set of objective possibilities which each element possessed within the general movement; it becomes impoverished. Thus the relation of this partial totality to the total totality takes the form of conflict; absolute integration requires that every particular determination should be eliminated to the extent that it threatens to constitute a new plurality. Conversely, inertia and the necessities of partial integration require each part of the relative totality to resist the pressures of the whole. Finally, the determination of a partial totality, within the detotalised totality, must also determine the ensemble which remains outside this integration, as a partial totality, albeit negatively. The unity in exteriority of those regions which lie outside the zone of partial integration (in the first instance, those which have not been integrated) is transformed into a unity of interiority, that is, into an integrating determination, simply because, within a totality, even exteriority is expressed by relations of interiority. At the same time, the relation of the new totalisation to the whole varies: it may start to posit itself for itself, in which case the developing totalisation is completely shattered; it may identify itself with the whole itself and strive to reabsorb the new enclave; finally, it may be torn apart by contradiction, positing itself both as the whole, or at any rate, as the very process of totalisation, and as a partial moment which derives its + +determinations from its opposition to the Other. + +3 Labour + +Man, who produces his life in the unity of the material field, is led by praxis itself to define zones, systems and privileged objects within this inert totality. He cannot construct his tools - and this applies to the agricultural tools of primitive peoples as much as to the practical use of atomic energy - without introducing partial determinations into the unified environment, whether this environment is the whole world or a narrow strip of land between the sea and the virgin forest. Thus he sets himself in opposition to himself through the mediation of the inert; and, conversely, the constructive power of the labourer opposes the part to the whole in the inert within the 'natural' unity. We shall come across many examples of this later. It follows, in the first place, that negation becomes internal in the very milieu of exteriority, and secondly, that it is a real opposition of forces. But this opposition comes to Nature through man in two ways, since his action constitutes both the whole and its disruption. Labour of any kind always exists only as a totalisation and a transcended contradiction. Once it has constituted the environment as the milieu in which the labourer produces himself, every subsequent development will be a negation precisely to the extent that it is positive. And such negations can be grasped only as moments which posit themselves for themselves, since the force of inertia increases their separation' within the whole. Hence the subsequent task of labour must be to put the created object back in contact with the other sectors within the whole and to unite them from a new point of view; it negates + +separation. + +But this new process, the negation of the negation, derives its intelligibility, once again, from the original totality. In a realist and materialist system there can be no justification for asserting, a priori, that the negation of a negation must give rise to a new affirmation, as long as the type of reality in which these negations occur remains undefined. Even in the human universe, the universe of totalities, there are quite definitive and classifiable situations in which the negation of the negation is a new negation, because in these special cases there is interference between totality and recurrence. But this is not our present + +concern. At all events, it is clear that the negation of a negation produces an indeterminate ensemble unless it is regarded as arising within a totality. But even within a totality the negation of the negation would be a return to the starting point if it did not involve a totality being transcended towards a totalising end. The elimination of the partial organisations of the instrumental field would simply bring us back to the original non-differentiation of the unified environment (as when one destroys the traces of an event, an experience or a construction), unless the movement to eliminate them is accompanied by an effort to preserve them - that is, unless they are regarded as a step towards a unity of differentiation in which a new type of subordination of the parts to the whole and a new co-ordination of the parts with one another is to be achieved. And this is what has to happen given that the aim is not to preserve the unity of the field of action in and for itself, but to find in it material elements capable of preserving or restoring the organic totality it contains. Thus, in so far as body is function, function need and need praxis, one can say that human labour, the original praxis by which man produces and reproduces his life, is entirely dialectical: its possibility and its permanent necessity rest upon the relation of interiority which unites the organism with the environment and upon the deep contradiction between the inorganic and organic orders, both of which are present in everyone. Its primary movement and its essential character are defined by a twofold contradictory transformation: the unity of the project endows the practical field with a quasi-synthetic unity, and the crucial moment of labour is that in which the organism makes itself inert (the man applies his weight to the lever, etc.) in order to transform the surrounding + +inertia. + +The oscillation which opposes the human thing to the thing-man will be found at every level of dialectical investigation. But the meaning of labour is provided by an end, and need, far from being a vis a tergo pushing the labourer, is in fact the lived revelation of a goal to aim at, and this goal is, in the first instance, simply the restoration of the organism. Eventually, action really converts the material surroundings into a real whole on the basis of which an organisation of means to an end is possible. In the simplest forms of activity, this organisation is given by the end itself: that is to say, it is merely an exteriorisation of function. The totality defines its means through its lacks : the hunter or fisherman lies in wait; the food-gatherer searches: the field has been unified so as to provide a basis on which the object sought may be + +more readily apprehended. Thus labour organises itself by synthetic determinations of the ensemble, by discovering or constructing tighter and tighter relations within the practical field so as to convert what was originally only a vague relation of the parts to the whole and to one + +another into a complete circle of conditioning. + +Determination of the present by the future, oscillation between the inert and the organic, negation, transcended contradictions, negation of the negation - in short, developing totalisation: these are the moments of any form of labour, until - at a dialectical level that we have yet to consider - society develops the division of labour to the point of the specialisation of machines. The process is then inverted : the semi-automatic machine defines its environment and constructs its man, so that the inorganic comes to be characterised by a false but effective interiority, and the organic by exteriority. Man becomes the machine's machine; and to himself he is his own exteriority. But in all other cases, the dialectic appears as the logic of labour. To consider an individual at work is a complete abstraction, since in reality labour is as much a relation between men as a relation between man and the material world. I do not claim to have revealed the historically primary moment of the dialectic: I have merely tried to show that our most everyday experience, which is surely labour, considered at the most abstract level, that is as the action of an isolated individual, immediately reveals the dialectical character of action. Or, to put it another way, even if we accept the molecular theories of analytical rationalism, the dialectic is already present, even at the highest level of abstraction, in the elementary but complete form of a law of development and a schema of intelligibility. It goes without saying that, although the real existence of organic totalities and totalising processes reveals a dialectical movement, the existence of organic bodies can in no way be derived from the dialectic. However biology may develop in future, organic bodies can never be regarded as any more than de facto realities ; we have no means of establishing their existence by reason alone. The theory that they originate from unorganised matter is a reasonable and economical hypothesis, on which even Christians can agree. But this hypothesis is no more than a belief. Thus neither analytical Reason, which applies to relations in exteriority, nor dialectical Reason, which derives its intelligibility from totalities, and which governs the relations of wholes to their parts and of totalities to one another in a process of increasing integration, can establish a statute of intelligibility for organised bodies. If they emerged from + +inorganic matter, there was a passage not only from the inanimate to + +life, but also from one rationality to the other. + +It might be thought that this merely brings us back to the irrationalities of Engels. But it is not so. For Engels, it is the laws which are irrational - opaque formal principles of thought and nature. For us, however, what is contingent is the existence of certain objects. But just as analytical Reason is not qualified to ask why matter exists instead of nothing, so dialectical Reason is not bound to inquire why there are organised wholes rather than merely inorganic matter. These questions may become scientific (for one cannot set a priori limits to science), but at present they are not. The essential point is, however, that if there are organised wholes, then their type of intelligibility is the dialectic. Since the individual worker is just such a totalisation, he can only understand himself in his acts, and in his relation to Nature (and indeed, as we shall see, in his relations with others) ifhe interprets every partial totality in terms of the overall totalisation, and all their internal relations in terms of their relations to the developing unification, the means in terms of the end and the present in terms of the relation which links the future to the past. On the other hand, his praxis is dialectical and contains its own intelligibility. To take but one example, the law of the interpenetration of opposites, baldly proclaimed by Engels, becomes perfectly intelligible when related to a praxis seen in the light of its future totalisation and of the completed totalities which surround it. Within a totality (whether completed or developing), each partial totality, as a determination of the whole, contains the whole as its fundamental meaning and, consequently, also contains the other partial totalities; the secret of each part therefore lies in the others. In practical terms, this means that each part determines all the others in their relations to the whole, that is to say, in their individual existence. At this level, the truly dialectical type of intelligibility appears, combining the direct conflict between the parts (to tlle extent that dialectical Reason includes and transcends analytical Reason) with the constantly shifting hidden conflict which modifies each part from within in response to internal changes in any of the others, and establishing alterity in each part both as what it is and as what it is not, as that which + +it possesses and as that by which it is possessed. + +With these remarks I have merely described the form of connection proper to these objects, namely the bond of interiority. At this level, dialectical investigation may be difficult to describe, but it is universal and constant. It is true that most people speak according to the rules of + +analytical rationality, but this does not mean that their praxis is not conscious of itself. In the first place,4 dialectical Reason includes analytical Reason, just as totality includes plurality. In the process of labour, the practical field must already be unified before the worker can undertake an analysis of its problems. An 'analysis of the situation' is carried out in accordance with the methods and mode of intelligibility of analytical Reason; and though indispensable it presupposes totalisation. Ultimately it leads to the underlying plurality, that is, to the elements as united by the bonds of exteriority. But the practical movement, which transcends this molecular dispersal of conditions, will recover a unity through itself, in creating both the problem and the solution. Moreover, this unity was never lost, since it was wz"tAin it that the dispersal was sought. But the analysis is initially carried out by discourse and thought, even if it requires a material expression later; the production of the object, on the other hand, is entirely practical. And although praxis is self-explanatory and transparent to itself, it is not necessarily expressible in words. In fact, knowledge appears as the explanation of the practical field of perception by the end, that is to say, by future non-being. It would be a simple task, though too lengthy to undertake here, to show that only the dialectic can establish the intelligibility of knowledge and truth because neither knowledge nor truth can be a positive relation of being to being; they are, on the contrary, negative relations mediated by a nothingness. The transcended and its transcendence can be explained only in terms of a future which does not yet exist, and within the practical unity of a developing totalisation. But such a discovery can only be practical; in a society which, as a whole, confuses knowledge and contemplation, it cannot be frozen in discourse. Thus we all try to express our dialectical investigation of everything in the terms of analytical, mechanical rationality. Nevertheless, as long as we are aware of this situation, all of us can characterise our fundamental experience at any given moment. Man as a totalising project is himself the active intelligibility of the totalisations; and since alienation has not yet come into the picture (simply because we cannot deal with everything at once), doing and understanding are + +indissolubly linked. + +4. We shall see later that the dialectical investigation is not only permanent, in that men always have worked and always will, but also the result of becoming, in that it is the discovery at a particular point in time of the dialectic as the intelli- + +The investigation, however, in its elucidation of the logic of wholes and of the intelligibility of the relations of man to the universe, still cannot be regarded as apodictic. The full comprehension of act and object remains the temporal development bf a practical intuition, rather than apprehension of a necessity. For necessity can never be given in intuition, except as a horizon, an intelligible limit of intelli- + +gibility. + +Human Relations + +as a Mediation Between + +Different Sectors of Materiality + +z Isolated Individuals + +Immediate experience reveals being at its most concrete, but it takes it at its most superficial level and remains in the realm of abstractions. We have described the man of need and seen his labour as dialectical development. But we must not assume that there are no such things as isolated labourers. Isolated labourers, in fact, exist wherever the social and technical conditions of their work require that they work alone. But their very isolation is a historical and social characteristic: in a given society, and given a certain level of technical development, etc., peasants work in complete isolation at certain times of year and this is a social mode of the division of labour. And the labourer's work, his manner of producing himself, conditions not only the satisfaction of his + +need, but also the need itself. + +In southern Italy, the agricultural day labourers, the semi-employed bracciante, eat only once a day or even, sometimes, once every two days. In this situation, hunger ceases to exist as need (or rather, it appears only if it suddenly becomes impossible for the labourers to get their single meal every one or two days). It is not that hunger has ceased to exist, but that it has become interiorised, or structured, as a chronic disease. Need is no longer the violent negation which leads to praxis: it has passed into physical generality as exis, as an inert, generalised lacuna to which the whole organism tries to adapt by degrading itself, by idling so as to curtail its exigencies (exigences). In spite of this, given that the labourer is alone, and given that he chooses this or that piece of work and decides on his order of means, (at the present time, in present society, and given his particular objectives and the tools at + +his disposal), he can be made the object of a regressive investigation, and his praxis can be grasped and located as temporali5ing itself through all the conditionings. But it must be noticed that this moment of the regression, though true as a first approximation within a dialectical investigation, would be false and idealist if it were taken no further. Conversely, when our whole investigation is complete, we shall see that individual praxis, always inseparable from the milieu which it constitutes, and which conditions and alienates it, is at the same time constituent Reason (la Raison constituante) itself, operating + +within History seen as constituted Reason. + +For precisely this reason, the second moment of the regression cannot be directly the relation of the individual to social bodies (inert or active) and to institutions. Marx clearly indicated that he distinguished human relations from their reification or, in general, from their alienation within a particular social system. He says, in effect, that in feudal society, based on different institutions and tools, a society which presented different questions, its own questions, to its members, the exploitation of man by man did exist, together with the fiercest oppression, but that everything happened diff erently and, in particular, human relations were neither reified nor destroyed. It is obvious, however, that he was not trying to evaluate or compare two systems, both built on exploitation and institutionalised violence. He merely stated that the connection between the serf or the black slave and the proprietOl: is often personal (which, in a sense, makes it even more intolerable and humiliating) and that the relations between labourers and employer (or of labourers among themselves in so far as they are subject to forces of massification) is a simple relation of exteriority. But this relation of exteriority is itself inconceivable except as a reification of an objective relation of interiority. History determines the content of human relations in its totality, and all these relations, even the briefest and most private, refer to the whole. But History itself does not cause there to be human relations in general. The relations which have established themselves between those initially separate objects, men, were not products of problems of the organisation and division of labour. On the contrary, the very possibility of a group or society being constituted - around a set of technical problems and a given collection of instruments - depends on the permanent actuality of the human relation (whatever its content) at every moment of History, even between two separate individuals belonging to societies with + +This is why the habit of skipping the abstract discussion of the human relation and immediately locating ourselves in the world of productive forces, of the mode and relations of production, so dear to Marxism, is in danger of giving unwitting support to the atomism of liberalism and of analytical rationality. This error has been made by several Marxists: individuals, according to them, are a priori neither isolated particles nor directly related activities; it is always up to society to determine which they are through the totality of the movement and the particularity of the conjuncture. But this reply, which is supposed to avoid our 'formalism', involves complete formal acceptance of the liheral position; the individualistic bourgeoisie requires just one concession: that individuals passively submit to their relations and that these are conditioned in exteriority by all kinds of other forces; and this leaves them free to apply the principle of inertia and positivistic laws of exteriority to human relations. From this point of view it hardly matters whether the individual really lives in isolation, like a cultivator at certain periods, or whether he lives in highly integrated groups: ahsolute separation consists in the fact that individuals are subject to the historical statute of their relations to others in radical exteriority. In other words - and this amounts to the same thing, though it misleads certain undemanding Marxists - absolute separation is when individuals as products of their own product (and therefore as passive and alienated) institute relations among themselves (on the basis of relations established by earlier generations, of their own con- + +stitution and of the forces and requirements of the time). + +This brings us back to our problem in the first part of this book:5 what does it mean to make History on the basis of earlier conditions? I then said: if we do not distinguish the project, as transcendence, from circumstances, as conditions, we are left with nothing but inert objects, and History vanishes. Similarly, if human relations are a mere product, they are in essence reified and it becomes impossible to understand what their reification really consists in. My formalism, which is inspired by that of Marx, consists simply in recognising that men make History to precisely the extent that it makes them. This means that relations between men are always the dialectical consequence of their actiyicy to precisely the extent that they arise as a transcendence of dominating and institutionalised human relations. Man exists for man only in given circumstances and social conditions, so every human + +relation is historical. But historical relations are human in so far as they are always given as the immediate dialectical consequence of praxis, that is to say, of the plurality of activities within a single practical field. + +A good example is language. + +Words are matter. In appearance (an appearance which has its truth as such), words make a material impression on me, as disturbances of the air producing certain reactions in my organism, in particular certain conditioned reflexes which materially reproduce the words in me (I understand them in forming them at the back of my throat). Accordingly, one can say, more briefly, and with a measure of both truth and falsity, that words enter the interlocutors as vehicles of their meaning. They carry the projects of the Other into me and they carry my own projects into the Other. Language might well be studied on the same lines as money: as a circulating, inert materiality, which unifies dispersal; in fact this is partly what philology does. Words live off the death of men, they come together through men; whenever I form a sentence its meaning escapes from me, is stolen from me; meanings are changed for everyone by each speaker and each day; the meanings of the very words in my mouth are changed by + +others. + +There can be no doubt that language is in one sense an inert totality. But this materiality is also a constantly developing organic totalisation. Nor can there be any doubt that speech separates as much as it unifies; or that it reflects the cleavages, the stratifications and the inertias of the group ; or that dialogues are partly dialogues of the deaf. Bourgeois pessimism decided long ago to rest content with this observation; the original relation of men to one another would be reduced to the pure and simple exterior coincidence of immutable substances. This being so, it is obvious that a person's every word must depend, in its present meaning, on its references to the total system of interiority and that it must be the object of an incommunicable comprehension. But this incommunicability - in so far as it exists - can have meaning only in terms of a more fundamental communication, that is to say, when based on mutual recognition and on a permanent project to communicate; or rather, on the permanent, collective, institutional communication of, for example, all French people, through the constant mediation of verbal materiality, even in silence; and on people's actual projects of + +particularising this general communication. + +Every word is in fact unique, external to everyone; it lives outside, as a public institution; and speaking does not consist in inserting a + +vocable into a brain through an ear, but in using sounds to direct the interlocutor's attention to this vocable as public exterior property. From this point of view, the totality of language as a set of internal relations between objective senses is given, for and to everyone; words are simply specifications expressed against the background of language;6 the sentence is an actual totalisation where every word defines itself in relation to the others, to the context and to the entire language, as an integral part of a whole. To speak is to modify each vocable by all the others against the common background of the word (verhe); language contains every word and every word is to be understood in terms of language as a whole; it contains the whole of language and reaffirms it. But this fundamental totality can only be praxis itself in so far as it is directly expressed to others; language as the practical relation of one man to another is praxis, and praxis is always language (whether truthful or deceptive) because it cannot take place without signifying itself. Languages are the product of History; as such, they all have the exteriority and unity of separation. But language cannot have come to man, since it presupposes itself: for an individual to discover his isolation, his alienation, for him to suffer from silence or, fm that matter, to become integrated into some collective undertaking, his relation to others, as manifested in and by the materiality of lan- + +guage, must constitute him in his own reality. + +This implies that, if the praxis of the individual is dialectical, his relation to the other must be dialectical too and that it is contemporary with his original relation to materiality both inside and outside him. And this relation should not be seen as a potentiality present in everyone as a kind of 'opening to the other' which is actualised in a few particular cases. This would be to shut up these relations in 'natures' like boxes and to reduce them to mere subjective dispositions: and then we would relapse into analytical reason and molecular solipsism. 'Human relations' are in fact inter-individual structures whose common bond is language and which actually exist at every moment of History. Isolation is merely a particular aspect of these relations. The reversal of our investigation shows us the same men: but whereas we started by considering them in so far as each of them was ignorant of most (in fact, almost all) the others, we are now considering them in so far as each is bound by work, interest, family ties, etc., to + +6. It is in this sense that every vocable is the whole of actualised Language. + +Specification is totalisation. + +several others, each of these to others, etc. This is not really a totalisation, or even a totality; it is rather a changing indefinite dispersal of reciprocities. And our investigation is not yet in a position to comprehend the structures of this group; it still seeks the elementary bond which conditions all structurations. It is necessary to know at the simplest level, the level of duality and trinity, whether the relation between men is unique and, if so, in what respect it is so. This, like everything else, will have to be revealed in simple everyday praxis. Since we began with the dispersal of human organisms, we shall consider individuals who are completely isolated by institutions, by their social condition, or by accidents of fortune. We shall try to reveal in this very separation, and therefore in a relation which tends towards absolute exteriority, their concrete historical bond of interiority. + +2Duality and the Third Party + +From my window, I can see a road-mender on the road and a gardener working in a garden. Between them there is a wall with bits of broken glass on top protecting the bourgeois property where the gardener is working. Thus they have no knowledge at all of each other's presence; absorbed as they are in their work, neither of them even bothers to wonder whether there is anybody on the other side. Meanwhile, I can see them without being seen, and my position and this passive view of them at work situates me in relation to them: I am 'taking a holiday', in a hotel; and in my inertia as witness I realise myself as a petty bourgeois intellectual; my perception is only a moment of an undertaking (such as trying to get some rest after a bout of 'over-working', or some 'solitude' in order to write a book, etc.), and this undertaking refers to possibilities and needs appropriate to my pr�fession and milieu. From this point of view, my presence at the window is a passive activity (I want 'a breath of fresh air' or I find the landscape 'restful', etc.) and my present perception functions as a means in a complex process which expresses the whole of my life. Hence my initial relation to the two workers is negative: I do not belong to their class, I do not know their trades, I would not know how to do what they + +are doing, and I do not share their worries. + +But these negations have a double character. In the first place, they can be perceived only against an undifferentiated background consisting of the synthetic relations which support me together with them in an actual immanence: I could not contrast their ends with mine without recognising them as ends. The basis of comprehension is complicity in principle with any undertaking, even if one then goes on to combat or condemn it. Any new end, once determined, is set against the organic unity of all human ends. In certain pathological states (e.g. 'de-personalisation') man appears as the representative of an alien species because he is no longer seen in his teleological reality, that is, because the link between the patient and his own ends is temporarily broken. To anyone who believes himself to be an angel, the activities of other people will seem absurd, because he tries to transcend the + +human undertaking by having nothing to do with it. + +But it would be a mistake to suppose that my perception reveals me to myself as a man confronted by two other men: the concept of man is an abstraction which never occurs in concrete intuition. It is in fact as a 'holiday-maker', confronting a gardener and road-mender, that I come to conceive myself; and in making myself what I am I discover them as they make themselves, that is, as their work produces them; but to the extent that I cannot see them as ants (as the aesthete does) or as robots (as the neurotic does), and to the extent that I have to project myself through them before their ends, in order to differentiate their ends from mine, I realise myself as a member of a particular society which determines everyone's opportunities and aims; and beyond their present activity, I rediscover their life itself, the relation between needs and wages, and, further still, social divisions and class struggles. In this w�y, the affective quality of my perception depends both on my social and political attitude and on contemporary events (strikes, threats of civil or foreign war, occupation of the country by enemy + +troops or a more or less illusory 'social truce'). + +Secondly, every negation is a relation of interiority. By this I mean that the reality of the Other affects me in the depths of my being to the extent that it is not my reality. My perception provides me first with a multiplicity of tools and apparatuses, produced by the labour of Others (the wall, the road, the garden, the fields, etc.) and it unifies them according both to their objective meaning and to my own proj ect. Every thing maintains with all its inertia the particular unity which a long forgotten action imposed upon it; things in general are indifferent to the living, but ideal act of unification which I perform in perception. + +the Other does not see, of exposing the object through a special kind of work, establishes a relation of reciprocity in my perceptual field which transcends my perception: each of them constitutes the ignorance of the Other. Of course these mutual ignorances would not come into objective existence without me: the very notion of ignorance presupposes a questioning or knowing third party; otherwise it could be neither experienced nor described; the only real relation would be contiguity, or co-existence in exteriority. But my perception makes me a real and objective mediation between these two molecules : if I can, in effect, constitute them in a reciprocity of ignorance, it is because their activities jointly affect me and because my perception defines my limits by revealing the duality of my internal negations. Even my subjectivity is objectively designated by them as Other (another class, another profession, etc.), and in interiorising this designation, I become the objective milieu in which these two people realise their mutual + +dependence outside me. + +It is important not to reduce this mediation to a subjective impression : we should not say that for me the two labourers are ignorant of one another. They are ignorant of one another through me to the extent that I become what I am through them. In the same way, each enters into the environment of the Other as an implicit reality; each sees and touches what the other would see and touch in his place, but each reveals the world through a particular practice which regulates this process. Thus, by limiting me, each constitutes the limit of the Other, and deprives him, as he deprives me, of an objective aspect of the world. But this mutual theft is nothing like the haemorrhage they make in my own perception: they are both manual workers, and they are both from the country; they differ from each other less than they differ from me and, in the last analysis, their reciprocal negation is, for me, a kind of + +deep complicity; A complicity against me. + +In fact, in the moment of discovering either of them, the project of each displays the world, as the objective envelope of his work and his ends : and this spherical unveiling returns to him so as to situate him in relation to what lies behind him as much as to what lies in front of him, in relation both to what he sees and to what he does not see. The objective and the subjective are indistinguishable; the worker produces himself through his work as a certain exposure of the world which objectively makes him the product of his own product. Thus each of them, as the objectification of selfin the world, reaffirms the unity of the world by inscribing himself in it through his work and through the + +particular unifications which this work brings about; thus each of them can discover the Other, as an object actually present in the universe, within his own situation. And - as these possibilities can be objectively seen from my window, as my mediation suffices to uncover the real routes which might bring them closer - separation, ignorance, and simple juxtaposition in exteriority appear as mere accidents concealing the fundamental, immediate and permanent possibility of mutual dis- + +covery, and, therefore, the existence of a human relation. + +At this fundamental level, I myself am picked out and put in question. Three objective possibilities are given in my perception: the first is to establish a human relation with one or the other; the second is to become a practical mediation enabling them to communicate with one another, or, in other words, to be revealed by them as the objective milieu which I already am; the third is to play a passive part in their meeting and to observe them constituting a closed totality from which I am excluded. In the third case, I am directly inyolyed in the exclusion and it forces a practical choice on me: either I submit to it or I adopt it and co-operate with it (for example, I close the window and go back to my work) or I myself enter in to collaboration with them. But in this way I change them in changing myself.9 However, whichever choice I make each of the two men, in his ignorance of the Other - an ignorance which becomes real through me10 - will interiorise in his behaviour what was an exteriority of indifference, even if they never meet. The hidden existence of a human relation relegates physical and social objects, or the world of inertia, to the level of inessential reality. This permanent inessentiality exists as a passive possibility: either simple recognition abolishes distance, or work projects onto matter the in- + +animate movement of convergence. + +In short, the organisation of the practical field in the world determines a real relation for everyone, but one which can only be defined by the experience of all the individuals who figure in this field. This comes down to unification through praxis; and everyone, unifying to the extent that his acts determine a dialectical field, is unified within this field by the unification of the Other, that is to say, in accordance with the plurality of unifications. The reciprocity of relations - which we will + +9. See below, section 3· + +10. When I count on it, it becomes a reality. If a military leader uses the enemy's ignorance to destroy two units which do not know their relative posi- + +tions, this ignorance becomes lack of co-ordination, incompetence, etc. + +examine in detail later - is a new moment of the contradiction between the unifying unity of praxis and the exteriorising plurality of human organisms. This relation becomes inverted in that the exteriority of multiplicity is a condition of the synthetic unification of the field. But multiplicity also remains a factor of exteriority since, within this multiplicity of totalising centralisations, each eluding the Other, the only true bond is negation (at least as the moment we have now reached). Each centre stands in relation to the Other as a point of flight, as an other unification. This is a negation of interiority, but not a totalising negation. Everyone is not the Other in an active, synthetic manner, since not to be someone is in this case to make him serve, in a more or less differentiated way, as an object - an instrument or a conflicting purpose - in the very activity which grasps the unity of the practical field, since it is both to constitute this unity against him (in so far as he is himself constituent) and to deprive him of an aspect of things. The plurality of doubly negated centres at the level of practical unification becomes a plurality of dialectical movements, but this plurality of exteriority is interiorised in that it characterises every dialectical process in interiority, simply because a dialectical development can be recognised from the inside only by characteristics which are dialectical + +(that is, synthetically organised within the whole). + +Thus, this new stage of the investigation reveals the human relation within pure exteriority in so far as objective exteriority turns out to be lived and transcended in the interiority of my praxis, and to indicate an elsewhere which escapes me and escapes all totalisation because it is itself a developing totalisation. Conversely, one might say that I find that this negative rudiment of the human relation is an objective and constituent interiority for everyone in so far as I find myself in the subjective moment of praxis to be objectively characterised by this interiority. In this elementary sense, the individual's movement from the subjective to the objective no longer involves knowing his being from the point of view of matter as it used to do; it now involves realising his human objectiyity as the unity of all the negations which connect it internally to the interior of others, and of his project as the positive unification of these negations. It is impossible to exist amongst men without their becoming objects both for me and for them through me, without my being an object for them, and without my subjectivity getting its objective reality through them as the interiorisation of my + +human objectivity. + +perpetual determination of everyone by the Other and by all is neither an a priori communication engineered by a kind of Great Telephone Operator, nor the indefinite reiteration of essentially separate patterns of behaviour. This synthetic connection, arising always for particular individuals at a definite moment of History and on the basis of determinate relations of production, but which also turns out to be a priori, is simply praxis, that is, the dialectic as the development of living action in everyone in so far as it is pluralised by the multiplicity of men within a single material {one. Every existent integrates the other into the developing totalisation and thereby, even if he never sees him, and in spite of barriers, obstacles and distances, defines himself in relation to the actual totalisation which the Other is perform- + +ing. + +But it should be noted that the relation revealed itself through the mediation of a third party. It is through me that ignorance became reciprocal. And yet this reciprocity no sooner came into being than it repulsed me; as we saw, it closed in upon itself. If the triad is necessary in the extreme case of a relation stranded in the universe, and actually linking two individuals who are ignorant of each other, it is broken up by the exclusion of the third party as soon as people or groups either help one another or fight one another deliberately and self-consciously. The human mediator cannot help transforming the elementary relation whose essence is to be Jived with no other mediation than matter into something else. (The meaning of this metamorphosis will become clear later.) But this is not all. Even when men are face to face, the reciprocity of their relation is actualised through the mediation of this + +third party and at once closes itself off from it. + +Following Mauss, Levi-Strauss has shown that potlatch is 'supraeconomic' in character: 'The best proof ... is that ... greater prestige results from the destruction of wealth than from its distribution, because however liberal it may be, distribution always requires a similar return.'ll And it cannot be denied that in this case the gift has + +1 I. The Elementary Structures of Kinship, (1 949), London and Boston, 1969, p. 55. Levi-Strauss emphasises, of course, the fact that its economic aspect persists, 'although it is always limited and qualified by the other aspects of the institution of exchange'. By way of objection, one might refer to some interesting observations made by Georges Bataille (La Part maudite) to the effect that, in certain societies and in certain conditions, extravagance (which is tightly bound up with other institutions of a political-religious character) is an economic function. Economics as the science of the production, distribution and consump- + +a basic quality of reciprocity. But it should be noted that in its destructive form the gift is not so much an elementary form of exchange as a mortgage of the one for the other: the period of time which separates the two ceremonies, even if reduced to a minimum, masks their reversibility; in effect, the first donor issues a challenge to the second. Mauss has emphasised the ambiguous character of potlatch being an act both of friendship and of aggression. In effect, in its simplest form, the act of giving is a material sacrifice whose object is to put the absolute Other under an obligation. When, in the course of a migration, members of a tribal group come across a strange tribe, they suddenly discover man as an alien species, that is, as a fierce carnivorous beast who can lay ambushes and make tools.12 This terrified discovery of alterity necessarily implies recognition: human praxis confronts them as a hostile force. But this recognition is crushed by the quality of strangeness which it itself produces and supports. And the gift, as a propitiatory sacrifice, is offered both to a god whose anger is being appeased, and to a beast which is tamed by being fed. It is the material object which, by its mediation, sets reciprocity free. But it is not experienced as such: whoever receives a gift, provided he agrees to receive it, conceives the gift both as proof of non-hostility and as an obligation on himself to treat the newcomers as guests; the threshold is crossed, + +that is all. + +The importance of temporality cannot be overemphasised: the gift is and is not an exchange; or, to put it another way, it is exchange experienced as irreversibility. So that its temporal character can be dissolved in absolute reciprocity, it must be institutionalised, that is to say, apprehended and located through an objective totalisation oflived time. Duration then appears as a material object, as a mediation between two acts which determine one another in their interiority; it may be defined + +tion of goods in a context of scarcity ought to pay attention to gratuitous expendi- + +ture in consumption societies. + +12. Cf. Levi-Strauss's excellent descriptions of the relation between strangers who are forced to share the same restaurant table or the same railway compartment in our society (p. 59). 'A conflict exists ... between the norm of privacy and the fact of community.' See also his description of the former markets of the Chukchee. 'Everyone came armed, and the products were offered on spear points. Sometimes a bundle of skins was held in one hand and a bared knife in the other so that one was ready for battle at the slightest provocation. The market was also formerly designated by the one word, Elpu'rIrkln "to exchange", + +by reference to tradition or law, so that the homogeneity of instants conceals the heterogeneity of succession. But institutions, such as marriage between cross-cousins, are themselves manifested against the background of the 'dualistic organisation' of which Levi-Strauss has given such a striking description, and whose origin lies in a reaction against the pluralisation of primitive groups. Migratory movements 'have introduced allogenic elements', the absence of central power has encouraged 'fissions', etc. Thus a dualistic ordering is 'superimposed' on a plurality of clans and 'sections' and functions as a 'regulating principle'. The Mekeo of New Guinea themselves say that the 'apparent confusion of their groups' actually conceals a dualistic order based on reciprocal tributes. This is because reciprocity as a relation within the totality can be conceived only from the point of view of totality, that is, by each group in so far as it can claim to be integrated with all the others. The whole precedes the parts, in this case, not as a static substance but as a turning totalisation. We shall come back to this point later. But what has emerged clearly here is that duality, both as a general rule and in each particular case, is released by a sort of commutative trinity which presupposes plurality: it is only the third party in fact who can, through his mediation, show the equiyalence of the goods exchanged and consequently of the successive acts. For this exterior third party, the use-value of the goods exchanged is clearly transformed into exchange-value. Thus to precisely the extent that he is not an agent in the operation, he negatively determines the potlatch, and, for those who do it, he illuminates their reciprocal recognition. And here, whatever the society, the third party is everyone and everybody; thus reciprocity is lived by everyone as diff use ohjectiye possibility. But as soon as it is actualised, or rather unmasked, it closes in upon itself. The dualistic ordering is based on the ever turning totalisation and + +negates this totalisation as soon as it is established.I3 + +Similarly, reciprocity becomes isolated as a human relation between individuals; it presents itself as the fundamental, concrete lived bond. If I try to locate myself in the social world, I discover around me various ternary or binary formations, the first of which are constantly disintegrating and the second of which arise from a turning totalisation and may at any moment integrate themselves into a trinity. Thus it is inconceivable that a temporal process should begin with a dyad + +13. As we shall see, it will lay claim to it again at a later moment of its develop- + +treat the human person, in myself and in the Other, as an absolute end; nor on a purely contemplative intuition revealing 'Humanity' to everyone as the essence of his fellows. It is the individual's praxis, as the realisation of his project, which determines his bonds of reci- + +procity with everyone. + +And the quality of being a man does not exist as such: this particular gardener recognises in this particular road-mender a concrete project, which is expressed in his behaviour and which others have already recognised by the very task which they have set him. Thus everyone recognises the Other on the basis of a social recognition to which his clothes, his tools, etc., passively bear witness. From this point of view, the mere act of speaking, the simplest gesture, and the elementary structure of perception (which, moving from future to present, from totality to particular moments, discloses the behaviour of the Other) imply mutual recognition. And capitalist exploitation and oppression are no counterexample to this. The swindle of capitalist exploitation is based on a contract. And though this contract necessarily transforms labour, or praxis, into an inert commodity, it is, formally, a reciprocal relation; it is a free exchange between two men who recognise eaclz other in their freedom; it is just that one of them pretends not to notice that the Other is forced by the constraint of needs to sell himself as a material object. The clear conscience of the employer is based entirely on that moment of exchange in which the wage-labourer appears to offer his labour-power in complete freedom. And if he is not free in relation to his poverty, he is juridically free in relation to his employer, since, at least in theory, the employer does not put any pressure on the workers when he hires them, and merely fixes a top rate and turns away those who ask for more. Here, once again, competition and antagonism between workers moderate their demands; the employer himself has nothing to do with it. This example shows clearly enough that man becomes a thing for the Other and for himself only to the extent that he is initially posited as human freedom by praxis itself. Absolute respect for the freedom of the propertyless is the best way of leaving him at the mercy of material constraints, at the moment of the contract. As for oppression, it consists, rather, in treating the Other as an animal. The Southerners, in the name of their respect for animality, condemned the northern industrialists who treated the workers as material; but in fact it is animals, not 'material', which are forced to work by breaking-in, blows and threats. However, the slave acquires his animality, through the master, only after his humanity has been + +recognised. Thus American plantation owners in the seventeenth century refused to raise black children in the Christian faith, so as to keep the right to treat them as sub-human, which was an implicit recognition that they were already men: they evidently differed from their masters only in lacking a religious faith, and the care their masters took to keep it from them was a recognition of their capacity to acquire it. In fact, the most insulting command must be addressed by one man to another; the master must have faith in man in the person of his slaves. This is the contradiction of racism, colonialism and all forms of tyranny: in order to treat a man like a dog, one must first recognise him as a man. The concealed discomfort of the master is that he always has to consider the human reality of his slaves (whether through his reliance on their skill and their synthetic understanding of situations, or through his precautions against the permanent possibility of revolt or escape), while at the same time refusing them the economi c and political status which, in this period, defines human beings. + +Thus reciprocity, though completely opposed to alienation and reification, does not save men from them. As we shall see later, a dialectical process produces these inhuman relations out of their opposite. Reciprocal ternary relations are the basis of all relations between men, whatever form they may subsequently take. Though reciprocity is often concealed by the relations which are established and supported by it (and which may, for example, be oppressive, reified, etc.), it becomes evident whenever it manifests itself that each of the two terms is modified in its very existence by the existence of the Other. In other words, men are bound together by relations of interiority. It might be objected that this reciprocal relation is unintelligible: for we have tried to show that the intelligibility of the synthetic bond either manifests itself in the process of a totalising praxis, or remains congealed in an inert totality. But in this case there is neither totality nor totalisation, and these relations manifest themselves as plurality within exteriority. The primary answer to this objection is that, while we are at this stage of the investigation, we are not dealing with one dialectic, but with the external relation between several, a relation which must be Datil dialectical and external. In other words, the relation of reciprocity and the ternary relation are neither of them totalising: they are multiple adhesions between men which keep a 'society' in a colloid state. Besides, in order to gain comprehension, we must - in this as in every other case - make use of the totality of the moments of the investigation which have already been established. It + +is true that the dialectical materiality of everyone is not sufficient to account for a reciprocity; the least that is necessary is a quasi-totality. And this quasi-totality, as we know, exists in the form of worked matter in so far as it mediates between men; it is on the basis of this negative inert unity that reciprocity arises. This means that it always arises on an inert foundation of institutions and instruments by which + +everyone is already defined and alienated. + +We must not suppose that we have entered the kingdom of ends and that, in reciprocity, everyone recognises and treats the Other as an absolute end. This would be formally possible only in so far as everyone treated himself, or treated the human person in himself, as an unconditioned end. Indeed this hypothesis would throw us back into absolute idealism: only an idea amongst other ideas can posit itself as its own end. But man is a material being set in a material world; he wants to change the world which crushes him, that is, to act on the world of materiality through the mediation of matter and hence to change himself. His constant search is for a different arrangement of the universe, and a different statute for man; and in terms of this new order he is able to define himself as the Other whom he will become. Thus he constantly makes himself the instrument, the means, of this future statute which will realise him as other; and it is impossible for him to treat his own present as an end. In other words, man as the future of man is the regulative schema of every undertaking, but the end is always a remoulding of the material order which by itself will make man + +possible. + +Or, to approach the question from a different angle, Hegel's mistake was his belief that within everyone there is something to objectify and that work reflects the individuality of its author. In fact, however, objectification as such is not the goal, but the consequence attached to the goal. The aim is the production of a commodity, an object of consumption, or a tool, or the creation of a work of art. And it is through this production, this creation, that man creates himself, or in other words detaches himself gradually from things as he inscribes his work in them. Consequently, in so far as my project is a transcendence of the present towards the future, and of myself towards the world, I always treat myself as a means and cannot treat the Other as an end. Reciprocity implies, first, that the Other is a means to the extent that I myself am a means, that is to say, that the Other is the means of a transcendent end and not my means; second, that I recognise the Other as praxis, that is to say, as a developing totalisation, at the same time as + +integrating him as an object into my totalising project; third, that I recognise his movement towards his own ends in the same movement by which I project myself towards mine; and fourth, that I discover myself as an object and instrument of his ends through the same act + +which constitutes him an objective instrument of my ends. + +In this way, reciprocity can be either positive or negative. In the first case, everyone may make himself a means within the project of the other so that he becomes a means within his own project; and in this case the two transcendent aims remain separate. This is what happens with exchange or the provision of services. Alternatively, the end may be shared (a collective undertaking or work), everyone making himself the Other's means in order that their collective effort shall realise their single transcendent aim. In the case of negative reciprocity, the four necessary conditions are fulfilled but on the basis of a reciprocal refusal : each refuses to serve the Other's end and, while recognising his own obj ective being as a means within the adversary's project, he uses his own instrumentality in others to make them an instrument of his own ends in spite of themselves. This is struggle; in it, everyone reduces himselfto his materiality so as to act on that of the Other; through pretences, stratagems, frauds and manoeuvres everyone allows himself to be constituted by the Other as a false ohject, a deceptive means. But here again it would be quite wrong to think that the aim is the annihilation of the adversary or, to use Hegel's idealist language, that each consciousness seeks the death of the Other. The origin of struggle always lies, in fact, in some concrete antagonism whose material condition is scarcity (la rared),14 in a particular form, and the real aim is objective conquest or even creation, in relation to which the destruction of the adversary is only the means. Hatred - a form of recognition - even if it is posited for itself, is really only a mobilisation of all one's strength and passions in the service of an aim which requires such total commitment. Hegel, in other words, ignored matter as a mediation between individuals. Even if one uses his terminology, one has to say that while each consciousness is the counterpart of the Other, this reciprocity can take an infinity of different forms, positive or negative, and that it is the mediation of matter which deter- + +mines these forms in every concrete case. + +But this relation, which comes to all from each in so far as he makes himself a man amongst them, contains a contradiction: it is a totalisation + +rhythm as precisely as possible, the common rhythm, in the light of the objective end, appears as the living unity which animates the two workers. Thus the movement of objectivity is inverted: what the timekeeper initially sees as the meaning and unity of his own project, is the aim which he pursues. He has to measure speeds; and through this relation which is definitive of his praxis, he grasps the end which is imposed upon the workers in its full objectivity; for it is not the same as his own end though it is intimately linked with it. As the end of Others it is the essential means for him to do his job. The objective and subjective connection between his own end and that of others makes him see the rhythm as his object and the workers as the means of maintaining or increasing its speed. Reciprocity as the real bond of a double heterogeneity is relegated to another level; this interiority without a centre, this intimacy lived in separation, is abruptly dislocated and torn apart so as to become a single praxis whose end lies outside itself. This end which belongs to Others, reveals itself as their end and as his means and is presented to the witness in its objective totality. And as it discloses its content, which refers back to the activity of the whole factory and to the entire social system, it reveals itself as a structure of control set up from outside by technicians in accordance with the requirements of production. It is this disclosure which defines the relation of the timekeeper to the two workers and to his superiors, or in other words, which designates his objective being in his very subjectivity: he is the one through whom the end is posited as a structure of transcendence in relation to the workers. Thus he reveals it as an autonomous object. But this structure of control refers, in its very objectivity, to the subjectivity of those whom it controls: this goal has to he achieved, it imposes itself on them as a common imperative. This imperious goal, though entirely present in the objective field, cannot be grasped by the witness; it closes in on the two subjectivities which it equalises and shows them its inner surface - which the timekeeper has to see as pure meaning, as a dimension of flight at the heart of plenitude. Objectively, the totality includes the two simultaneous actions; it defines and limits them at the same time as enveloping them, and so masking them from direct perception. It is a structure of the world, which exists through itself; it is expressed and sustained by a double praxis, but only in so far as this is subjected to the pre-established imperative which conditions it. Objectively, and through the third party, the independence of the end turns reciprocity into a binding together of movement, and mutual adaptation into the internal self-determination + +of praxis; it transforms a double action into a single event which controls the two workers as secondary structures whose particular relations depend on overall relations and who communicate through the mediation of the whole. This living totality, comprising men, their objects and the material on which they work, is both an event as a temporalisation of the objective imperative and - though this amounts to the same thing - the regressive disclosure of the end (from the future + +to the present) as the concrete unity of the event. + +Subjectivities are enveloped within this moving totality as necessary but elusive significations; but they define themselves as a common relation to a transcendent end rather than as each apprehending its own ends in a reciprocity of separations. Thus these significations, in their objective meaning, become homogeneous, and come together and merge into one another in their recognition of the transcendent imperative. Thus this imperative is expressed, through the mediation of the Other, as essential, and subjectivity becomes its inessential means of making itself felt as imperative. In this way, subjectivity is merely the internal milieu which mediates the imperative as the interiorisation of control; in this milieu the individual appears as an a posteriori and arbitrary determination of the subjective substance. As in wave mechanics, the principle of individuality is not really applicable. Whatever their external differences, individuals are defined on the basis of the end as a complete interiorisation of the entire imperative, and therefore by the + +presence in them of the whole of subjectivity. + +Here the social group appears reduced to its simplest expression. It is the objective totality in so far as it defines its subjectivity simply by interiorisation of values and objective ends and, within a given undertaking, controls real individuals as simple interchangeable modes of subjective praxis. Through the intervention of third parties, the subjectivity of the group is shown to be indivisible, and circulates freely within the object as milieu, substance and pneuma; it expresses itself in self-temporalising objectivity as intersubjective reality. And intersubjectivity expresses itself in the most fortuitous and temporary groupings; for a taxi-driver looking at some people staring into a river, they are united by one and the same curiosity. And their active curiosity (they push one another, lean over, and stand on tiptoe) shows the existence of a transcendent, but invisible end: there is something that has to be looked at. The mediation of the third party reanimates the objective significations, already inscribed in things, which constitute the group as a totality. These crystallised significations already represent + +the anonymous praxis of the Other and produce, in matter, a solidified revelation. In awakening them the third party makes himself a mediator between objective thought as Other and concrete individuals; through + +him a rigid universality constitutes them by its own activity. + +Thus duality is unified from outside through the praxis of the third party; and we shall see in a moment how the members of a group interiorise it. At present it is still a transformation which transcends him. True, the relation of the third party to the dyad is one of interiority in that he modifies himself in modifying it. But this relation is not reciprocal: in transcending the dyad towards his own ends, the third party shows it to be an object-unity, that is a material unity. Of course, the relation of the integrated terms is neither external nor molecular, but, in so far as each of them excludes the Other through their actual recognition, or in so far as this relation can only link but not unify, unity is imprinted from outside and, in the first moment, passively received. The dyad becomes a team not by producing its totality, but, initially, + +by being subjected to it as a determination of being. + +It will no doubt have been noticed that this Trinity seems like an embryonic hierarchy: the third party as mediator is a synthetic power and the bond between him and the dyad is unreciprocal. It will therefore be asked what this spontaneous hierarchy is based on, given that we are considering it in the abstract, as a synthetic bond, without examining the historical circumstances in which it arises. The answer to this question is provided by two points, and these will enable us to make further progress in our regressive investigation. First, if there is no reciprocity between the dyad and the third party, this is because of the very structure of the third party relation; but this does not generate any a priori hierarchy since any member of the Trinity might become the third party in relation to the Other two. Only the conjuncture (and therefore History in its entirety) can determine whether this changing relation shall be commutative (each member becoming the third party in turn, like in children's games where everyone takes turns at being the general or the bandit chief) or whether it is to be fixed in the form of a primitive hierarchy. It is already fairly obvious, in fact, that the problem will become infinitely complex since social reality compri ses an indefinite multiplicity of third parties (because the relation changes even if the number of individuals is finite) and an indefinite multiplicity of reciprocities; and also because individuals can constitute themselves as group third parties, and there can be reciprocities of reciprocities, and reciprocities of groups; finally, individuals or groups + +can be engaged in reciprocal actions even while defining themselves as + +third parties. + +At present we are not equipped to th.ink these moving, indefinite relations in their intelligibility, for we have not yet mastered all our instruments. But it is worth recalling, to conclude, that the human relation really exists between all men and that it is no more than the relation of praxis to itself. The only origin of the complication which gives birth to these new relations is plurality, that is, the multiplicity of actiYe organisms. So, quite apart from any question of antagonism, every praxis both affirms and negates the other, in so far as it transcends it as its object, and also causes itself to be transcended by it. And every praxis, as a radical unification of the practical field, adumbrates, in its relation to all others, the project of unifying them all by eliminating the negation of plurality. This plurality is none other than the inorganic dispersal of organisms; and given that this plurality always arises within an existing society, it is in fact never wholly natural and, as we have seen, is always expressed in techniques and social institutions - which transform it to the extent that it occurs within them. But, although natural dispersal cannot be any more than the abstract sense of real, social dispersal, it is always the case that, within a given society, the negative element of mechanical exteriority always conditions that peculiar relation of reciprocity which negates not only plurality, through the adhesion of activities, but also unity, by a plurality of recognitions, and also the relation of a third party to a dyad, which defines itself as exteriority within pure interiority. Moreover, the designation of a third party as the actualisation in a given individual of this universal relation always occurs, as we have seen, in a given practical situation and under the pressure of material circumstances. Thus our investigation is reversed: starting from the isolated worker, we showed individual praxis to be the complete intelligibility of dialectical movement; but, moving on from this abstract moment, we have found that the first relation between men is the indefinite adherence of each to each; and these formal conditions for all History are immediately seen to be conditioned by inorganic materiality, both as the fundamental condition determining the content of human relations, and as an external plurality within the commutative reciprocity and within the Trinity. It can also be seen that this commutativity, though by degrees it unites each to all, is in itself incapable of realising totalisation as the movement of History, since the jelly-like substance which constitutes human relations involves the infinite interiorisation of + +bonds of dispersive exteriority, rather than their elimination or totalising transcendence. No doubt it does transcend them, but only because the discrete multiplicity of organisms happens to be engaged in a kind of dance with an unlimited, circulating multiplicity of epicentres. This ambiguity accounts well enough for our private relations with friends, companions, casual customers or chance acquaintances, and even with colleagues (in an office, or a factory) in so far as they are both the living milieu which unites us to everyone and the mechanical indifference which separates them from us when work is over. But this ambiguity cannot explain the structured relations which at all levels produce active groups, classes, and nations, any more than it can explain institutions or the complex ensembles known as societies. The reversal of the investigation takes place through historical materialism: if totalisation is a historical process, it comes to men through matter. In other words, praxis as the free development of the organism has now totalised the material environment in the form of a practical field; and in a moment we shall see the material milieu as the first totalisation + +of human relations. + +3 + +Matter as Totalised Totality + +- A First Encounter + +with Necessity + +IScarcity and Mode of Production + +Pure, non-human inorganic matter - that is, not matter in itself but matter from the point of view of the praxis in which it is the object of scientific experiment - is governed by laws of exteriority. If it is true that matter effects an initial union between men, this can only be so to the extent that man has already made a practical attempt to unify it, and that it has passively received the seal of that unity. In other words, a passive synthesis whose unity conceals a molecular dispersal conditions the totalisation of organisms whose deep bonds of interiority cannot be masked by their dispersal. This synthesis, therefore, represents the material condition of historicity. At the same time, it is what might be called the passive motor of History. Human history - an orientation towards the future and a totalising preservation of the past - is in fact also defined in the present by the fact that something is happening to + +men. + +As we shall see later, the inert totality of worked matter, which, functioning as an inert universal memory, records and conserves the forms impressed on it by earlier labour, is the only factor in any given social field which allows every particular historical situation to be transcended by the total process of History. In addition, as a kind of material synthetic judgement, it makes possible the continuous enrichment of historical events. But since inorganic materiality which has received the imprint of praxis appears as a passiye unity (unite subie), and since the unity of interiority which belongs to the dialectical moments of action returns into itself and can only be preserved through exteriority (that is to say, to the extent that there is no external force to destroy + +it), it is necessary, as we shall soon see, that human history should be lived, at this level of the investigation, as non-human history. This does not mean that historical events are going to appear to us as an arbitrary succession of irrational facts; on the contrary, it means that they are going to assume the totalising unity of a negation of man. History, at this level, has a fearful and depressing meaning: it appears as though what unites men is an inert demonic negation, taking away their substance, that is to say, their labour, and turning it against all men in the form of active inertia and totalisation by extermination. We shall see that this peculiar relation, together with the initial alienation which results from it, will produce its own dialectical intelligibility, as soon as the relation of a multiplicity of individuals to the practical field which surrounds them is investigated, in so far as this relation is for everyone a univocal relation of interiority, and as soon as it is linked dialectically + +to the reciprocal relations which unite them. + +At the same time, it is worth pointing out that this univocal relation of surrounding materiality to individuals is expressed in our History in a particular and contingent form since the whole of human development, at least up to now, has been a bitter struggle against scarcity. Thus at every level the basis of the passive actions of worked and socialised materiality will turn out to be the original structure of scarcity as a primary unity transmitted to matter through men and returning to men through matter. But we should not be disturbed by the fact that the relation of scarcity is contingent. It is indeed logically possible to conceive of other organisms on other planets having a relation to their environment other than scarcity. (However we are completely incapable of simply imagining such a relation, and supposing that there is life on other planets, it is most likely that it too would suffer from scarcity.) Above all, although scarcity is universal, at a given historical moment it may vary from one region to another. (And while some of the causes of these variations, such as over-population or underdevelopment, are historical, and are therefore fully intelligible within History itself, others, such as climate, or the richness of the sub-soil, given a certain level of technical development, condition History + +through social structures without being conditioned by it.) + +The fact is that after thousands of years of History, three quarters of the world's population are undernourished. Thus, in spite of its contingency, scarcity is a very basic human relation, both to Nature and to men. In this sense, scarcity must be seen as that which makes us into these particular individuals producing this particular History and + +defining ourselves as men. It is perfectly possible to conceive of a dialectical praxis, or even of labour, without scarcity. In fact, there is no reason why the products required by the organism should not be practically inexhaustible, while a practical operation was still necessary in order to extract them from the earth. In that case, the inversion of the unity of human multiplicities through the counter-finalities of matter would still necessarily subsist. For this unity is linked to labour as to the original dialectic. But what would disappear is our quality as men, and since this quality is historical, the actual specificity of our History would disappear too. So today everyone must recognise this basic contingency as the necessity which, working both through thousands of years and also, quite directly, through the present, + +forces him to be exactly what he is. + +In the progressive moment of our investigation, we shall study the problem of the contingency of History; and we shall see that the problem is particularly important from the point of view of a future for man. In the case which we are considering, scarcity appears to grow less and less contingent in that we ourselves produce new forms of it as the milieu of our life, On the basis of an original contingency - which shows, one might say, both the necessity of our contingency and the contingency of our necessity. Nevertheless, an attempted critique must distinguish between this determinate relation and the general relation, independent of historical determination, between dialectical, multiple praxis and materiality. However, since scarcity is a determination of this general relation and the latter is manifested to us only through the former, it will be safest to discuss scarcity first and then to let the universal relations between the dialectic and the inert emerge later. + +Our description of the relation of scarcity will be brief, because there is nothing new to say about it. In particular, historical materialism, as the interpretation of our History, has provided the necessary explanations here. But what has never been attempted is a study of the type of passive action which materiality as such exerts on man and his History in returning a stolen praxis to man in the form of a counterfinality. The point must be emphasised: History is more complex than some kinds of simplistic Marxism suppose; man has to struggle not only against nature, and against the social environment which has produced him, and against other men, but also against his own action as it becomes other. This primitive type of alienation occurs within other forms of alienation, but it is independent of them, and, in fact, is their foundation. In other words, we shall reveal, through it, that a + +permanent anti-praxis is a new and necessary moment of praxis. If we do not try to define this moment, historical intelligibility - that is, certainty within the complexity of temporal development - loses one of its essential moments and is transformed into unintelligibility. + +(i) Scarcity and History + +Scarcity is a fundamental relation of our History and a contingent + +determination of our univocal relation to materiality. + +Scarcity, as the lived relation of a practical multiplicity to surrounding materiality within that multiplicity itself, is the basis of the possibility of human history. But this calls for two explicit qualifications. First, for a historian situated in 1957, scarcity is not the basis of the possibility of all History. We have no way of telling whether, for different organisms on other planets - or for our descendants, if technical and social changes shatter the framework of scarcity - a different History, constituted on another basis, and with different motive forces and different internal projects, might be logically conceivable. (By this I do not simply mean that we cannot tell whether the relation of organic beings to inorganic (inorganises) ones might somewhere be something other than scarcity; first and foremost, I mean that it is impossible to know a priori whether the temporalisation of such beings would take the form of a history.) But to say that our History is a history of men is equivalent to saying that it is born and developed within the permanent framework of a field of tension produced by + +scarcity. + +The second qualification is this. Scarcity is the basis of the possibility of human history, but not of its reality. In other words, it makes History possible, but other factors (yet to be determined) are necessary if History is to be produced. The reason for this restriction is that there are some backward societies which, in a sense, are more prone than others to famine or to seasonal depressions of food resources, but which are, nevertheless, correctly classified by ethnographers as societies with no history, societies based on repetition.16 This means + +J6. In fact, as we shall see, they have begun to interiorise our History, because they have been subjected to colonialism as a historical event. What historialises + +them, however, is not a reaction to their own scarcity. + +that scarcity can exist on a very large scale. If a state of equilibrium is established within a given mode of production, and preserved from one generation to the next, it is preserved as exis - that is to say, both as a physiological and social determination of human organisms and as a practical project of keeping institutions and physical corporate development at the same level. This corresponds ideologically to a decision about human 'nature'. Man is a stunted misshapen being, hardened to suffering, and he lives in order to work from dawn till dusk with these (primitive) technical means, on a thankless threatening earth. We shall see later that certain scarcities can condition a moment of History, if, in the context of changes of technique (which will themselves have to be explained) , they take the form of abrupt changes in the standard of living. History is born from a sudden imbalance which disrupts all levels of society. Scarcity is the basis of the possibility of human history - and of no more than its possibility - because, through the internal adaptation of organisms, it can, within certain limits, be lived as an equilibrium. From this point of view, there is no logical (dialectical) absurdity in the idea of a country with no History, where human groups would vegetate and never break out of a cycle of repetition, producing their lives with primitive techniques and + +instruments and knowing absolutely nothing of one another. + +Some people, of course, have said that these societies with no History are in fact societies whose History has come to a halt. That is quite plausible, since they do indeed have their techniques, and, however primitive their tools may be, there must have been a temporal process to bring them to this degree of efficiency, by means of social forms which themselves, in connection with this process, are in spite of everything differentiated, so that they, too, refer back to this temporalisation. But this way of presenting matters disguises the a priori desire of some ideologists,!7 idealists as well as Marxists, of basing History on some essential necessity. From this point of view, non-historical societies would in fact be very special moments in which historical development had slowed itself down and stopped, by turning its power + +against itself. + +For the critical position, however, this conception, though pleasing in that it reinstates necessity and unity everywhere, is unacceptable simply because it offers itself as a conception of the world which the facts could neither confirm nor refute. (It is true that many groups + +which here settled into repetition have a legendary history; but this is irrelevant, for legend is a negation of History, its function being to reintroduce the archetype into sacred moments of repetition.) The only conclusion we can draw from the examination of the validity of a dialectic is that scarcity could never be sufficient by itself either to initiate a historical development or, in the course of a development, to burst some log jam which has transformed History into repetition. On the contrary, it is always scarcity, as a real and constant tension both between man and his environment and between man and man, which explains fundamental structures (techniques and institutions) - not in the sense that it is a real force and that it has produced them, but because they were produced in the milieu of scarcity18 by men whose praxis interiorises this scarcity even when they try to transcend it. Scarcity can be seen, in the abstract, as a relation of the individual to the environment. Practically and historically, that is, in so far as we exist in particular situations, the environment is a ready-constituted practical field, which relates everyone to collective structures (we shall explain what this means later). The most fundamental of these structures is scarcity as the negative unity of the multiplicity of men (of this concrete multiplicity). This unity is negative in relation to men because it is transmitted to man by matter in so far as matter is nonhuman (that is to say, in so far as its being human is possible only through struggle on this earth). This means, therefore, that the first totalisation effected by materiality manifests itself (in a given society and between independent social groups) hath as the possibility of universal destruction and as the permanent possibility that this destruction through matter might come to any individual through the praxis of other men. This first aspect of scarcity can condition the unity of the group, in that the group, taken collectively, may organise itself to react collectively. But this dialectical and properly human aspect of praxis cannot possibly be contained within the relation of scarcity itself, precisely because the positive dialectical unity of a common action is the negation of negative unity as surrounding materiality turning on the individuals who have totalised it. In fact, scarcity as tension and as force-field is the expression of a quantitative fact (more or less strictly defined). There will be an insufficient quantity of a + +18. As we shall see, scarcity is a milieu in that it is a unitary relation of a plurality of individuals. In other words, it is an individual relation and a social + +milieu. + +particular natural substance or manufactured product in a particular social field, giyen the number of members of the groups or inhabitants + +of the region. There is not enough for eyeryhody. + +Thus the world (the ensemble) exists for anyone in so far as the consumption of such and such a product elsewhere, by others, deprives him here of the opportunity of getting and consuming something of the same kind. In examining the indefinite and universal relation of indeterminate reciprocity we have noticed that men can be united with each other indirectly through a series of adhesions, without having the slightest ide;;> of the existence of this or that other person. In the milieu of scarcity, however, even if individuals are unaware of each other, even if social stratifications and class structures completely sever reciprocity, everyone within the particular social field still exists and acts in the presence of everyone else. Perhaps this member of this society does not even know how many individuals it contains. He may not know the exact relation of man to natural substances, to instruments and to human products - the relation which strictly defines scarcity. And he may account for present poverty in ways which are completely untrue and absurd. All the same, the other members of the group do exist for him collectiyely, in that each one of them is a threat to his life - in other words, in that the existence of every one of them is the interiorisation and absorption by a human life of the environment as a negation of mankind. But this individual member, if he realises himself, through his need and praxis, as being amongst men, will see everyone in terms of the object of consumption or the manufactured product, and, on this basic level, he will recognise them as the mere possibility of the consumption of something he himself needs. In short, he will find each of them to be the material possibility of his being annihilated through the material annihilation of an object of primary + +necessity. + +Of course, these remarks describe a still very abstract moment of our regressive investigation: in reality, all the social antagonisms in a given society are qualified and structured, and the society itself defines the bounds of scarcity, at least within certain limits, both for each of its constituent groups, and in the fundamental matter of collective scarcity - that is, in terms of an original relation between forces and relations of production. But the important thing for us now is simply to record, in order, the structures of dialectical intelligibility. Now, from this point of view, it is easy to see that the totalisation effected by scarcity is circular. Scarcity is not the absolute impossibility of the human + +organism surviving (although, as I have shown, one might wonder whether this statement would remain true in this form: the radical impossibility of the human organism surviving without labour). But in a given situation, whether it be the raft of the Medusa,19 an Italian city under siege, or a modern society (which, of course, discreetly selects its dead simply by distributing items of expenditure in a particular way, and which, at its deepest foundations, is already in itself a choice of who is well provided for and who is to go hungry), scarcity makes the passive totality uf individuals within a collectivity into an impossibility of co-existence. The group or the nation is defined by its surplus population (ses excedentaires); it has to reduce its number in order to + +survIve. + +This numerical reduction, of course, though always present as a practical necessity, need not take the form of murder. People can simply be allowed to die, as was the case with surplus children under the Ancien Regime. Or birth control can be used, in which case the potential child, as a future consumer, is designated as undesirable. This may be conceived either, as in bourgeois democracies, in terms of the impossibility of continuing to feed its brothers in an individual family, or, in a socialist nation such as China, in terms of the impossibility of maintaining a certain rate of population growth until a certain rate of production growth can be reached. But when there is no question of controlling the birth rate, the negative requirements of materiality take a purely quantitative form: the size of the surplus population can be determined, but not their individual characters. 20 Here we see the full force of commutativity, whose importance will become clearer later, and which marks each member of the group both as a possible survivor and as a dispensable surplus member. And each member is constituted in this way in his objectivity both by himself and by everyone. The direct movement of need affirms him unconditionally as having to survive; this is the practical message of hunger and labour; and a direct challenge to it is inconceivable since it itself expresses man's transcendence of a radical threat by matter. But at the same time the individual's being is put in doubt by everyone, and by the very + +19. Reference to the sinking of the Medusa in 1816. [Ed.] + +20. As I have said before, social institutions will be seen later as a society's stratified inert selection of its dead - though, of course, this is only one aspect of them. But even when this choice is made, even when an oppressed and exploited class has to submit to it, there is still indeterminacy both within the class and at + +the level of individuals. + +human in so far as this same man appears as radically Other - that is to say, as threatening us with death. Or, to put it another way, we have a rough understanding of his ends (for they are the same as ours), and his means (we have the same ones) as well as of the dialectical structures of his acts ; but we understand them as if they belonged to another species, our demonic double. Nothing - not even wild beasts or microbes - could be more terrifying for man than a species which is intelligent, carnivorous and cruel, and which can understand and outwit human intelligence, and whose aim is precisely the destruction of man. This, however, is obviously our own species as perceived in + +others by each of its members in the context of scarcity. + +This, at any rate, is the basic abstract matrix of every reification of human relations in any society. At the same time, it is the first stage of ethics, in so far as this is praxis explaining itself in terms of given circumstances. The first movement of ethics, in this case, is the constimtion of radical evil and of Manichaeism; it values and evaluates the breaking of the reciprocity of immanence by interiorised scarcity (though we cannot go into the production of values here), but only by conceiving it as a product of the praxis of the Other. The anti-human (Ie contre-homme) in fact tries to destroy men by sharing their ends and adopting their means. The break occurs the moment this deceptive reciprocity reveals the deadly danger which it contains, or, in other words, when it reveals that it is impossible for all those bound by reciprocal links to stay on the soil which supports and feeds them. And let us not make the mistake of thinking that this interiorised impossibility characterises individuals subjectiyely; on the contrary, it makes everyone objectiyely dangerous for the Other and makes the concrete existence of each individual endanger that of the Other. Thus man is objectiyely constituted as non-human, and this non-humanity is expressed in praxis by the perception of evil as the structure of the Other. '"{'he somewhat confused clashes, whose origin is highly ambiguous, which take place between nomadic tribes when they happen to encounter one another, have for this reason been interpreted by historians and ethnographers as a challenge to some of the elementary truths of historical materialism. It is certainly true that the economic motive is not always essential, and is even sometimes not to be found at all. These wandering groups have the whole savannah to themselves; they do not trouble one another. But this is not the point. It is not always necessary for scarcity to be explicitly involved; but, in each of these tribes, the man of scarcity encounters, in the other tribe, the man of scarcity in the + +form of the anti-human. All of them are so constituted by their struggle against the physical world and against people (often within their own group) that the appearance of strangers, which presents them both with the bond of interiority and with the bond of absolute exteriority, makes them see man as an alien species. The strength of their aggressiveness and hatred resides in need, and it makes very little difference if this need has just been satisfied: its constant renewal and everyone's anxiety mean that whenever a tribe appears, its members are constituted as famine being brought to the other group in the form of a human praxis. And, when there is a clash, what the adversaries try to destroy in each other is not the simple threat of scarcity, but praxis itself in so far as it is a betrayal of man in favour of the anti- + +human. + +For this reason, I believe that, at the level of need and through it, scarcity is experienced in practice through Manichaean action, and that the ethical takes the form of the destructive imperative: evil must be destroyed. And at this level, too, yiolence must be defined as a structure of human action under the sway of Manichaeism and in a context of scarcity. Violence always presents itself as counter-yiolence, that is to say, as a retaliation against the violence of the Other. But this yiolence of the Other is not an objective reality except in the sense that it exists in all men as the universal motivation of counter-violence; it is nothing but the unbearable fact of broken reciprocity and of the systematic exploitation of man's humanity for the destruction of the human. Counter-violence is exactly the same thing, but as a process of restoration, as a response to a provocation: if I destroy the non-humanity of the anti-human in my adversary, I cannot help destroying the humanity of man in him, and realising his non-humanity in myself. I may try to kill, to torture, to enslave, or simply to mystify, but in any case my aim will be to eliminate alien freedom as a hostile force, a force which can expel me from the practical field and make me into 'a surplus man' condemned to death. In other words, it is undeniable that what I attack is man as man, that is, as the free praxis of an organic being. It is man, and nothing else, that I hate in the enemy, that is, in myself as Other; and it is myself that I try to destroy in him, so as to prevent him + +destroying me in my own body. + +These relations of exteriority in reciprocity, however, are complicated by the development of praxis itself, which re-establishes reciprocity in the negative form of antagonism, as soon as a real struggle develops. In terms of the concrete necessities of strategy and tactics, + +one is bound to lose if one does not recognise the enemy as another human group, capable of inventing traps, and of getting out of them, and of allowing itself to be caught by some of them. Conflicts of scarcity, from nomad wars to strikes, are always oscillating between two poles, one of which turns the conflict into the Manichaean struggle of men against their terrifying counterparts, while the other reduces it to human proportions as a dispute which is being resolved by violence because the possibilities of reconciliation have been exhausted or because mediation has broken down. The important point here is that, as soon as it is constituted as the action of an army, a class, or even of a lesser group, praxis in principle transcends the reifying inertia of the + +relations of scarcity. + +This shows, I think, that the inert morality of Manichaeism and radical evil presupposes a suffered distance, a lived impotence, and, in a way, the discovery of scarcity as destiny - in short, a veritable domination of man by the interiorised material environment. So it is not a permanent structure, in the sense that it must always remain rigid and inert at a given level of human density, but rather a certain moment of human relations, which is constantly being transcended and partially destroyed, but which is always being reborn. In fact, this moment is located midway between the destruction of positive reciprocities by scarcity (to whatever degree of social praxis this destruction goes) and the reappearance, under the sway of scarcity, of negative and antagonistic reciprocities. And this intermediate moment is identical with the first moment and the productive schema of the complex process of reification. In this moment, the individuals belonging to a given social field live in a false relation of reciprocity with the environment (that is to say, they allow themselves and others to be defined by matter as pure quantity), and they carry this relation into the social milieu by living their reciprocity as human beings as a negated interiority or, in other words, by living it falsely in exteri- + +ority. + +It may be said that we have not explained how matter as scarcity can unite men in a common practical field when free human relations, abstracted from economic constraint, reduce themselves to constellations of reciprocity. In other words, given that the possibility of totalising comes from praxis, how can matter control totalising actions through scarcity so as to make them totalise every individual totalisation? The question contains its own answer. It must be recognised that neighbouring groups, though differing in structure - like, for example, + +Chinese peasants and nomads on the frontiers of China during the T'ang dynasty - can in fact be materially united in one and the same place, defined by a particular material configuration, and by a particular state of techniques, especially communications. The nomads have a limited freedom of movement and always remain on the edge of the desert; while the pioneering army of Chinese peasants advances step by step seizing a little more arable land from the unproductive desert every day. The two groups are aware of each other: they are both divided and united by an extreme tension. For the Chinese, the nomads are robbers capable only of stealing the fruit of the labour of others; and for the nomads, the Chinese are pure colonialists, gradually driving them into an uninhabitable desert. For each group, as praxis, the Other is an object in the unity of its practical field (we shall return to groups later); and everyone is aware of being an object for the Other's group. This utilitarian knowledge will be expressed in such things as the peasants' precautions against surprise attack, and the nomads' care in preparing their next raid. And it is precisely this that prevents the two movements of practical unification from constituting two different fields of action in the same environment. For each of them, the existence of the Other as the object for which it is itself the object, simply constitutes the material field as undermined, or as having a double foundation. In this co-existence, the only duality is a duality of meanings for every material object. The field is practically constituted as a means which can be used by the Other; it is a mediation between the two groups in that each makes it a means against the means of the Other. Everything is both a trap and a display; the secret reality of the object is what the Other makes of it. And while the pure surrounding materiality becomes the contradictory unity of two opposed totalisations, each group, as an object among objects, that is to say, as a means chosen by the Other to achieve his own ends, is objectively totalised as material fragility along with all the other material structures of the field. As a praxis which has been transcended and outwitted, as a freedom which has been misled and used against its will (I sketched these relations in The Problem of lvlethod), every individual and every village will realise itself as objectively characterised by the inertia of the surroundings; and these objective characteristics will become more and more clear as the peasants who dread the raids take stricter measures to avoid them by transcending their environment. In a solitary praxis, as we have seen, the farmer makes himself into an inert object in order to act on the soil; but at this point, his inertia reappears, transmitted to + +him through other people. But, if the balance of forces in some clash is favourable to him, he will find a new form of labour (for war is a labour of man upon man) in the shape of power. And this means something entirely new, namely the power of one human praxis, through matter, against the praxis of the other, and the possibility of transforming an objectifying object into an absolute one. But what is particularly interesting from our point of view is that every square metre of the practical field totalises the two groups and their two activities for all their members, in so far as the terrain presents itself as a permanent possibility of alienation for everyone. The negative unity of scarcity, which is interiorised in the reification of reciprocity, is reexteriorised for us all in the unity of the world as the common locus of our antagonisms; and we will re-interiorise this unity in turn, in a new negative unity. We are united by the fact that we all live in a world + +which is determined by scarcity. + +It goes without saying that scarcity, as indeed we have already seen, can be the occasion for the formation of new groups whose project is to combat it. Man, in fact, produces his life in the midst of other men who are also producing theirs, or at least causing others to produce it; he produces his life in the social field of scarcity. I do not intend to study the types of groups, collectives and institutions which arise within this social field; I am not trying to reconstitute the moments of History or the descriptions of sociology. Besides, this is not the place for a description of those human fields which are unified under the pressure of an active organisation of multiplicity, with differentiated functions. We must pursue our investigation in the regressive order and return to materiality as the inert synthesis of human plurality. However, we must not move on from this stage of our inquiry without making some observations about those groups which are united and differentiated in a unique way by struggling against scarcity and by being conditioned in their structures by scarcity. They constitute and institutionalise themselves not because scarcity appears to everyone in need through the need of Others, but because it is negated, in the unified field, by praxis, by labour. This obviously means that labour, as we have seen, is primarily the organism which reduces itself to a controlled inertia so as to act upon inertia and satisfy itself as need. Clearly this does not in itself mean either that labour exists in the field of scarcity, or that it must be defined as a struggle against scarcity. But given a social field which is defined by scarcity, that is, given the historical human field, labour for man has to be defined as praxis + +and as scarce. His expendability is immediate; and his scarcity appears in the most primitive forms of practical association and creates a constant tension in any given society. But in particular societies, with particular modes of production, the scarcity of men in relation to tools can be transformed, as a result of its own effects, into a scarcity of tools in relation to men. But the basic issue is the same. For a given society the quantity of tools in itself defines the producers, and thus the combination of producers and means of production defines the limits of production and the margin of non-producers (that is to say, of rejected producers) which the society can permit itself. The remaining non-producers represent a surplus which can either vegetate in + +malnutrition or disappear. + +It goes without saying that this new form of scarcity presupposes a society based on particular kinds of work performed in common by an organised group. But this is not sufficient to define any particular historical society. Chinese society in imperial times (in so far as it was conditioned primarily by its rivers), and Roman society (in so far as it secured domination of the Mediterranean world by constructing an enormous system of communications), both satisfy the necessary conditions just as well as capitalism, although this type of scarcity has essentially developed as part of the process of modern industrialisation. But, in the same way, in certain structured historical situations, the institutionalised inequality of classes and conditions can cause a complete reversal of the situation - a scarcity of consumers in relation to products. Of course such relative scarcity is caused both by some material rigidity of production (which must not fall below certain levels) and by the institutionalised social choice of consumers (or rather of the hierarchy of consumers, which itself reflects the social structures which crystallise around the mode of production - what Marxists call 'relations of production'). It is all too clear that this reversal is particularly marked in our capitalist society and that it is an expression of its fundamental contradiction - over-production. And it is the absence of home markets capable of absorbing the entire product which has forced maritime societies since antiquity to trade by sea in order to search for new products or raw materials ; it is this which has forced the continental powers into military imperialism. But this scarcity of man in relation to the product, the final twist of the dialectic of scarcity, presupposes as its essential condition the scarcity of the product in relation to man. And this scarcity is a fundamental determination of man: as is well known, the socialisation of + +production does not put an end to it except possibly through a long dialectical process of which we cannot yet know the outcome. The scarcity of consumers in relation to a particular product is conditioned by the scarcity of all products in relation to all consumers. Indeed, it is because of this fundamental scarcity that certain relations of production have arisen, defined on the basis of the mode of production, which institutionally exclude certain social groups from full consumption, reserving it for other groups, insufficient in number to + +consume everything. + +There would be no point in expounding the dialectic of 'overproduction' and its crises here. But it is important to notice that, taking the process as a whole, the capitalist is ruined, because of lack of outlets under competition, precisely to the extent that the proletariat is impoverished, that is to say, to the extent that the process produces a scarcity of objects of primary necessity. It is perfectly logical, at this level of the contradiction, for a given society to destroy some of its members as surplus to requirements at the same time as destroying part of its product because production exceeds consumption. And of course even if these products were distributed free to those whom society would otherwise allow to die, this would scarcely improve their lot. There would have to be a change at the level of the mode of production and of the basic relations to which it gives rise if the scarcity of consumers were to be made absolutely impossible and the reality of basic scarcity eliminated in the long term. The important thing, from the point of view of the logical structures of History ,is that the historical process is constituted in the field of scarcity; and if it actualises all its dialectical possibilities, this is because of its actual contingent materiality, the outcome of an original contingency. But although, if we consider each case in isolation, it would have been possible for some of these dialectical moments not to have developed (we have only to consider peoples with no history, or those Asiatic nations which were forced to interiorise the fundamental relation of man to machine in the form in which the capitalist West initially imposed it on them in colonialism), once these moments appear as structures of intelligibility in a developing history, they alone enable it to be seen as a total + +rationality. + +(ii) Scarcity and Marxism + +It should be noted that Marx21 - so clear and intelligible in his dialectical reconstruction of the capitalist process and in demonstrating its necessity - always refused, and rightly so, to present Marxism as 'a general historico-philosophical theory the supreme virtue of which consists in being supra-historical'. 22 But at the same time, he believed correctly, though without historical proof - that historical materialism was applicable to every moment of the historical process. In a remarkable passage, he criticised our contemporary Marxists and their dog- + +matism. + +'(The plebeians) of ancient Rome were originally free peasants, each cultivating his own piece of land on his own account. In the course of Roman history they were expropriated. The same movement which divorced them from their means of production and subsistence involved the formation not only of big landed property but also of big money capital. Thus one fine morning there were to be found, on the one hand, free men stripped of everything except their labour power and on the other, the owners of all the acquired wealth ready to exploit this labour. What happened? The Roman proletarians became not wage labourers but a mob of do-nothings ... and alongside them there developed a mode of production which was not capitalist but based on slavery. Thus events strikingly analogous but taking place in different historical surroundings led to totally different results. By studying each of these forms of evolution separately, and then comparing them + +one can easily find the clue to this phenomenon ... .'23 + +This passage clearly shows that, for Marx, the history of the non- + +21. Since Marx constituted the materialist dialectic out of and in opposition to the bourgeois economists of scarcity, the discussion which follows is necessary, though it may appear to be a digression. Its aim is to re-integrate scarcity into human history as a human fact, rather than as the malignity of a cruel Nature. 22. Karl Marx, Letter to the editorial board of the Otechestvenniye Zapiski, Nov. 1877, in Marx and Engels, Selected Correspondence, Moscow, 1975, p. 294. + +[Ed.] + +23. Ibid. The object is to show that the proletarianisation of the Roman plebs, despite its similarity to the proletarianisation of a section of the contemporary peasant class, does not produce the same results and that, consequently, the march of Russia towards socialism will be different from that of the advanced + +Engels regarded this particular contingency as irreducible - irreducible, for example, to the more general contingency of there being a history, which we will discuss more fully later. What is certain is that in the cases under consideration we are confronting vast hypotheses about the succession of events which have no dialectical intelligibility. But let us see how Engels himself described the dissolution of village communities. Here are two passages from the same work. In the first + +we read : + +'Private property • . . already existed, though limited to certain objects, in the ancient primitive communes of all civilized peoples. It developed into the form of commodities within these communes, at first through barter with foreigners. The more the products of the commune assumed the commodity form, that is, the less they were produced for their producers' own use and the more for the purpose of exchange, and the more the original natural division of labour was extruded by exchange also within the commune, the more did inequality develop in the property owned by the individual members of the commune, the more deeply was the ancient common ownership of the land undermined, and the more rapidly did the commune develop towards its dissolution and transformation into a village of small- + +holding peasants'. 27 + +Exactly. This is an example of a law in the positivist sense, that is to say, of a function and the determination of its variable. Y = I(X). The rate at which a commune changes into a village of property-owning peasants is directly proportional to the rate at which increasing numbers of 'natural' products are transformed into commodities. But then, because this law, like every law of Nature, merely describes a universal relation between possibilities, its content is non-historical; on the contrary, it is for History to explain how and why in a given society the rate suddenly accelerates while in another there is practically no change. And this History must provide its own intelligibility as a temporal process; no analytical law can explain it. And it is striking that Engels tried in the sentence that follows to provide just such an example of this dissolution as historical intelligibility, and that he took the example from the Asiatic communes. The sentence, in fact, has already been quoted. It says that these communes managed to resist everything except the entirely modern competition of large-scale industry. Of course this sentence must be taken in context; Engels was rightly + +Here the explanation is historical, and this is what makes it possible to see what is wrong with it. To begin with, it is clear that past societies - those which belong to 'written' History and are therefore characterised by classes - are divided into a plurality of classes, whose number tends to be gradually reduced by their struggles, rather than into the schematic duality which does not apply even today in industrialised countries. Besides, how can we accept the idea that the upper class is initially constituted as a ruling class and frees itself from directly productive labour by means of its new function when Engels himself says that the institution of slavery frees the majority of 'free men' from a part of the constraints of labour? Or when the moment of the expropriation and concentration of landed property, according to Marx, follows that of the individual ownership of land by peasants; and when this moment in fact creates a defenceless proletariat confronting a class of big proprietors (together with other intermediary classes)? Similarly, in the Middle Ages, as Marc Bloch has said, a noble was originally aperson who owned a horse; and if the peasants gathered around the castle, accepted the constraints of serfdom, forced labour and the communal kitchen, this was indeed due to a certain division of labour, but not the one Engels mentions. The peasant asks the noble to undertake the labour of war, that is to say, to defend him with violence + +against violence in the milieu of scarcity. + +What is striking in Engels' interpretations, and often in Marx's too, is that the references to scarcity are almost incomprehensible and, what is more, ambiguous. We find traces of it in this explanation of class duality; but the imagined society is assumed to produce a little more than necessary. And the scarcity is not a scarcity of goods, or of tools or of men, but of time. Of course, this scarcity reflects the others: if time is scarce for the worker (because he does not have enough of it to exercise his own sovereignty), we must obviously conclude that scarcity of goods and producers has been transposed and converted into scarcity of time. But this quintessentialised form does not take account of the reality of malnutrition which is universal today even under socialist regimes. The historical interpretations of Marx and + +that the dominant class produces the State as one of its organs. No doubt this is not a contradiction, but the 'circularity' is very suspicious. A class which developed on the basis of its political and judicial sovereignty would not have the characteristics of the owners of landed property or of the bourgeoisie of the + +Ancien Regime. + +Engels, taken literally, would have us believe that societies always have enough of what is necessary, given the instruments at their disposal and the needs which have become stratified in their organisms; and that it is the mode of production which, through the institutions that it conditions, produces the social scarcity of its product, that is to say, class + +inequali ty. + +In Wage Labour and Capital Marx wrote: 'In production, men not only act on nature but also on one another. They produce only by cooperating in a certain way and mutually exchanging their activities. In order to produce, they enter into definite connections and relations with one another and only within these social connections and relations does their action on nature, does production, take place. '31 And a little further on: 'The relations of production in their totality constitute what are called the social relations, society. '32 I entirely agree with Marxism on this point. Given the existence of classes, that is to say, once 'cooperation' has revealed the deep antagonism which underlies it, it provides us with the bases for a true intelligibility. The entire problem - and we can now see that there is only one problem here, the problem of the historical · disintegration of agricultural communes being merely an aspect of it - is how, within Marxism, to conceive the transition from positive to negative. In Engels, we see workers creating their administrators; and in Marx, we see the direct co-operation of individuals around a mode of production which determines its conditions. But why must these direct transformations, which even look something like a Rousseauan contract, inevitably become antagonisms? Why should the social division of labour, which is a positive differentiation, be transformed into class struggle, that is, into a negative differ� entiation? After all, today, militant trade unionists are the organisers and administrators of the working class; and in certain countries they have taken on too much importance, or the leadership is becoming bureaucratic; the workers, however, have not claimed that they form a class or are going to become one. Is this because the differentiation occurs within the exploited class and against other classes? Undoubtedly. But when a group which is absorbed in labour which takes up all its time, produces apparatuses for supervision, management and control, these apparatuses, according to Engels, are maintained within this rudimentary society and their purpose is to counter internal + +31. Marx, 'Wage Labour and Capital', Selected Works, Vol. I, p. 89. [Ed.] + +32. Ibid., p. 90. [Ed.] + +forces) for an entirely negative event (the liquidation of surplus population by famine or emigration). This is just the conclusion he wanted to reach: in the capitalist period the mode of production itself produces scarcity (surplus population in a given society, decrease of purchasing power for each of them), because it comes into contradiction with the + +relations of production. + +This means that, according to Marx, the Revolution - which he believed to be imminent - would not simply be the heir of bankruptcy, and that, by transforming the relations of production, the proletariat would soon be in a position to reabsorb this social scarcity into a new society. The truth will appear later on when new contradictions will arise in a socialist society owing to the gigantic struggle against scarcity. It is this positive certainty which prevented Marx and Engels from emphasising scarcity as a negative unity through matter in labour and man's struggles. And it was this same certainty which gave such uncertainty to Engels's reflections on violence. For, in a sense, he saw violence everywhere and, like Marx, made it the midwife of change; and if words have any meaning, struggle involves violence. But in another sense, Engels refused, quite rightly, to follow Diihring when he tried to base property and exploitation on violence. Now Diihring was a fool, and his robinsonades are absurd; but Engels did not see that his idealist and romantic ideas and all their follies required the presence of the negative in History. And this is what Diihring meant by 'violence' : the historical process cannot be understood without a permanent element of negativity, both exterior and interior to man. This is the perpetual possibility in man's very existence of being the one who sends Others to their deaths or whom Others send to his - in other words, of + +scarcity. + +The errors of the classical economists and of Diihring are exact opposites. The former, like everyone else at the time, believed in human nature. They placed man in situations of scarcity - this is what defined the economy - and tried to study his behaviour and the resulting relations between the objects of the economy. But it is assumed that man is what he is at the outset and that scarcity conditions him externally. Diihring, on the other hand, immediately attributed to man a capacity for violence and a will to use it which could only come from his enslaved will. This wicked creature's behaviour when there is no bread is not difficult to imagine. But violence is not necessarily an action; and Engels succeeded in showing that as an action it is absent from a great many processes. Nor is it a feature of Nature or a hidden + +hunger. So it is immediately obvious that administrative, managing and ruling groups are both the same as those they administer (in so far as the latter accept them) and other than them. For not only are they responsible for determining the Others in the group, that is, for choosing the victims of the new system of distribution; but also, they are themselves the Others in the sense that they are completely dispensable, consuming without producing and constituting a pure threat for everybody. In the context of scarcity, the differentiation of functions (however this takes place, for Engels saw it in a very simplistic way) necessarily implies the constitution of a dispensable (but accepted) group and the formation, by this group, with the complicity of many Others, of a group of under-nourished producers. Conversely, the unproductive groups, which are perpetually in danger of liquidation because they are the absolute Other (living off the labour of Others), interiorise this ambivalent alterity and behave towards individuals either as if they were Other than man (positively, as gods) or as if they alone were men in the midst of a different, sub-human species. As for the sacrificial group, its relation with Others can truly be described as struggle. For even if violence is not used, such a group will be negated by everyone, that is, by scarcity in everyone and it will reply by negating this negation - not, however, at the level of praxis, but + +simply through that negation of negation which is need. + +We shall see later how in reality these acts and attitudes become beings, or collectives. We shall also see the true structure of groups. But it has been important to explore the primary conditioning of men by interiorised matter, this first, constant reassertion of control by the inertia of exteriority which contradicts praxis within praxis itself. This provides a foundation for the intelligibility of that cursed aspect of human history, both in its origins and today, in which man constantly sees his action being stolen from him and totally distorted by the milieu in which he inscribes it. It is primarily this tension which, by inflicting profound dangers on everyone in society, by creating diffused violence in everyone, and by producing the possibility for everyone of seeing his best friend approaching him as an alien wild beast, imposes a perpetual statute of extreme urgency on every praxis, at the simplest level, and, whatever its real aim, makes the praxis into an act of aggression against other individuals or groups. If one grants Marx and Engels the idea of class struggles, that is, of the negation of classes by one another; in other words, if one grants them negation, then they are able to comprehend History. But then we still have to + +reality - not only in the context of the capitalist process, but also at every other moment of the historical process. Marx explained the material conditions for the appearance of capital, a social force which ultimately imposes itself on individuals as anti-social. But our concern is to carry out a concrete investigation of the general, dialectical conditions which produce a determinate inversion in the relations of man and matter as a moment of the overall process; and which produce, within that determinate moment, through the praxis of Others, and through his own praxis as Other, the domination of man by matter (by this particular already-worked matter) and the domination of matter by man. It is within this complex of dialectical relations that the possibility of the capitalist process constitutes itself as one of the pos- + +sible historical moments of alienation. + +In other words: we have seen how production establishes itself and how it makes alterity a characteristic of the relations of production in the context of scarcity, or the negation of man by materiality as an inert absence of matter, and we shall now investigate how alienation becomes the rule of objectification in a historical society to the extent that materiality, as the positive presence of worked matter (of the tool), conditions human relations. We shall then understand, through the connection of these two dialectical moments, how classes are possible. But in the moment in which our praxis experiences its alienation, an internal and external structure of objectification appears, and this is precisely Necessity. So the rest of the regressive investigation need not be confined to displaying the intelligibility of class formation (on the basis of the mode of production and in the context of scarcity, as complex structures of stratified alterities, of interiorised and subsequently\_ re-exteriorised contradictions and of antagonisms); it also + +introduces us to its first structure of apodicticity.35 + +3 ). It must be clearly understood here that the rediscovery of scarcity in this investigation makes absolutely no claim either to oppose Marxist theory, or to complete it. It is of a different order. The essential discovery of Marxism is that labour, as a historical reality and as the utilisation of particular tools in an already determined social and material situation, is the real foundation of the organisation of social relations. This discovery can no longer be questioned. What we are arguing, however, is this: the possibility of these social relations becoming contradictory is itself due to an inert and material negation re-interiorised by man. We are also arguing that violence as a negative relation between one praxis and another characterises the immediate relation of all men, not as a real action but as an inorganic structure re-interiorised by organisms and that the possibility of reification is present in all human relations, even in the pre-capitalist period, and + +2 Worked Matter as the Alienated Objectification of + +Individual and Collective Praxis + +It is important to be clear about what is meant by saying that a society designates its undernourished producers and selects its dead. It sometimes happens than an organised power consciously and deliberately decides to overpower and exploit certain groups for the advantage of others. This is the case, for instance, when one nation conquers another, and plunders and enslaves the defeated. But this is certainly not the most usual kind of case; on the contrary. Engels was right to say that very often, when two groups engage in a series of contractual exchanges, one of them will end up expropriated, proletarianised and, often, exploited, while the other concentrates the wealth in its own hands. This takes place in yiolence, but not by violence: and experiencing exchange as a duel in this way is characteristic of the man of scarcity. + +even in family relations or relations between friends. As for scarcity itself, it has a formal dialectic which we have already sketched: scarcity of products, scarcity of tools, scarcity of workers, and scarcity of consumers; it also has a historical, concrete dialectic about which we will be silent since it is for historians to retrace its moments. Indeed, it would be necessary to show the double transition, under the influence of production itself, from scarcity as the dispensability of each individual in relation to all, to scarcity as the designation by society of groups of under-consuming producers. At this point the relation between groups becomes violence - not necessarily because it was established by violence - Engels is right about this - but because it is in itself a relation of violence between violent men. The second aspect of the transition is from absolute scarcity, as a determinate impossibility of all the members of the group existing together in certain definite material conditions, to relative scarcity, as the impossibility that the group, in certain circumstances, should grow beyond a certain limit without any change in the mode or the relations of production (that is to say, scarcity in the form of the discreet liquidation of non-producers in a given society according to certain rules, and also as the selection of undernourished producers). This relative scarcity, which itself has a historical dialectic (an intelligible history), acquires, in class societies, the status of an institution. The analytical study of institutions of scarcity is political economy. This implies that in giving due weight to scarcity we are not reverting to a pre-Marxist theory of the pre-eminence of 'consumption', but merely throwing into relief negativity as the implicit motive force of the historical dialectic and making it intelligible. In the context of scarcity all the + +Though the result is appropriated in violence by the dominant class, + +it is not foreseen by the individuals who compose it. + +The striking thing about Marxist descriptions, however, is not so much exchange as the constraints of tools. Late eighteenth and nineteenth century society was completely dependent on the iron and coal complex. In other words, coal as a source of energy itself conditioned the means of harnessing that energy (for instance, the steam engine) and, through these new tools, it conditioned new methods of working iron. (The meaning and intelligibility of this observation will become clear later.) In this way, mankind came into possession of a source of accumulated energy derived from vanished vegetable matter; one might describe it as capital bequeathed to mankind by other living beings. But at the same time every proprietor was eating away his own capital ; for mines are not inexhaustible. This peculiar feature of mining, as well as favouring industrialisation in its initial stages, made this first moment of industrial capitalism violent and feverish in character. All exploitative activities come to be based on the mode of exploitation of the mines; they are constituted in the perspective of rapid, brutal gains before the raw material is exhausted. And this gave rise to steam transport, railways (which are very directly linked to mining since their original function was to serve it), gas-lighting, etc. And within this complex of materials and instruments, there had to be a division of labour: mines and factories created their capitalists, their technicians + +and their workers. + +Marx and many later thinkers have shown the meaning of these constraints of matter - how the iron and coal complex presents itself at the basis of a society as the condition for class mobility, for new functions and institutions, for more extreme differentiations and for changes in the system of property, etc. But the undeniable result of what has sometimes been called the 'palaeo technical' period was the partial destruction of the structures of the old society, the proletarianisation of certain groups and their subjugation to the two inhuman forces of physical fatigue and scarcity. And as a result of all this, a new kind of men came into being, 'iron and coal men' , produced by mining and by new smelting techniques, the industrial proletarians (and, of course, industrialists and technicians, etc.). All this is well known. But still, it seems paradoxical that the ruthless proletarianisation of the peasants, which continued throughout the century, arose and developed from an incredible growth in the wealth of mankind and from absolute progress in its techniques. The historical reasons for this are well known. + +To take just two well understood examples, it has been shown hundreds of times how industry under the Second Empire itself produced a concentration of landed wealth, once industrialists had decided to construct the agricultural implements which enabled rich peasants to get richer while forcing poor, ruined peasants to sell their land and migrate to the towns. It has also been shown how steam ships caused the demographic transformation of England at the end of the last century by causing an unprecedented agricultural crisis simply by + +bringing Argentinian corn within a few days of England. + +From the point of view of intelligibility, the important thing is to comprehend how a positive fact, such as the large scale use of coal, could become the source of deeper and more violent divisions between people within a working society, a society which was also seeking to increase its social wealth by all available means; and to understand, too, how the constraints of the material complex which men inherit can negatively define the new expropriated, exploited and undernourished groups. Of course, this new mode of production could not have abolished scarcity, so it was not even conceivable that the means of production should be socialised. But this negative explanation is no more valuable than the attempt to explain the emigration of ancient Greeks by reference to their ignorance of the sciences of Nature. It would be both more reasonable and more intelligible to exhibit industrialisation as a process which developed out of previous scarcity, which is a real factor in History (in so far as it is crystallised in institutions and practices), and therefore on the basis of the negation of men by matter through other men. It is obvious, for instance, that the first people to work in factories and mines in England were paupers, that is to say, peasants who had been designated, sometimes from father to son, as dispensable, surplus population as a result of the complex movement of agricultural economies and the hard policies of bourgeois land-owners. It was left to machines to shatter the last positive bond: the parish had formerly fed its poor; this was an ethico-religious practice, and the only vestige of feudal relationships built around the Church. (And as is well known, Marx said that in these relationships, oppression and exploitation did not altogether hide a non-reified human relation.) Industry, and the political representatives of industrialists, in so far as they made themselves political servants of industrialisation, however, condemned the poor. They were torn from their villages, and immense movements of population took place, and individuals were reduced to interchangeable units of an abstract labour power, the same in everyone. This labour + +power itself became a commodity, and finally massification constituted workers in ' this first aspect: mere inert things who relate to other workers through competitive antagonism, and to themselves through the 'free' possibility of selling that other thing, their labour power, which also means the possibility of working as a man rather than an animal, of organising one's praxis so as to contribute more to production, and of being a man in general, since praxis is the real humanity of man. In all these specific negations, scarcity and pre-capitalist social structures are no longer to be found, although of course the new negations were based on the old ones; they actually owe their negative character to the mode of production in so far as it rests on this incredible wealth. In an altogether different context, and with a very different intention, Engels noted this paradoxical character very + +clearly: negation as the result of positivity. + +'The natural division of labour within the family cultivating the soil made possible, at a certain level of well-being, the introduction of one or more strangers as additional labour forces. This was especially the case in countries where the old common ownership of the land had already disintegrated . ... Production had developed so far that the labour-power of a man could now produce more than was necessary for its mere maintenance; the means of maintaining additional labour forces existed; likewise the means of employing them; labour power acquired a value. But the community ... yielded no available, superfluous labour forces. On the other hand, such forces were provided by war, and war was as old as the simultaneous existence alongside each other of several groups of communities. Up to that time, .. , prisoners of war ... had ... simply been killed . . .. But ... now ... the prisoners acquired a value; one therefore let them live and made use of their labour .... Thus force, instead of controlling the economic situation was on the contrary pressed into the service of the economic situation. + +Slavery had been invented.'36 + +Considered in the context of economic evolution, slavery represents progress, and therefore in itself it expresses a positive response to the positive conditions which gave rise to it: after all, it iS Jrue that it was the basis of Ancient Greece and of the Roman Empire. Again, considered in itself, it can also be seen as a humanisation of war and a positive element in that prisoners of war acquired value on account of their potential labour (on the highly dubious assumption that slavery + +can be explained in such simplistic terms). But from the first point of view, we could also say that, as far as the technical and even ethical progress of humanity are concerned, the industrial proletariat is a positive gain, because industrialisation involves proletarianisation and because the worker thus produced is destined to carry out the sentence + +which capitalism passes on itself. + +Marxism in no way conflicts with this; however, today, from the point of view of making History, it presents the positive character of the proletariat as the negation (human negation = praxis) of a negation. Similarly, from the point of view of the entire ancient world, the emancipation of the few through the enslavement of the many presents itself as the negation of the enslavement of all, and as an enslavement imposed only on some. Slavery prevents a possible enslavement. But when Engels shows us the origins of slavery, (or what he takes to be its origins), slavery appears as the negative result of a positive development of production. Free men, working for themselves and their communi ty, are reduced to their labour power, are forced to use it entirely for the advantage of some foreigner. That this negative side was perfectly evident to groups in which slavery existed is sufficiently proved by the frequent wartime oaths to die rather than become a slave. So it would be absolutely wrong to say that the massacre of prisoners, when it occurred, expressed the victor's indifference about the defeated. What it expressed was, rather, a certain statute of violence, in which death was a bond of antagonistic reciprocity; slavery was seen as positive in that positive extra labour power was actually present in exploitation, and it was seen as a negation of war, under the threat of war, perpetually, as the danger of a new statute being imposed on everyone. Besides, even if the transformation in the fate of prisoners of war due to economic development is, in this simplistic form, romanticised history, it is nevertheless clear that, when the practice became institutionalised, a complex system was constituted in response to the scarcity of slavery, involving a multiplication of wars and raids for the sake of conquering + +slaves, and also for the organisation of the slave-trade. + +It would be pointless for us to take up a moral position - which would be entirely meaningless - and to condemn the ancient system of slavery. Our concern has simply been to show that Engels wrote his paragraph on slavery using exclusively positive words and expressions, as against Duhring, who saw enslavement as simple violence and therefore as nothing but a fundamental negation of man by man. But Engels's collection of positive propositions does not conceal the fact + +that slavery originally appeared as a choice of a category of undernourished sub-humans, by men who were conscious of their own humanity and that, as such, in spite of the false, specious argument based on war, it appeared as negativity. But should this negativity be attributed to a displacement of scarcity? Scarcity of labourers, replacing a scarcity of tools and raw materials? Yes indeed; but this only takes us back to the heart of the problem, since this displacement of scarcity, as a negation which had to be negated, emerged out of a positive process. And this production of negativity did not result directly from scarcity felt as need, since it occurred in groups (in particular, families) which were quite 'well off'. They could conceive it only as a lack which had to be acquired, that is, in so far as it was expressed - in tools, in cultivation, and in the technical organisation of familial exploitation - as a positive possibility creating its own negation in its very positivity. In this case, the materiality revealed by action is really entirely positive : in the practical field, the soil is revealed as soil to be cultivated. This means that materiality also indicates the means of cultivation - it reveals itself as such through the tools and organisation which have actually cultivated some other part of the same soil. But this positive ensemble is lived as a negative turning back, and conditions all negativity (the raid in which men are captured like animals, and the statute which assigns them to a place in the new society as both necessary producers and dispensable consumers reduced to underconsumption and which, in constituting the Other as sub-human, makes of the slave-owner a + +man other than man).37 + +37. This is not a return to Hegelianism, which makes the Slave the Truth of the Master. Apart from the idealism of the celebrated passage on 'Master and Slave', Hegel can be criticised for describing the Master and the Slave, that is to say, ultimately, for describing the relations of a master with his slave through universals, without reference to their relations to other slaves or other masters. In reality, the plurality of masters and the serial character of every society cause the Master as such, even in idealist terms, to find a different truth within the ensemble of his class. Slaves are the truth of masters, but masters are also the truth of masters, and these two truths oppose one another as do these two categories of individuals. Besides, except at the time of great concentrations of landed wealth, in Rome and later, the ' Master also worked. So the problem was no longer to compare an idle whim with slave labour (which thereby became identified with labour in general), but rather, (to take for example a Greek artisan), to compare free (manual) labour with the slave labour which is its condition (but which is no longer identified with labour in general, since the slave is only given unpleasant tasks requiring no skill). If the slave possesses the secret of the master this is + +Within praxis, therefore, there is a dialectical movement and a dialectical relation between action as the negation of matter (in its present organisation and on the basis of a future re-organisation), and matter, as the real, docile support of the developing re-organisation, as the negation of action. And this negation of action - which has nothing in common with obstruction - can be expressed in action only in terms of action itself; that is to say, its positive results, in so far as they are inscribed in the object, are turned against and into it in the form of objective, negative exigencies. This should surprise no-one; everyone understands the necessity of social transformations in terms of material and technical complexes. Today, everyone finds a true intelligibility in the objective process (which is much more complex than Engels'S Marxism portrayed it) which adumbrates the slave as the sub-human future of still undetermined individuals on the basis of a technical progress and an increase in wealth which will rescue certain groups (including, in many cases, ones which will be reduced to slavery) from what Engels called the constraint of animality. Today everyone understands, or can understand, how machines, by their structure and functions, determine the nature of their servants as the rigid and imperious future of undetermined individuals and, thereby, create men. It is true that the intelligibility and objective necessity contained in the whole process sustain and illuminate our knowledge of it; but, on the other hand, they remain hidden in so far as they are absorbed by a material content which then reveals them to knowledge through its own temporalisation and as the special rule of its historical development. We are unable to give a dialectical account of our social and historical language. In his excellent book, Mumford says : 'Since the steam engine requires constant care on the part of the stoker and engineer, steam power was more efficient in large units than in small ones .... Thus steam power fostered the tendency toward large industrial plants ... . ' 38 I do not wish to question the soundness of these observations, but simply to note the strange language - language which has been ours since Marx and which we have no difficulty in understanding - in which a single proposition links finality to necessity so indissolubly that it is impossible to tell any longer whether it is man or machine which is a + +because his labour is destined to approach a moment where it will cost more than + +it produces, thereby bringing about the ruin of the ancient world. + +38. Lewis Mumford, Technics and Civilization, 1934, p. 162. The italics are + +practical project. We all feel that this language is correct, but also realise that we cannot explain or justify this feeling. Similarly, when we learn that gas-lighting, which was a consequence of the use of coal as a source of energy, enabled employers to make their workers work fifteen or sixteen hours a day, we do not quite know whether it was the industrial ensemble dominated by coal which, through the medium of the men it produced, required a working day of sixteen hours, or whether it was the industrialist, in the coal-based economy, who used gas-lighting to increase production or, again, whether the two formulations do not refer to two aspects of a single dialectical circularity. It is precisely at this level that a dialectical investigation must supply its own intelligibility, as the general condition of the relation of praxis to tools and, generally speaking, to materiality. This means that the translucidity of the individual praxis as the free, re-organising transcendence of particular conditionings, is really an abstract moment of the dialectical investigation - even though this moment can develop as a concrete reality in any particular undertaking, even in the wage earner's manual labour (for instance, when a skilled worker, though conscious of having sold his labour power, remains the organiser of his professional praxis). The deepening of the investigation must also be a deepening of praxis. It is in praxis itself, in so far as it objectivises itself, that we will find the new moment of dialectical intelligibility, which constitutes the result of a negation of the undertaking. This new structure of rationality can be called dialectical intelligibility because in its immediate purity it is simply a new dialectical determination produced on the basis of existing structures, and without any new factors apart from those it itself produces on the basis of these structures as the totalisation of their transcendence and as the strict necessity + +of this transcendence. 39 + +39. After the transcendence the totalisation itself becomes particular, both as an alienated objectification and in relation to the transcended structures which still exist, also in freedom (that is to say, in the strict conditioning of their reciprocal determinations and beyond all transcendence). So the particularised totalisation becomes, with others, the object of a new totalising transcendence which we shall have to discuss later. By way of an example, I would refer the reader to the observations I made in The Problem of Method (p. 72) on some studies by Kardiner, in particular the inquiry into the natives of the Marquesas + +islands. + +of their activity is the deforestation which has been going on for centuries. This praxis is living and real, and retains a traditional aspect: even recently the peasant was still tearing up scrub to clear a place for millet. But, at the same time, it inscribes itself on nature, both positively and negatively. Its positive aspect is that of the soil and the division of cultivation. Its negative aspect is a signification of which the peasants themselves are not aware, precisely because it is an absence - the absence of trees. A European flying over China today is immediately struck by this feature; China's present leaders have perceived it and are aware of the seriousness of the danger. But traditionalist Chinese in previous centuries could not perceive it since their goal was conquest of the soil. They saw only the plenty represented by their harvests and had no eyes for the lack, which was for them, at most, a simple process of liberation, the elimination of an obstacle. On this basis, deforestation, as a passivised practice which had become characteristic of the mountains, particularly those that dominate Szechwan, transformed that physico-chemical sphere which can be called 'wild' in the sense that it begins where human practice leaves off. To begin with, this wild sector is human in that it expresses the historical limit of society at a particular moment. But above all deforestation as the elimination of obstacles becomes negatively a lack of protection: since the loess of the mountains and peneplains is no longer retained by trees, it congests the rivers, raising them higher than the plains and bottling them up in their lower reaches, and forcing them to overflow their banks. Thus, the whole history of the terrible Chinese floods appears as an intentionally + +constructed mechanism.40 + +If some enemy of mankind had wanted to persecute the peasants of the Great Plain, he would have ordered mercenary troops to deforest the mountains systematically. The positive system of agriculture was transformed into an infernal machine. But the enemy who introduced the loess, the river, the gravity, the whole of hydrodynamics, into this destructive apparatus was the peasant himself. Yet, taken in the moment of its living development, his action does not include this rebound, either intentionally or in reality. In this particular place, and for this particular man cultivating his land, all that ex isted was an organic connection between the negative (removal of the obstacle) and the positive (enlargement of the arable sector). The first thing that is necessary for counter-finality to exist is th at it should be adumbrated + +by a kind of disposition of matter (in this case the geological and hydrographic structure of China) . It seems that in order to remove the danger of flooding completely it would not have been sufficient not to deforest. From ancient times, reforestation would have been necessary. Second, human praxis has to become a fatality and to be absorbed by inertia, taking on both the strictness of physical causation and the obstinate precision of human labour. Destruction by Nature is imprecise: it leaves little islands, even whole archipelagos. Human destruction is systematic: a particular farmer proceeds on the basis of an approach to a limit which conditions his praxis - quite simply, the idea that every tree growing in his field should be destroyed. Thus the absence of trees, which is an inert and thus a material negation, also has the systematic character of a praxis at the heart of materiality. Last, and most important, the activity must be carried on elsewhere: peasants eyerywhere must burn or uproot the scrub. These actions, which are legion and, as actions, both identical and irreducible, are united by the matter they unify. Through molecular homogeneity, the multiplicity of actions is diffused in the 'community' of being. Imprinted on the red soil, which offers itself as an infinite deployment of materiality, particular actions lose both their individuality and their relation of identity (in space and time) : they spread themselves out without frontiers, carried along by this material deployment, and lose themselves + +in it; there is just one seal impressed on just one land. + +But the passive movement of this deployment is itself the result of an initial praxis; the changing links between groups, by river, canal and road created closeness and distance within an initial unity, which was the life lived in common under the same geographical conditions by a society already structured by its tools and its labour. Thus deforestation as the material unity of human actions is inscribed as a universal absence on an initial inert synthesis, which itself is already the materialisation of the human. And passive unity, as the synthetic appearance of pure dispersal and as the exteriorisation of the bond of interiority, is for praxis its unity as Other and in the domain of the Other.41 On this basis, deforestation as the action of Others becomes everyone's action as Other in matter; objectification is alienation, and at first this primitive alienation does not express exploitation, though it is inseparable from it, but rather the materialisation of recurrence. There is no joint + +41. Obviously my example can be understood only in the context of scarcity + +and as a displacement of it. + +undertaking, but still the infinite flight of particular undertakings inscribes itself in being as a joint result. By the same token, Others are fused, as Others, in the passive synthesis of a false unity; and, conversely, the Oneness stamped on matter reveals itself as Other than Oneness. The peasant becomes his own material fatality; he produces + +the floods which destroy him. 42 + +Thus human labour, though only just 'crystallised', is enriched with new meanings precisely to the extent that it eludes the labourer through its materiality. At this elementary stage, by inscribing itself in the natural milieu, it extends to the whole of Nature and incorporates the whole of Nature within itself: in and through labour Nature becomes both a new source of tools and a new threat. In being realised, human ends define a field of counter-finality around themselves. Through the unity of this counter-finality, deforestation negatively unites the enormous masses who people the great plain of China: it creates universal solidarity in the face of a single danger. But at the same time it aggravates antagonisms, because it represents a social future both for the peasants and for the land-owners. This future is both absurd, in that it comes to man from the non-human, and rational, in that it merely accentuates the essential features of the society. Future floods are /iyed as a traditional feature of Chinese societies. They bring about a perpetual shift of fortunes, and equalisation through catastrophe followed by renewed inequality; - hence the immemorial feudalism in which repetition replaces transformation, and in which, apart from the great landowners, the rich man is almost always a nouyeau riche. Later, when it is recognised as the foremost danger, deforestation remains a threat to be eliminated, in the form of a common task whose success will give + +benefits to all. + +This first relation of man to the non-human - where Nature becomes the negation of man precisely to the extent that man is made anti- + +4�. The extraordinary separation of rural workers in China, which the commune system has only recently caused to disappear, is obviously linked with the primitiveness and stagnation of techniques. These facts condition and express a definite system of social relations and a definite form of property. But although exploitation as alienation is inscribed in materiality with its own characteristics and mingles there indissolubly with alienation through recurrence, the latter cannot be reduced to the former. The former defines the relation of forms of production to productive forces in a concrete historical society; the latter, although it appears in the relevant aspect only at a certain technical level, is a permanent type of separation against which men unite, but which attacks them even when + +united. + +everyone the passive indication of a definite if temporary purchasing power. Obviously we do not intend to make an economic or historical study. But, given the work of historians and economists on the circulation of precious metals in the Mediterranean world during the Renaissance, we will try to grasp the intelligible bond of exteriority and of interiority in real life within that circulation, observing how, in the case of gold and silver as materiality, and in the case of man as the product of his product, it transforms human praxis into anti praxis, that is to say, into a praxis without an author, transcending the given towards rigid ends, whose hidden meaning is counter-finality. I shall apply myself, therefore, to an example, drawn from Spanish history, which has the advantage of showing the process of the inversion of praxis in all its clarity. It goes without saying that this process develops in class societies with class divisions. But it is not classes which we will be trying to understand in it, but rather, other things being equal, the dialectic of antipraxis as an objective relation between matter and man. On the basis of this inquiry, we shall, perhaps, be able to determine the conditions for the dialectical intelligibility of the constitution of classes + +as schism and conflict within a given grouping. + +In the example we have chosen, as in those quoted above, a social heritage turns into a disaster; and plenty itself becomes negativity (as also happened later, in the age of mining). The discovery of the Peruvian mines seemed at the time to be an increase of wealth and, in the middle of the sixteenth century, it caused a new technique of metallic amalgamation to be perfected. The continual increase in stocks of precious metals in Spain, however, eventually resulted in an increased cost of living on the whole of the Mediterranean seaboard, worsening poverty for the exploited classes, the paralysis of business and the ruin of many merchants and industrialists. The Spanish terror, caused by the outflow of gold, must be seen, finally, as containing not only the prophetic announcement of the decline of Spain and the Mediterranean, but also its result and one of its conditions. How can the affirmation of + +an affirmation produce a negation? + +As soon as the first Spanish gold coins had been struck, a l + +iving bond + +between them, other Spanish coins, and the coins of all other countries, and also between all these and all the gold mines established itself, through the apparatus and structures of mercantile capitalism and the historical praxis of Charles V and Philip II. The bond was initially a human one: mining, transport, melting down, minting - so many modalities of labour - defined techniques and social structures. Circu- + +lation and hoarding are forms of praxis. It was the labour in the Peruvian mines, the long and difficult journey along the routes crossing the isthmus of Panama, and the comings and goings of the Spanish fleet which, under the Ancien Regime, placed Spanish currency as a whole in a permanent relation with mining as the source of constant, limited expansion . But it was the instruments of mining, the means of transport, the techniques of minting, etc. which, at least in part, accounted for the reserves of money at any particular moment in the reign of + +Philip II. + +At the beginning of the sixteenth century, the Mediterranean suffered a 'gold famine' : African sources were exhausted. America was replacing them, and up to 15 50, Spain was importing both gold and silver. But in the second half of the century, silver predominated, and this was because Bartolomeo de Medina had introduced a new amalgamation process into the American mines. Between 15 80 and 1630 imports of precious metals increased tenfold. This is a case of matter acting on matter: the treatment of silver ore with mercury conditioned the whole evolution of money up to the middle of the following century. But this instrumental materiality was materialised practice. Later, as prices rose, the effects of the increase were felt particularly in Florence and in Castille. Braudel explains why: 'Continental prices reflected the constant tension in economies affected by the hostile distances separating them from the sea.'43 But these hostile distances also express materialised praxis: distance as materiality is a function of the state of the roads, of the means of communication, and of conflicts between towns: Florence was now close to the sea. In short, at this level, matter as a limit to signification becomes a mediation between significations. It is in and through matter that significations (crystal- + +lised praxis) combine into new but still inert syntheses. + +American gold and silver took on their true character within these passive totalisations. Coins became human quantities under the influence of the inert actions surrounding them. In a sense, indeed, quantity was already in them, since it cannot be separated from materiality, nor, + +43. F. Braudel, The Mediterranean and the Mediterranean World in the Age of Philip !! (1 949). [English translation of second edition by Sian Reynolds, Collins, 1972 - Ed.] The whole of the exposition which follows is no more than a commentary on this admirable work. See, in particular, Part Two. 'Collective Destinies and General Trends', chapter two, 'Economies: Precious Metals, Money and Prices' . [The sentence quoted by Sartre is on p. 413 of the first, F,ench + +above all, from being in exteriority. But it was not a differentiated quantum; and, above all, it did not concern coin s as such. I am not referring to the value of coins, which is something we shall come to later. If it were only a question of their weight, even that would have its concrete reality only in relation to the galleons which transported them and the carts which brought them to the capital from the coast. And how could their number be determined except in relation to a definite vessel in which they accumulated without being able to escape? Such a vessel existed: it was Spain itself, 'a country traditionally protectionist, fenced around with customs barriers .... So, in principle, the huge American treasure was being drawn into a sealed vessel.'44 It was the unity of the vessel, the customs barriers and the authoritarianism of the absolute monarchy which allowed the amount of coins or precious metal to be checked and counted. It was in relation to this unit that this quantity would be reckoned as abundance or as scarcity. It was at the bottom of this crucible that the heavy burden of ingots and coins began to weigh; it was in and through it that real relations came to be established between this mineral and other material objects - manufactured products, food-stuffs, etc. Should this crucible, this unbreakable vessel (unbreakable in theory at least) be called material, on the grounds that the very nature of the Spanish frontiers (the sea, the Pyrenees) constitutes in itself a natural barrier, and that institutions, social structures and the system of government are crystallised practices ? Or should it be called praxis, on the grounds that governments pursuing a precise policy and supported by the ruling classes appointed quite definite people - administrators, policemen, customs officials, + +etc. - to keep watch over the outflow of gold and silver? + +In reality, it is completely impossible to separate the first interpretation from the second: at this point we reach concrete and fundamental reality. Matter as the receptacle of passivised practices is indissolubly linked to lived praxis, which simultaneously adapts to material conditions and inert significations, and renews their meaning, re-constituting them by transcending them, if only to transform them. At this level, the process of revelation is constitutive in the sense that it realises a unity which, without man, would be instantly destroyed. Spain was the living unity of an undertaking, and restored their value and meaning to the signs inscribed in a sector of matter: and, at the same time, it was a material entity, a set of geographical, geological and + +freedom of its sea-routes, etc. In transcending his material condition man objectifies himself in matter through labour. This means that he loses himself for the sake of the human thing,46 and that he can rediscover himself in the objective as the meaning for man of his product. Two types of human mediation must, however, be distinguished. The first is communal, premeditated, synthetic praxis uniting men (whether exploited or not) in a single enterprise aimed at a single object. Such - to return to our example - was the policy of Philip II's government, in particular, in relation to precious metals. This concerted undertaking47 led to the accumulation of ingots and coins in the depths of the crucible of Spain. Through this mediation matter directly produced its own idea. But this has nothing to do with philosophical or religious conceptions, constituted at the level of 'superstructures' as dead possibilities far removed from reality. The idea of the thing is in the thing, that is to say, it is the thing itself revealing its reality through the practice which constitutes it, and through the instruments and institutions which define it. In the sixteenth century, the use of colonial mines necessarily meant importing unprocessed products from the colonies into the metropolitan country, and therefore accumulating precious metals in Spain. But this very practice revealed gold and silver as commodities, and this, moreover, corresponded to the mercantilism of the age. Money revealed itself as a commodity because it was treated as a commodity: since the necessities of colonisation implied the accumulation of gold in the colonising country, it is obvious that the labour expended on transport defined gold as real wealth. But it is even more obvious that the density and material opacity of the object, its weight and brilliance also turned it into an autonomous substance which was apparently sufficient to itself; the physical reality of the coin proved its bonitas intrinseca.48 Price became an intrinsic relation between the values of two commodities : that of the object you wished to buy and that of the monetary unit. 46. Hence the profundity of Zola's title for one of his most famous novels, La Bete Humaine - the humanised machine, man with his animal needs, man as prey + +to the machine and the machine acquiring a parasitic life from man. + +47. In due course we will come back to these collective undertakings in so far + +as they make history. But we do not yet have the means to think them. + +48. On the other hand it would not have occurred to anyone in 1792 to regard assignats (promissory notes) as commodities. However, the mctalist theory being then at its height, they were regarded as fiduciary signs backed by money-commodities which themselves served to mediate between the note and the national + +wealth. + +recurrence and made of it a sort of spontaneous resistance on the part of matter to the wishes and practices of men. In this case, inertia itself merged with alterity, and became a synthetic principle producing new forces. But these forces were negative: gold took on a 'life of its own' mediating between real praxis, whose unifying power and negativity it absorbed, and the mere succession of physical phenomena, whose dispersal in exteriority it re-affirmed. The characteristics of this magical liJe, which turns praxis back on itself and transforms ends into counter-ends, cannot be analysed here; but I will examine one example, + +which I shall call bewitched quantity. + +The Spanish government accumulated gold, yet the gold flowed out. On this plane, we have first a positive, logical action of quantity: it seems, in short, that gold flowed out faster and more abundantly as the monetary potential of the country rose. Hence Braudel's metaphor: 'Spain was a reservoir'. If this action was negative, it was so only in relation to human undertakings. But this only means that the action's powers of destroying accumulation have to be seen in the same light as, for instance, the limits on the size of a galleon's cargo. If the galleon foundered, the shipwreck was due to the positive action of overloading; the more ingots it carried, the more it weighed. In reality this is not so clear, since any given current contains negativity. But, after all, a historian or an economist may use a physical symb o l to + +describe the phenomenon as a whole. + +However, it is the other aspect of the complex fact of 'accumulationoutflow' that we shall refer to as a 'bewitchment of quantity'. American wealth stayed for a while in Spain, and was then discharged into other Mediterran�an countries; for nearly a century the Spanish reserves were reconstituted and increased by new imports. Here a contradiction arises between the material idea of the money-commodity and economic reality. The quantitative notion enters into the idea; if the value of the monetary unit is fixed, then the greater the sum, the greater its value. And as I have shown, this is always true for the individual. But, while for him every new quantity increases his wealth, in the national community it devalues the unit; and thus individual wealth constantly deteriorates in the hands of the merchant or the industrialist, and his own increasing prosperity is partially responsible. Without any doubt, there are physical laws stating functional relations between two quantities, one of which increases as the other diminishes. This is what allowed the metalists of the liberal period to present the phenomenon of devaluation in terms of a relation between two variables, the money- + +The process as a whole retained a human meaning in Spain because, in a way, everything from the outflow of gold to the outbreak of epidemics, including the price rises, can be regarded as the result of the deliberate and persistent practice of monetary accumulation. In the other Mediterranean countries, however, precious metal appeared, through various individual frauds, as an invasion. Governments had no legal means of encouraging the influx of mOney ; the most they codd do was to close their eyes to this automatic accumulation. In this case, money appeared in its material dispersal, in small separate sums54 or on the occasion of legal transactions, but with no other relation than temporal co-existence. Once again, the unity is human: the 'hunger for gold'. But this means a diffuse need on the part of Mediterranean industry and trade, felt through individuals unknown to one another. The unity was not a lived reality for anyone; it was a material reality expressed by a cloud of particular demands. In a sense, every merchant + +personal desires and needs are objectified and alienated in the use-values of the thing in which they become quantities. But, at the same time, the 'units' (doses) are no longer forced to co-exist like coins in a stocking; or rather, their coexistence becomes an internal relation. The 'marginal unit' - that with the lowest use-value - determines the value of all the others. And this is not a real synthesis, but a phantom interiorisation. In areal synthesis, the relation would establish itself between real, concrete and individuated parts. In marginalism, the final unit could be any one of them. Any of my ten gold coins can be regarded as the one which I shall use last; each of the employer's ten workers can be regarded as the last one, and his labour can always be seen in terms of its marginal productivity. But what makes this link of interiority commutative is the materialisation of need. It is this which, through the decomposition due to Gossen's law, impregnates the sum of marginal units with its unitary project. The truth of marginalism does not lie outside, in pure quantity; nor does it lie inside, in the 'psychological': it lies in the dialectical uncovering of a constant exchange between interiority and exteriority which bases a pseudo-mathematics on a pseudo-psychology and crystallises the lived time of satisfied need in a hidden ordinalism of cardinals. This pseudo-mathematics is in fact more like a logistic. There is nothing to prevent the construction of a symbolism once some universal relations of pseudointeriority have been defined. It is sufficient that exteriority should be present somewhere. It is the true interiority of relations - that is to say, the individuated part's concrete membership of the whole - which is always absolutely unarnenable to symbolisation. In other words, certain moments of the dialectic can be expressed algebraically; but the dialectic itself in its real movement lies beyond + +Jny mathematics. + +54. 'In J 554 ... Don Juan de Mendoza searched the passengers travelling on his galleys from Catalonia to Italy. The result was the confiscation of 70,000 + +ducats, most of it on Genoese merchants,' (Braude!, op. cit., p. 478.) + +transformed into the mechanical, and the mechanical is raised to a kind of parasitic life; it is our inverted reflection, and in it, to make use of a celebrated phrase of Hegel's, 'Nature appears as the Idea in the form of Otherness'. There is, simply, no Idea here at all, but only material actions performed by individuals. Matter is this changing reflection of exteriority and interiority only within a social world which it sur- + +rounds completely and penetrates, in so far as it is worked. + +If materiality is everywhere and if it is indissolubly linked to the meanings engraved in it by praxis, if a group of men can act as a quasi-mechanical system and a thing can produce its own idea, what becomes of matter, that is to say, Being totally without meaning? The answer is simple: it does not appear anywltere in human experience. At any moment of History things are human precisely to the extent that men are things. A volcanic eruption destroys Herculaneum; in a way, this is man destroying himself by the volcano. It is the social and material unity of the town and its inhabitants which, within the human world, confers the unity of an event on something which without men would perhaps dissolve into an indefinite process without meaning. Matter could not be matter except for God and for pure matter, which is absurd. But does this lead us back to dualism? Not at all. We situate man in the world, and we simply note that for and through man this world cannot be anything but human. But the dialectic is precisely aform of monism, in that oppositions appear to it as moments which are posited for themselves for an instant before bursting. If we were not wholly matter, how could we act on matter, and how could it act on us? If man were not a specific entity which lives its condition in totalising transcendence, how could there be a material world? How could we conceive of the general possibility of any activity whatever? We always experience material reality as a threat to our lives, as resistance to our labour, as a limit to our knowledge and also as actual or possible instrumentality. But we experience it in society, where inertia, automatism and impenetrability act as a brake on our action, as well as in inert objects which resist our efforts. In both cases we experience this passive force within a process of signifying unification. Matter eludes us precisely to the extent that it is given to us and in us. The universe of science is a strict chain of significations. These are produced by practice and return to it in order to illuminate it. But each of them appears as temporary; even if it is still in the system tomorrow, the permanent possibility of the overthrow of the ensemble will modify it. The monism which starts .from tlte human world and situates man in + +pure matter in experience, he would have to be either a god or a stone; and in either case, it would not affect him: either he would produce it out of the incomprehensible fulguration of his intuitions, or else action would disappear and be replaced by mere energy equations. The only temporal movement would be decay, that is to say, an inverted dialectic moving from the complex to the simple, from the concrete wealth of the earth to the indifferentiation of a perfect equilibrium: in short there would be involution and dissolution instead of evolution. In our example we saw how things can absorb the whole of human activity, and then materialise and return it: it could not be otherwise. Nothing happens to men or to objects except in their material being and through the materiality of Being. But man is precisely the material reality from which matter gets its human functions. Every effect of Spanish money was a transformation and reflection of human activity: wherever we find that an action of gold disrupts human relations with-Out being willed by anyone, we discover an underlying profusion of human undertakings, directed towards individual or collective ends anel metamorphosed through the mediation of things . In the indissoluble couple of 'matter' and 'human undertakings', each term modifies the other: the passive unity of the object determines material circumstances which the individual or group transcend by their projects, that is, by a real and actiYe totalisation aimed at changing the world. This totalisation, however, would be pure negation if it were not inscribed in Being, if Being did not take hold of it as soon as it occurred, so as to transform it again into the pseudo-totality of the tool, and relate it as a finite determination to the whole universe. The totalising extraction from inert meanings involves a more or less profound and explicit decoding and understanding of the signifying ensemble. A project awakens significations; it momentarily restores their vigour and true unity in the transcendence which finally engraves this totality in some completely inert but already signifying material, which might be iron, marble or language, and which others animate with their movement from beneath, like stage-hands creating waves by crawling around under a piece of canvas. Everything changes and becomes confused; different meanings come together and merge in a passive recomposidon which, by substituting the fixity of Being for the indefinite progress of the actual totalisation, encloses the totality-object within its limits and produces the ensemble of contradictions which will set it in opposition to the Universe. For it is not comprehension which solidi- + +etc. It is not only the social memory of a collectivity, but also its transcendent but interior unity, the totality made up of all its dispersed activities, the solidified threat of the future and the synthetic relation of alterity by which men are connected. It is both its own Idea and the negation of the Idea, and in any case the perpetual enrichment of all. Without it, thoughts and actions would disappear, for they are inscribed in it as a hostile power, and it is through it that they act materially or mechanically on men and on things, and in it that they are subjected to the mechanical action of things and of reified ideas. A coin as a human object in circulation is subject to the laws of Nature through other human objects, such as caravels, waggons, etc. These laws of Nature are unified in it in so far as its circulation is a parasitic inertia which vampirises human actions. Through this changing unity of natural laws, as through the strange human laws which result from circulation, it produces an inverted unity of men. This can be summarised in one word: praxis as the unification of inorganic plurality becomes the practical unity of matter. Material forces gathered together in the passive unity of tools or machines perform actions: they unify other inorganic dispersals and thereby impose a material unification on the plurality of men. The movemen t of materiality, in fact, derives from men. But the praxis inscribed in the instrument by past labour defines behaviour a priori by sketching in its passive rigidity the outline of a sort of mechanical alterity which culminates in a division of labour. Precisely because matter mediates between men, men mediate between materialised praxes, and dispersal orders itself into a sort of quasisynthetic hierarchy reproducing the particular ordering imposed on + +materiality by past labour in the form of a human order. + +At the level which we have now come to, our investigation has already reached richer meanings, but is still abstract. Obviously the human world contains more than this non-humanity; and it will be necessary to pass through further layers of intelligibility before completing our dialectical investigation. Nonetheless, whatever its relations with other moments of the investigation, it is correct to present this moment as the determination of a specific structure of real History, namely the domination of man by worked matter. But, in so far as we have been able to follow the movement of this domination in our example, we have seen the expression of that terrible aspect of man in which he is the product of his product. (We have also seen that, at this stage of the inquiry, he is nothing more than this.) We must now study this within the unity of this moment of the investigation and in close + +poses itself between labourers to precisely the extent that it is indispensable for their work; the living solidarity of the group is destroyed even before it can take shape. What one man expects of another, if their relation is human, is defined in reciprocity, for expectation is a human act. There can only be such a thing as passive exigency between them if, within a complex group, divisions, separations and the rigidity of the organs of transmission replace living bonds by a mechanical statute of materiality (we shall come back to this point later). For it is possible for praxis as such to unite itself to praxis in reciprocal action, and for everyone to propose his own end in so far as he recognises that of the Other; but no praxis as such can even formulate an imperative, simply because exigency does not enter into the structure of reci- + +procity.59 + +As for sovereignty, which, as we shall see, is possessed by the third party, it is, as I shall try to show, nothing but freedom positing itself for itself. On the other hand, the expectation of others, affecting the individual labourer through the machine, is qualified by the machine itself. Simply by virtue of its structure, the machine says what task is to be performed. But even while human expectation - at least provided it achieves self-consciousness, and the group is not too large - relates to the worker in person, with his name and character, etc., the machine absorbs and depersonalises it, translating it into anyone's expectation; that is, into the expectation of the worker himself, in so far as he is not himself, but is defined by a universal pattern of behaviour, and is therefore other. In this way, it also makes his comrades Other than themselves, since they are merely the men who happen to be serving other machines, and by means of its demand it refers to the demand made on Others by other machines;. so that it ends up as a group of machines imposing a demand on any men, regardless of who they are. But this demand on the part of a tool designed to be used in a particular way, with particular rhythms, etc., is also transformed by its very materiality: it becomes exigency through receiving the double quality of + +alterity and passivity. + +Exigency, in fact, whether in the form of an order or a categorical imperative, constitutes itself in everyone as other than him. (He cannot modify it, but simply has to conform to it; it is beyond his control, and he may change entirely without it changing; in short, it does not + +59. We shall see below how the individual can affect himself with inertia by + +means of a pledge; exigency then becomes possible. + +men animating it with their labour power; and, for the manual labourers, it is the very object of which they are the objects and in which their actions are inscribed in advance. But this machine arises in the milieu of industrial c ompetition: it is the product of this competition and serves to intensify it. Competition as recurrent antagonism determines even the employer as Other than himselfin so far as it determines his action as a function of the Other and of the Other's action on Others. It was imported into France as Other, and was to inaugurate new destinie� and antagonisms for all and between all. (Consider, for example, the ' first cautious importation of English machinery around r830 by afew producers in the textile industry.) These defined classes and milieux within this perspective by necessarily constituting them as Others. (We shall see that about 1830 labourers and artisans, disqualified and proletarianised by these machines, lived their destinies like a conjuring trick which reduced them to ruins and completely transformed them without touching them.) There can be no doubt that a particular machine of aparticular type, which by its form expresses the techniques and social structures of the age, is, in itself, and as a means of realising, maintaining and expanding a certain sector of production, exactly what I said, namely, the Other in the milieu of the Other. Nor can it be doubted that, in this milieu, it has already absorbed into itself both the tensions of competition, so as to reflect them to the employer as exigency, and those of need and social constraint so as to turn them into exigencies in relation to the workers. In this way, every object, in so far as it exists within a given economic, technical and social complex, will in its turn become exigency through the mode and relations of production, and give rise to other exigencies in other objects. The basic intelligibility of this transformation at a distance of one material object by others naturally lies in the serial action of men; but this intelligibility requires precisely that the action of man should be constituted as inessential, that is, that it should take note of its own impotence and make itself a means to the accomplishment of some non-human end - that of worked matter in so far as it presents itself as passive activity, and sole producer of goods in the name of which it appears as a social force, as a social power and + +as unconditioned exigency. + +Admittedly it is logically and abstractly possible to consider material exigencies as hypothetical imperatives, such as 'If you want your wages .. .' or 'If productivity is to be increased and the number of workers reduced .. .' But this abstract view belongs in the milieu + +But, in so far as coal had become the main exigency of an industrial world in the process of equipping itself, the necessity of 'devouring oneself' affected both the mine and its owner, in so far as they were Others, fused by demand into a common alterity. Common exigency, then, arose out of the mine, as if matter itself could interiorise the exigency of other material sectors as a new imperative. To reduce costs, water had to be removed from the deep galleries; and the labour of men and beasts was not sufficient for this. In the eighteenth century, the first steam pump, which was made in England, inscribed itself within a tradition of effort and research which was itself crystallised in material objects, in experiments to be repeated and meanings deposited in books. In other words, the exigency of matter working through its men ended by nominating the material object it required. Papin and Newcomen had defined that particular exigency, and had thereby established the schemata and general principles of the invention before it was made: in this way, sustained by the growing consumption of coal and the gradual exhaustion of certain galleries, it was the object itself, as defined but not yet made, which became an exigency of being. And, through competition, the exigency which put every engineer under an obligation to make one, became, through Others, a matter of urgency for all potential inventors: a pump had to be made as quickly as possible. So, when Watt constructed his steam-engine, it already existed and his invention was no more than an improvement involving + +the separate condensation chamber. + +But this improvement was also a realisation, in that it was a means of increasing output - this being the justification for the industrial production of such machines. The same years (roughly the last decade of the eighteenth century) saw the appearance of other essential objects, in particular steamboats. The fundamental exigency determined similar exigencies in other sectors: it was negatively totalising, as inert matter must be. At the same time it produced exigency-man; that is, new generations, or certain groups within them, interiorised, as their own exigencies, the diffuse exigencies of materiality which previous generations had lived as t!leir limits. The inventor is a technician who makes himself into an exigency-man, an inessential mediation between present materiality and the future it demands (exige). A man who invents a steam-engine must himself be a steam-engine, as an inert ensemble of known principles relating to it; he must himself be the lack of a sufficiently powerful pump, as the old, but still real, exigency of the mine, and the future objectification of past praxis in a realisation + +steam-engines, concentration of workers around towns, etc.) involved air pollution for the constantly growing urban populations. It goes without saying that the biological effects were essentially harmful to the workers, in the first place because their habitat and mode of work brought them closer to the sources of the pollution; and secondly, because their starvation wages forced them to work all the time so that they had to stay in the smoke of the factories year in year out; and lastly, because the poison would have more effect on exhausted and undernourished bodies. In this sense, this counter-finality simply reproduces the class struggle (whose existence we are assuming, though we have not yet established its intelligibility): it is one aspect of that struggle. All the same we must notice that air pollution presupposes the iron-coal complex and, although it is obvious that this complex conditions one particular aspect of the class struggle and no other, air pollution is another consequence of the complex, contemporaneous + +with the structuring of the class but of a different order. + +And, in fact, pollution is also a counter-finality for the employer, or so, at least, one might think. Admittedly, he has sufficient means to spend his evenings and his Sundays out of town, in his country cottage. But still he does not breathe in less coal dust during the days. In a way, there was appreciably less inequality from the point of view of air pollution during working hours between the employer and the wageearners, and between the office clerks and the labourers. Bourgeois children themselves suffered in their development from this pollution, which sometimes reached truly cataclysmic proportions. (For example, in 1930 in the Upper Meuse region an excessive concentration of noxious gas produced a suffocating cloud which spread throughout the + +whole region killing sixty-five people.) + +Moreover, to stay with our example, coal fumes contain another definite counter-finality from the point of view of the employers. They are costly, as the following figures prove. In order to maintain the normal standard of cleanliness of any industrial city, Pittsburgh is committed to extra expenditure (over and above the average cleaning expenses for a city of its kind and with its population) amounting to 1,500,000 dollars for household washing, 7,500,000 dollars for general cleaning and 360,000 dollars for curtains. And in order to estimate the total cost we should have to add losses due to the corrosion of buildings, additional electricity consumption for those periods when concentrations of gas over the city make it necessary to switch on the + +So what is the difference between the bourgeoisie and the working class in this case? In the first place, from the beginnings of urban concentration the workers have been aware of the danger which threatens their lives. (The contrast is obvious for proletarianised peasants.) But before union organisations had been formed the demand for a hygiene policy was a luxury which the first resistance and combat groups could not afford: it was quite hard enough to prevent wages from falling. Besides, their impotence at that time made them prefer the factory, with all its counter-finalities, which allowed them to sell their labour power, to the disappearance of the factory, which would necessarily lead to the total destruction of dispensable groups. In the end, therefore, as a result of their situation at the time, counterfinality threw them back on the employers as a universal exigency which constituted the employers as a special group to precisely the extent that they failed to satisfY it. In other words, the nineteenth century industrialists, indifferent to the mortal dangers which threatened the working population, and to the real danger and even to the real costs that public squalor represented for them, were truly characterised as a special group by their refusal to constitute this effect of industrialisation as a universal counter-finality, though it could have been constituted as such through a well defined praxis. (Of course, this is not what made them a special group; but it was in this, amongst other things, + +that their distinctiveness was expressed.) + +From the outset means were in fact available of lessening the pollution if not of ending it entirely. Franklin had already suggested that coal smoke could be reused, since it was really just incompletely consumed carbon. Ultimately, smoke expressed the limitations of the machine at this time. Ninety per cent of the heat generated was lost as the fuel escaped up the chimney. But the failure to see this human and technical exigency, or to see it and take it seriously, is precisely what characterises the praxis of the bourgeoisie at this time. (Today the ensemble of safety and health measures is due to union pressures; and in the most advanced countries, the initiative sometimes reverts to the employers, in so far as they want to increase the productivity of labour; but the problems in this case are different.) Mines, as capital subject to a gradual process of exhaustion, created the first employing class (patronat), a curious mixture of traditionalist prudence and of wastage (wastage of human lives, of raw materials and of energy). They were constituted as a class (in this particular respect) by a refusal to see the effects of air pollution on the other class as a counter-finality. But they + +hide his wealth from the world; through his very life, as we have seen, he communicates a certain unity to the ensemble; he lays out his memory in drawers or on tables, until in the end it is everywhere, as is the ensemble of his practices and habits; when everything is outside him, sheltered behind the walls, in rooms where each piece of furniture is the materialisation of a memory, one can say that his interior life (Ia vie interieure) is literally none other than his home life (Ia vie d'interieur) and that his thoughts are defined by the inert and changing relations between his various pieces of furniture. But at the same time the exteriority of the thing becomes his own human exteriority. The inert separation which encloses his intimate life as a signifying materiality between four walls constitutes him as a material molecule among molecules: the relation he has, on this level, with other human beings, taken as a social, institutionalised practice, is in effect the absolute negation of any relation of interiority in the positive guise of mutual respect for possessions (and consequently for private life). It then becomes possible for the proprietor to assert that 'human beings are impenetrable', because he has given them in his person the impenetrability of matter (that is to say, the impossibility of distinct bodies occupying the same place at the same time). What we have here is an everyday phenomenon of reification; but the proprietor will find his truth and reality more completely in the thing possessed, which already addresses him as his own visible and tangible essence, the more he experiences, in his direct relation with this metamorphosis into an inanimate power, his mechanical isolation in the midst of a molecular + +dust. + +However, this dual, complementary aspect of private property is as yet no more than an abstraction: this property exists in a particular society, at a particular moment of History, and is dependent on the institutions of this society, which are themselves based on the development of the mode of production. Beneath the molecular relation between owners, we discover their serial conditioning within a structured social field and within a certain general movement of History. For example, in the case of rural properties, it may happen that the movement of investments which have been diverted, for other historical reasons, from agricultural enterprises results in disposable capital being concentrated for a time in rapidly developing industries. At this stage, agriculture, deprived of capital, will stick at the same technical level, the yield of the land will not increase, nor, consequently, its value. But by gradually improving the means of communication the + +development of industry may have the effect of raising land values. And if a sector of industry starts producing new agricultural tools, yields will increase and there will be a concentration of land, accompanied by expropriation. Throughout all these transformations, our proprietor's income and the value of his possessions will change (or at least they may change) from one year to another and they will change, as it were, in his hands, even if, like Gustave Flaubert, he is a bachelor and an artist and remains entirely passive. In other words, this interiorbeing as possessed materiality turns out to be conditioned by the whole of exteriority. His real person as an isolated molecule is separated from all others by an absolute vacuum and his personality-matter, as the object that he is, is subjected to the shifting laws of exteriority, as a perverse and demoniac interiority. Lastly, throughout the ups and downs, the crises and the good years, everything drives him back into need, through the fear of privation (in negative moments), or into expansion of his property as a real intensification of his powers. In other words, the negative moment sends him back to the immediate and absolute exigency of the organism as such; the positive moment becomes his own possible expansion as inert materiality, or as exigency. As soon as an objective ensemble is posited in a given society as the definition of an individual in his personal particularity and when as such it requires this individual to act on the entire practical and social field, and to preserve it (as an organism preserves itself) and develop it at the expense of the rest (as an organism feeds itself by drawing on its + +exterior milieu), the individual possesses an interest. + +But the material ensemble, being practico-inert, is already of itself a passive action on the practico-inert world around it; it reflects the exigencies of this world in the negative unity of passivity, and as its own exigencies, while at the same time it is already a teleological process acting on the whole of the field and reflected as an exigency by all sectors of materiality. In this way, to the small extent that the individual can escape or act, he becomes, in fact, the mediation between the exigencies of the material totality (mediated by everyone) and those of the limited totality which is himself. His being-outside-himself has become essential and, in so far as its truth lies in the practico-inert totality, it dissolves within him the characteristics of pseudo-interiority which appropriation gave him. Thus the individual finds his reality in a material object, conceived initially as an interiorising totality which functions, in effect, as an integrating part of an exteriorised totality; the more he tries to conserve and increase the object which is himself + +class interest in terms of the subjective characteristic of one individual coinciding with the subjective characteristics of all the Others, one would in fact have to begin by forgetting the dialectic of aIterity which renders this agreement as sur::h impossible. But, even if this could be done, it would still be necessary to understand the agreement of these molecular subjectivities: if one begins by positing them as different, it is not clear why a common exterior situation should not aggravate these differences; indeed, in the true milieu of alterity, in particular conditions, a common danger may, by its very urgency, accentuate antagonisms and conflicts. On the other hand, it is easy enough to point out that special interest as a material object in the world already has a structure of generality because it offers itself as the same for everyone in that it is this sameness that creates antagonisms in the milieu of alterity. But of course this is not altogether true: interest does not begin the same, and then divide into an infinity of oppositions; rather, in so far as the unity of the same equipment, the same techniques, and the same skills, constitutes the fundamental practical basis of all antagonism, it is the oppositions in a given social field which, through one another and in their confrontation, define the unity of all of them, in so far as they negate each of them as the universal characteristic of particular + +interests. + +Thus, classical economics tried to define identical interests as if they existed equally in every individual member of a group, and it did not take account of the fact that this very identity was the result of a serial process. In other words, when they stated some obvious truth, for example, that in a capitalist system the interest of the producer is, at least within limits, to intensify production and lower costs, they took themselves to be stating logically an analytical, Aristotelian truth, of the same kind as 'all men are mortal'. But, in fact, it is something quite different, partly because this interest involves a structure of serial aIterity of the individual being-outside-himself, and partly because it cannot be acquired by an individual except in certain totalising conditions, and through others. (For instance, in a France where a sort of tacit understanding and very real, if secret, agreements stifled any competition which small enterprises would have been unable to resist, in the name of Malthusianism, the interest of the employer, which seldom situated itself in a European or world context, was to increase productivity without increasing production; and thus this interest came to him from Others.) Thus the universality of particular interests can appear only to a form of thought (a rationality) which I will define + +Now, the individual thus signified by material practice is, in a different sense, reduced to a nonentity: he need only satisfy a few universal conditions (being an expropriated peasant, or a peasant in danger of being expropriated, or the son of a large, penurious peasant family, etc.); as a worker he is no more than a particular labour power used for various tasks, and renewed each day by his daily wage. Thus not only does his being exist before and outside him, in the movement of the economy, and ultimately in this particular machine (or these tools) which lay claim to him; but also, this Being represents the pure abstraction of himself. His object-being awaits him and patiently produces him from a distance: for example, the industrialisation of certain agricultural processes, by gradually preparing the ruin and expropriation of his father, patiently shapes the son until penury turns him into afree worker - an exploited man whose exploitation resides entirely in freedom of contract. The machine shapes its man to precisely the extent that man shapes machines (I shall deal with this process of shaping more extensively below). This means that it constitutes its servant, by a temporal, teleological process, as a machine for operating machines. It inverts the relations within the practical agent; it is a categorical imperative, which makes him an absolute but conscious means (in that he knows the imperative); a distributor of wages, which transforms his praxis (or labour power) into a commodity, that is, an inert product, while preserving for him the power of unifying a practical field. Indeed, to the extent that he makes himself a force of inert exteriority (or uses his substance in energy transformations which are inorganic in nature), it itself becomes a living thing and a pseudo- + +organism. + +Thus the machine defines and produces the reality of its servant, that is to say, it makes of him a practico-inert Being who will be a machine in so far as the machine is human and a man in so far as it remains, in spite of everything, a tool to be used: in short, it becomes his exact complement as an inverted man. At the same time, it determines his future as a living organism, just as it defines that of the employer. The difference is that it defines him negatively as an impossibility of living in the more or less long term. The machine does this not only through the counter-finalities which we have described (air pollution, destruction of the environment, occupational diseases, etc.), but also through representing,for him, in so far as it develops his being in the practical field of industrialisation, a permanent threat of reduced wages, of technological unemployment and of becoming disqualified. + +struggle, it struggles against particular effects of the private ownership of machines in the development of a specific moment of the historical process, as a fundamental relation of production, the praxis of the group, through the practical negation of its being-outside-itself as destiny, constitutes its destiny as future interest (through the material object), and as exigency contained in the destiny-materiality of + +changing itself into interest-materiality. + +The contradiction of the machine in the capitalist period is that it both creates <'nd negates the worker; this contradiction is materialised into a general destiny and becomes a fundamental condition of the assumption of consciousness, that is to say, of the negation of the negation. But the only negation which is possible as the unity of all, is not the negation of the machine in itself (which was attempted, about 1830, by craftsmen thrown out of work and by disqualified workers whose wages were steadily falling) and, consequently, of the worker in so far as he is its product and in so far as it is his being; it is the negation of the machine in so far as it is destiny in exteriority for the man it produces because, within a given social system, it controls him and he cannot control it in return. Thus all the worker can wish for is that the means of production and products as a whole should represent the material expansion of his class (there is no need to show here how this praxis moves towards the exigency of a classless society), that is to say, that this ensemble, simply through the movement which negates its character as destiny (organisation and struggle), should become his + +interest. + +This does not mean that a real socialisation of the means of production must, in a particular historical development, lead to the total elimination of interest itself as linking men in alterity through matter. On the contrary, interest arises, as always, out of alterity as the primary human practical relation, but as deformed by the matter which mediates it; and it maintains itself in the milieu of alterity. There are several workers' interests, but only one working class interest. This is because the employers, by introducing new machines within the framework of capitalism and appropriating them as their interest, constitute the destiny of the workers as the interest of the Other, controlling them in the form of counter-interest (destiny), and because in the moment of social struggle, that is to say, of the negation of the negation, the real material objective can only be the negation of the capitalist's interest in so far as it has become the worker's destiny, that is to say, the negation of the interest of the other as negation. And so, at a particular historical + +effectively supervised by trade unions in matters of hygiene, security and even of management. But the workers' interest never appears to the worker as an inert object of contemplation, but rather as the variable, practical meaning of his daily struggle against the necessary consequences of the capitalist process, and therefore both as present (to the extent that any successful action, however local, presents itself as the human negation of a destiny and, concretely, as the practical, negative use of machines against the employer in the milieu of liberal competition itself);65 and as future in a perspective whose opening and depth are conditioned by praxis itself as it assumes its total historical meaning. Thus, though we are not yet able to answer our questions: how can a class be dialectically intelligible, and how can a practical group be formed; and what type of dialectical reality can it represent? our investigation already gives us the rational certainty that workers do not have particular interests (as individuals subjected to forces of massification) and that their unification, if it occurs, is indissolubly bound up with the constitution of general interest (as such still unde- + +termined) as class interest. + +It is on this basis that class interest arises amongst employers: the moment which is, in effect, passed over in silence in the constitution of their material property as their private interest, is that neither land nor machines on their own can be productive; or, in other words, they need human means in order to be made to work. When I say 'passed over in silence', this does not imply any particular reflection on the attitude of employers to workers: in false innocence they may believe in the absolute value of the free wage contract; or, while having no illusions as to the nature of profit, they may believe that the workers are massified and too impotent to initiate anything. This abstract position, while making it possible to merge the worker and the machine in the real symbiosis of their common social activity, legitimates for them the constitution of a single social field : that of the employers, whose properties, as materials and means of production, oppose one another in their practico-inert being and thus oppose them. In a way, the multiplicity of these antagonisms has always been integrated into the ab- + +65. Strikes, as the collective refusal to use machines, turn machines - in so far as they require a certain level of production in particular circumstances - into the workers' weapon against the employers and, if the strike continues and shows signs of succeeding, the employer in turn will discover his destiny as a distant future possibility (for succeeding generations if not for him) through the medium + +of his present interest. + +stract forms of unity and universality. Although divided to the extent that each of them produces the same commodity as the other, NO industrialists will, in one way or another, affirm their positive unity as producers of wealth for mankind as a whole. This is the true meaning of Calvinism since the sixteenth century and of Puritanism up to the twentieth: the bourgeois is the man of God because God has put him on earth to continue the work of creation; and the pride of the Victorian industrialist watching his factory chimneys poisoning his native town involves a collective structure: even if he is the most powerful, he is not alone and, indeed, he needs other powerful men in order to be + +more powerful than them. + +What these abstract integrations really express is simply the otlter side of particular interest: based on the diversification of production and causing an increasingly extreme division of functions and of labour (at least in the nineteenth century), the private ownership of a factory implies solidarity in matter between the industrialist, his suppliers and his customers. We are in fact still in the domain of the practico-inert: it is the machine which requires certain materials (and which is thereby affected, for example, by improvements in communication) , and again, it is the machine which demands certain markets (that is to say, at a certain level of production, customers who are themselves producers). This is expressed in the practical field, and under the aberr:lnt appearance of 'private life', in social relations between employer-suppliers and employer-customers. (This is an extreme simplification because these social relations in fact concern the entire social field of production in so far as it is the private interest of the capitalists, and because such 'private' social relations also connect financiers and senior civil servants.) But these social relations - simple activities aimed at establishing the human relations between employers that their machines demand - are in fact eroded by exteriority (in so far as it is reconstituted in competition). Nothi�g really connects a particular supplier to a particular customer, other than a material situation which is itself given as variable (it only requires a lowering of transportation costs for it to become the particular interest of tltis particular customer to obtain his supplies elsewhere) . In this sense, the negative unity of 'everyone follows his own interest' erodes and neutralises the positive unity of their supposed solidarity in differentiation. In the drawing-rooms of the rich bourgeois, machines pay visits on one another and manifest their temporary concord. The concrete unity of the bourgeois class can be realised only through a common opposition to the common praxis of the workers. + +The exploited classes manifest themselves as exploited simply through the unity which, in the class milieu, makes the worker appear a man: for the employer, isolated in his private interest, the absolute refusal of the exploited to regard the machine as their destiny manifests itself as the possibility. that his own interest will be transformed into a destiny for him - not only through the still distant socialisation of the means of production, but also simply through the workers' resistance (to wage cuts, raising of norms, etc.), which in principle implies a reduction of profits, and therefore possible ruin (through competitors). But the unity of the workers' praxis, though the geographical dispersal of factories in the social field, gives each employer the possibility of a destiny, in so far as this possibility applies to him both as a general individual and as a particular moment of the capitalist process in its totality. In this sense, it is through the unity of the workers that the capitalists realise capital as the totality of the process instead of as a mere dispersal of interests which sometimes support and sometimes contra- + +dict one another. + +This change occurred towards the end of the eighteenth century and it can be observed in a number of writings of that period. Nasmyth wrote at the time that 'strikes do more good than harm because they serve to encourage inventions'. And Ure said: 'If capital takes science into its service, the recalcitrant labourer will be forced to be docile.' In reality, there is a circle here: the machine causes strikes precisely in so far as it aims to eliminate workers. The crucial fact is that capital becomes self-conscious in so far as it is unified in the milieu of the Other, and therefore in so far as it is an other totality; its general (and total) interest comes to it therefore as other, and negatively, as the need to destroy any possibility of the other class transforming its destiny into interest. This emerges very clearly in a remark by another classical economist: 'As far as most of our tools and powerful, automatic machines are concerned, industrialists could be led to adopt them only when forced to do so by strikes.' This, too, is only partially true: it is equally true, in fact, that in a period of competition the machine produces the machine, since it is the machine which determines the flow of investments. But this admission is historically interesting, in the sense that it shows the historical development of capital as producing itself for the bourgeois themselves under pressure from the Other class. And, in so far as the machine becomes an exigency for the capitalist himself, to the extent that it is his private interest, and in so far as the expansion of production directly or indirectly defines all the social and political + +activities of a human grouping, and in so far as the discovery of new sources of energy in certain countries becomes an external destiny for less favoured countries, the totality of 'capital', as the common interest of the capitalist class, also controls everyone as his destiny. At this level the State, as a class organ, represents an apparatus of struggle against capital as the destiny of the capitalists; and it is at this level, too, that the organs of the workers' struggle will create, in the other class, as an Other for itself, agreements and employers' organisations whose structure is determined by that of the workers' organisations. However, as long as the competitive system is not directly challenged by employers' organisations struggling against the counter-finalities of capital itself,66 the fractured unity of the social field of the capitalists is due to the fact that they can unite only to impose the changing multiplicity of their contradictions. In short, the capitalists' class interest, up to the end of the nineteenth century, was to maintain a system ruled by the conflict of private interests. Or, to take them in their being-outsidethemselves, their interest was the material totality of production goods - in so far as this totality, in its social materiality, negated the + +66. In this sense; monopolies, cartels, agreements, and even State intervention, in so far as they define the semi-competitive system in which we live, derive hoth from the transformation of the means of production (electric power, etc.) and from the working class itself in so far as, by the same process, it becomes one of the essential markets for mass-production. However, it should be remarked that this is an attempt on the part of industry to mitigate a structural contradiction of the capitalist process in itself. Producers find that, in themselves and as consumers, they are the destiny of capital, to precisely the extent that the capitalists' need to reinvest most of their profits has the contradictory double result of expanding production and diminishing the overall buying power of the working masses. Thus the destiny of the workers, as the negation of their standard of living by machines, becomes the destiny of the machine (in the social field of capitalism) as the negation of the possibility of selling its products; and this destiny exercises its control through crises. The policy of paying high wages in the context of controlled mass-production (which implies at least a partial negation of the competitive system), in the 'second industrial revolution', was undoubtedly an attempt at conscious organisation by the employers, in certain sectors of industry and in the most advanced countries, to transcend the deep contradictoriness of the capitalist process by making the producers themselves the consumers of their own products. At this level of the investigation, a new theoretical conflict will set Marxists (who think that the contradiction is simply veiled) in opposition to technocrats (who claim that it has been overcome) . We cannot go into this here; but it was worth explaining the reversal which, for the capitalists, transforms the destiny of the proletariat (even in grinding poverty) + +practical totalisation which the class without property wanted (namely, socialisation) and in so far as it affirmed the negative dispersal of the owners of capital with the whole of its practico-inert being. Thus everything becomes Other: for the possessors the threat of Others constitutes their general interest as Other, and this material interest is the exigency that relations between capitalists should be relations of Other to Other or, ih other words, the exigency that in so far as it determines the relations of production, the capitalist mode of production cannot unite the members of the dominant class except through their radical alterity. Thus we see, in effect, how particular interests ultimately express material being-outside-itself in the medium of the + +Other and one's own coming to oneself as Other than self. + +These formal remarks cannot, of course, claim to add anything at all to the certainty of the synthetic reconstruction which Marx carried out in Capital; they are not even intended to be marginal comments on it. By its very certainty, the reconstruction in effect defies commentary. But my remarks, though they are possible only on the basis of this reconstruction, which simultaneously recreates its method and its object, belong, logically, before this historical reconstruction, at a higher level of greater indeterminacy and generality: in so far as they have fixed certain relations of the practico-inert field in its generality, their purpose is simply to define the type of intelligibility which is involved in the Marxist reconstruction. I have simply tried to establish without prejudice (the inquiry is not yet complete) the basic relations between praxis and the material environment (in so far as it organises a practical field and defines the relations between men through their objects, and the relations between objects through men) in which a rational foundation for the certainty of dialectical investigations (l ' evidence de l' experience dialectique), which any reader of Marx can experience, can be found. And, as for conflicts of interest, in particular, my own investigations, as conducted in this book, have provided a means to pay off the hedonistic, utilitarian mortgage which makes of interest an irrational mixture of subjective conatus and objective con- + +ditions. + +There is a choice: either 'everyone follows his interest', which implies that divisions between men are natural - or it is divisions between men, resulting from the mode of production, which make interest (particular or general, individual or class) appear as a real moment of the relations between men. In the first case, interest as a fact of nature is an entirely unintelligible datum; indeed, the induction which posits + +structures of capitalist society, and which, as we have seen, relates only very indirectly to need itself, although need is always present as tension. The same would apply to a kind of quasi-socialist idealism which represented the employers as necessarily rapacious, that is to say, if the pursuit of profit, power, etc. (which exists only in and through a particular society and whose character and even intensity depend on the historical situation as a whole and on particular institutions) was treated as the natural force which moves individuals. We would then find, as we often do, the same unintelligible heterogeneity when confronted with workers grouped into unions and acting in accordance with the interests of their class against vampire-employers giving in to + +their rapacious instincts. + +In both these cases, the transition from false individual objectivity (conatus conceived as an external force) to the objective, abstract generality of the process simply becomes incomprehensible. And if the workers were fundamentally these interests posited in divergence and antagonism as natural realities, if their class interest were not negatively inscribed for everyone in the destiny prefabricated by machines, no propaganda, no political or union education, no emancipation would be possible. For every individual or class, interests are constituted in and through matter itself in so far as it defines and produces, as instruments, the men and relations suited to serving it (to serving production). For the men or groups under consideration their interests do not differentiate themselves from their being-outs ide-themselves in matter at work in so far as this being-outs ide-themselves controls the Other as destiny (through other men or groups). The structure of the material equipment alone determines what kind of interests are opera� tive. (It is this structure which creates a practical field of individual interests for one class and a field of general interest as its only possibility for another.) From this point of view, conflicts of interest are defined at the level of relations of production, or rather, they are these relations themselves: they appear as directly caused by the movement of worked matter, or rather as this matter itself in its exigencies and movement, in so far as each group (or person) struggles to regain control of it (in order to control production in and through their being-outside-themselves-in-it, that is to say, through the inert but powerful objectification of themselves in it) and to wrest this control + +from the Other. + +In this sense, it is not diversity of interests which gives rise to conflicts, but conflicts which produce interests, to the extent that worked + +matter imposes itself on struggling groups as an independent reality through the temporary impotence which emerges from their balance of forces. And, in this sense, interest is always a negation not only of the Other but also of the practico-inert being both of matter and of men in so far as this being is constituted by everyone as the destiny of the Other. But, in the same moment, it is precisely this interchangeability of man and his product in the medium of the practico-inert. The contradiction of interest is that it reveals itself in the individual or collective attempt to rediscover the original univocal bond between man and matter, that is to say, free constituent praxis, but that it is already in itself the perversion and petrification of this attempt by matter as the false counterpart of human action. In the practico-inert field, in other words, active man, inert in his product, becomes the only way of preventing his interest from becoming destiny, or of transforming his destiny into interest. But, as destiny and interest are two contradictory statutes of being-outside-oneself, and as these two statutes always exist together (although the one may enclose the other and veil it), they mark the limits of the practico-inert field, in so far as worked matter produces, as means to its ends, its men with their conflicts and their work relations, that is to say at that moment of the dialectical investigation in which man, defined by his being-outsidehimself (whether this is the seal he impresses on matter or the prefabrication of his functions by the coming together and passive organisation of material exigencies), is defined as bewitched matter (that is, precisely as an inorganic, worked materiality which develops a nonhuman activity because its passivity synthesises the serial infinity of + +human acts which sustain it). + +Thus for this being who reveals himself in the perpetual appropriation of his praxis by the technical and social environment, destiny threatens as a mechanical fatality ; and his struggle against destiny as such cannot itself be conceived as free human affirmation: it must appear as a means of safeguarding, or at least serving, his interest. Interest therefore appears as the inorganic materiality of the individual or group seen as an absolute and irreducible being which subordinates itself to praxis as a way of preserving itself in its practico-inert exteriority. In other words, it is the passive, inverted image of freedom, and the only way in which freedom can produce itself (and become conscious of itself) in the shifting hell of the field of practical passivity. + +JNecessity as a New Structure of Dialectical + +Investigation + +At its most immediate level, dialectical investigation (l' experience dialectique) has emerged as praxis elucidating itself in order to control its own development. The certainty of this primary experience, in which doing grounded its consciousness of itself, provides us with one certainty: it is reality itself which is revealed as presence to itself. The only concrete basis for the historical dialectic is the dialectical structure of individual action. And, in so far as we have been able provisionally to abstract this action from the social milieu in which it is in fact embedded, we have discovered a complete development of dialectical intelligibility as the logic of practical totalisation and of real temporalisation. But this investigation, just because it is its own object, provides us with complete transparency but not necessity. Since man becomes dialectical by acting on matter, and since knowledge is action in so far as action is knowledge, this constitutes an indubitable fact. Indubita- + +bility, however, is not necessity. + +And as soon as we tried to reach the more complex, more concrete reality of everyday life, we discovered a multiplicity of discrete quantities, which is capable of being studied by analytical Reason. The fact that this multiplicity reveals itself on the level of totalising synthesis rather than on that of simple living organisms is irrelevant; and so is the fact that the origin of dispersal is itself dialectical: the plurality of human actions is still a negation of the dialectical unity of each praxis. But since these actions as a whole - of which some are done by groups, and others by individuals - act on a single material field (an isolated Indian village in the virgin forest of Brazil, or the soil and sub-soil of a country or of the whole world), and since this field, which was originally united by its bond of univocal practical interiority to everyone is, in its passivity, the basis and support of the multiplicity of determinations, we have discovered, by deepening our investigation, that men unwittingly realise their own unity in the form of antagonistic al terity through the material field in which they are dispersed and through the multiplicity of unifying actions which they perform upon + +this field. Thus while the plurality of bodies and actions, i f i t is conceived directly, produces isolation, it is transformed into a unifying + +factor if it is reBected to men through worked matter. + +This is apparent in the most everyday objectivity: from my window I can see men who do not know each other walking across a square to jobs which, at least at the present level of the investigation, isolate them from one another; I can also see a group of people waiting for a bus, while none of them pays the slightest attention to the others - all eyes are turned towards the rue de Rennes, looking out for the bus which is about to arrive. In this state of semi-isolation, it is obvious that they are united by the street, the square, the paving-stones and the asphalt, the pedestrian crossings, and the bus, that is to say, by the material underside of a passivised praxis. But this unity is itself that of a material system, and in this sense it is highly ambiguous. It can be called dialectical in so far as the ensemble under consideration has been totalised by actions; and also in so far as scarcity, in any form, transforms separation into antagonism. But from another point of view, if dialectic is totalisation, materiality cannot be said to totalise: the avatars of Spanish gold did not totalise the practices of the nations and cities of the Mediterranean; they absorbed them and gave them the passive unity of interpenetration. Moreover, the inversion of activity into passivity, combined with the transformation of the diverse into a totalised inertia, has the effect of inverting both relations of exteriority and relations of interiority: quantity controls reified men in so far as these same men magically haunt quantity. Everything changes its sign when we enter the domain of the negative; from the point of view of this new logic, the unity of men through matter can only be their separation. In other words, separation ceases to be a pure relation of exteriority and becomes a bond of lived interiority. People are separated by alteri�y, by antagonisms, by their place in the system; but these separations, such as hatred, Bight, etc., are also modes of connection. However, since matter unites men in so far as it binds them together and forces them to enter a material system, it unifies them in so far as they are inertia. We have already seen how, through its quality as inorganic inertia, the organism can come into contact with the non-organised world; what we find here is passive materiality, as an elementary structure of the human organism, in thrall to an inorganic matter which has taken away its power of transcendence towards organised action. To stop at this level would lead to a very elementary and very false picture of the materialist dialectic - which is, unfortunately, most widespread: + +jected to constraint as to an exterior force, with all the contingent opacity of a fact; it appears as violence in so far as it opposes itself to free praxis. Nor is the discovery of necessity to be found in that gradual confinement of action which finally reduces the number of possibilities to one, in relation to a given end, and on the basis of certain already constructed means. When only one course is possible (for moving a material ensemble from one state to another, for going from one place to another, or from one person to another, or from one idea to another), and when this course exists and opens or offers itself, then praxis will conceive of itself as creating it - and rightly so, since, without it, neither the possibilities nor the means would exist as such. Thus the synthetic, royal road to comprehension, in the domain of thought, is a synthetic advance which is given negatively, as incapable of being otherwise, through the positive consciousness of becoming everything it can become. The unfolding of action and the conformity between the result achieved and the result intended cannot in fact give rise to any apodicticity except of the Other and by means of the + +Other, and on another level of the investigation. + +This shows that the first practical experience of necessity occurs in the unconstrained activity of the individual to the extent that the final result, though conforming to the one anticipated, also appears as radically Other, in that it has never been the object of an intention on the part of the agent. This elementary type of necessity is already to be found in mathematics ; at the end of a proof, the last proposition is transformed into an other which is just a statement of the theorem to be demonstrated. The difference is that the mathematician uses the dialectical fact of the transformed result as a method. The moment of necessity in practical experience is the simultaneous recognition of the same as Other and of the Other as the same. Let there be no misunderstanding: a solitary activity involving a tool undergoes transformations due to the nature of the chosen instrument or of the object on which it is used. But these transformations, transcended, corrected and controlled, do not alter praxis, even if they force it to modify itself, to make deviations, etc. : the metamorphoses of praxis are dialectical and form part of praxis as inevitable, living moments linked by relations of interiority; failure itself is integrated into the movement, as a final term and destruction of the dialectic in the same way as our death may be said to be part of our life. Moreover, in the case of solitary activity, failure returns to throw light upon the whole of the praxis and reveals within it the real reasons for our defeat: + +we were wrong to undertake it, or we chose the wrong means. In general, failure, illuminating past movement, shows us that we were already certain to fail, or, in other words, that an objectively inappropriate action produces in interiority in one form or another (stubbornness, haste, etc.) the knowledge of its inappropriateness. But when this knowledge is absent, failure still exists within praxis itself as a + +dialectical possibility of negation. + +Necessity appears in experience when we are robbed of our action by worked matter, not in so far as it is pure materiality but in so far as it is materialised praxis. In this moment, the tool made by an Other represents an element of exteriority in the dialectical field of interaction; but this exteriority does not derive from the external connections which are characteristic of inorganic materiality. All these connections are effectively taken up in the practical field of action. Exteriority exists to the extent that the tool as materiality is part of other fields of interiority. Finally, it is primarily a matter not of fields determined by the deliberate praxis of individuals or groups, but of the quasidialectical field whose fugitive unity does not come from anyone, but proceeds from matter to men who mediate between different sectors of materiality. In this way, a magical field of quasi-dialectical counterfinality comes to be constituted: everything acts on everything else from a distance, and the slightest novelty produces complete devastation, just as if the material ensemble were a true totality. And the instrument used by a given individual or community is transformed + +externally within the very hands which use it. + +During the period of Spanish hegemony, for example, gold could be real power for a person or collectivity. And, in so far as a historical agent is defined by his obj ective reality, and therefore by his objectification, this precious metal became, for a given society, this objectification itself; and objectifying praxis came to be defined, in turn, by its use of gold, that is to say, by the distribution of wealth (capitalisation, the financing of enterprises, items of expenditure, etc.). But in addition to being the mode of exteriorising interiority for particular individual or collective agents, what gold represented for the agent was existence in total exteriority, since its value at any particular time ,was determined by the whole of History; and in this way, to the extent that a prince or merchant realised his objective reality, it eluded him. But this exteriority refers back to material totalities in which every element acts at a distance as in an organic whole (the discovery of a mine, a massive influx of precious metals, the discovery of a new technical process, + +etc.). In this WClY, the haemorrhage of objective reality, which is emptied of its meaning in the hands of the agent, takes on a definite meaning when interpreted in terms of the developing totality. The ruin of a particular Genoese merchant can be interpreted from within his praxis, but in order for it to be intelligible it must also be seen as coming from outside as a result of the accumulation of stocks of precious metals, etc., to the extent that the Mediterranean is, as Braudel says, a + +material unity. + +There is no a priori reason why the transformation of the result should be understood by the agent: everything depends upon the instruments of thought provided for him by hi" period, class and historical circumstances. On the other hand, at the present level of development of our knowledge, it is possible to claim that this transformation is always intelligible, provided one has the necessary instruments at one's disposal; in other words, it defines its own type of rationality. The point is to conceive the praxis and its result from nvo inseparable points of view: that of objectification (or of man acting on matter) and that of objectivity (or of totalised matter acting on man). It is necessary to grasp how the concerted result of a practice, as a new fact, can produce a universal modification in the material quasitotality, and how it can receive from this moving, inorganic totality a sort of passive modification which makes it Other than it is. The example of deforestation is very clear: uprooting a tree in a field of sorghum becomes deforestation from the point of view of a large plain and of terraces of loess, united by the work of separate men; and deforestation as the real meaning of the individual action of uprooting is simply the negative union of all those who are isolated by the material totality which they have produced. Thus the transformation of the act is completely intelligible from the point of view of a process of comprehension which, having evaluated its end in isolation, strives to comprehend it in terms not only of the massification of the peasants (identity of work, repetition), but also of the constitution of a material totality which abolishes separations in the common unity of a destiny (floods) and, lastly, of new material totalities created on this basis and separately. Although this doubly referring work can be done by an isolated agent only with difficulty, there is no reason in principle why he should not do it; in other words, it is possible for anyone to comprehend himself in his action both from the outside and from within: this is proved by the fact that the Chinese government's propaganda against deforestation explained the totalised meaning of his familial + +praxis to everyone. The experience of necessity is all the more obvious, all the more blinding, to the extent that every moment of the praxis has been clear and conscious, and that the choice of means has been deliberate. And it should be remembered that, as it becomes richer, praxis gradually reduces the number of possibilities to one and, in the end, eliminates itself, as dialectical unfolding and as work, in favour of + +a result inscribed in things. + +We have seen that the agent's real aim, and (this comes to the same thing) the age:lt himself, can only be assessed in the light of the result. It is Madame Bovary who i lluminates Flaubert, not the reverse. But if an other, broader result, bound up with the present totality, always superimposes itself on the result which has been intended and achieved, then what is assessed from the point of view of totalised objectivity is not only the aim, but also the agent himself in so far as he is nothing Other than his objectification through praxis. It is therefore necessary to recognise oneself as Other in one's own individual objectification on the basis of an other result. And this recognition is an experience of necessity because it shows us an unconstrained irreducibility inside the framework of intelligibility. This individual experience can occur only through the freedom of praxis (as I defined it in The Problem of Method); it is the free fullness of successful action providing me with the objective result as irreducibility: if I have made mistakes or been subject to constraints, it is always possible that they have falsified the result. But ifI take full responsibility for the operation, I shall discover necessity as ineluctable. In other words, the basic experience of necessity is that of a retroactive power eroding my freedom, from the final objectivity to the original decision, but nevertheless emerging from it; it is the negation of freedom in the domain of complete freedom, sustained by freedom itself, and proportional to the very completeness of this freedom (degree of consciousness, instruments of thought, practical success, etc.). In this sense, it is the experience of the Other, not in so far as he is my adversary, but in so far as his dispersed praxis, totalised by matter, turns back on me in order to transform me; it is the historical experience of matter as praxis without an author, or of praxis as the signifying inertia which signifies me. We shall find that this experience becomes more complex as our investigation progresses, but for the present we may say: the man who looks at his work, who recognises himself in it completely, and who also does not recognise himself in it at all; the man who can say both: 'This is not what I wanted' and '} understand that this is what I have done and that I could not do + +anything else', and whose free praxis refers him to his prefabricated being and who recognises himself equally in both - this man grasps, in an immediate dialectical movement, necessity as the destiny in exteri- + +ority of freedom. + +Should we describe this as alienation? Obviously we should, in that he returns to himselfas Other. However, a distinction must be made: alienation in the Marxist sense begins with exploitation. Should we go back to Hegel who sees alienation as a constant characteristic of all kinds of objectification? Yes and no. We must recognise that the original relation between praxis as totalisation and materiality as passivity obliges man to objectify himself in a milieu which is not his own, and to treat an inorganic totality as his own objective reality. It is this relation between interiority and exteriority which originally constituted praxis as a relation of the organism to its material environment; and there can be no doubt that as soon as man begins to designate himself not as the mere reproduction of his life, but as the ensemble of products which reproduce his life, he discovers himself as Other in the world of objectivity; totalised matter, as inert objectification perpetuated by inertia, is in effect non-human or even anti-human. All of us spend our lives engraving our maleficent image on things, and it fascinates and bewilders us if we try to understand ourselves through it, although we are ourselves the totalising movement which + +results in this particular objectification. + +68 + +68. It is the necessity for the practical agent to discover himself in the organised inorganic as a material being, and this necessary objectification as grasping himself in the world and outside himself in the world, which makes man into what Heidegger calls a 'being of distances'. But it is very important to notice that he first discovers himself as the real object of his praxis in a milieu which is not that of his practical life, so that his knowledge of himself is knowledge of himself as inertia stamped with a seal (whereas, in fact, he is the movement by which he transcends material conditioning through the act of placing his seal on the inorganic). Thus the practical agent is an organism transcending himself by an action, and his objective perception of himself presents him as an inanimate object, the result of an operation, whether it is a statue, a machine or his particular interest. For those who have read Being and Nothingness, I can describe the foundation of necessity as practice: it is the For-Itself, as agent, revealing itself initially as inert or, at best, as practico-inert, in the milieu of the In-Itself. This, one might say, is because the very structure of action as the organisation of the unorganised primarily relates the For-Itself to its alienated being as Being in itself. This inert materiality of man as the foundation of all knowledge of himself by himself is, therefore , an alienation of knowledge as well as a knowledge of alienation. Necessity, for man, is conceiving oneself originally as Other than one is + +belongs to the employers, is unimportant; and we can say with assurance that this is how capitalism saw itself at the beginning of the first industrial revolution: an inert milieu in which transmutations of energy could take place provided they were produced by an exterior energy source. However, this need not correspond to any particular manufacturer's judgement of himself when he tries to know himself as an individual: on the contrary, he will regard himself as a bold innovator (if he has just bought a new machine, if his factory is expanding) or as a wise man (if he is refusing to take an interest in some invention). Employers as Other, (the ensemble of his competitors, suppliers and clients) however, he will judge in this way; but this Other body of employers exists in him as his own (relative or total) powerlessness to change anything ('Personally, I would be only too happy to .. .'). Thus he will rediscover in himself, as his negative social being and as caused impotence, the inertia which he considers to be a constituent + +characteristic of the being of Others. + +He is not entirely mistaken. It must be recognised that his impotence is created for him out of the inertia of Others, and is lived by Others as an other inertia reducing them to impotence. It should also be understood that, for him and for Others, impotence is simply the level of his production in so far as it is conditioned by total production in terms of the system and the conjuncture. It is on the basis of this being-outside in a field of unifying materiality on the part of everyone that Marx can describe the process of capital as an 'anti-social force' developed within a definite social field and positing itself for itself. But this inertia of impotence, in so far as it can also be conscious of itself as impotence through inertia (circumstances, or a competitor's innovation can define ' a manufacturer's pseudo-impotence as inertia for him: 'I should have suspected something, I should have accepted so and so's proposal,' etc.). And in so far as it constitutes itself as the reality of the individual (or group), and as the negative medium in which external transmutations of energy produce praxis in the form of a transformation of energy conditioned from the outside but producing itself as human value, we can regard it as the social Being of man at the fundamental level, that is to say, in so far as there are several people within a practical field totalised by the mode of production. At an elementary level of the social (and we shall see that there are others), everyone must become conscious of lzis being as the inorganic materiality of the outside interiorising itself in the form of a bond linking him to everyone else. We shall try to see social Being from the point of view of the practico- + +complex activity, and membership of a class. At the ongm of this membership, there are passive syntheses of materiality. And these syntheses represent both the general conditions of social activity and our most immediate, crudest objective reality. They already exist; they are simply the crystallised practice of previous generations: individuals find an existence already sketched out for them at birth; they 'have their position in life and their personal development assigned to them by their class'. 69 What is 'assigned' to them is a type of work, and a material condition and a standard of living tied to this activity; it is a fundamental attitude, as well as a determinate provision of material and intellectual tools; it is a strictly limited field of possibilities. Thus Claude Lanzmann is right when he says: 'A working woman who earns 25,000 francs a month and contracts chronic eczema by handling Dop shampoo eight hours a day is wholly reduced to her work, her fatigue, her wages and the material impossibilities that these wages assign to her: the impossibility of eating properly, of buying shoes, of sending her child to the country, and of satisfying her most modest wishes. Oppression does not reach the oppressed in a particular sector of their life; it constitutes this life in its totality. They are not people plus needs: they are completely reducible to their needs. There is no distance between self and self, no essence is hidden within the bounds of interiority: the person exists outside, in his relation to the world, and visible to all; he coincides exactly with his objective reality.'70 + +But this objective reality involves an obvious contradiction: it is both the individual and his predetermination through generality: the working woman is expected in bourgeois society, her place is marked in advance by the capitalist 'process', by national production requirements and by the particular needs of the Dop shampoo factory. Her life and destiny can be determined before sl,e gets her job, and this prefabricated reality must be conceived in the mode of being, in the pure materiality of the in-itself. The role and attitude imposed on her by her work and consumption have never even been the object of an intention; they have been created as the negative aspect of an ensemble of directed activities; and as these activities are teleological, the unity of this prefabrication remains human, as a sort of negative reflection of ends pursued outside it, or, in other words, as a result of counter- + +69. The German Ideology, Moscow, 1964, pp. 69-70. + +70. Les Temps Afodernes, special issuc on the Left, Nos 11 2-1 3, (195 5), p. + +1647. + +finality. At the same time, this material apparatus in which everything is meticulously controlled as if by a sadistic will is the working woman herself. This is what Marx elucidated in The German Ideology: 'The conditions under which individuals have intercourse with each other, so long as the above-mentioned contradiction is absent, are conditions appertaining to their individuality, in no way external to them; conditions under which these definite individuals, living under definite relationships, can alone produce their material life and what is connected with it, are thus the conditions of their self-activity and are + +produced by this self-activity.'71 + +Marx here refers to the contradiction which opposes the productive forces to the relations of production. But this is really the same contradiction as that mentioned above, which forces the working woman to live a prefabricated destiny as her reality. She would try in vain to take refuge in intimate 'privacy' ; such a remedy would betray her directly, and become simply a mode of subjective realisation of objectivity. When semi-automatic machines were first introduced, investigations showed that specialised women workers indulged in sexual fantasies as they worked: they recalled their bedrooms, their beds, the previous night - everything that specially concerns a person in the isolation of the self-enclosed couple. But it was the machine in them which was dreaming of love : the kind of attention demanded by their work allowed them neither distraction (thinking of something else) nor total mental application (thinking would slow down their movements). The machine demands and creates in the worker an inverted semiautomatism which complements it: an explosive mixture of unconsciousness and vigilance. The mind is absorbed but not used ; it is concentrated in lateral supervision; and the body functions 'mechanically' while yet remaining under surveillance. Conscious life overflows the job; the minutes of false distraction have to be lived one by one ; they must be lived without concentration, and there can be no attention to detail, or to systematic ideas ; otherwise the lateral function of supervision would be impeded, and movements would be slowed down. It + +is therefore appropriate to sink into passivity. + +In similar situations, men have less tendency to indulge in erotic fantasies; this is because they are the 'first sex', the active sex; if they were to think of 'taking' a woman, their work would suffer; conversely, work, by absorbing their total activity, cuts them off from sexuality. + +through men, and if material circumstances are preserved in it as significations, it is not because it is homogeneous with them (and passive like them), but on the contrary because human praxis has given it ahuman future by projecting it (as transcended and preserved) into this future. On the contrary, precisely because they have been worked and assembled by men, who have made them anti-human, the machine and the combination of exigencies contain the movementof transcendence in themselves and, in connection with this inert movement, the future of the ensemble is the mechanico-practical meaning of this totality in so far as it functions (that is to say, in so far as an exterior force enables it to realise itself as a pseudo-organic function). Thus the reason why past being cannot be transcended is that it is itself the inscription in being of a praxis which produces, beyond any particular human praxis, its own meaning as transcendent being. So the human praxis which lives in symbiosis with this inert practice and which is controlled by it as exigency constitutes itself as a mechanical means (in exteriority) of introducing mechanics amongst its characteristics as a human undertaking. It remains entirely what it is (if one takes it abstractly as a pure, isolated praxis) but its own future as transcendence of its past being is transcended by thisvery past-being in so far as it is already signified by + +the future. + +As I have said already, if the stratagems of the enemy lead a regiment to retreat towards an emplacement which seems protected but which has in fact been heavily mined, the practical freedom of the commanders who execute this retreat remainsunimpaired in each of its dialectical moments, but their ignorance of the trap the enemy has prepared for them means that their free praxis is the necessary means selected by the enemy of bringing this military unit to inevitable destruction. Thus some other freedom, supported by powerful material means, may force a praxis into the role of a blind process leading men toward a passive future which cannot be transcended: that of their own destruction. And, if we assume that - as is usually the + +case - + + the commanders could not know that the field wasmined, their praxis should not even be described as playing this role, but rather as objectively being this necessity itself. In any case, it should be noted that a praxis can constitute itself in this way only in the milieu of a praxis which transcends it and knows it better than it knows itself. Of course, it often happens that, in trying to avoid some annoyance, we fall into worse trouble; but if nobody has deliberately arranged the first danger in order to lead us into the second through the complicity + +of our personal activity, this involves nothing more than the inherent uncertainty of praxis; for every praxis, to some degree, takes account of its areas of ignorance, reckons on probabilities (in the strict sense of + +the term), makes wagers, and takes risks. + +The freedom of an action which ends in failure is simply freedom which fails, since the fundamental relation of the organism to its environment is univocal. Matter does not make a constitutive return to praxis in order to transform it into a controlling fatality. In the case of a trap, however, it is clear that the freedom of the enemy, through the complex of material means involved, from the initial shot to the mine field, has given our own freedom a negative aspect (envers), and has made it objectively a practico-inert process of counter-finality: so much so that the soldier who falls into the trap will, if he escapes, discover an extraordinary (but easily understood) paradox, conveyed by the colloquial expression: 'We've really been had.' To have: that is, to possess an enemy in so far as he is an inalienable praxis (and not, fol.'" example, because one is stronger or better armed). This petrification of freedom as such is obvious in military stratagems because once the material machine which forces us to destroy ourselves is set in motion, it is sustained and controlled by the living, practical freedom of the enemy. In the case of class-being as inertia which infiltrates freedom, the thing seems less obvious : for one thing, the workers who created the machines through their work are absent, perhaps dead; and in any case, it is not they but others - their exploiters - who desired our enslavement; indeed they did not desire it directly, but were essentially trying to increase their profit; besides, the empty position which each worker is expected to fill derives thereby from the diverse variety of exigencies which have come together without any particular action having presided over the process. Thus there is not really a freedom on the part of the employers to constitute the negative aspect in itself of the workers' praxes. But tlle univocal relation of interiority has transformed itself through the medium of the real meanings and real exigencies whose material object has been provided by human practices, whether multiple or unified, in false reciprocal interiority. And this false interiority, along with the prefabricated ends which cannot be transcended but which praxis must freely realise, is sufficient to transform this transcendence of Being into transcendence transcended by the Being to be transcended. Thus in the complex movement of alienated labour we have the inert Being of machinery as a material circumstance to be transcended, transcendence by praxis (setting in + +motion, use, and supervision) and transcendence of praxis (in so far as some exterior norm transfuses it as inert exigency) by that same Being, + +but to corne as an other meaning realising itself. + +This will apply on every plane and not just that of production. The worker is socially constituted as a practico-inert object to the extent that he receives a wage: he becomes a machine that has to be maintained and fed. Now, in deciding his budget in accordance with the needs created in him by his work (by satisfying above all his hunger, to the detriment of clothes and lodging), the nineteenth-century worker made himself what he was, that is to say, he practically and rationally determined the order of priority of his expenditure; he therefore decided in his free praxis, and through this very freedom he made himself what he was, what he is, and what he must be: a machine whose wages simply represent maintenance costS.74 At this level we will encounter the questions raised in The Prohiem of Method. We can now see why transcending one's class condition effectively means realising it. And since praxis, as the transparent movement of action, cannot alienate itself, we find different actions in everyone : one worker reads, another agitates, another finds time to do both, another has just bought a scooter, another plays the violin, and another does gardening. All these activities are constituted on the basis of particular circumstances, and they constitute the objective individuality of each person. But still, in so far as they are located, in spite of themselves, inside a framework of exigencies that cannot be transcended, they simply realise everyone's class being. Everyone makes himself signify by interiorising, by a free choice, the signification with which material exigencies have produced him as a signified being. Class-being, as practico-inert being mediated by the passive syntheses of worked matter, comes to men through men; for each of us it is our being- + +74. I say 'the nineteenth-century worker' because contemporary economists increasingly tend to regard wages as the portion of the national income socially assigned to each individual. We may well wonder whether this ethical conception of wages - based on old 'solidarist' theories - has anyadvantage other than 'drowning the fish' - that is to say, passing over class struggle in silence; whether, in effect, family allowances, social security, etc., do not represent what one might call a social portion of wages. It should be observed however that even so it is far from being the case that society as a whole provides this national contribution. In any case, the contemporary worker has entirely different characteristics, in many fields, than previous generations . But the problem of class-being, as a logical and dialectical problem of rationality, remains the same for all that. + +to imagine different forms of struggle, at the same time as giving their self-affirmation (that is to say, their ethico-practical reinteriorisation of the machine's exigencies and the temporalising development in action of structures prefabricated by it) the form of the only effective struggle that was possible in these circumstances and against these employers. In this situation, Being became the prefabricated Future as a negative determination of temporalisation. In other words, it appeared in action (at least to some people, in some circumstances, such as, for example, certain antagonistic relations with unskilled workers) as its solidified but incomprehensible contradiction, as an impossibility of going further, of desiring or comprehending any more, like an iron wall in translucidity. In a way, indeed, the limit is given and even interiorised by praxis itself (in our example, it appears inside individual relations themselves: work relations, politico-social relations, personal relations) of both skilled and unskilled workers; it even affects a simple greeting between a skilled and an unskilled worker, just as the relation between classes in the same period is visible in the greeting between an indus- + +trialist and one of his workers. + +For us, who belong to another society (still capitalist, but one whose structures are governed by new energy sources, new machines and mass production), these interiorised limits appear as the objective meaning of structural relations in the period of anarcho-syndicalism. Of course, we can neither see nor hear these men, and the meaning of their everyday individual praxis eludes us. But it is expressed everywhere in the collective actions of which society retains some memory, in the institutions which they produced, in the sectarian conflicts within the unions, in the speeches which express them and even in the dreams of certain anarchist journalists. Elsewhere I have quoted some statements by syndicalist leaders which affirm quite blandly that the exploitation of man by man is more deplorable the more skilled the work (there are thousands of such statements). This can be taken to mean that the exploitation of an illiterate labourer - who has no skill, but who exhausts himself in carrying enormous loads from one end of the workshop to the other - is not completely unjustified. Above all, this proves that such syndicalists (whatever they may have said or written) did not really understand that this i!Jiterate, possibly stupid labourer had been marked by society, even before he was born, as incapable of becoming a skilled worker. So for us the meaning of this is blindingly obvious; and this is a measure of our distance from them; and we too com prehend it in terms of our invisible walls: we can understand every + +petrified limit of human relations in terms of the invisible limit which reifies our own. I am not saying that for them this objective meaning was a priori incapable of being achieved : for example, the contacts between two societies with different structures, though always degrading for the underdeveloped society, lead certain groups in the underdeveloped society to see certain relations which were formerly simply produced in their objectivity. Supposing, for example - though it is historically absurd - that in the name of another trade union movement, established on the basis of mass production in advanced capitalist countries, foreign workers were able, in the course of an international dialogue, to point out to the anarcho-syndicalists certain ossified structures of social praxis, there is no a priori reason for denying that certain groups or individuals might have become conscious of them (at least it is not logically impossible). However, this does not in any way imply that they would have wanted to alter these structures; it is more likely that they would have engaged in the kind of secondary activity which might be called practices of justification. But, in any case, contacts - between differently structured proletariats - could not have had such a simple meaning at the beginning of the twentieth century, when, unknown to itself, the second industrial revolution was taking place. Today, such contacts exist, but they have a different meaning (France: for a long time backward in its development, with a more homogeneous working class in certain key-industries, and still a hierarchised one in other sectors; the United States: advanced capitalism, a destiny which was for a long time rejected in France, both by + +Malthusian employers and by the working class). + +The fact remains that it is always abstractly possible for any practico-inert limit to a human relation to reveal itself to the men it unites as the objective Being of their relation. But at this very moment, their experience of this meaning as real Being shows them that it has always existed, interiorised but petrified, in living praxis, even at the moment of subjectivity. It is simply that it then appeared both as an incomprehensible nothingness in the full development of some reciprocal activity and as a positive qualification of this practical fullness (suzerainty lived in the relation between the skilled and unskilled worker as the basis of the responsibilities of the suzerain and even of his love for the vassal). And precisely for that reason, the discovery of our Being is frightening (since it generally occurs in the midst of failure and conflict) - because it reveals that what one did not know was something one knew all along, in other words, because it retrospectively consti- + +positing freedom; but in so far as the end projected is in fact an inert, un transcendable meaning of the prefabricated future, value acquires an independent passive being. Instead of being pure praxis, laying down its own laws (which would deprive it of its characteristics of interior exteriority, that is, of transcendence in immanence, and which would reduce it to a mere act of awareness (prise de conscience)), it isolates itself. But, since its inertia necessarily makes it transcendable, and since its practico-inert characteristic is that it cannot be transcended, it posits itself as the transcendent unity of all possible transcendences, (depassements), that is to say, as the term which is untranscendable (because it is situated at infinity) and towards which every action transcends the material conditions which occasion it. In the case of anarcho-syndicalist humanism, for example, skilled labour became human value as soon as the conditions which had made it necessary began to make it impossible even to conceive of a different mode of being, constituted on the basis of unskilled labour. If he became conscious of himself, without this a priori limit and as a mere historical agent, the skilled worker would certainly have come to see his work as the dialectical, translucent development of human praxis within an exploitative system, in short, as the historical, dated actualisation of his reality as a man. But labour became impossible to trar.scend in him, because it also appeared as other; that is, when the actual praxis of the worker constituted itself as having to realise itself as other than itself, as a particular embodiment of an inert meaning which, even when embodied, would remain alien to it, or in other words, would remain the sign of all transcendences. However, value is different from exigency. They are two different structures within a single process. The imperative character of exigency is due to the fact that materiality is animated by the praxis of the other and to the fact that this praxis is revealed to me as both human and alien: it signifies me and awaits me, but it is not mine: it is myself as nothing. Value, on the other hand, is in a double movement: both the revealing of my praxis in its free development in so far as it posits itself as other within immanence, and the revealing of a future signification as an inertia which necessarily refers back to my freedom. In either case, the original structure is worked materiality as a bond between men, and praxis as absorbed and inverted by this matter. But in the first case, the inversion directly signifies me in so far as I am the means of realising a material aim; whereas in the second case, which arises at a different level of the investigation, I apprehend primarily my praxis, but only in so far as it transcends itself in its very freedom towards the Other-Being of all praxis; and, consequently, in so far as a controlling and created limit affects it with materiality. This new structure implies that the experience of praxis as the creator (or realiser) of value is new (originale): there is not any constraint in this case, but rather an (alienated) awareness of an identity between praxis itself, at its highest level of conscious translucidity, and a particular inert meaning which absorbs it and gives it its practico-inert statute as materiality. In short, value is not the alienation either of the aim or of realised objectivity; it is the alienation of praxis itself. In other words, it is praxis unwittingly revealing the inertia with which the practico-inert being of the practical agent affects it. From the point of view of ethics, this means that values are bound up with the existence of the practico-inert field, in other words with hell as the negation of its negation (which shows that their pseudo-positivity is entirely negative) and that if a liquidation of these structures is to be possible - a question + +Thus we have seen class-being as the practico-inert statute of individual or common praxis, as the future sentence, petrified in past being, which this praxis itself has to carry out and in which it must finally recognise itself in a new experience of necessity. But this practico-inert being appeared to us as a real moment of the individual or as the passive statute of an active group or, conversely, as the active pseudo-unity of an inert material ensemble. In order to understand it better, we must investigate a new structure, conditioned by the preceding ones and conditioning them in turn: for, as we have seen, classbeing is not a mere characteristic of untranscendable materiality existing as a separate quality in discrete entities isolate2 from one another (like, for example, height or colour of hair). In fact claSS-being, far from manifesting itself as an identity of being between independent realities, appears in this investigation (experience) as the material unity of individuals or, in other words, as the collective basis of their individuality. Our examples were designed to show that individuals realise their class statute through one another: from elementary praxis, from working in a workshop, everyone's class-being, in so far as it is a practico-inert exigency of machines, comes to him not only from the class which exploits him, but also from all his comrades; or rather, it comes to him from the class which exploits him and the machines which require him through the medium of his comrades and their universal character as + +exploited. + +At the same time, claSS-being defines itself for everyone as an inert (untranscendable) relation with his class comrades on the basis of certain structures. Destiny, general (and even particular) Interest, Exigency, Class Structures, Values as common limits, all necessarily direct our attention not only to a type of individual being which we have already described, but also, through it, to a type of collective being as the basis of all individual reality. I am not referring here to those active collectivities which organise themselves for a definite purpose and which we will study later under the name of groups. Nor am I referring to those ensembles which are both hot and cold, like an army, because they possess both the practical and historical activity of an organisation and the inert materiality of an institution. Rather, at a deeper level, as the basis of all individuation as well as all unity, I am + +experience and in various forms, in all the moments of activity and of alienation, not only as signs, as exigencies in the tool, hut also as a revelation of the world + +through this tool by labour, etc. + +occur in the practico-inert field and precisely to the extent that they are not individual organisms, or in other words, in so far as worked materiality itself makes itself into a synthesis (or false synthesis) of their being-outside-themselves-in-it. This is clearly reflected in our language, when an individual is said to be born into the working class or to have sprung from the proletariat (if he has emerged from it) or to belong to it, as if the class as a whole was a matrix, a milieu and a sort of passive weight (the idea of class viscosity is used to explain a worker's son's chances of emerging from the working class). In a word, class as collective being is in everyone to the extent that everyone is in it, and before 'getting organised' and 'producing apparatuses', it appears in the contradictory aspect of a sort of common inertia as a synthesis of multiplicity. These considerations, which normally satisfy sociologists, obviously cannot establish the intelligibility of fundamental socialities. We must abandon such vague descriptions and try to extend our dialectical investigation to include them. But, although class, as a fundamental structure, represents at a certain level the very substance of which groups and passive socialities are determinations, and although every collection of human beings, at the present time, expresses this substance in one way or another, or manifests the class divisions of society - both within themselves and in their inertia or praxis - we will not immediately attempt a definition of the practico-inert sociality of class. We shall examine the most obvious, immediate and superficial gatherings of the practical field, as they appear in everyday experience. And, since many of them arise as simple internal determinations of a substance with which they are homogeneous, they can be treated formally not in their particularity, but in so far as through themselves they are social beings in the practico-inert field: through themselves they will manifest to us what might be called their ontological intelligihility, and in a later moment we will be able, through them, to understand and fix this more fundamental reality, class. In The Problem of Method I called these inorganic social beings collectives. + +On this basis, it is possible to grasp our relations to the object in their complexity. On the one hand, we have effectively remained general individuals (in so far as we form part of this gathering, of course). Therefore the unity of the collection of commuters lies in the bus they are waiting for; in fact it is the bus, as a simple possibility of transport (not for transporting all of us, for we do not act together, but for transporting each of us). Thus, as an appearance and a first abstraction, a structure of universality really exists in the grouping; indeed, everyone is identical with the Other in so far as they are waiting for the bus. However, their acts of waiting are not a communal fact, but are lived separately as identical instances of the same act. From this point of view, the group is not structured; it is a gathering and the number of individuals in it is contingent. This means that any other number was possible (to the extent that the individuals are considered as arbitrary particles and that they have not collected together as a result of any common dialectical process). This is the level where conceptualisation has its place; that is to say, concepts are based on the molecular appearance of organisms and on the transcendent unity of + +the group (common interest). + +But this generality, as the fluid homogeneity of the gathering (in so far as its unity lies outside it), is just an abstract appearance, for it is actually constituted in its very multiplicity by its transcendent unity as a structured multiplicity. With a concept, in effect, everyone is the same as the Others in so far as he is himself. In the series, however, everyone becomes himself (as Other than self) in so far as he is other than the Others, and so, in so far as the Others are other than him. There can be no concept of a series, for every member is serial by virtue of his place in the order, and therefore by virtue of his alterity in so far as it is posited as irreducible. In arithmetic, this can be demonstrated by reference to numbers, both as concepts and as serial entities. All whole numbers, or integers, can be the object of the same concept, in so far as they all share the same characteristics; in particular, any whole number can be represented by the symbol n + I (if we take n = 0 for the number one). But for just this reason, the arithmetical series of integers, in so far as all of them are constituted by adding one to the preceding number, is a practical and material reality, constituted by an infinite series of unique entities; and the uniqueness of each number is due to the fact that it stands in the same relation to the one that precedes it as this one does to the one preceding it. In the case of ordinals, alterity also changes its meaning: it manifests itself in the + +synthetic: everyone is identical with the Other in so far as the others make him an Other acting on the Others; the formal, universal structure of alterity produces the formula of the series (la Raison de la sirie). In the formal, strictly practical, and limited case that we have been examining, the adoption of the serial mode remains a mere convenience, with no special influence on the individuals. But this simple example has the advantage of showing the emergence of new praticoinert characteristics: it reveals two characteristics of the inactive human gathering. The visible unity, in this case, in the time of the gathering (the totalised reality which they comprise for someone who sees them from a window or from the pavement opposite), is only an appearance; its origin for every observer to whom this totality is revealed, is integral praxis in so far as it is a perpetual organisation of its own dialectical field and, in practico-inert objectivity, the general, inert link between all the people in a field which is limited by its instrumentality, in so far as it is social - that is to say, in so far as its inert, instrumental materiality ultimately refers back to the order of historical movement combined with their true being-outside�themselves in a particular practical object which, far from being a symbol, is a material being which produces their unity within itself and imposes it on them + +through the inert practices of the practico-inert field. + +In short, the visible unity of a gathering is produced partly by accidental factors (accidental at this level of the investigation - their unity will be restored in a broader movement of totalisation), and partly by the real but transcendent unity of a practico-inert object, in so far as this unity, in the development of a directed process, produces itself as the real material unity of the individuals in a given multiplicity, which it itself defines and limits. I have already said that this unity is not symbolic; it is now possible to see why. It is because it has nothing to symbolise; it is what unites everything. And if, in special circumstances, it is possible to see a symbolic relation between the gathering, as a visible assembly of discrete particles (where it presents itself in a visible form), and its objective unity, this is to be found in the small visible crowd which, by its presence as a gathering, becomes a symbol of the practical unity of its interest or of some other object which is produced as its inert synthesis. This unity itself, in so far as it is practico-inert, may present itself to individuals through a larger praxis of which they are either the inert means, the ends or the objects, or a combination .of these, and which constitutes the true synthetic field of their gathering and which produces them in the object wiTh + +their new laws of unified multiplicity. This praxis unifies them by producing the object in which they are already inscribed, in which their forms are negatively determined, and, in so far as it is already other (affected by the entire inertia of matter), it is this praxis which + +produces them in common in other unity. + +The second point to be made is that the apparent absence of structure in the gathering (or its apparent structures) does not correspond to objective reality: if they were all unaware of each other and if they carried their social isolation behaviour to the limit, the passive unity of the gathering in the ohject would both require and produce an ordinal structure from the multiplicity of the organisms. In other words, what presents itself to perception either as a sort of organised totality (men huddled together, waiting) or as a dispersal, possesses, as a collecting together of men by the object, a completely different basic structure which, by means of serial ordering, transcends the conflict between exterior and interior, between unity and identity. From the point of view of the activity-institution (the exact meaning of these terms will be clarified later), which is represented in Paris by the RATP (the public transport authority), the small gathering which slowly forms around the bus stop, apparently by a process of mere aggregation, already has a serial structure. It was produced in adyance as the structure of some unknown group by the ticket machine attached to the bus stop. Everyone realises it for himself and confirms it for Others through his own individual praxis and his own ends. This does not mean that he helps to create an active group by freely determining, with other individuals, the end, the means, and the division of tasks; it means that he actualises his being-outside-himself as a reality shared by several people and which already exists, and awaits him, by means of an inert practice, endowed by instrumentality, whose meaning is that it integrates him into an ordered multiplicity by assigning him + +aplace in a prefabricated seriality. + +In this sense, the indifferentiation of beings-outside-themselves in the passive unity of an object exists between them as a serial order, as separation-unity in the practico-inert milieu of the Other. In other words, there is an objective, fundamental connection between collective unity as a transcendence which is giyen to the gathering by the future (and the past), and seriality as everyone's practico-inert actualisation of a relation with Others in so far as this relation determines him in his being and already awaits him. The thing as common heing produces seriality as its own practico-inert being-outside-itself in the + +plurality of practical organisms; everyone realises himself outside himself in the objective unity of interpenetration in so far as he constitutes himself in the gathering as an objective element of a series. Or again, as we shall see more clearly later, whatever it may be, and whatever the circumstances, the series constitutes itself on the basis of the unity-object and, conversely, it is in the serial milieu and through serial behaviour that the individual achieves practical and theoretical + +participation in common being. + +There are serial behaviour, serial feelings and serial thoughts; in other words a series is a mode of being for individuals both in relation to one another and in relation to their common being and this mode of being transforms all their structures. In this way, it is useful to distinguish serial praxis (as the praxis of the individual in sa far as he is a member of the series and as the praxis of the whole series, or of the series totalised through individuals) both from common praxis (group action) and from individual, constituent praxis. Conversely, in every non-serial praxis, a serial praxis will be found, as the practico-inert structure of the praxis in so far as it is social. And, just as there is a logic of the practico-inert layer, there are also structures proper to the thought which is produced at this social level of activity; in other words, there is a rationality of the theoretical and practical behaviour of an agent as a member of a series. Lastly, to the extent that the series represents the use of alterity as a bond between men under the passive action of an object, and as this passive action defines the general type of alterity which serves as a bond, alterity is, ultimately, the practicoinert object itself in so far as it produces itself in the milieu of multiplicity with its own particular exigencies. Indeed, every Other is both Other than himself and Other than Others, in so far as their relations constitute both him and Others in accordance with an objective, practical, inert rule of alterity (or a formal particularisation of this + +alterity). + +Thus this rule - the formula of the series - is common to all precisely to the extent that they differentiate themselves. I say common, but not identical: for identity is separation, whereas the formula of the series is a dynamic scheme which determines each through all and all through each. The Other, as formula of the series and as a factor in every particular case of alterity, therefore becomes, beyond its structure of identity and its structure of alterity, a being common to all (as negated and preserved interchangeability). At this level, beyond the concept and the rule, the Other is me in every Other and every Other in me + +and everyone as Other in all the Others; finally, it is the passive Unity of the multiplicity in so far as it exists in itself; it is the reinteriorisation of exteriority by the human ensemble, it is the being-one of the organisms in so far as it corresponds to the unity of their being-inthemselves in the object. But, in so far as everyone's unity with the Other and with all Others is never given in him and the Other in a true relation based on reciprocity, and in so far as this interior unity of all is always and for everyone in all the Others, in so far as they are others and never in him except for Others, and in so far as he is other than them, this unity, which is eyer present but always elsewhere, again becomes interiority lived in the milieu of exteriority. It no longer has any connection with molecularity: it is genuinely a unity, but the unity of a + +flight. + +This can best be understood in the light of the fact that in an active, contractual and differentiated group, everyone can regard himself both as subordinate to the whole and as essential, as the practical local presence of the whole, in his own particular action. In the case of the bond of alterity, however, the whole is a totalisation of flight; Being as material reality is the totalised series of not-beings; it is what everyone causes the other to become, as his double, out of reach, incapable of acting on him directly, and, simply in its transformation, subject to the action of an Other. Alterity, as the unity of identities, must always be elsewhere. Elsewhere there is only an Other, always other than self and which seems, from the point of view of idealist thought concerning other real beings, to engender them by logical scissiparity, that is to say, to produce the Others as indefinite moments of its alterity (whereas, in reality, exactly the opposite occurs). Ought we to say that this hypostasised serial reason simply refers us back to the practico-inert object as the unity outside themselves of individuals? On the contrary, for it engenders it as a particular practical interiorisation of beingoutside through multiplicity. In this case, must we treat it as an Idea, + +that is to say, an ideal label? Surely not. + +The Jew (as the internal, serial unity of Jewish multiplicities), or the colonialist, or the professional soldier, etc., are not ideas, any more than the militant or, as we shall see, the petty bourgeois, or the manual worker. The theoretical error (it is not a practical one, because praxis really does constitute them in alterity) was to conceive of these beings as concepts, whereas - as the fundamental basis of extremely complex relations - they are primarily serial unities. In fact, the being-Jewish of every Jew in a hostile society which persecutes and insults them, and + +opens itself to them only to reject them again, cannot be the only relation between the individual Jew and the anti-semitic, racist society which surrounds him; it is this relation in so far as it is lived by every Jew in his direct or indirect relations with all the other Jews, and in so far as it constitutes him, through them all, as Other and threatens him in and through the Others. To the extent that, for the conscious, lucid Jew, being-Jewish (which is his statute for non-Jews) is interiorised as his responsibility in relation to all other Jews and his being-in-danger, out there, owing to some possible carelessness caused by Others who mean nothing to him, over whom he has no power and every one of whom is himself like Others (in so far as he makes them exist as such in spite of himself), the Jew, far from being the type common to each separate instance, represents on the contrary the perpetual being-outsidethemselves-in-the-other of the members of this practico-inert grouping. (I call it this because it exists within societies which have a non-Jewish majority and because every child - even if he subsequently adopts it with pride and by a deliberate practice - must begin by submitting to + +his statute.) + +Thus, for example, if there is an outbreak of anti-semitism, and Jewish members of society are beginning to be accused of 'getting all the best jobs', then for every Jewish doctor or teacher or banker, every other banker, doctor or teacher will constitute him as dispensable (and conversely). Indeed it is easy to see why this should be so: alterity as everyone's interiorisation of his common-being-outsidehimself in the unifying object can be conceived as the unity of all only in the form of common-being-outside-oneself-in-the-other. This is because totalisation as an organised form of social relations actually presupposes (in the abstract and in extreme cases, of course) an original synthetic praxis whose aim is the human production of unity as its objectification in and through men. This totalisation - which will be described below - comes to men through themselves. But the totality of the gathering is only the passive action of a practico-inert object on a dispersal. The limitation of the gathering to these particular individuals is only an accidental negation (since, in principle, as identities, their number is not determined). Transformation into a totality is never the aim of a praxis; it reveals itself in so far as men's relations are governed by object-relations, that is to say, in so far as it comes to them as a practico-inert structure whose sealed exteriority is revealed as the interiority of real relations. On this basis, and in the context of exigency as an objectivity to be realised, plurality becomes unity, alterity + +becomes my own spontaneity in the Other and that of everyone in me, and the reciprocity of flights (as a pseudo-reciprocity) becomes a human relation of reciprocity. I have taken the simple and unimportant example of the passengers on the bus only in order to show serial structure as the being of the most ordinary, everyday gatherings: as a fundamental constitution of sociality, this structure does in fact tend to be neglected by sociologists. Marxists are aware of it, but they seldom mention it and generally prefer to trace the difficulties in the praxis of emancipation and agitation to organised forces rather than to seriality as the material resistance of gatherings and masses to the action of + +groups (and even to the action of practico-inert factors). + +If we are to encompass the world of seriality, if only in one glance, or to note the importance of its structures and practices - in so far as they ultimately constitute the foundation of all seriality, even that which aims to bring man back to the Other through the organisation of praxis - we must abandon the example we have been using and consider what occurs in a domain where this basic reality discloses to our investigation its true nature and efficacity. I call the two-way relation between a material, inorganic, worked object and a multiplicity which finds its unity of exteriority in it collective. It defines a social object; it is a two-way relation (false reciprocity) because it is possible not only to conceive the inorganic object as materiality eroded by serial flight, but also to conceive the totalised plurality as materialised outside itself as common exigency in the object. Conversely, one can start either from material unity as exteriority, moving towards serial flight as a determinant of the behaviour which marks the social and material milieu with the original seal of seriality, or from serial unity, defining its reactions (as the practico-inert unity of a multiplicity) to the common object (that is to say, the transformations they bring about in the object). Indeed, from this point of view the false reciprocity between the common object and the totalised multiplicity can be seen as an interchangeability of two material statutes in the practico-inert field; but at the same time it must be regarded as a developing transformation of every one of the practico-inert materialities by the Other. In any case, we can now elucidate the meaning of serial structure and the possibility of applying this knowledge to the study of the dialecti- + +cal intelligibility of the social. + +2Indirect gatherings: the radio broadcast + +In order to understand the rationality of alterity as a rule of the social practico-inert field, we must, in effect, understand that this alterity is more complex and concrete than in the superficial and limited example in which we have observed it. Following up our investigation, we may find that some new characteristics emerge as seriality comes to be constituted in a larger field, and as the structure of more complex collectives. First, it should be noted that, in accordance with their own structure and passive action, practico-inert objects produce the gathering as a direct or indirect relation between the members of the multiplicity. The relation based on presence will be referred to as direct. And presence will be defined as the maximum distance permitting the immediate establishment of relations of reciprocity between two individuals, given the society's techniques and tools. (This distance obviously varies. In particular, there is the real presence of two people speaking on the telephone, each in relation to the other; similarly, an aeroplane can remain in a permanent relation of presence, by radio, + +with all the technical services which ensure its security.) + +There are, of course, different kinds of presence, and they depend on praxis (some undertakings require that everyone should be present in the perceptual field of the Other - without the mediation of instruments) but, in any case, I define gatherings by the co-presence of their members, not in the sense that there must be relations of reciprocity between them, or a common, organised practice, but in the sense that the possibility of this common praxis, and of the relations of reciprocity on which it is based, is immediately given. Housewives queueing in front of a baker's shop, in a period of shortage, are characterised as a gathering with a serial structure; and this gathering is direct: the possibility of a sudden unitary praxis (a riot) is immediately given. On the other hand, there can be practico-inert objects whose structure is completely determinate but which, within the indeterminate multiplicity of men (of a city, a nation, or the world), themselves constitute a given plurality as an indirect gathering. And I define such gatherings by absence; by which I mean not so much absolute distance (in a given society, at a given moment in its development) which is, in reality, only an abstraction, as the impossibility of individuals establishing + +relations of reciprocity between themselves or a common praxis, in so far as they are defined by this object as members of the gathering. But the important point is not whether a particular radio listener possesses his own transmitter and can make contact, as an individual, later, with some other listener, in another city or country: the mere fact of listening to the radio, that is to say, of listening to a particu lar broadcast at a particular time, establishes a serial relation of absence between the different listeners. In this way, the practico-inert object not only produces a unity of individuals outside themselves in inorganic matter, but also determines them in separation and, in so far as they are separate, ensures their communication through afterity (and the same applies to all 'mass media') . When I listen to a broadcast, the relation between the broadcaster and myself is not a human one: in effect, I am passive in relation to what is being said, to the . political commentary on the news, etc. This passivity, in an activity which develops on every level and over many years, can to some extent be resisted: I can write, protest, approve, congratulate, threaten, etc. But it must be noted at once that these activities will carry weight only if a majority (or a considerable minority) of listeners who do not know me do likewise. So that, in this case, reciprocity is a gathering with one voice. Moreover, radio stations represent the point of view of the government or the special interests of a group of capitalists; so the listeners' activities (about programmes or about the opinions that are + +expressed) are unlikely to have any effect. + +It often happens that political and social events which occur at all levels and throughout the country suffice to bring about changes in programmes or in controversial comment. From this point of view, the listener who disagrees with the policy of the government, even if, elsewhere, as a member of organised groups, he plays an effective part in opposing this policy, will see his passive activity - his 'receptivity' as impotence. And, in so far as this voice gives it exactly the limits of its powers (there was an excessively bad drama or music programme), the public can act. Not entirely, however, as many examples have shown: the listener's indignation may simply be the lived discovery of his impotence as a man confronting a man. (The same applies if he is enthusiastic; I am taking the negative case because it is simpler, but the same impotence exists if I am delighted by some speaker or singer and demand that he be given a regular programme or that he broadcast more frequently.) For, in a sense, the voice, with its particular inflections and intonations, is the individual voice of a particular person, who + +has prepared his audience by a series of precise, individual actions. At the same time, there can be no doubt that the voice is addressed to me. To me and to Others, the voice says: 'Dear listeners.' But, although the speaker at a meeting addresses everyone present, each of them is in a position to contradict or even insult him (on condition, of course, that he takes certain risks in certain cases, with the more or less clearly defined intention, according to the circumstances, of ' changing public opinion'). Thus the public speaker really does address us, in that both individual reciprocity (I shout out my approval or my criticism) and collective reciprocity (we applaud him or shout our disapproval at + +him) are perfectly conceivable. + +The broadcaster's voice, in contrast, in its reality as a human voice, is, in principle, mystifying: it is based on the reciprocity of discourse, and therefore on a human relation, but it is really a reifying relation in which the voice is given as praxis and constitutes the listener as the object of praxis; in short, it is Cl univocal relation of interiority, similar to that of the organism acting on the material environment, but one in which I, as an inert object, am subjected as inorganic matter to the human work of the voice. Yet I can, if I wish, tum the knob, and switch off the set or change stations. But here the gathering at a distance emerges. For this purely individual activity changes absolutely nothing in the real work of this voice. It will continue to echo through millions of rooms and to be heard by millions of listeners; I will merely have rushed into the ineffective, abstract isolation of private life, objectively changing nothing. I will not have negated the voice; I will have negated myself as an individual member of the gathering. And, especially in the case of ideological broadcasts, it is really as Other that I will have wanted this voice to be silent, that is to say, in so far as it can, for example, harm Others who are listening to it. I may be perfectly sure of myself, I may even belong to some active political group, sharing all its views and adopting all its positions. Nevertheless, the voice is unbearable for me in so far as it is listened to by Others - Others who, to be precise, are the same in so far as they listen to the radio and Others in so far as they belong to different milieux. I tell myself that it may convince them. In fact, I feel as though I could challenge the arguments put forward by this voice in front of these Others, even if they do not share my views; but what I actually experience is absence as my mode of connection with the Others. In this case, my impotence does not lie only in the impossibility of silencing the voice: it also lies in the impossibility of convincing, one by one, the listeners + +Others who control the mass media) and who are influenced by the mere fact that this policy has the power to propagate itself publicly; and finally, it is Other for those who support government policy, in thatfor everyone in isolation it is backed up by the approval of Others (those who share his opinion) and by its effect on waverers. For them, the voice expresses their own thinking, but as Other, in that it is uttered by an Other, expressed in other terms (better than they could have done and differently) and in so far as it exists simultaneously for all Others as an Other-Thought. The reactive behaviour occasioned in the listeners by the Other-Thought as the meaning of the Other-Voice is always the behaviour of alterity. By this I mean that it has neither the immediate structure of an individual praxis, nor the concerted structures of a common, organised praxis. It is occasioned immediately - as the individual's free reaction - but he cannot produce it under the influence of the collective except in so far as it is itself a lateral totalisation of seriality (indignation, ironical laughter, impotent anger, fascination, enthusiasm, the need to communicate with Others, shock, collective fear,80 etc.). In other words, the individual, as a member of aseries, exhibits behaviour which is altered (altedes), and every part of which is the action of the Other in him, which means that of itself + +it is recurrence taken to its limit (that is to say, to infinity). + +In developing this example our investigation (experience) of seriality has grown richer. From the very fact that some objects can establish indirect bonds of alterity between individuals who are unaware of each other as such, we can see how the possibility emerges of a series being either finite, indefinite or infinite. When a multiplicity, though numerically determined in itself, remains practically indeterminate as a factor of the gathering, it is indefinite. (This applies, for example, to the radio: there is a definite number of individuals listening to a particular programme at a given moment, but it is as an indeterminate quantity that the broadcast constitutes the seriality of its listeners as a relation of each of them to the Others.) When the multiplicity is + +80. In so far as collective fear is manifested as serial behaviour in an isolated listener, it occurs if the broadcast seems audacious or shocking; then it is the fear of anger or of others, it is sacred fear, for it is the fear that these words should have been spoken in the indefinite milieu of seriality, and also the fear in the milieu of the Other of having heard these words. These others, in me, condemn this moment of receptivity in which, by my individuality as a practical organism, these words have existed here in t!Jis room; alterity condemns in me my personal + +reality, and the Other passes sentence on the Same . + +gathered together by a movement of circular recurrence, we have a practically infinite series (at least provided the circular movement continues). Each term, in effect, in so far as it produces the alterity of Others, itself becomes Other to the extent that Others produce it as Other, and that it helps modify them in their alterity in turn. + +But we have also noticed that pure, formal alterity (as our first examples showed) is only an abstract moment of the serial process. It is true that it occurs in any group which, for example, is ordered in some way or other (a group of shoppers, for example, when there is a scarcity of goods or staff). But the formal purity is maintained here by a deliberate action - the refusal to discriminate between individuals on any basis other than alterity, itself constituted as a rule of succession. Otherwise, that is to say when alterity is not itself a means of selection, individuals in the serial milieu have a few special characteristics which vary among them or from one ensemble to another. Of course, the fundamental structure remains the same: the radio listeners at this moment constitute a series in that they are listening to the common voice which constitutes each of them in his identity as an Other. But it is precisely for this reason that an alterity of content arises between them. This alterity is still extremely formal, for it constitutes them on the basis of the object (the voice) and in accordance with their possible reactions to it. It goes without saying that in order to ground these reactions, one would have to enter more deeply into the differences, find other collectives and interests and groups, and, finally, one would have to totalise the historical moment together with its past. But in so far as the gathering is created by the radio, it remains at the level of the practical alterity of listening behaviour. It is on this basis that alterity as the formula of the series becomes a constituent force of each and for all; for in everyone, the Other is no longer mere formal difference in identity; in everyone, the Other is a different reaction, other behaviour, and everyone is conditioned in the fleeting unity of alterity by these different kinds of behaviour of the Other in so far as he cannot modify them in the Other. Thus everyone is as effective in his action on the Other as if he had established human relations with him (either direct and reciprocal, or organised), but his passive, indirect action derives from his very impotence, in so far as the Other lives it in himself as his + +own impotence as Other. + +3Impotence as a bond: the free market + +This material, but still abstract, determination of the variable content of alterity (in other words, of a synthetic alterity which by itself creates a practico-inert world of alterity) leads us logically to the investigation (experience) of impotence as a real bond between members of a series. A series reveals itself to everyone when they perceive in themselves and Others their common inability to eliminate their material differences. We shall see how, in certain special conditions, a group constitutes itself as the negation of this impotence, that is to say, of seriality: I feel my impotence in the Other because it is the Other as Other who will decide whether my action will remain an individual, mad initiative and throw me back into abstract isolation or whether it is to become the common action of the group; in this way, everyone awaits the Other's action and makes himself the Other's impotence in so far as the Other is his impotence. But this impotence, as a constituent presence in everyone in the series, does not necessarily correspond to the pure, passive immobility of the ensemble. On the contrary, it may become un organised violence: precisely to the extent that I am impotent through the Other, it is the Other himself who becomes an active power in me. Incapable of changing the Other's indignation (when I witness a scene which some people find shocking), this indignation, lived in)mpotence, becomes for me an other-indignation, in which the Other in me is angered and guides my action. Provocateurs apart, there is no difference between Scandal and the Fear of Scandal. In other words, Scandal is the aggressive Fear of the Other's Scandal. In other words, Scandal is the Other himself as the transcendent reason of the serial propagation of acts of violence caused by the fear of Scandal. But in order to simplify the structure of collectives, we have so far assumed that series are constituted by isolated terms, whose only, and fleeting, unity was alterity as impotence. Series of this kind actually exist; generally speaking, readers of Le Figaro or radio listeners would be an example. But other cases are more complex: for human relations of reciprocity define the co-existence of men as well as the statute of massified dispersal. And as these relations constitute complex chains and polyvalent systems, every individual relation, through the medium of the surrounding material reality, is conditioned by + +between a totality of worked objects, a unity of inert exteriority (the sixteenth arrondissement of Paris, etc.), and the quasi-plurality which is signified by it and which produces unity in it as an absence. My relation with my customer arises in the bourgeois milieu of retailing (and more specifically of a particular retail trade, in a particular town, etc.) and contributes to determining it while actualising a predetermined structure; but the milieu which unites us is revealed as an active, synthetic force (in the course of business) only in so far as precise relations link one term to another, and link the relation itself to other terms and relations (deals between big companies which are trying to lower prices and ruin small businesses or simply approaches to one of my customers by a competitor), on which practical influence is incon- + +ceiyable. + +Thus the true structures of the milieu, those which produce its real force in the practico-inert field, are in fact structures of alterity. It is true that every relation is linked to every other, but only in particular ways : every element is linked to all elements, but from its place in the series and through its fleeting link with all the intermediate elements, just as any number is linked to every other number through precise relations which presuppose that every one of them is related to the others through the series of numbers which separate them - that is, on the basis that one of them is (n + I ) and the other (n + I) + I, etc. Similarly, there is the unity of the milieu, which can, in certain cases, be a terrifying collective force. (It can be measured objectively, at least in some cases, by the chances of an individual in the milieu emerging from it, and inversely by the chances of an individual from a particular social category entering it, apart from any constraint exerted by his own milieu.) But the unity of the milieu exists precisely in so far as it does not reside in its terms as the whole in the part, in so far as it realises itself for each relation as those relations which elsewhere condition its concrete existence and its content. It is true that in the serial behaviour of terms which are present, the totality of the others arises as a milieu and as a general conditioning of behaviour. But this totality must not be confused with a positive, concrete totality, with a real presence: it is not the result of the unification of a practical field. On the contrary, it is a real extrapolation of an infinite series of relations which are both identical and other in so far as everyone conditions the Other by his absence. The totality here is the practicoinert totalisation of the series of concrete negations of every totality. The totality manifests itself in every reciprocity as its other-being, in + +other nineteenth-century commercial markets in major international products (wheat, cotton, etc.). If we examined all the conditions affecting markets in general, our conception of 'collectives' as recurrences would be confirmed, but the problem would go beyond the limits of this study. The market has an undeniable reality; it is imposed on everyone in so far as the price and volume of transactions are necessarily determined (in terms of constant elements and within determinate limits) by the quantities on offer, the prices asked, the quantities needed and the prices people want to pay. Now, it is easy to see that the necessity which imposes itself on a merchant in his relation with an individual consumer arises from the concrete relations between other tradesmen and their customers, and from the relations between other buyers and this seller (who, for them, becomes Other than he was for the customer in question) and, finally, from the very fact that the consumer as such appears on the market as Other than himself and acts as Other on the direct human relation which he tries to form with the seller. The price corresponds to the intersection of the supply and demand curves, as everyone knows: this means that the quantities supplied and demanded at this price are equal. If the seller set his price at a lower level, demand would exceed supply; if he set it higher, supply would exceed demand. But there is no direct agreement between two men or two groups, understanding one another directly. A dealer never actually fixes his prices himself. And the mathematical rig our of the object demonstrates precisely that it is the objective representation + +of a line of flight. + +The table opposite is of quantities supplied and demanded. + +According to what we have just said, 11,000 units will be sold at the + +price of 6 francs. + +First, it goes without saying that the justification for this quantitative law lies neither in purely mathematical principles, nor in the essential characteristics of quantity. The heart of the proof (that if the price were lower, demand would be higher than supply, and inversely) must refer us back to the seller and to his real action, to the buyer and his real demand. Demands cannot be higher than supply precisely because buyers who are in a position to pay more will make new offers and this wiIl have the effect of raising prices. Supply cannot be higher than demand, because the better placed merchants (with lower production costs) will drop their prices immediately. Thus men are considered as forces of buying and selling. To simplify matters, let us assume that one buyer corresponds to each unit of demand, and that one seller + +corresponds to each unit of supply. Now, of the 27, 500 supposed sellers, we can see that only 11 ,000 are prepared to drop the price to 6 francs per unit. And, of these, only 8,500 would go to 5 francs. Of 27, 500 sellers, therefore, there are just 2, 500 who can go down to 6 francs but no lower, and these 2, 500 determine the price for everyone + +Price Quantity demanded Quantity supplied + +18,500 0 + +2 16,500 ° 3 15,000 3,000 4 13,500 6,000 5 12,250 8,500 6 11,000 11,000 7 10,000 13, 500 8 9,000 15 ,500 9 8,250 17,250 10 7,500 19,000 II 6,750 20,500 12 6,000 22,000 13 5,250 23,2 50 14 4,750 24,250 15 4,250 25,250 16 3,750 26,000 17 3,2)0 26,750 18 2,750 27, 500 + +else. On the one hand, by lowering the price, they effectively exclude from the market 16,500 sellers, who, for one reason or another, cannot match this price reduction. On the other hand, by setting the price at 6 francs, they enable 8,500 sellers to avoid going down to 4 francs a unit, and 3,000 to avoid going to 3 francs. Thus, to confine our attention to them, these 3,000 receive a seller's profit, that is to say, they realise 3 francs a unit above their minimum expectations. How, then, do we explain the fate of the 25 ,000 people, of whom some have sold + +determines both himself and the Other in so far as he is Other than the Other and Other than himself. And everyone observes his direct action deprived of its real meaning in so far as the Other governs it, and in his turn hastens to influence the Other, over there, without any real relation to his intention. There must be a false unity. And it exists : it is the market as a gathering (whether it is a physical place or a system of telecommunications informing everyone of supplies, demands and prices).82 At the outset, everyone yields to the gathering; he already determines it (in alterity) by his expectations, and it already eludes him and determines him. Consequently, the market exists through him On itself and for him) as an object of expectation and as the fleeting determination of his action; but he himself sees it as an ensemble of juxta- + +posed persons. The totality of the market is thus detotalised. + +To take the simplest examples (flower markets, cattle markets, etc.), the unity of place shows that all the individuals are united in that they devote themselves to the same direct operation, which allows itself to be determined in exteriority and alterity by all the other similar operations, so that this determination in alterity finally turns them into the object itself and reality: everyone's expectations, in a market that is supposed to be competitive, depend on the hypothesis that atomisation will remain the typical social link at least for the duration of the exchange. Thus, the unity cannot be conceived as a unifying synthesis, but as a form of dispersal as such, when this dispersal is seen as a rule and means for action. Two essential facts must be noted. First, the real difference between the physical molecule and the social molecule is that the first is purely and simply an element of numerical dispersal, while the second is a factor of dispersal only in so far as it begins as a factor of unity. The human molecule does not remain in multiplicity: through its action it organises the multiplicity into a synthetic unity (it is the market as the aim and condition of its activity). Dispersal intervenes in the second degree: there is a multiplicity, not of simple isolated molecules, but of unifications of purely physical multiplicity which have already been practically (and sometimes even consciously) realised. Everyone unifies, and perceives, and manipulates the market as a total reality (he perceives it through local traditions, habit, periodicity, his own material existence, his project as a producer-seller, etc.). But these unifications are separated from one another by a real + +82. The market as a gathering (practico-inert place) itself becomes the price in + +so far as it grounds the practico-inert activity of the series. + +vacuum, that is to say, by the fact that, physically and practically, everyone is not the other, that walls really do separate them, as well as practical antagonisms or their real ignorance of their reciprocal existence. And the market is not the synthetic unity of a multiplicity, but the dispersive, real multiplication of its own unity. The unity of the market is not only the foundation of the operation which everyone tries to carry out, but also something which eludes him because the very action of this atomicity is alienating; and, finally, it is the fact that the centre of a market is always elsewhere as well as always present (as the place of the gathering or as all the information about prices); and it is this very contradiction which creates the social object. It is precisely this contradiction that enables the unity of the gathering to be not simply transcended by common action (as happens when there is a direct agreement between producers or consumers), or even by indidual action, but on the contrary to present itself both as the common object of an action and as the rigid, external law of every particular action, that is to say, to exist in the manner of an instrumental object, 'to hand', 'before one's eyes' and as an objective but alien necessity in every one of us. It is this second point which has to be emphasised. If prices are agreed between unions (or co-operatives) and monopolies, the price tends to lose its reality as a constraint: Obviously production costs and real wages indicate objective limits of variation; but these conditions are material and visible and can be confronted head-on; the profit margin, in contrast, can be reduced or increased by the direct relation between the forces present. At this level, selling price becomes a 'reciprocal object', that is to say, its opacity for one is based on the direct resistance of the other, and it affords us a glimpse, in its depths, + +of the action and needs of trusts or co-operatives. + +Under Roosevelt's presidency, Americans refused to buy meat in order to struggle against the claims of the trust of slaughter-house owners. In such a situation - as long as the boycott lasts - price remains an ideal sign, since nobody either sells or buys and its meaning refers directly to the trust's will to struggle; it is a mere statement of the trust's determination, of their will to 'hold out' and of the material conditions which occasion or necessitate their attitude. But this is because the unification of the two groups makes a direct relation between them possible. (And as I have said, this unification only displaces recurrence.) When unification does not occur, for example in a competitive market, the price derives its objective and practical reality from the physical and mental separation of the agents; it is real + +because it gathers within it all the real factors of separation - the inadequacy of the available means of communication, the stone walls which separate the retail stores, or the actual time needed to reach one's neighbours and persuade them to transcend antagonism towards co-operation; but above all, it is based on a certain type of human relations, which might be called indirect, or lateral. Its strength derives from the impotence (whether temporary or absolute) of every buyer (or seller) in relation to the series of other buyers (or sellers); it corresponds to the necessity that if the seller (or buyer) wanted to try to defend himself, he would have to undertake a serial action, passing, that is, from one individual to the next. This serial action must be both indeterminate (for the number of persons to be directly reached is not given), and circular (for the individual with whom I make direct contact becomes other for me again, as soon as I move away from him in order to reach another; and it will be necessary to + +return to him). So it is a case of infinite recurrence. + +The type of arithmetical reasoning which demonstrates that all the elements of a series possess the same property is well known. It can be divided into three operations. First, we establish a simple universal proposition: if the property exists for any number a, it necessarily exists for the number b (which comes immediately after a in the series); secondly, we verify that some number of the series does, in fact, possess the property in question; and lastly, we proceed to a sort of artificial totalisation, in other words, a sort of passage to the limit which dispenses with an infinite series of operations. (It is true of a, and therefore it is true of b; if it is true of b, then it is true of c, therefore c possesses the property; but if it is true of c, it is true of d, etc.) Thus collective objects originate in social recurrence: they represent totalisations of impracticable operations. But they do not appear at first as an object of knowledge: above all, they are realities which we are subjected to and which we live, and we learn them, in their objectivity, through acts which we have to do. The price imposes itself on me, as a buyer, because it imposes itself on my neighbour; it imposes itself on him because it imposes itself on his neighbour, and so on. But, conversely, I am not unaware that I help to establish it and that it imposes itself on my neighbours because it imposes itself on me; in general, it imposes itself on everyone as a stable collective reality only in so far + +as it is the totalisation of a series. + +The collective object is an index of separation. This would emerge more clearly if we took as our example a more complex market (in + +persistence of coinage alongside paper money introduced a bi-monetary system (2,000 million in coin, 2,000 million in paper) and, as is well known, in such situations bad money chases good, that is to say supply exceeds demand, and it devalues rapidly; lastly, we must take account + +of speculation, forged notes from abroad, etc. 85 + +But, apart from the fact that many of them can be effective only in so far as they are lived (for example Gresham's law necessarily refers to confidence - good money disappears because people hoard it, and they do so because they have no confidence in each other) , historians recognise the importance of political factors in the decline of the assignat: confidence in it was all the weaker because it was issued by a revolutionary power, which might be overthrown. The failure of the assignat therefore reflects the flight of Louis XVI, the retractions of the Constituent Assembly, the defeat of the revolutionaries at the end of 1791 and, after the first defeats of 1792, the fear of the restoration of absolute monarchy. For the men who came together to struggle against these different events, in so far as they are historical, were directly subjected to them; it was an organised response to the king's treason which expelled him from the Tuileries on 10 August. The collapse of the assignat, however, gives expression to these events in so far as they had lateral effects on everyone, lived as the dispersed reaction of Others, in recurrence and impotence. The same person might belong to a J acobin club, approve enthusiastically of 10 August, and keep his gold without noticing that the same facts are appearing to him at two distinct levels and that he reacts in contradictory ways depending on the level at which he considers them. As far as the assignat is concerned, the Revolution crumbles in his hands, and he helps it to do so; but as far as the motion which he helped to get carried at his club is concerned, he sees himself as carried along by revolutionary fervour. And supposing someone was aware of the contradiction, would he receive payment in assignats but pay for things in coin? Recurrence intervenes here; such an act could serve neither as propaganda, nor as an example; hardly anyone would notice it, and the only result would be that if the patriot was a merchant he would he ruined, while if he was a producer, though he would no doubt be saved, he + +8). All these factors relate, of course, to the praxis of the bourgeoisie, to its economic liberalism (its refusal to give the assignat a power equal to that of coin, a refusal to decree compulsory circulation (this was to come later) and a refusal + +to shoulder the expenses of war). + +would be helping (though to a negligible degree) to maintain the bi- + +monetarism which was undermining the Revolution. + +So must this revolutionary be worried, and suspicious? Yes, profoundly; defiance of the Other, and a vague awareness of recurrence are necessary concomitants of the first steps of a revolution. The suspicion calls for unity against recurrence (and not, as some people think, against mere multiplicity), and for totalisation against indefinite flight (and not, as Hegel says, universality against specific difference): it is suspicion which engenders and sustains Terror as an attempt at subjective unification. Eut this suspicion, governed by the suspicion of Others, is also counter-revolutionary and presents it.,elf in the collapse of the assignat as an alien object. At this level, we come back to money as materiality. But this time, we can consider it in the context of practical relations of reciprocity. Its meaning sums up the totality of the historical process up to the present moment, but it does so by mechanising it; and the agents do not conceive of it as a positive characteristic of the material object (like the Genoese merchants when they carried off the Spanish gold), but as an infinite and regressive absence. Today, the rapid succession of inflations and devaluations has shown everyone the double character of all money, as material presence and as indefinite flight. The real value of a given banknote can be determined only in a specific, dated historical conjuncture; it must refer to the capitalist system, to the relations of production, to the relative strengths of classes, to the contradictions of imperialism and to the relation between France and other bourgeois democracies. But this complex is a flightjor me; I see it in the 5-franc piece in so far as it is lived by the Other, either the buyer who stockpiles in the expectation of war, or the seller who raises his prices, or the producer who reduces his own production. But this absence, this movement of perpetual regression, can be manifested only in a material object of which it constitutes the human reality. The diabolical appearance of the coin (or note) is that it is apprehended (at successive moments) in its material identity and that I can take it, hold it, and hide it; but that in its very immobility it is affected by an absent change, which always occurs elsewhere and which reflects to me the image of my impotence through + +atomisation. + +I shall develop the example of money in a later work. Here, I simply wish to draw attention to the fact that money, in each of its concrete units, has the double infinity of the universal and of recurrence. This particular banknote is constituted in my hands as a + +and takes on an impenetrable depth in so far as it also exists for a nOI1 member, for the sans-culottes, for the provincial towns, for the countryside, and for Europe itself (how often revolutionary orators declared: 'The eyes of the world are upon us I'). Originally, this relation is a direct one: the Convention, with its powers, its authority, its tasks, its deputies, exists as a direct object for the elector, for the Jacobin, and for the representant en mission; it is both the organ of government and the elected assembly which is accountable to the nation; it is suffered and res?sted, venerated and detested. But what makes us relapse into recurrence is the fact that, in spite of the political clubs, the citizens were not organised in any way, and that, in a way, the Assembly was in the position of a monopoly facing dispersed buyers. This dispersal creates both the power and impotence of the rulers: it reduces the possibility of organised resistance (strikes against maximum wages, etc.) to a minimum, but, at the same time, it erodes its unifying decrees and dissolves them in itself (the crisis in foodstuffs, the collapse of the assignat, etc.). Representations and beliefs, always coming from elsewhere, bear in themselves the mark of recurrence, they are 'overflowing' ideas (idees 'debordantes'): no doubt they express everyone's real situation, but they express it in flight, and mythically; their inconsistency makes them impenetrable and invincible. When the member of the Convention tries to understand the Convention, as a changing utldertaking,for his electors or for the country, it will elude him completely: the object is there, enlarged to the frontiers of France, real, + +constricting, but, strictly speaking, unthinkable. + +4 Series and Opinion: the Great Fear + +These last remarks enable us to see a few characteristics of another collective - a most important one from the point of view of rulers. This is public opinion. In the context of the process of temporalisation and totalisation, there is undoubtedly such a thing as opinion, and it is expressed in words and deeds which refer to certain meanings. It is an everyday matter for some of these words and deeds to form the subject of police reports to the head of government. It is for the leaders themselves to interpret their meanings as objective realities and as an + +effective ideological materiality. Then there will be talk of the discontent of a particular social category, of the tension developing amongst individuals and groups (in so far as it is expressed in speech and action - brawls, lynchings, etc.). At this level it will be determined whether public opinion does or does not make a direct connection between two facts or objective meanings (for example, between the refusal of the bourgeoisie to finance the war of 1792 from taxation and the fall of the assignat) or whether, in contrast, it creates - rightly or wrongly - a single meaning with two different meanings. So public opinion tends to be seen as a collective consciousness arising from the synthetic unification of the citizens into a nation, and imposing its representations on everyone as an integral part of the whole, just as the totality is + +present in each of its parts. + +The discontent of retailers (as revealed both in common actions and in wholly distinct ones), the distrust of the government amongst industrialists and bankers (as expressed in the refusal of loans), the revival of anti-semitism (after a defeat or a national humiliation): all these objective realities should be regarded as totalising schemata. But we should realise that every one of them, in itself and for everyone, is the Other, that its signifying structure is infinite seriality, and that it has the practico-inert unity of an index of separation. For example, in so far as retailers have produced their own organs of defence and can affect the government, it is inappropriate to speak of discontent: they fight ministerial power and try to change it. Everything is praxis: if it succeeds, everything will be settled amicably. On the other hand, when the isolated small shopkeeper sees taxes and wholesale prices rising when he is unable to raise his retail prices, he feels, in his verY, person, the fear of ruin and hunger. But his reaction would be pure terror, rather than discontent, unless, in his very fear, he discovered the same discontent among other shopkeepers as a serial totality of impotence, that is to say, unless he discovered himself as dispersed in the seriality of the Other, as affected by the impotence of Others, and as affecting the Others (that is to say, himself as Other to infinity) with his impotence. For this reason, the common material ohject (for example, tax or the index of wholesale prices) in its practico-inert development, creates the unity of the discontent. But it creates it outside, in him. In the multiplicity of individuals, this discontent realises itself in the theoretical and practical protests of isolated, discontented individuals (who do not know one another as individuals), as the index of their separation. In this sense, it is a social reality; it is a force (as impotence + +lived individually, it may lead a person to sell his business, to commit suicide, etc.; and in circumstances which will be defined below, it can serve as a basis for regroupment) and this force is simply the practicoinert power of hundreds of thousands of people as potential energy. But this force does not reside in anyone, and it is not the product of everyone; it is alterity itself to precisely the extent that, for everyone, it + +is elsewhere. + +In specific cases where discontent (or some other affective state) has spread through the country, then, rather than being felt and expressed by everyone in his own right, people take part in serial propagations which clearly illuminate its character as alterity. One need only recall the Great Fear of 1789, of which Lefebvre has provided such a remarkable study.87 First he shows that the fear did not break out everywhere at the same time and that it did not cover the whole of France, contrary to what some historians have claimed in the name of a spontaneous organicism. He shows that five different waves of fear ought to be distinguished, and that certain regions were never affected. Finally, he shows that these waves, the origins of each of which can be localised and dated, were propagated serially, from town to village and from village to town, and that their routes were determined by quite precise conditions. But the most striking thing in his book is that one constantly feels driven to discovering the intelligibility of a movement in the rationality of the Other. I will simply recall a few observations: the fiar arose in very specific conditions, but what it expressed, in the provinces and the countryside, was above all a structure of alterity in relation to Paris. News was scarce, slow to arrive, and impatiently awaited: it eventually reached the towns, but it spread unevenly and confus<:dly in the countryside (it was already stale and distorted when the peasants heard it on market days). Thus the contrast between the rapidity of events in the capital and Versailles and the scarcity of information showed everyone his passivity in relation to those Others (aristocrats, deputies of the Third Estate, the Parisian people) who made History in Paris. Later, Jacobin societies tried to organise the provinces and even the countryside. But at this time, these men disturbed, anxious and impatient - all felt themselves as Others (who suffered History) in so far as they could have no effect on the subjects + +The conditions which gave rise to the Great Fear must therefore be seen in the context of everyone's discovery of himself as Other (as an object of a History made by others). But it is striking that the fear was essentially born out of 'fear of bandits' . Begging, in fact, was the chronic sore of the countryside: there were beggars and tramps everywhere. Basically, these were just ruined peasants or the children of over-large families. Nevertheless, the farmers did not regard them favourably. The smallholders and even the day-labourers saw them as an agricultural 'lumpen-proletariat' at the same time as recognising themselves in the vagabonds, in that a permanent possibility threatened them too with ruin, with vagabondage, and with being Others. But, for the peasant, the true other, the other class, was, of course, the landed aristocracy with its feudal rights. Now it is remarkable that, on the news that an aristocratic plot was feared in the towns, the synthetic link between aristocrats and vagabonds suddenly became apparent. Of course, one might offer a reasonable explanation: the aristocrats had had the vagabonds in their pay in order to crush the country people. But this interpretation rationalises retrospectively a movement whose intelligibility lies in the process of alterity itself and which makes the vagabond appear as absolute Other, that is to say, as doubly Other (Other as a pauper, and Other as a hireling of the oppressing class), combining in himself, in the dimension of alterity, both crime as the anti-human activity of the Other than man, and oppressive domination as. a praxis aiming to reduce the peasant to a sub-human state. The proof that it was essentially a synthetic union of all alterities in the absolute Other (a cruel man reducing his fellow-men to sub-humanity, a cruel beast exactly like men except that his sole aim is to eliminate them) is that, in regions where memories of the ravages caused by the Hundred Years War still lingered on, bandits were known as 'Englishmen' and that, almost everywhere, with no concern for coherence, the vagabondhirelings were known as foreigners. The 'aristocrat's plot', supported by a professional army, initially had meaning, in fact, only in Paris and Versailles: it was conceivable that the aristocracy would use the troops massed around Paris to break the resistance of the Third Estate and of the people (and certain aristocrats actually attempted to impose this policy). But, in the new form that this policy assumed in the eyes of the peasant, it became perfectly absurd. Nevertheless it was the same, but seen in the milieu of the Other by individuals whose impotence had dragged them into the world of objects, of Others. Bandits were the aristocratic plot as Other, seen in the original milieu of the Other + +and seriality had to propagate itself by becoming actualised. At first, indeed, what appears is always taken for something else. This does not in any way mean that one object is mistaken for another, as in the case of a sensory error: the object correctly conceived actually returns as an other meaning in the very movement of propagation. A gang of daylabourers in the Oise valley protest because the farmer refuses to pay what they demand. 'The news,' said a local newspaper, 'spread and grew. Bells were rung in all the parishes.' In the same region another newspaper offered a different interpretation: 'from a distance,' a group of surveyors had apparently been mistaken for bandits. Elsewhere, town militias or soldiers were mistaken, from a distance, for bands of assassins. From a distance means: when the information was so poor that it was impossible to know who was coming. In such a case, that is to say, whenever witnesses could choose between a positive and a negative interpretation, between reciprocity and aiterity, between man and anti-man, they chose the Other, the no, the anti-human. Anyone seen from a distance was other than man because the observer felt + +himself to be other in this developing History. + +We must now show how alterity creates its own laws: the truth becomes obvious for everyone not only in so far as it is negative and relates to the Other, but also in so far as it is transmitted by an Other in so far as he is Other. These are the rules of belief: what everyone believes of the Other is what the Other conveys in so far as he is Other(or in so far as the news comes to him already from an Other). In other words, it is negative information in that neither the person who receives it, nor the one who gives it, could or can verify it. Their impotence is simply seriality itself as a negative totality, and it should not be supposed that everyone believed his informer in spite of it. On the contrary, this impotence in each of them as Other supports and sustains the belief in the Other as a means of propagating truth as Other. If I believe my informer, it is not because I cannot check what he says, or because I trust him (which would re-establish a direct relation of reciprocity), or because, while I may check it sometime it is more prudent to be prepared for the worst. I believe him because, as Other, the truth of a report is its seriality, that is to say, the infinite series of impotences which will be, or are being, or have been actualised, and which constitute me through Others as a practico-inert conveyor of the truth. I believe it because it is Other (that is to say, in accordance with the principle that History is really the history of the Otherthan-man and that the worst is always certain), because it shows the + +man it describes as an alien species, and because the mode of its communication is other, and has no reciprocity. The informer propagates amaterial wave; he does not truly inform; his report is a panic; in a word, the truth, as Other, is transmitted as a state hy contagion; it is quite simply the Other-state of the Other in the face of Others, and it is this contagion which grounds it for everyone, in so far as it is ultimately the Other-Being of the series which realises itself through it in him; if! believe a madman whom I see approaching, running and shouting, when I am already aware of my own impotence, I become the same for another and run like a madman towards my neighbour. Belief, in a process like the Great Fear, is alterity itself in so far as it temporalises itself in the actualisation of an already constituted series. Thus the contagious fact is unintelligible apart from the collective and recurrence. Whatever the fundamental historical conditions which gave rise to it, it would never have produced itself as a chain-disintegration unless it had taken place in the structured temporality of the practicoinert field and unless the infinite complex of serialities had already heen produced as the very grain and web of this field. Indeed, it was in terms of seriality and alterity that contemporaries explained it when they tried to slow it down. One simply changes level: newspapers and local authorities explain that foreigners are spreading rumours to the effect that there are bandits (or else are passing themselves off as bandits) in order to spread panic. This amounts to saying: if you plunge into the milieu of the Other, you are playing the game of the ahsolute Other. I have used this example in order to exhibit a new temporal object: a series in the process of actualisation. It is not an historical event in the ordinary sense of the term, that is to say, a developing totalisation of antagonistic and concerted actions, but rather a process. However, in so far as the practico-inert field is the field of material exigencies, of counter-finalities and of inert meanings, its unity necessarily remains teleological and signifying. Thus, the Great Fear appeared to contemporaries either as the practical result of a revolutionary agitation which aimed to set the peasants against the feudal lords (and, in fact, looting and rioting, as the first group reaction against the impotence of the collective, did increase; and, a little later, the project of federation also appeared as a reaction against the impotence of the masses), or as the result of an attempt by representatives of the aristocracy (and a section of the lower clergy) to demoralise the peasant masses and to set them against the bourgeoisie of the Third Estate. In actual fact, it involved this double counter-finality only because the series lived + +History as Other and on the basis of human impotence. The opinions of public opinion arise like the Great Fear, in that everyone makes himself Other by his opinion, that is to say, by taking it from the Other because the Other believes it as Other, and makes himself the informer of the Others. At this level, the Idea is a process; it derives its invincible strength from the fact that nobody thinks it. That is to say, it does not define itself as the conscious moment of praxis - that is to say, as the unifying unveiling of objects in the dialectical temporalisation of action. Instead, it defines itself as a practico-inert object whose self-evidence, for me, is the same as my double inability to verify it and + +to transform it in Others. 88 + +88. There are also other forms of ideas in the collective: for example, the Ideaexis. As we have seen, the practico-inert object (the gold coin, for example) produced its own Idea in the general movement of practice, that is to say, the passive unity of its materiality was constituted by practice as meaning. In so far as this object becomes the common-being-outside-itself of a series, the Idea, as such, becomes the unity of the series as its reason or its index of separation. This is how colonialism, as a material system in the practico-inert field of colonisation, in other words as the common interest of the colonists, produced its own Idea in its very development: it became a means of practical choice between those who are the exploited by essence, and those who have become exploiters through merit. And if it does designate the exploited by their essence (that is to say, as exploitable sub specie aeternitatis), it is because it cannot allow any change in their condition, however minimal, without destroying itself. Colonialism defines the exploited as eternal because it constitutes itself as an eternity of exploitation. In so far as the inert sentence passed on the colonised peoples becomes the serial unity of the colonialists (in its ideological form), or their link of alterity, it is the Idea as Other or the Other as Idea; it therefore remains an Idea of stone, but its strength derives from its ubiquity of absence. In this form of alterity, it becomes racism. The essence of racism, in effect, is that it is not a system of thoughts which might be false or pernicious - and the same applies to thousands of other 'theses'; I simply took the first example to come to mind. It is not a thought at all. It cannot even be formulated. And the attraction of racism for intelligent, well-meaning people (for example, in the form of an innocent pride: 'One has to admit that the Mediterranean races ... , etc.') is normally experienced by them (and in an objectively observable way) as the attraction of stupidity, that is to say, as the secret hope that thought is a stone. In reality, racism is the colonial interest lived as a link of all the colonialists of the colony through the serial flight of alterity. As such, like the living Idea, it presents itself as infinite depth. But this depth is both petrified and strictly formal, because it is limited to producing itself as a negation of everyone by serial infinity: in other words, it gives itself in the abstract as other than each of its particular formulations. At the same time it realises itself constantly in every relation between the colonists and the colonised through the colonial system and, as the basic activity of the colonists amongst themselves, it + +is reduced to a few phrases, which have almost no content, but are uniquely guaranteed by alterity in that the Other-Idea guarantees them in a negative way by negating its reduction, as a totalised seriality, to these particular expressions. These determinations of discourse are very familiar: 'The native is lazy, dishonest, and dirty; he doesn't work unless he is forced to; he's an eternal child quite incapable of controlling himself; in any case, he lives on nothing, he never thinks of the next day; the native is properly understood only by the colonialist, etc.' These phrases were never the translation of a real, concrete thought; they were not even the ohject of thought. Furthermore, they have not by themselves any meaning, at least in so far as they claim to express knowledge about the colonised. They arose with the establishment of the colonial system and have never been anything more than this system itself producing itself as a determination of the language of the colonists in the milieu of alterity. And, from this point of view, they must be seen as material exigencies of language (the verhal milieu of all practico-inert apparatuses) addressed to colonialists as members of a series and signifying them as colonialists both in their own eyes and in those of others, in the unity of a gathering. It is pointless to say that they circulate, that people repeat them to one another in some form; the truth is that they cannot circulate because they cannot be objects of exchange. They have a priori the structure of a collective and when two colonialists, in conversation, appear to be exchanging these ideas, they actually merely reactualise them one after the other in so far as they represent a particular aspect of serial reason. In other words, the sentence which is uttered, as a reference to the common interest, is not presented as the determination of language by the individual himself, but as his other opinion, that is to say, he claims to get it from and give it to others, in so far as their unity is based purely on alterity. (Of course, it is possible to imagine colonialist groups associating for the organised defence of their colonial interests; indeed, there have been plenty of cases of it. Naturally, these groups multiply as tension between colonists and colonised increases. But we are here considering only the colonial milieu. It is enough to indicate - and we shall come back to this in the next chapter - that the presence of groups constituted from the gathering itself must complicate any real + +description.) + +In fact, the affirmative force of this opinion derives from the fact that, in and through everyone, it is the invincible stubbornness of others; and the certainty of the person who affirms it rests on his (cheerfully accepted) inability to occasion any doubt about this subject in any other members of the series. The Idea as a product of the common object has the materiality of a fact because no one thinks it. Therefore, it has the opaque indubitability of a thing. But in the moment where a particular colonialist is pleased to relate to it as to a thing, that is to say, as an unthinkable thought, he presents it as a spontaneous rediscovery, a fresh, new re-creation elsewhere (anywhere in the colony): for example, there is this colonial administrator, a nice chap, but terribly young and so foolishly idealistic, and he is just learning the job ... ; in him and through him, the idea becomes a hypothesis, a key to decipher an experience, etc. Elsewhere, and therefore in the Other, the inert formula which everyone repeats recovers its pristine force as a discovery; in other words this particular colonialist, as Other, here repeats a stereotyped formula in the certainty that he himself, in an Other and as an Other, is rediscovering it. But, in fact, he has neither the means nor the intention of renewing his experience + +for himself, of testing the Idea, in order to guarantee it anew: the Idea as a living praxis emerges in action and as a moment of action as an ever contestable key to the world. But there is no need to contest it since the common object is based on the practical avoidance of all testing. The strength of this particular colonialist lies in the fact that the Idea (as a common bond) comes to him as the thought of the Other, of totalised alterity, and that he is entirely the Other as infinite flight, frozen at the moment he repeats it, while this absolute certainty becomes work, unification and translucidity in Others - in the young, etc. He affirms himself as the Other who really thinks it elsewhere by making himself the Other who repeats + +it here without thinking. + +In connection with this opacity conceived as obviousness and the inability to change the Other conceived as indubitability, it should be remembered that each of these Ideas is imposed on everyone as a practico-inert exigency, that is to say, as a categorical imperative. In this sense, it is common interest constituting itself as the solidarity of the colonialists against the colonised; but this solidarity, at the level of seriality, can only have a negative form: it is determined in alterity. On this basis, it arises as the (negative) fact that, amongst the small number of colonialists who maintain themselves by force and against the colonised, everyone is in danger in the Other; that is to say, everyone is impotently in danger of suffering the consequences of some pernicious act occurring somewhere in the series. In fact, in this particular example, the serial unity of the colonists comes to them from the Absolute Other which is the colonised people; and it reflects them as an active grouping (a synthetic, positive unity of plurality). The impotence of the series constitutes itself as a magical power of the colonised people. They are oppressed and, in a way, still impotent - otherwise the colonialists would no longer be there; but, at the same time, 'they know everything, they see everything, they spy on us, they communicate among themselves instantly, etc.'. In this magical milieu of the colonised Other and of the participation of every native in the whole, seriality is revealed in its impotence as the threat to each by all, and consequently as an obligation for everyone to maintain the Other-Action, which means: not that which has been established by universal agreement, but that which he would like any other to maintain. This act, of course, is the Other itself as the formula of the series of colonialists; in other words, it is the colonialist in so far as he is always the model who inspires me in an Other. The colonialist produces himself in the Other without weakness; he imposes himself within me as a prohibition: show no weakness to the native staff; and this brings us to the exigency of the system: no change for the colonised without the destruction of the colonial apparatus. The colonialist is a particular being who needs to be realised through me in so far as no one can realise him and in so far as he must remain outside as the negative formula of the series. In a way, every colonialist spontaneously and constantly realises him by his free activities in so far as they express his particular interests as an exploiter in the milieu of the exploited; but at this level, he is not a being. He becomes one when the threat of insurrection becomes more concrete. But in this case, his practicoinert relation to everyone is imperative precisely because it produces itself as everyone's responsibility towards the Other in so far as every Other is responsible for everyone. Hence that strange magical bond through the virgin forest of seriality: I try to realise the Other - that is to say, to make myself more deaf, ruthless, and negative to the claims of the native, than my plantation as my own + +I have described serial being as the determination of the bond of alterity as a unity of plurality by the exigencies and structures of the common object which in itself defines this plurality as such. We have seen that this being is practical because it is sustained in reality by the relations which are established in the practico-inert field between the individual activities of men. But at the same time as it produces itself as collective in and through the real behaviour of every practical organism, this serial being is constituted as a negative unity and a threatening (or paralysing) interdependence by the impotence of each real action in so far as it derives from the actions of the others through the practical field. Its reality, then, is in itself practico-inert and its transformations are born of a simple dialectic. (Activity is sometimes constituted as collective passivity by failures due + +interest actually requires - so that my attempt becomes, for some other who might be tempted to make a concession to the natives, the real presence of the Other, as a magical force of constraint. In fact, of course, there is nothing irrational in this: the Other as the presence-constraint of a negative unity is given t('l all the members of the series; it is the same imperative for all. In actualising it in my action I actualise itfor all those present and, by degrees, (by a real series of propagation, which, however, like all movements, exhausts itself ) for the serial totality. In fact, the example is in no way the direct unification of the multiplicity of a gathering by the real activity of a single individual (although the existence of the group will complicate its structures). Originally, the example was quite simply the actualisation in one term of the relation of seriality. In this Other, who behaved correctly in public (that is to say, as the Other that he is and that I am) towards the native, I discover myself as Other (an identity determined in seriality). Conversely, this particular Other, who has shown himself so perfectly as the Other in all his opacity, becomes for me the common interest as my particular imperative: the Other that I have to be. This makes it clear that racist ideas, as structures of the collective opinion of the colonialists, are petrified actions (petrified from the beginning) which are manifested as imperatives in the context of the Other to be realised by me. As perpetual exigencies of reaffirmation by individual verbal acts, they indicate the impossibility of a real totalisation of these affirmations, that is to say, the intensity of the imperative is directly proportional to the index of separation. In short, by the very act of repeating them, one shows that it is impossible for everyone to unite simultaneously against the natives, that it is merely shifting recurrence, and that in any case such a unification could occur as an active grouping only so as to massacre the colonised people, which is the perpetual, absurd temptation of the colonialists, and which, if it were possible, would amount to the immediate destruction of colonisation. In this way, the racist idea, both as an unthinkable idea and as a categorical imperative, can serve us as a typical example of the serial idea as an act of alterity which realises in urgency (and for lack of anything better) the practico-inert unity of the gathering, and, in contradiction with the original exigency, manifests this unity as a fundamental negation, + +to impotence, that is to say, to a qualification and a transformation which come to the agent from others; serial being becomes immobility through innumerable impotent activities, or activities of impotence. And sometimes, as in the case of the colonialists, impotence presents itself as a unitary exigency of action; but, in this case, action is not really praxis; it is practico-inert because it realises the Other as a fleeting and prefabricated passivity.) In this way, serial being, as a practico-inert reality, can be defined as a process, that is to say, as a development which, though orientated, is ca4sed by a force of exteriority which has the result of actualising the series as the temporalisation of a multiplicity in the fleeting unity of a violence of impotence. These observations have shown us that the collective is not simply the form of being of certain social realities,89 but that it is also the being of sociality itself at the level of the practico-inert field. And I have been able to describe this being as social being in its elementary, fundamental structure because it is at the practico-inert level that sociality is produced in men by things as a bond of materiality which transcends and alters simple human relations. Besides, a collective is in itself a sort of scale model of the practico-social field and of any passive activity carried out in it. It is constructed, moreover, on the false reciprocity of the practical agent and of worked matter; in reality, worked materiality, in bearing the seal of an other activity (and entering into human action under the impulse of a series of dispersed praxes), becomes in the collective the practico-inert unity of the multiplicity of which it is the common object. Thus the unity of the gathering, far from being organic or practical, manifests itself with all the characteristics of sealed materiality; in other words, inorganic materiality comes to the gathering as such from its inert (or practico-inert) unification by the interiorisation of the seal of its common object. But this materiality, as an inorganic materiality which produces itself in and through practical relations, takes on the determination of alterity. Thus, in the dialectical movement which characterises this structure of false reciprocity within the collective, seriality as the seal of the common object projected onto the human multiplicity turns back on the common object and determines it by the action of everyone as an other-object (objet autre) (that is to say, a common object as the objectification of the Other or as Other objectivity). It is in this dialectical moment that the object produces its men (as workers, owners, etc.), as the others whose alterity it is and who act on it or suffer its action in so far as it becomes for each of them his Other Destiny or his Other Interest, that is to say, in so far as the activity of everyone - in so + +far as it responds to the exigencies of the common object - also reveals the impotence of everyone in the objective form of the inflexibility of the object. The celebrated inexorable laws of bourgeois economics in the nineteenth century have never been anything but the effect of scarcity appearing in a practico-inert field of serial impotence. Indeed, from this point on, the same practico-inert notions (solidified finality, simultaneous inversion of the dialectical laws of human praxis and of the analytical quantitative laws of inorganic materiality) apply within the collective, to matter as the sealed unity of men, to the gathering as the material negation of molecular dispersal and of the human relation, and to the acting individual in so far as his free praxis constitutes itself as inessential in relation to the practico-inert activity of the Other and to the practico-inert exigencies of the worked thing. In fact, we rediscover here a real and universal mode of discourse, in so far as discourse itself is a practico-inert designation of the practico-inert field. These verbal structures are genuine tools of thought for thinking the world of passive activity and active passivity; all that is necessary is that a direct, organised practice (on the part of an individual or a group) should take them in their practico-inert heing and use them, as is only proper, as replacements for things. And in so far as they have been invented by nobody, and in so far as they are language organising itself as passive activity in the milieu of alterity, these verbal structures are, in a collective, the collective itself, that is to say, the common object in so far as it is produced (under everyone's real actions) as a material Idea of the being of man or of the acting individual in so far as he acts and speaks as Other in the milieu of serial impotence. These verbal structurations (practical schemata for constructing an indeterminate series of sentences) are characterised by an absolute refusal to make a distinction at any level between the agent (or agents) as member of a series and the object as producing men as its products. In fact, in the collective, exigency really is in the object, because some men have put it there and others maintain it there on the basis of the entire historical process; and it really is inhuman, because inorganic matter, as the conducting medium, necessarily inverts the structures of praxis. Conversely, it is really human in everyone (in so far as it is grounded on need, etc., and in so far as it manifests itself through a project which transcends past and present conditions towards the future), but it is dehumanising in so far as it produces itself as the unification of the gathering by the thing: its reality therefore produces itself in everyone as inflexible in so far as it produces impotence as the negative and totalising link of the series as materiality; furthermore, the structure of alterity which is manifested on the basis of this impotence forces man to demand, as Other and as conditioned by Others, (and as conditioning them as an Other) so + +imposed on the multiplicity which composes it. But a few points still remain to be cleared up. We shall return for a moment to the example of the French proletariat as produced by industrialisation in the first + +half of the nineteenth century. + +5 Series and Class: The French Proletariat + +As collectives are both a result of particular undertakings and a radical inversion of finality, they have peculiar powers which may have made it possible to believe in their subjective existence, but which need to be studied in objectivity. Because the economic system of a society is a collectiYe, it can be conceived as a system which functions of itself, tending to persevere in its being. In particular, what Marx calls the process of capital must necessarily be understood through the materialist dialectic and in accordance with his rigorous interpretation of it. But if it is true that this process is partially responsible for 'the atom isation of crowds' and also for recurrence,92 it is also true that it can + +92. There is no trace of aromisation in medieval communities. They have their own structures, grounded on the relation of man to man (personal dependence). In this period, writes Marx: 'The social relations between individuals in the performance of their labour, appear at all events as their own mutual personal relations, and are not disguised under the shape of social relations between the products of labour ... .' (Capital, I, p. 77) . Yet this feudal constitution did nothing to prevent alterity or circular recurrence or even in certain cases the perspective of flight: this is what creates, for example, the reality of the Church, which is certainly something more than the set of the personal relations amongst the clergy and between the clergy and the laity. If the enormous, real substratum of religious alienation existed, and weighed on the whole of Europe with the weight of its properties and its privileges, this is not because it was tending to realise its unity as a subjective community of believers, but rather because it remained a detotalised totality and because any attempted action on it, whether from outside or inside, lost itself in a perspective of indefinite flight. The real problem - which we cannot go into here - relates not so much to the past, where recurrence and alienation have always existed, as to the future: to what extent will a socialist society do away with atomism in all its forms? To what extent will collective objects, the signs of our alienation, be dissolved into a true inter-subjective community in which the only real relations will be those between men, and to what extent will the necessity of every human society remaining a detotalised totality maintain recurrence, flights and therefore unity-objects as limits to true unifica- + +exist as 'a relation determined by production' only in and through this milieu of recurrence which it helps to maintain. 'Capital is a collective product, and only by the united action of many members, nay, in the last resort, only by the united action of all members of society, can it be set in motion. Capital is, therefore, not a personal, it is a social + +power, + +' we read in the Communist Manifesto.93 But this social power will impose itself as 'a thing existing outside individuals' through what Marx called an 'interversion and a prosaically real and in no way imaginary mystification'. And a passage in Capital explains the origin of this interversion itself: 'In the form of society now under consideration, the behaviour of men in the social process of production is purely atomic. Hence their relations to each other in production assume a material character independent of their control and conscious individual action. These facts manifest themselves at first by products as a general rule taking the form of commodities .... Hence the riddle presented by the money-fetish is but the riddle presented by the commodity-fetish.'94 Thus it is not so much, as Marx says somewhat unfortunately in the Manifesto, 'the united action of many members', but above all their separation and atomisation which endows their real relations of production with the inhuman character of a thing. + +Yet this 'uniting of action' does occur; the proof is that bourgeois economists speak quite readily of the solidarity of the interests of workers and employers. Thus, the finished product is presented as if it were the result of a concerted undertaking, that is to say, of an action and work group comprising management, technicians, office staff and workers. But the bourgeois economist does not wish to see that this solidarity is expressed in inert matter as an inversion of the real relations ; this false unity, as the inert seal which supposedly signifies men, can, in fact, refer only to relations of antagonism and seriality. It is the object and the object alone which combines human efforts in its inhuman unity: and if it can make people believe in the existence of an original agreement where there is, in fact, only an anti-social (practico- + +tion? Must the disappearance of capitalist forms of alienation mean the elimination of all forms of alienation? This brings us to the question posed by Jean Hyppolite in his Etudes sur Marx et Hegel (Paris, 1 95 5; translated by John + +O'Neill as Studies on Marx and Hegel, Basic Books, 1969. [Ed.]) + +93. Marx and Engels, Selected Works, Moscow, 1962, Vol. I, p. 47. [Ed.] 94. Capital, Vol. I, pp. 92-3. The emphases are Sartre's and the translation is slightly amended. [Ed.] The passage is missing from the French translation. See Maximilien Rubel, Karl Marx. Essai de hiographie intellectuelle, p. 35 0. + +inert) force, this is because its passive unity, in its radical heterogeneity, cannot refer to any kind of human unification. In other words, it leaves the social origin of a machine as such totally indeterminate (at a particular moment of Histnry there is no way of telling, for example, whether a particular machine was produced in a country with a capitalist system or in one where the means of production are socialised).95 How can one fail to see that 'reification' comes to man through recurrence, that is to say, precisely as that which makes him act as Other than himself and which determines his real relations on the basis of relations between Others? We have seen how price stabilises as a result of recurrence, and how it immediately imposes itself on everyone without haviI).g been wished as such by anyone; we have also seen how the concrete relation of the buyer to the seller is relegated to being an inessential appearance : entering the shop, saying hello, asking the price, haggling, hesitating, and buying something: all these supposed moments of the act are no more than gestures; the exchange is settled in advance, the price imposes itself; it is things that determine the relations of men. If, as Marx has often said, everything is other in capitalist society, this is primarily because atomisation, which is both the origin and the result of the process, makes social man an Other than himself, conditioned by Others in so far as they are Other than + +themselves. + +In so far as the worker is a product of capitalism, that is to say, in so far as he works for wages and produces goods which are taken from him and uses industrial machinery which belongs to individuals or to private groups, the negative common object of the working class in the first half of the nineteenth century was, as we have seen, its total national production, that is to say, machines as capital requiring the worker to produce, through them, an expansion of capital. We have also seen that the common interest of the class can only be the negation of this negation, that is to say, the practical negation of a destiny which + +95. On the other hand, the same machine as such may yield information about contemporary means of production, about techniques and, in this way, about certain ossified structures which worked matter establishes amongst its servants. But, in so far as the means of production are the same everywhere, these inert structures are everywhere the same. It is at the level of the group that one can tell whether a common praxis has returned to these structures and made them more flexible, or balanced them in other areas (reduction of working hours, organisation of leisure, cultural activities, etc.) or whether they have been left to fend + +for themselves. ' + +is suffered as common inertia. We must therefore recognise that practical organisation, as human exigency, is, in itself, and even in the practico-inert field, a constitutive structure of relations amongst workers (this will become clearer in the next chapter). And this organisation is both a means and an end, since it presents itself hoth as a means of struggling against destiny (that is to say, against the men who in a particular system make this particular destiny out of the machine), and as the future reinteriorisation of the practico-inert field and its projected dissolution within a perpetually active social organisa. tion which, as a concrete totality, will govern both the means of pro- + +duction and production as a whole. + +The worker will be saved from his destiny only if the human multiplicity as a whole is permanendy changed into a group praxis. His only future, therefore, is at the second degree of sociality, that is to say, in human relations as they arise in the unity of a group (and not in the disunity of th� gathering-milieu). This is what Marx meant when he spoke of the sociality of the worker. Yet it should be noted that this sociality appears as the joint negation of two reciprocal aspects of the practical field: a negation of the common object as destiny and a connected negation of multiplicity as seriality. In other words, sociality as a still individual project of transcendence (in the organised group) of the multiplicity of individuals reveals seriality itself as a link of impotence; this seriality is the being-to-be-transcended towards an action tending to socialise the common object. On the other hand, this sociality, in so far as it was determined in everyone by the very structure of the collective in which he produced himself, and in so for as it initially produced no result (that is, during the first quarter of the nineteenth century and, basically, right up to the revolt of the Lyon silk-weavers) or was limited to the creation of reciprocal relations, appeared in everyone as a structure peculiar to his own project and thus decomposed into a multiplicity of identical projects, before producing active organisations through itself. Thus it emerges as a process of isolation precisely to the extent that it is fundamentally a transcendence of plurality towards unity. This means, quite simply, that the organising project in everyone begins by being negated by that which it transcends and negates, that is to say, by seriality as a link of impotence. When we look at it more closely, we can see that the necessity of some common action can arise only out of an existing link between men and can present itself only as the transcendence and inversion of this fundamental link. If it were possible to conceive real (but abstract) + +individuals in a pure state - and I do not mean the social atoms of liberalism - in so far as they are united by bonds of reciprocity, and if one could abstract from the object's transformation of reciprocity into a link of alterity, it would be impossible to understand how the infinite dispersal of human relations could of itself produce the means of pulling itself together again. This conception is completely inapplicable to human history, but it retains some sense as a logical possibility, provided the idea mentioned above of living organisms, which depend on the universe, but are not affected by the contraction which is caused by scarcity as a fundamental, contingent characteristic of our History, is consistent. In the practico-inert world based on scarcity, however, the object brings men together by imposing the violent, passive unity of a seal on their multiplicity. And in the very moment where this object is a threat (for the colonised, or the exploited), in the very moment where this object, as positive interest, is threatened (for the colonists or the exploiters), the unity .of impotence transforms itself into a violent contradiction: in it, unity opposes itself to the impotence which negates it. We shall discover the intelligibility of this moment later. For the time being, what needs to be emphasised is that impotence, as a force of alterity, is primarily unity in its negative form, primarily action in the form of passivity, and primarily finality + +in the form of counter-finality.96 + +Thus, as we have seen, there is a sort of common mode of hehaviour amongst the white minority in a city where the majority are black: quite simply this behaviour is common in that it is imitated by everyone but never adopted by anyone (not counting the creation of organisations). All the same, the practical unity of men can never arise or originate in the domination of worked matter over man, from such unity itself. In this sense, the common class-heing of the workers in 1830, in the presence of Machine-Destiny and of the organs of oppression and constraint, was the seriality of their relations of reciprocity, in that this profound impotence was also a unity. In fact, the existence of a labour market created a link of antagonistic reciprocity between workers, in which separation was lived as opposition and alterity: in the negative ensemble of individuals selling their labour power, we have seen everyone featuring both as himself and as Other. It is also clear that labour itself, according to the mode of production, + +96. I see these three notions as socialities. It has been obvious from the beginning of our dialectical investigation that the original foundation of unity, of + +engenders relations either of positive reciprocity or of dispersal. Although in the nineteenth century capitalist concentralisation tended to bring workers together, dispersal remained a crucial factor (the dispersal of industries throughout France, the dispersal of residential groups, etc.). Yet the worker tended to become aware of the objective characteristics which made a worker of him and which defined him by his labour and by the type of exploitation to which he was subjected. He gradually became aware of his objective reality and, thus, of that of his comrades. But their common characteristic of being the product of their product and of the society which was organised around this product, however apparent it may have been to some of them, could not create anything more than an abstract, conceptual identity amongst + +them, unless it was lived in action. + +By this I mean that this common characteristic was manifested each day in the reciprocal and contradictory double link of antagonism on the market and of solidarity in labour, and above all on the occasion of local retaliatory actions, through their first failures and surrenders. In these early days of the workers' movement, when resistance was spontaneous , impotent and rapidly repressed, the defeated realised themselves in this impotence and lived it as the serial dispersal of men in their condition; but this objective condition realised itself through their everyday relations with their comrades, and it was this that held back all their efforts to take common action. This indefinite plurality of contradictory relations is both what defined their condition as workers (in particular, the fact that they competed with their comrades) and what created class as an indefinite series whose serial unity lay everywhere in the impotence of the individuals who composed it, just because this impotence derived from their separation. Exploitation was revealed as the passive unity of all (and not simply as an identity of condition) , in so far as everyone lived the isolation of Others as his own isolation and their impotence through his own. Class as a collective became a material thing made out of men in so far as it constituted itself as a negation of man and as a serial impossibility of negating this negation. This impossibility makes class a factual necessity: it is un- + +action, and of finality is individual praxis as the unifying and reorganising transcendence of existing circumstances towards the practical field. But we also know that this individual praxis can no longer he recognised at the most concrete level of the practico-inert and that it exists there only to lose itself, to the advantage of the + +changeable destiny. It is not a practical solidarity but, on the contrary, the absolute unity of destinies brought about by lack of solidarity. Every worker feels himself confirmed in his inertia by the inertia of all the Others; every small organised group feels its own class as a universal flight, which neutralises all its efforts. For this proletariat in the process of formation, the Other is primarily the serial totalisation of Others (in which he features as an Other), that is to say, of all those, including himself, who represent for everyone the possibility of being out of work or of working for lower wages; in short, it is himself as Other, in so far as his serialised and totalised antagonisms manifest themselves in the fact that on the labour market he is his own counterfinality, who emerges as the Other who forces demands to be lowered. This serialised antagonism, or negative seriality (which, for reasons of space, we have not examined thoroughly except in relation to the market) constitutes an initial structure of alterity, based on the reciprocity of antagonism, and constitutes every worker for every Other as himselfin so far as he is his own enemy. But in the same moment the serial unity of these oppositions posits itself as a contradiction of the same and of the Other demanding a unifying praxis. Now, paradoxically, but very logically, it is not these antagonisms as such which make unity-praxis so difficult; on the contrary, as we shall see, their truth lies in the transcendence which integrates them in the common unity of demands. What made the workers impotent, in the first half of the last century, was alterity as spatial and temporal stratification. At the level of positive reciprocity in labour (which is the structure of alterity which contradicts the former and creates the true practico-inert tension of class), it is in effect dispersal which creates impotence. At this level, in fact, everyone's objective grasp of his class-heing as the practico-inert reality of his own praxis (which was examined above) implies a reciprocal grasp of his comrade in his particular class-being; this was achieved practically (and not theoretically, at least at that time) by friendship, mutual aid, work relations, etc. And, in so far as this reciprocity spread through France in constellations and chains of constellations (including, through their relations with other groups, the villages from which some of the proletarians came and the political groups of the republican petty bourgeoisie), class posited itself- as the + +But this milieu was not an ohjective representation of the worker: it constantly realised him as practical impotence. If he learnt that a workers' newspaper had been founded, as a practical determination of + +class action, he would produce himself as directly affected by this group, which, from within the practico-inert, affected him in his being as an imperative order97 to negate the structure of impotence and separation in this being. But, at the same time, because this limited undertaking was constituted at the horiton (he did not work in the town where it was constituted, a comrade from there told him about it, showed him a copy of the paper), it produced itself as a negative determination of itself and of everyone: in itself, it was in fact a proof that the totalisation of the milieu by class-action was always possible, and that it is the profound truth of the passive totality. But, by the same token, it defines itself as not being this totalisation, as being nothing in relation to class-totalisation and in a way as negating it through the simple fact, which is in any case inevitable, of positing itself for itself: it therefore refers back by itself to the class-gathering as an inert unity of multiplicity. As for the worker in Lyon who, in a moment of defeat, learnt of the initiative of his Parisian comrades, he himself was constituted as inertia, as rooted in impotence by sheer distance (connected in fact with eyerything), which prevented him from joining them and by circumstances which meant that the moment to imitate their action had not yet arrived at Lyon. At the same time, in this period of uncertainty, he remained hesitant about the content of the initiative: he has not completely thrown off Christian ideology, and he knows that his Parisian comrades are not entirely free of it either, so that his relation to the object produced (the newspaper, the ideas it supports, its propaganda, etc.) remains indeterminate. Here again it is common class-being which realises itself in this contradictory relation: in this collective, in effect, if a group, however small, constitutes itself, and if this group becomes known, then the unity of the group is lived negatively by everyone as a sort of intermediary between serial inertia and the active organism: everyone is united with the Others, passively but directly, in sofar as he is determined as a moment of a total totalisation by the movement of partial totalisation which, somewhere else, and through a few people, negates the class-gathering as everyone's inert being-there. Between him and the groupuscule, through the inert density of the milieu, a synthetic link of univocal interiority (which proceeds from the group to the individual) establishes itself; but at the + +97. Clearly the imperative character which collective action presents to someone who has not joined the group is the only way in which human freedom can + +same time, both his own indeterminacy and the thorough indeterminacy of the group action, mean that this relation remains indeterminate (neither negative nor positive), so that the bond of synthetic interiority allows itself to be absorbed by the serial bond of common mem- + +bership of the milieu. + +On the other hand, through the failures of local attempts which had not been suppor-ted and followed through, or sustained and continued, every group saw active class solidarity as an inert exigency of the classobject on the basis of the rediscovery, in the defeat of negative solidarity, of destiny as serial flight. What was at stake here was not a conflict of interests between workers, but rather their separation. Faced with this indefinite milieu which needed to be agitated by serial methods, the group became aware of its smallness, its impotence and its fragility. In other words, it came to be seen as a fragile mode of the common substance and, by the same token, it produced itself in its vacillating activity as the relation of a 'micro-organism' (I am not using this term in an organicist or Gestaltist sense) to the substance which it determines, and which gives it its depth and fragility. Naturally, classbeing manifests itself as a temporalised separation, not only because any political education and agitation presupposes a hysteresis originating in the 'passivity of the masses'; that is to say, in the seriality of the classgathering, but also because the workers are at different levels of politicisation arid liberation depending on their individual histories and + +because spatial dispersal is reinforced by temporal dispersal. + +In any case, in so far as the historical reality and specific structure of the class had been defined in certain men produced by the mode of production through the relations of production, it derived its general structure and intelligibility from the fact that its common object constituted it as a serially structured milieu and that other classes, through the contradictions which opposed them to it, through the same practicoinert ensemble, made the negative unity of alterity into the leaven of its orgamsing praxis. In the example of the archaic proletariat, the worker is in the class in so far as he is conditioned by Others, that is to say, to the extent that he is himself, for himself, always Other, and that his labour power, as a commodity, is Other than him, that is to say, alienated. He is in the class in so far as his own inertia is based on the inertia of Others and becomes the class itself in everyone as the inertia of the Other as Other. And this class-being is normally expressed in the serial, negative practices of abstentionism, defeatism, demoralisation or surrender. These practices in everyone are seriality as a whole. + +In this way, common-class-Being manifests itself in all its rigidity in periods when workers are 'on the defensive'; on the basis of the contradictions of the individual, and of the material conditions of his life, it becomes, in everyone, destiny producing itself as the Other-Being of the worker in relation to himself and to all the Others. In this sense, common-class-Being as an interiorised common object is neither a totality imposing itself on its parts but differing from them, nor a word connoting the indefinite repetition of particular class-being as a universal reproduction of the identical, nor a way of designating the set of conditions common to everyone and which are sometimes called the 'condition of the working class'. At the most superficial level of the investigation, everyone is in the class, in so far as the indefinite series of relations is realised as a milieu by the human terms between which these relations hold. But at first this milieu as such is no Other than men and their objects making themselves into the milieu of man or, in other words, it is reciprocity as a relation amongst workers making themselves through things not only humanity but also a homogeneous, inert container of all. But in any case, at a later stage of the investigation the milieu will dissolve and reveal serially structured multiplicities of multiplicities. At this moment, common class-heing is no longer, for everyone, heing-in-the-milieu-of-class: it is, in fact, everyone's heingelsewhere in so far as he is constituted as the Other by the progressive series of Others, and as the Other-Being of everyone in his position in the series in so far as he constitutes the Others. Class exists as a + +totalised series of series. + +This is why it is not really very significant to find (or to think one can find) continuous transitions from one class to another, intermediaries, and unclassifiable groups : if class were to be treated as a total, synthetic form, enclosing its members, it would indeed be highly embarrassing to admit those imperceptible passages from one class to another which bourgeois economists are so happy to describe, and the aporias which this new scepticism claims to have found (and whose logical structure resembles that of the old arguments about the bald man, etc.). But, if class is a serial totality of series and if the ensemble of these series corresponds roughly both to the worker's class-being and to his Other-Being, it does not matter if these series finally disappear, decompose or become .Other; on the contrary, it is of the essence of seriality (as a determination of the practico-inert) to be infinite or indefinite; thus it is of the essence of class-being, as the absolute elsewhere of impotence, to disappear at the horizon and to allow itself to + +be determined in its Other-Being-to-infinity, by the Other-Being of other individuals belonging to other classes. These mediations do not affect the true weight of class and are practically ineffective: in cases of tension (which is to say, permanently), alterity sticks at the level of mediation, and nothing gets through any more, or the intermediary explodes and the two freed series define themselves by their struggle. Conversely, if one could define precisely the historical reality of a class and if this definition could be applied to all its members and to them alone, the series would still be infinite, because they would be circular. But the seriality of class makes the individual (whoever he is and whatever his class) into a being who defines himself as a humanised thing and who, in the practico-inert universe, is strictly interchangeable, in given conditions, with some material product. And what finally characterises the working class (this being our example) is that the organised praxis of a militant group originates in tpe very heart of the practico-inert, in the opaque materiality of impotence and inertia as a transcendence of this materiality. Thus the other form of class, that is to say, the group which totalises in a praxis, originates at the heart of the passive form and as its negation. A wholly active class, all of whose members are integrated into a single praxis and whose apparatuses organise themselves in unity rather than conflicting with one another, is realised only in very rare (and revolutionary) moments of workingclass history. Even without going into the question of the development of the working-class experience and of its objective organisation (which are one and the same thing) , it is therefore dear, from the point of view of the intelligibility of the practico-inert, that the proletariat, in so far as it is both Destiny and the Negation of Destiny, constitutes in its very form a changing and contradictory reality, or in other words, that it is always, to a degree which is determined bv the historical situation, a group praxis (or, usually, a multiplicity of group activities) which erodes the inert unity of a common-class-being. It is therefore a class which produces itself as a contradictory double unity, for the inert-being-of-seriality, as the basis and material of every other combination, is really the unity of workers in their being and through Being, in so far as their destiny owes its rigidity to their dispersal, 98 and + +98. The dispersal of which I speak here has no historical connection with the process of concentration, although the latter can help to decrease it by increasing contacts; dispersal is fundamentally only the impotence of alterity in so far as it is lived by a necessarily dispersed plurality, although the field of dispersal may be + +more or Jess extensive. + +increases it; whereas an active organisation constitutes itself against Being, and its unity is purely practical; in other words, praxis, as the organising transcendence of inert being towards the reorganisation of + +the s + +bcial field, is the unity of the multiple as a perpetual labour. However, a number of points should be noted. First, that collective praxis can occur only on the basis of a fundamental common-being; secondly, that it will remain structured by the being which it transcends and which determines it up to its limits and efficacity (as we saw, trade-union practice about 1900 was structured in its very temporalisation by the practico-inert characteristics of the proletariat as they had been produced under the pressure of universal machines) ; thirdly, that it stands in a relation of alterity and, through antagonisms, of seriality to other organisations independent of it and that the conducting medium of this new seriality is the class as a collective; fourthly and lastly, that any organisation, as we shall see, is in constant danger of dissolving into seriality (the bureaucratic nature of certain unions in some countries) or of falling straight back into the inertia of common-being, while, at the same moment, the class-collective, as worked matter, with all its inertia, supports the practical unities, which have become unitiesof-being and inert meanings, as a seal. Thus, whether or not organisation has progressed beyond the series, the working class in its contradiction represents the most resolute and visible effort of men to reconquer themselves through one another, that is to say, to rescue themselves from Being to the extent that it gives them the statute of a human thing amongst other human things which are their inanimate products ; and the field of practico-inert being is constantly closing up or threatening to do so; Being petrifies their actions in full freedom. This new moment of the investigation shows us that the practico-inert field is no + +more than a still abstract structure of History; - + +indeed, it cannot + +constitute itself unless the world of alterity produces as a serial unity the condition and principle of its own transcendence. We must now examine this transition from being to organisation. Having grasped the dialectical intelligibility of individual praxis and of the passive activity of the collective, we must now grasp and fix that of collective praxis. + +covering whether this place of violence, darkness and witchcraft actually has dialectical intelligibility or, in other words, whether some strict rationality underlies the strange appearance of this world. It is now clear that it does : not only do all the objects and processes which occur there obey rules of dialectical development, thus making comprehension always possible, but also the structuration of the experience in the practico-inert field realises itself through the appearance of necessity within certainty (iyidence) and, therefore, necessity at the heart of free individual praxis presents itself as the necessity of the existence of this field of inert actiyity. In other words, in the practical experience of a successful action, the moment of objectification presents itself as a necessary end of the individual practical dialectic - which is submerged in it as in its object - and as the appearance of a new moment. And this new moment (that of the practico-inert or of fundamental99 sociality) comes back to the total, translucid dialectic of individual praxis and constitutes it as the first moment of a more complex dialectic. This means that in every objectified praxis the practico-inert field becomes its negation in favour of passive activity as a common structure of collectives and worked matter. Thus the moment of objectivity defines its dialectical necessity as organic activity which has been transcended and preseryed by inertia precisely to the extent that, both for the individual agent himself and in the apodicticity of the investigation, it presents itself as the transcendence of individuality, in this agent and in everyone, by a suffered original statute of reifying sociality. And we have carried the study of this sociality far enough to discover in it, through a new kind of investigation, the principles of an inversion, which refers from necessity to a different freedom (that of unification) + +as a third moment. + +But this dialectical movement, as I have described it - and as it superficially appears - has no intelligibility; or rather, if we were to neglect its real conditions, we would fall back into an external dialectic (dialectique du dehors). Only Magic or Fate could explain how individual praxis, absorbed in the object, could be the source of a new negation by which it transforms itself into the first moment of a dialectic of collectivity, if we really had to accept that the intelligibility of the practico-inert field and of its negation by the group resides in the action of a dialectical force expressed through free praxis and developing + +through changes in the field and different kinds of action. The intelligibility of individual praxis as translucidity cannot in any way be the same as that of the practico-inert field, and, similarly, it would be absurd or idealistic to imagine that individual praxis, inert activity and common action are the three moments of the development of a single force conceived as human praxis, for example. In reality, there are two quite distinct dialectics: that of individual practice and that of the group as praxis - and the moment of the practico-inert field is in fact that of the anti-dialectic. It is, in effect, contained between two radical negations: that of the individual action which meets it in itself, in so far as it still adheres to its product, as its negation; and that of the unification into groups which occurs in collectives as a practical rejection of seriality. If one can nevertheless apply the term 'dialectical' to this material field of the anti- dialectic, it is precisely because of this double negation. In this field, everyone's action disappears, and is replaced by monstrous forces which, in the inertia of the inorganic and of exteriority, retain some power of action and unification combined with a false interiority. And conversely, the simple movement of unification, as it developed in the working class in the course of the last century, was sufficient to constitute the class, far beyond its precarious, limited initial unifications, as an impotence which was haunted by an invincible human power, + +as the serialisation of a fundamental totality. + +The intelligibility of practico-inert processes therefore rests on a few simple, clear principles which are themselves the synthetic contraction of the obvious characteristics of the univocal relation of interiority as a basis of individual praxis and of the plurality of agents within the practical field. In fact, objectification always directly involves alteration. When they say that, in a socialist society, man will be his own product instead of 'the product of his product ' , Marxists mean that if man is his own product, he will be his only objectification (in himself and in Others) ; thus objective being will be homogeneous with the practice of objectification. But if the individual's reality lies in a material object, an anti-dialectic starts : sealed inorganicism appears as man's being. Now, this very special situation obviously depends on the multiplicity of individuals co-existing in the field of scarcity. In other words, only the free praxis of the Other on the basis of material circumstances, through some worked matter, can limit the efficacity and freedom of my praxis. In this sense the explanation of classes in Anti-Duhring is correct, although it hardly has any historical value. But, paradoxically, it is correct as a dialectical schema of intelligibility + +rather than as a reconstruction of a particular social process. Engels claimed in fact that classes (that is to say, the collective as a practicoinert type of sociality) begin to constitute themselves in an agricultural community when the products of labour become commodities. I have shown that his examples are all irrelevant, because they concern communities disintegrating under the impact of bourgeois societies which surround them or which have commercial relations with them. Butfrom the point of view of intelligibility these examples are adequate: for the characteristic of being a commodity comes to the product of peasant labour from the outside. Engels assumes that the land is common property and that every peasant produces in order to feed himself and his family, and we shall make the same assumption. At this moment of rural labour, the product is neither an aim nor an objective limit: it is the aim of labour only to the extent that it is a means of getting food. It is on the basis of exchange - and in particular of exchange as practised between bourgeois societies and under-developed societies - that objective demand, as a moment of a free praxis of the Other, constitutes the product as Other; that is to say, it removes it from the closed circle of the 'production/consumption' cycle and posits it in itself as an independent object, which has absorbed labour and is capable of being exchanged . Of course, this is not some ideal structure conferred on the product by the mere desire of the future purchaser; these changes occur in the course of a common action (colonisation, semi-colonisation, and an overall movement to enclose the community, and turn it into an enclave) performed by bourgeois groups, and through a set of serial processes which effect the disintegration of the village through a society which trades with it. The product really becomes a commodity. But the important point here is that this transformation imposes itself on free individual praxis: objectification becomes production of the object in so far as it posits itself for itself; in this case, the product becomes the man and as such the product. But this transformation is wholly intelligible. If we ignore for the moment the serial processes and transformations of the practicoinert field, two things remain. First, a praxis (that of a buyer or a group of buyers) has appropriated the freedom of the producer: it is as the object of this free enterprise that the producer will find himself to be producing commodities rather than objects of immediate consumption. Objectification becomes other because it produces its object in the free field of another's action. It is freedom limiting freedom. But secondly, two practical freedoms can confront one another only in the practical + +field and through the medium of materiality as a whole. If circumstances enable one praxis to appropriate the meaning of the other praxis, this only means that the object in which the latter objectifies itself takes on a different meaning and a counter-finality (for its producer) in the practical field of the former and through a reorganisation of this field. The original situation therefore presents itself as follows : the univocal relation of interiority enables the buyer to manipulate the peasant's practical field; in effect, the peasant's relation to his environment that is to say his labour - is an interiorisation in so far as praxis is a unifying organisation and in so far as the organism has its being-outside -itself in Nature. But of itself produced materiality cannot transform anything since it stands in a univocal relation with the producer. On the other hand, as soon as it is given another meaning for the producer hy an other whose relation with it is also a relation of interiority though in a different way, a false relation of reciprocal interiority establishes itself between the product and the producer, because the former signifies the latter and because the producer behaves as signified hy his product. Now, all this is perfectly clear, because, through this product and in so far as he is this product, a human praxis directs itself at the worker and tends to make him work for others when he is still working for himself. On the other hand, it is no less clear that the product, in becoming a commodity, allows itself to be constituted according to the laws of its passivity: it is its very inertia which sustains its new unity, and which transforms the praxis of the buyers into an exigency in so far as it becomes its own independent meaning (signification) against the worker. And it is through this independence (as an absence of human relations, lived in interiority as a synthetic relation of inhumanity) that, as a product which posits itself for itself as a commodity-exigency it becomes that which the worker has made, and therefore what he is, in the world of the object and a5 an object. Destructive power is simply a structure of praxis as individual dialectic; but the confrontation offreedoms, by the double constitution of the intermediate object, cannot become an objective, material contradiction unless the inertia of the object makes the two unities which are conferred on it into + +real, inert negations, that is to say, into passive forces. + +This simple example contains all the conditions of the intelligibility of the practico-inert field: the only practical dialectical reality, the motive force of everything, is individual action. When a field of scarcity determines the confrontation of real agents, a new statute is imposed on the worlced Thing by the activities which confront one another. In + +everyone's practical field (in so far as it is everyone's), it takes on secret, multiple meanings which indicate the directions of its flights towards Others; and as means and end of a particular undertaking (that of transforming the freedom of the Other into a docile means to my own freedom, not by force but by manipulating the practical field), it converts the praxis of the one who is winning into an inert and fascinating hold over the practical freedom of the loser. In the univocal milieu of interiority it re-exteriorises the praxis of the conqueror as the interiorising synthesis of the practical field. And as significationexigency it reflects his heing to the producer as the inert exteriority of a slave in the milieu. of interiority. But, by mortgaging the worker's freedom by its imperative inertia, it transforms, through itself, the free praxis which confronts the worker into a mere inertia of exigency. And, in a way, every freedom, both in the milieu of the Other and in its own milieu of interiority, experiences its own inertial limit, that is to say, its necessity. As soon as multiplicity becomes indefinite (in the practical and serial sense), the multiplication of actions and responses is unified in the object which posits itself for itself as a negation of everyone by everyone (and, later, as a common object). And when I say that the object, as inorganic, sealed inertia, posits itself for it!lt!lf, I mean this literally, although we are grasping the process in its full intelligibility: the fleeting unity of the object which affirms itself in opposition to everyone is in reality the negation of everyone, and of everyone for everyone in everyone's practical field, in so far as it becomes a negative, inert unity in the object (for example, everyone's impotence revealed in the ohject and through every attempt to change its structures) . + +The ensemble of living structures must, therefore, be recomposed in each case, according to the rule of the particular process, if we are to reach the schemata of intelligibility we are looking for: first, the univocal relation of interiority within free praxis as the unification of the field; second, the equivocal relation of a multiplicity of practical activities each of which tries to appropriate the freedom of Others by the transformations which it imposes on the object (practices are hoth negative reciprocal relations, and therefore relations of interiority, and, through the mediation of the inert object, indirect relations of exteriority) ; third, the transformation of every free praxis (in so far as it is absorbed and returned by the object) into an exis; fourth, the inevitable transformation of every exis of worked Things into a passive activity bi the free praxis of an Other, whoever he may be, whose projects and overall point of view are other; fifth, the transformation of + +intelligibility as the transcendence of necessity towards a common freedom, if, indeed, the dialectical origin of the group lies in the passive unity of aiterity in so far as it negates itself as passivity, then, apart from assessing their concrete situation and their history within totalising History, there is no way of telling whether given individuals or gatherings will emerge from their abstract condition as practico-inert beings. In other words, for some men and some multiplicities, in so far as both of them are concrete realities, the possibility of remaining, within the limits of one life or of a set of lives, under the statute of Being and of passive activity, is itself a real, concrete possibility. There is no guarantee that a given bureaucrat or clerk will one day, by integration into a group, cease to be an Other both for himself and for Others. At this moment, manipulated by things (his office, as a collective, his boss as an Other), he is for other men a factor of aiterity, of passivity and of counter-finality, as ifhe were a thing (a Spanish ducat) circulating through men's hands. There is no guarantee that, in itself and for him, this situation contains the seed of a contradiction. + +This contradiction would be inevitable, however, if the freedom of practice came into conflict with constraints, with interiorised exterior prohibitions, in everyone. Such cases do occur: but they are not relevant to our present concerns. Mystification, in fact - as a real process rather than a concerted undertaking - is unfortunately so deep that the reified individual remains in possession of his free praxis. Or rather: to be alienated, or simply altered, a man must be an organism capable of dialectical action; and it is through free praxis that he will discover necessity as a transformation of his product, and of himself by his product, in the Other. The constraints of need, the exigencies of the worked Thing, the imperatives of the Other, and his own impotence his praxis will reveal all these to him and interiorise them. His free activity, in its freedom, will take upon itself everything which crushes him - exhausting work, exploitation, oppression, and rising prices. This means that his liberty is the means chosen by the Thing and by the Other to crush him and to transform him into a worked Thing. Hence the moment of the free contract by which, in the nineteenth century, the isolated worker, a prey to hunger and poverty, sold his labour power to a powerful employer who imposed his own rates, is both the most shameless mystification and a reality. It is true that he has no other way out; the choice is an impossible one; he has not the ghost of a chance of finding better-paid work and in any case he never even asks himself the question: what is the point of it all? He goes and + +sells himself at the factory every morning (in the good old days, they made one day contracts to keep workers), by a sort of sombre resigned exis which scarcely resembles a praxis. And yet, in fact, it is a praxl:r: habit is directed and organised, the end is posited, the means chosen (if he learns that there will be a lot of workers offering themselves for hire, he will get up an hour earlier in order to be there before the others); in other words, the ineluctable destiny which is crushing him + +moves through him. + +It would be true to s�y - and I said it above - that the semi-automatic machine dreams through the women workers, lost in some day dream and moving in a rhythm external to them - which is everyone's work itself as other. But, at the same time, these dreams are quiet, private behaviour, carrying out the machine's sentence by pursuing its own ends (the valorisation of the physical person against devaluation by the alien universality of exigency, etc.). And as for this rhythm, which is so alien to the personal rhythms of her life that for the first few days it seemed absolutely unendurable: the woman worker wanted to adapt herself to it, she made an effort, took advice from her friends, and invented a personal relation of interiority applying to herself alone (given her height, strength, other physical characteristics, etc.); and this, one might say, is the best means of individual adaptation. It is perfectly clear that this involved giving herself to the machine, and that the latter, as the work of Others in the negative unity of a destiny, took possession of her work and made it other: ultimately, the total adaptation to semi-automatism meant the destruction of her bodily rhythms and the interiorisation of a rhythm whicJ:! was absolutely other. But the moment in which the girl emerged as the ohject of the machine that is to say, when mystification revealed itself in objective alienation - was also the moment in which her adaptation was accomplished (within the narrow limits assigned her). There is nothing in this that she could have avoided (except, perhaps, by failing to adapt and getting herself eliminated, first of all from the labour market, and then, as surplus population, from society, through sickness): the initial constraints (the fact that her family could not survive without at least three people working at the factory) ; the constraints which put her in the factory, on the production line, etc., are ineluctable, and they reinforce one another. But these constraints derive from things only in so far as things become transmitters of human actions lying behind them. There is the multiplicity of workers and their false unity through the factory - that is to say, through a destiny which they have to negate + +(Demography, for example, is necessarily the study of both an exis and a praxis: number appears as the product of a certain mode of production and of the institutions it produces, and also as the movement of production, and its exigencies produce demographic differentiations between different sectors of the population. And these conditions are interiorised for everyone through their individual practices - birth + +control, or the Christian prohibition of it.) + +From this point of view, for an isolated individual - that is to say, for every one of us, in so far as we receive and interiorise the statute of isolation - the consciousness of our praxis as free efficacity remains, through every constraint and exigency, our own constant reality in so far as we are the perpetual transcendence of our ends. And the individual does not recognise that it is in direct contradiction with his Other-Being because this untranscendable Other-Being reveals itself in praxis itself, either as a motivation of this praxis (in exigency or in value systems), or as an object of a possible transcendence. !t is clear, in fact, that the Other-Being of the individual as the common structure of the collective derives its being for everyone from its U1I.transcendahility. But precisely to the extent that it is freedom which reveals untranscend ability as a necessary structure of alienated objectification, it does so in the milieu of freedom as transcendable untranscendability. Indeed, for an exploited man who, in a period before any important developments of proletarian organisation, became aware, through his own praxis as his own reality, of his fatigue, of his occupational diseases, of price rises, of the obsolescence of his trade through machinery, etc. , as the statute which defined him in his sub-humanity, the reality he grasps is simply the set of his impossibilities (the impossibility of living humanly or, perhaps more radically, of living at all). Clearly this reality of his Being is precisely that of his impotence; it defines itself, in and through the series of exploited men, as alterity or as an index of separation in negative unity. But in so far as everyone perceives his own impossibilIty (that is to say, his inability to change or reorganise anything) through his praxis (which posits itself in its dialectical structure as a permanent possibility of transcending any actual circumstances), this impossibility inside freedom appears to him as + +temporary and relative. + +Of itself, no doubt, praxis does not occur as a concrete, material transcendence of impossibility towards a particular reorganisation: this, indeed, is what proves that the statute cannot be transcended. But the mere exposure of the impossibility makes it confront itself as the + +pure, abstract, and ideal negation of every given by a transcendence towards an end. Confronted with the real impossibility of living humanly, it affirms itself in its generality as human praxis. This affirmation is neither more than nor other than the action itself in so far as it transcends the milieu in order to reproduce life: and its affirmative power is simply the material power of the organism striving to change the world. But for lack of any real objective and of real means of attaining the end, the praxis reveals itself as a pure negation of negation (or of affirmation) universally; and, to be more precise, what it immediately grasps is not its formal structure, but, in the reality which crushes it, the impossibility of the impossibility of man. In fact, the impossibility of man is given as an individual determination of life; but the praxis which reveals it cannot see it as its own impossihility: it sees it in action - which is, of itself, an affirmation of man as an impossibility which is in some way impossible. In fact, praxis, as the praxis of an organism which reproduces its life by reorganising the environment, is man - man making himself in remaking himself. To make oneself and to produce oneself on the basis of one's own possibility are one and the same thing; but it is at the level of the practico-inert, in the real production of man, that the impossibility of man reveals itself as his being. This impossibility refers to pure, formal transcendence as an affirmation without an object. 'It is impossihle that this should continue; it is impossihle that it should be unchangeable; it is impossihle that there should be no way out, that I should continue to live like this.' Such formulas, which insist on the objective structure of possibilities, are very common. And there are also ones which refer to the subjective moment: 'I'll find a way out, I'll find a solution somehow', etc. After all, the contradiction would be in danger of exploding if it opposed two homogeneous moments. But the individual will change his reality, he will transcend it: he will occasionally have a chance to improve his lot. Thus the untranscendable comes to be transcended. But it is only an appearance: he has simply realised his being - the very thing he cannot change - in slightly different circumstances ; and these superficial differences make no difference to the Being which has been actualised. A particular worker leaves a factory where the working conditions are particularly bad and goes to work in another where they are a little better. He is merely defining the limits within which his statute allows a few variations (themselves due to general circumstances of production: manpower requirements, wage rises in a particular sector, etc.), but at the same + +time he is confirming his general destiny as exploited. A rise in wages in a particular branch of production occurs only in the general context of the search for profit and it is to be explained in terms of the historical totalisation and of the present conjuncture. He may, therefore, vary the implementation of the verdict, but he cannot transcend it. Concretely, however, things are not so simple: provided he breaks his bonds of impotence but avoids replacing them by union, he will be able to acquire, in a still indefinite society, a society which remains indeterminate in spite of serial structurations (and because of them), the efficacity of an imponderable, that is to say, of a disintegrated + +individual. + +In certain circumstances, in certain historical moments and in certain societies, there may be real possibilities of moving from one class to another. And these possibilities vary from sector to sector, and from country to country. In the patrician Venice of the sixteenth century, the bourgeois had absolutely no possible access to the patrician class; elsewhere - in France, for example - they were able to 'betray' their class and enter the noblesse de robe, and sometimes even + +slip into the noblesse d'ipie. 1 + +0 + +1 Thus, at this level, an individual may + +avoid being a class individual, and may sometimes transcend his classbeing and thereby produce for all the members of the class he has left the possibility of individually escaping their destiny. However, in foct though it took him a great deal of intelligence, work and patience to transcend the common destiny - all he has done is to realise, in his person, one of the possibilities in the structured field of his class possibilities . In other words, if he moves into the petty bourgeoisie or gets his son to do so, he practically realises - at the same moment as several other individuals - a possibility (statistically determinable and conditioned by the whole historical process) of his class of origin: in the structured social field of his possibilities and impossibilities (as destiny), this class, at a particular moment and in definite conditions and sectors, is also determined by the possibility that a definite proportion of its members may move into another class (return to the peasant class, move into the bourgeoisie, etc.). This can be called class viscosity. Thus the worker who becomes a bourgeois demonstrates the viscosity of his class: by thus escaping the untranscendable in his + +101. The noblesse de robe owed their patents of nobility to administrative or legal posts which they or their ancestors bought. The noblesse d' epee was the old + +preserve them in the name of their dialectical unity, precisely to the extent that, in labour and through instrumentality, it identifies itself + +with the practical inertia of the tool. + +These transformations are wholly material; or rather, everything really takes place in the physico-chemical universe and the organism's power of assimilation and of strictly biological selection exists at the level of consumption. But one will never understand anything of human history if one fails to recognise that these transformations take place in a practical field inhabited by a multiplicity of agents, in so far as they are produced by the free actions of individuals. Serial plurality, as the inorganic unity of inertia, comes to this multiplicity only through the mediation of worked matter in so far as it transforms individual labours into the negative unity of counter-finality. Thus praxis alone, as it appears between the inert (and abstract) multiplicity of number and the (equally abstract) passive exteriority of the physico...; chemical world, is, in its dialectical freedom, the real and permanent foundation (in human history up to the present) of all the I inhuman sentences which men have passed on men through worked matter. In praxis, multiplicity, scarcity, exteriority and the improbability of the continuation of life are interiorised and humanised as the internal inhumanity of the human race; through it, these same characteristics of the inorganic take on the practical and directed aspect of Fatum and their simple non-humanity becomes counter-finality or anti-humanity. Of course, it is possible to reverse the terms completely, and, as we did at a more abstract moment of the dialectical investigation, show worked matter in its primacy and inorganic materiality as governing men through it: this view is as correct, or perhaps more so, in so far as it refers directly from the non-organised physico-chemical world to the number of individuals as the inorganic materiality of the social; but it will remain abstract as long as the development of the investigation fails to show clearly that any relation between things, in so far as they mediate between men, is strictly conditioned by the multiple relations of human actions in so far as they mediate between + +things. + +From this point of view the problem of negation, as stated at the beginning of this chapter from a simple practico-inert point of view, is also completely explained. Our problem, in relation to the origins of the 'iron and coal complex', was to explain how it was that the discovery of techniques, which made the exploitation of fabulous wealth possible, took the form of a negation for most members of a nation (the + +gradual elimination of the English peasantry by expropriation and proletarianisation). We were acquainted with the historical explanation and it appeared obvious, provided it was based on an intelligible structure of the practico-inert field; that is to say, provided we could see its dialectical skeleton as matter constituting itself as the practicoinert negation of the praxis which works it and uses it in the context of multiplicity. We more or less know this much: that free praxis is the negation of every particular given, in the course of a particular action, and that it negates matter in so far as it reorganises it in its passive being in terms of a future objective originating in the satisfaction of needs. In fact, it is neither the presence nor the possible instrumentality of matter which is negated by the project, but simply its 'co-efficient of adversity', in so far as inertia presents it as a factual impossibility. And in its first moment, that is to say in its elementary structure, negation is a practical, univocal relation of interiority which man derives from matter through the need which explains it, and which matter derives from men in so far as the present material state (and not materiality) is always what has already been transcended. Thus in the practical field of man, as an individual worker, there appear tools which he himself made, or acquired in exchange for his labour, and these material tools are a practical, solidified negation, which is borne by matter and which refers to certain states of materiality in their passivity (that is to say, adversities, or counter-finalities). Thus, from the tool as a solidified product of past labour and a solidified inscription of future labour, to the Thing (which might itself be a tool - for example, one which needs to be mended), a negative signification establishes itself as solidified passivity. The future comes to objects through the tool, as a necessity that some material combinations should be realised and that others should disappear. In fact, it comes through freedom to the practical field in so far as it is already unified by need. But the negative structure as a relation of the worked object to nature and of tools among themselves nonetheless appears, in the field of scarcity, as a definite intra-material tension. Destruction, and destructability as a negation of man's materiality and of his goods, come to matter through man; they are designated and negated (wholly or partly) by the presence of the human tool. It is obvious that the tool has some positive, creative function, and + +In the next chapter we shall see the positive aspect of praxis: at present what interests us is that, even in productive labour, tools are the inert as a negation of the inert (combined with the permanent possi- + +bility of the organism acting in exteriority by becoming the tool of its tool). It is at this level that the matter to he worked, as passive resistance, makes itself a negation of man in so far as man negates the existing state of affairs; fatigue is heing in so far as it is distinct from knowledge and from praxis, in so far as its inert capacity can be reduced only through an expenditure of energy. It is the inertia of exteriority interiorised in the organism in so far as organic praxis exteriorises itself as the seal applied to the product. Negation is there in these fundamental relations of need and labour and in so far as, in the practical field, they constitute materiality as the negation of its own passivity as much as of human activity. It comes to matter in praxis and, through the development of this praxis, it turns back against the individual in so far as it becomes a double negation solidified by inertia (the ambivalence of the tool) . It is obvious, however, that the relation between two human activities is of itself indeterminate, as long as we have not defined the material conditions on the 'basis of which it arises. It is not true that 'each must aim at the death of the other'I02 - or his life, for that matter. Material circumstances as a whole (the set of tools and goods in the context of scarcity) settle it. In a word, if some free praxis becomes the negation of another praxis, this negation, which comes to them as a reciprocity of antagonism, produces itself in everyone as primary inertia, because it is the interiorisation of an exterior negation. It is in this senSe that there was competitive antagonism between workers on the labour market, at the beginning of the century, even hefore they had made it a moment of practice or rejected it in the name of unity of action. Thus, praxis as a fundamental relation of man to the environment structures the practical field as a set of inert, intra-material relations of negation. Negation as a force of inertia is a human inscription in the inorganic world. And the multiplicity of activities is constituted in its heing as a multiplicity of negative relations (antagonisms) because every praxis re-actualises for the Other, with all its signifying power, the inert negation of a particular part of the field by the Other in so far as this negation refers to the statute which makes one man the inert negation of an Other (in definite conditions and in a determinate form). Indeed, it might be said that negation comes to inert matter from individual labour and that negations come to men through worked matter as the matrix and receptacle of all passive negativity, through the inert numerical statute of their multiplicity. In counter-finalities, + +praxis inscribes itself in inertia and inertia returns as inverted praxis to dominate the very group which has objectified itself in this worked matter. Thus not only do individuals and groups receive their statute in inertia through matter-negation, in this inversion of action and passivisation; in addition, this very matter, in the development of dispersed actions, becomes their unity as the pure negation in everyone as Other both of himself and of all Others, in the name of an alterity which might, purely metaphorically, be called the perspective of t/te inorganic + +on man. + +These few observations enable us to elucidate one final point. We have claimed, in effect, that everyone has the practico-inert experience in his work and in his public life (and, to a lesser degree, in his private life) and that it is, in fact, characteristic of our everyday life. We also saw that it remained abstract because this inert bond of sociality does not explain the group, as an organised plurality, but that the universe of passive-activity was still, for particular individuals (depending on their function, their class, etc.) a field which they could not leave. Yet, at the same time, we saw that everyone's free praxis remained his translucid experience of himself, not in so far as it was the Other but in so far as it was produced by dialectical praxis - in the regulated change which it produces - as the same as itself (or as 'changing so as to remain the same'). It seems therefore that, for all of us, there are two contradictory experiences. In other words, although the critique of dialectical Reason can and must constitute the second as a negation of the first, but as deriving its intelligibility from it, in everyday reality our remarks might imply that the practico-inert field is not a synthetic blossoming and a reunification of the fundamental abstraction and its contradiction. Something is negated in misfortune; which means that negation itself is diverted and that all activities lose themselves in the practico-inert to the advantage of false, anti-human unities. How, it will be asked, is one to conceive of this duality of experiences, which is always possihle for everyone? Can we just pass from the translucid consciousness of our activity to the grotesque or monstrous apperception of the practico-inert, according to circumstances? My answer is not only that we can but also that we constantly do. There can be no doubt that at the moment of labour, and in so far as there remains, even in the case of a small section of work, the simple necessity of a control or, in the total subservience of the individual to specialised machines, a need for an eye or a hand, prior to automation, the action still appears - at least - as an adaptation of the body to a demanding + +situation. Similarly, if some worker agreed to work extra hard and thus to contribute to raising the norms, this result, from which he must necessarily suffer, will at first present itself to him as an almost unbearable work rhythm, which nevertheless he bears by a decision which anticipates the exigency of machines, that is to say, by a choice which may be disapproved of by his comrades. In this sense, the moment of freedom as unifying, translucid practice is the moment of the trap. By positing itself as free individual praxis, it contributes for its part, in itself and for all, to the realisation of the world of the Other. And this is precisely the practical moment in which it apprehends itself and sees + +only its reality. + +The terrible constraints which matter forces on both the factory worker and the agricultural worker never allow them to remain for long at this level of abstraction; but there is nothing to prevent a member of the middle class, in certain favourable circumstances, from fortifying himself within the consciousness of his individual praxis by using an interior monologue on freedom as a kind of solder. However, it is through the experience of alienation as necessity (that is to say, as the real, social being of one's being), that the practico-inert field is revealed. It is for . this reason that simplistic Marxists have calmly eliminated the moment of individual praxis as an irreducible experience of the dialectic or, in other words, as dialectic realising itself in practical experience. They have not seen that unless the fundamental reality of this moment is preserved the reality of alienation will have to be rejected. Their only excuse - and it is a feeble one - is that the moment of necessity throws experience into the universe of alterity. From the moment in which impotence becomes the meaning of practical power, and counter-finality the deep meaning of the aim pursued, when praxis discovers that its freedom is the means chosen elsewhere to reduce it to slavery, the individual suddenly finds himself back in a world where free action is the fundamental mystification; he no longer knows it except as a reality which is negated at this stage of the experience, absent or forever fleeing, and as the propaganda of the oppressors against the oppressed. But it is important to see that this experience is no longer that of the action, but that of the materialised result; it is no longer the positive moment in which one does, but the negative moment in which one is produced in passivity by what the practico-inert ensemble makes out of what one has just made. It is the moment, for example, when the worker who wished to raise his own work norm finds that this norm has become a general exigency and, + +thereby sees himself signified as an Other, that is to say, in this case, as his own enemy, as the agent of the employers and of exploitation. In this sense, the discovery of sociality as passive heing containing worked matter is not a plenary experience, comparable to the individual's experience of the action of his activity as a dialectical development. It occurs as a fleeting discovery, precisely because, through alienation as a passive result inscribed in social (worked) matter, it is the discovery of sociality as series, and because this series is flight (normally indefinite or infinite). Similarly, when anyone discovers his other-Being in so far as it is constituted by the serial absence of Others, he can realise it only as a negative, abstract meaning whose content he can express in language though he cannot hold it in a plenary intuition. The Being of this being is that it should be elsewhere. I do not mean by this that the alienation and the Other-Being which are manifested in it are essentially prohahle beings (as given to experience). It may, of course, happen that the otherness of my act remains obscure and probable for me: this depends on the circumstances of my experience and on the type of act in question; nevertheless alienation is the object of a necessary discovery, in the sense that the passivising reflection of objectified praxis is always given as necessary, even though the particular meaning (signification) of the alienation may remain confused and blurred. This means that the experience of alienation is not an instantaneous intuition - this would be meaningless but a process which temporalises itself and which the 'ways of the world' can always interrupt, either provisionally or definitively, from outside and within by the intervening transformation of the conditions of the experience. But, in the context of a shorter, uninterrupted experience, Other-Being may also manifest itself in its own content as necessary-heing. In short, it is possible to have a precise knowledge of it as the necessity that a given action will actualise a particular Other-Being. This knowledge, however, does not realise anything: the Other-Being which I am is in principle incapable of living in the dialectical development of praxis; it is the fleeting object of consciousness rather than consciousness itself; an abstract and precise limit of knowledge rather than a concrete presence to intuition. In this sense, my everyday experience of the Other-Being of Others realises itself as concrete experience only in moments when the necessity of the discovered alienation and the flight of alterity incite me to pursue this Other in his flight to the Others, for example, to realise my alterity through the + +But, this shifting, indefinite experience of the practico-inert field reveals the Elsewhere to me as a spatial structure of alterity, and shows me my Other-Being in this Elsewhere, fleeing from one to the other, as the Other to Others, that is to say, to reified man as Other than man, as well as to the worked Thing as Other than the Thing (as the antihuman being of man). This fleeting experience reveals its unity only in the form of common impotence as the negative cement of all the beings in a series or as the development to the limit (that is to say, the practical, abstract affirmation of a totalisation to infinity of the series by a recurrent, infinite transcendence). In this experience, which is constantly eluding itself, it is true that worked things come to us as men in the most everyday moment of life. (And the theatre has made great use, in melodrama, of the frightening effect produced by a door which opens by itself in an empty house, or - and this amounts to the same thing of a door which slowly opens and which we know to conceal the criminal, and which becomes the door-being of the criminal, etc.) But this is true only in so far as man has become, for us, pure flight, in us and in objects - in so far as the inanimate relation of a thousand-franc note to some absolutely necessary article may be altered at a distance by the serial ensemble of serialities (an alteration of my being-outsidemyself) just as my human relation to a comrade or to a member of my family m"y be alienated everywhere, in the ensemble of series which constitute my class - so that there is, in the end, a unity and fusion of all the meanings of practico-inert objects (men, things, relations of things, and relations of men) to the infinity of every Elsewhere. + +In this first form, as the limit which separates praxis from passive, alienated activity (that is to say, from the individual of sociality) necessity provides its own intelligibility, that is to say, the Reason of its being. We have seen that it could not even appear in individual praxis or in human relations of reciprocity (with or without a 'third parti) . But, in the same way, nobody, except by conceiving of natural laws in terms of a Platonic conceptualism, can imagine that such laws are a priori rules which impose themselves on matter and inflexibly govern transformations of energy. To the extent that scientific laws rest on experience, which constantly returns to them and modifies them, they are both statistical and contingent (at least for us and at this stage). In fact, we can now see that necessity is a particular meaning (signification) which links human action to the material thing in which it objectifies itself, on the basis of a univocal link of interiority between the organism and the environment. This is the moment where, through the very + +freedom which produces it, the Thing, transformed by other freedoms, presents, through its own characteristics, the objectification of the agent as a strictly predictable but completely unforseen alteration of the ends pursued. In this case, the characteristics of the object become the necessary foundation for any explanation of this alteration, because the action of other freedoms puts them in relief and manifests them: 'You should have realised that if you did this with that instrument, the result would be such and such, etc.' But the fixed characteristics (exigencies, instrumentality) of the instrument are precisely those of worked + +matter. + +Thus, as one might say, necessity is freedom as the exis of worked matter, or worked materiality as the freedom-exis of Others in so far as it is revealed within a free operation. And, from this point of view, we can conclude that necessity manifests itself neither in the action of the isolated organism, nor in the succession of physico-chemical facts : the reign of necessity is the domain - the real, but still abstract domain of History - in which inorganic materiality envelops human multiplicity and transforms the producers into its product. Necessity, as a limit within freedom, as blinding obviousness and as the moment of the inversion of praxis into practico-inert activity, becomes, once man has swung back into serial sociality, the very structure of all processes of seriality, that is to say, the modality of their absence in presence and of their empty obviousness. It is the shifting ensemble of unlucky materiality in so far as it is simultaneously affirmed and stolen away, for everyone and in any free act, by all free acts as Others; that is to say, as forging our chains. This is the only possible relation between practical organisms and their milieu and, through the milieu, between them, in so far as they have not achieved a new practical unity. It would be easy to show how so-called 'scientific' necessity - that is to say, the modality of certain chains of exact propositions - comes to science through practice and hy it as the limit-negation, through exteriority, of the dialectic, and how it appears by means of free dialectical research as its real and always Other objectification. But this is not our + +present concern. + +What we must retain from all this is that the practico-inert field is not a new moment of some universal dialectic, but the pure and simple negation of several dialectics by exteriority and plurality. This negation, however, operates not by destruction or dissolution, but by deviation and inversion. Thus this second moment of the in;vestigation (['experience) (but not of the dialectic) appears in itself as the anti- + +dialectic or, in other words, as the inorganic simulacrum, in and outside man, of the dialectic as free human activity. Thus, just as the dialectic transcends material conditions in preserving them in its very negation, so materiality as the inflexible necessity of the practico-inert transcends everyone's free praxis, that is to say, the multiple dialectics in their development, so as to preserve them in it as the only means of + +setting its clumsy machinery in motion. + +We have seen that the practico-inert field, considered in general and a priori, cannot, by any of its contradictions, occasion the form of practical sociality which we are about to study, namely the group. Groups always constitute themselves on the basis of certain particular contradictions which define a particular sector of the field of passiveactivity, while one cannot have any a priori assurance that the same applies everywhere. When such contradictions occur, then, as we shall see, the dialectical praxis of the individual puts itself on trial at the heart of the anti-dialectic which appropriates its results, and invents itself in another social space as the totalisation of multiple actions in, for an.d by a totalising objective result. This new approach is both reflexive and constituent: each praxis as a free individual totalising dialectic places itself at the service of a common dialectic whose very type is modelled on the synthetic action of an isolated worker. Thus the original dialectics are transcended towards an other dialectic, which they constitute on the basis of the anti-dialectic as an impossibility which cannot be transcended. In this sense, we might be said to be passing here from the nature-dialectic, as an original relation of interiority between the organism and its milieu, to the culture-dialectic, as an apparatus constructed against the power of the practico-inert. In other words, individual dialectics, after having created anti-physis as the power of man over nature and, in the same act, anti-humanity as the power of inorganic matter over man, create their own anti-physis by unification so as to construct human power (that is to say, free relations amongst men). It is at this level and on the basis of previous conditions that men totalise, and totalise themselves, in order to reorganise themselves into the unity of a praxis: in other words, we are approaching the third and last moment of our investigation (experience) - that which totalises the human world (that is to say, the world of men and their objects) in the historical undertaking. This new structure of the investigation presents itself as an inversion of the practico-inert field: that is to say, the nerve of practical unity is freedom, appearing as the necessity of necessity in other words, as its inexorable inversion. Indeed, in so far as the + +individuals in a given milieu are directly threatened, in practico-inert necessity, by the impossibility of life, their radical unity (in reappropriating this very impossibility for themselves as the possibility of dying humanly, or of the affirmation of man by his death) is the inflexible negation of this impossibility (,To live working or die fighting'); thus the group constitutes itself as the radical impossibility of living, which threatens serial multiplicity. But this new dialectic, in which freedom and necessity are now one, is not a new incarnation of the transcendental dialectic: it is a human construction whose sole agents are individual men as free activities. For this reason, in order to distinguish it from constituent dialectics, we shall refer to it as the + +constituted dialectic. + +Book II + +F rom Groups to History + +I + +The Fused Group + +The group - the equivalence of freedom as necessity and of necessity as freedom - the scope and limits of any realist dialectic + +1The Genesis of Groups + +As we have seen, the necessity of the group is not present a priori in a gathering. But we have also seen that through its serial unity (in so far as the negative unity of the series can, as abstract negation, oppose seriality) the gathering furnishes the elementary conditions of the possibility that its members should constitute a group. But this remains abstract. Obviously everything would be simpler in a transcendental, idealist dialectic: the movement of integration by which every organism contains and dominates its inorganic pluralities would be presented as transforming itself, at the level of social plurality, into an integration of individuals into an organic totality. Thus the group would function as a hyper-organism in relation to individual organisms. This organicist idealism is often to be seen re-emerging as a social model of conservative thought (under the Restoration, it was opposed to liberal atomism; after 1860, it tried to dissolve class formations into a national solidarity). But it would be a mistake to reduce the organicist illusion to the role of a reactionary theory. Indeed, it is obvious that the organic character of the group - its biological unity reveals itself as a particular moment of the investigation. As we approach the third stage of the dialectical investigation, we can describe the organic structure as above all the illusory, immediate appearance of the group as it produces itself in and against the practico-inert field. In two remarkable works! Marc Bloch has shown how, in and even + +before the twelfth century, the nobility, the bourgeoisie and the serfs to mention only these three classes - existed de facto if not de jure. In our terminology we would describe them as collectives. But the repeated efforts of rich bourgeois, as individuals, to integrate themselves into the noble class caused this class to close up: it moved from a de facto statute to a de jure one. Through a common undertaking, it imposed draconian conditions on anyone wishing to enter knighthood, with the result that this mediating institution between the generations became a selective organ. But this also conditioned the class consciousness of the serfs. Prior to the juridical unification of the nobility, every serf had regarded his situation as an individual destiny, and lived it as an ensemble of human relations with a family of landowners, in other words, as an accident. But by positing itself for itself, the nobility ipso facto constituted serfdom as a juridical institution and showed the serfs their interchangeability, their common impotence and their common interests. This revelation was one of the factors of peasant revolts in + +later centuries. + +The point of this example is simply to show how, in the movement of History, an exploiting class, by tightening its bonds against an enemy and by becoming aware of itself as a unity of individuals in solidarity, shows the exploited classes their material being as a collective and as a point of departure for a constant effort to establish lived bonds of solidarity between its members. There is nothing surprising about this: in this inert quasi-totality, constantly swept by great movements of counter-finality, the historical collectivity, the dialectical law, is at work: the constitution of a group (on the basis, of course, of real, material conditions) as an ensemble of solidarities has the dialectical consequence of makil1g it the negation of the rest of the social field, and, as a result, of occasioning, in this field in so far as it is defined as non-grouped, the conditions for an antagonistic grouping (on the basis + +of scarcity and in divided social systems). + +But the most important point here is that the non-grouped, on the outside, behave towards the group by positing it through their very pr=is as an organic totality. Thus every new collective organisation can find its archetype in any other older one, because praxis as the unification of the practical field objectively tightens the bonds of the objectgroup. It is striking that our most elementary patterns of behaviour relate to external collectives as if they were organisms. The structure of scandal, for example, is, for everyone, that of a collective taken as a totality: in a theatre, everyone, in confronting each speech of a scene + +which he finds outrageous, is in fact conditioned by the serial reaction of his neighbours. Scandal is the Other as the formula of a series. But as soon as the first manifestations of scandal have occurred (that is to say, the first acts of someone acting for the Others in so far as he is Other than himself), they create the living unity of the audience against the author, simply because the first protester, through his unity as an individual, realises th.is unity for everyone in transcendence (Ia transcendance). Moreover, it will remain a profound contradiction in everyone, because this unity is that of all the Others (including himself) as Others and by an Other: the protester was not revealing or expressing popular opinion; rather, he was expressing, in the objective unity of a direct action (shouts, insults, etc.), what still existed for everyone only as the opinion of the Others, that is to say, as their shifting, serial unity. But once the scandal has been reported and discussed, it becomes, in the eyes of those who did not witness it, a synthetic event which gave the audience which saw the play that night a temporary unity as an organism. Everything becomes clear if we situate the non-grouped who discover themselves to be a collective through their impotence in relation to the group which they reveal. To the extent that, through the unity of its praxis, the group determines them in their inorganic inertia, they conceive its ends and its unity through the free unifying unity of their own individual praxis and on the model of the free synthesis which is fundamentally the practical temporalisation of the organism. Indeed, in the practical field, all exterior multiplicity becomes, for every agent, the object of a unifying synthesis (and, as we have already seen, the result of this synthesis is that the ' serial structure of gatherings is concealed). But the group which I unify in the practical field produces itself, as a group, as already unified, that is to say, as structured by a unity which in principle eludes my unification and negates it (in so far as it is praxis relegating me to impotence). This free active unity which eludes me appears as the substance of a reality of which I myself, in my practical and perceptual field, have unified only its multiplicity as the pure materiality of appearance; or, to put it another way, I do not attribute inertia - which must constitute the real foundation of the group (as inertia which has been transcended and preserved) - to the active community; on the contrary, it is my praxis which, in its unificatory movement takes responsibility for it. And the common action, which eludes me, becomes the reality of this appearance, that is to say, the practical, synthetic substance, the totality controlling its parts, entelechy, life; or, at another level of perception + +and for other groups, a Gestalt. We shall encounter this naive organicism both as an immediate relation of the individual to the group and as an ideal of absolute integration. But we must reject organicism in every form. The relation of the group, as the determination of a collective and as a perpetual threat of relapsing into a collective, to its inertia as a multiplicity can never in any way be assimilated to the relation of + +the organism to the inorganic substances which compose it. + +But if there is no dialectical process through which the moment of the anti-dialectic can become by itself a mediation between the multiple dialectics of the practical field and the constituted dialectic as common praxis, does the emergence of the group contain its own intelligibility? Following the same method as we have used so far, we shall now attempt to find in our investigation the characteristics and moments of a particular process of grouping from the point of view of the purely critical aim of determining its rationality. In our investigation we shall therefore have to study successively the genesis of groups, and the structures of their praxis - in other words, the dialectical rationality of collective action - and, finally, the group as passion, that is to say, in so far as it struggles in itself against tlte practical inertia by which it is + +affected. + +I will begin with two preliminary observations. First, I have claimed that the inert gathering with its structure of seriality is the basic type of sociality. But I have not meant this in a historical sense, and the term 'fundamental' here does not imply temporal priority. Who could claim that collectives come before groups? No one is in a position to advance any hypothesis on this subject; or rather - despite the data of prehistory and ethnography - no such hypothesis has any meaning. Besides, the constant metamorphosis of gatherings into groups and of groups into gatherings would make it quite impossible to know a priori whether a particular gathering was a primary historical reality or whether it was the remains of a group which had been reabsorbed by the field of passivity: in either case, only the study of earlier structures and conditions can answer the question - if anything can. Our reason for positing the logical anteriority of collectives is simply that according to what History teaches us, groups constitute themselves as determinations and negations of collectives. In other words, they transcend and preserve them. Collectives, on the other hand, even when they result from the disintegration of active groups, preserve nothing of themselves as collectives, except for dead, ossified structures which + +scarcely conceal the flight of seriality. Similarly, the group, whatever it may be, contains in itselfits reasons for relapsing into the inert being of the gathering: thus the disintegration of a group, as we shall see, has an a priori intelligibility. But the collective - as such and apart from the action of the factors we are about to study - contains at most the mere possibility of a synthetic union of its members. Lastly, regardless of pre-history, the important thing here, in a history conditioned by class struggle, is to explain the transition of oppressed classes from the state of being collectives to revolutionary group praxis. This is particularly important because such a transition has really occurred in each + +case. + +But having mentioned class relations, I will make a second observation: that it would be premature to regard these classes as also being groups. In order to determine the conditions of their intelligibility, I shall, as with collectives, take and discuss ephemeral, superficial groups, which form and disintegrate rapidly, and approach the basic groups of + +society progressively. + +The upheaval which destroys the collective by the flash of a common praxis obviously originates in a synthetic, and therefore material, transformation, which occurs in the context of scarcity and of existing structures. For organisms whose risks and practical movement, as well as their suffering, reside in need, the driving-force is either danger, at every level of materiality (whether it be hunger, or the bankruptcy whose meaning is hunger, etc.), or transformations of instrumentality (the exigencies and scarcity of the tool replacing the scarcity of the immediate object of need; or the modifications of the tool, seen in their ascending signification, as necessary modifications of the collective). In other words, without the original tension of need as a relation of interiority with Nature, there would be no change; and, conversely, there is no common praxis at any level whose regressive or descending signification is not directly or indirectly related to this original tension. It must therefore be understood at the outset that the origin of any restructuration of a collective into a group is a complex event which takes place simultaneously at every level of materiality, but is trans- + +cended into organising praxis at the level of serial unity. + +But however universal the event may be, it cannot be lived as its own transcendence towards the unity of all, unless its universality is objective for everyone, or unless it creates in everyone a structure of unifying objectivity. Up to this point, in fact - in the dimension of the collective - the real has defined itself by its impossibility. Indeed, what is called + +the meaning of realities is precisely the meaning of that which, in principle, is forbidden. The transformation therefore occurs when impos sibility itself becomes impossible, or when the synthetic event reveals that the impossibility of change is an impossibility of life. 2 The direct result of this is to make the impossihility of change the very object which has to be transcended if life is to continue. In other words, we have come to a vicious circle: the group constitutes itself on the basis of a need or common danger and defines itself by the common objective which determines its common praxis. Yet neither common need, nor common praxis, nor common objectives can define a community unless it makes itself into a community by feeling individual need as common need, and by projecting itself, in the internal unification of a common integration, towards objectives which it produces as common. Without famine, this group would not have constituted itself: but why does it define itself as common struggle against common need? Why is it that, as sometimes happens, individuals in a given case do not quarrel over food like dogs? That is the same as asking how a synthesis can take place when the power of synthetic unity is both everywhere (in all individuals as a free unification of the field) and nowhere (in that it would be a free transcendent (transcend ante) unification of the plurality of individual unifications) . Indeed, let us not forget that the common ohject, as the unity of the multiple outside itself, is above all the producer of serial unity and that it is on the basis of this double determination that the anti-dialectical structure of the collectivity, or alterity, + +constitutes itself. + +2. Obviously it is not under a threat of mortal danger that anglers form their association or old ladies set up a system of swopping books: but these groups, which in any case respond to some very real exigencies imd whose objective meaning relates to the total situation, are superstructures, or, in other words, groups which are constituted in the general, permanent regroupment activity of collectives (class structures, class against class, national and international organisations, etc.). From the moment that the stage of the, dialectical regroupment of dialectics has been reached, totalising activity itselfbecomes a factor, a milieu and a reason for secondary groups. They are its living determination and therefore its negation; but, at the same time, they contain it entirely within themselves, and their dialectical conflicts take place through it and by it. In this way, as we saw in The Prohlem of Method, it is possible to study them either horizontally (and empirically) in so far as they determine themselves in a milieu in which the group structure is already objectively given, or vertically in so far as each of them in its concrete richness expresses the whole of human materiality and the whole historical process. Thus I need only concern myself here with the fundamental fact of grouping a� the conquest or reconquest of the collective by praxis. + +But this last observation may help us. If the object really produces itself as the bond of alterity between the individuals of a collective, then the serial structure of multiplicity depends, basically, on the fundamental characteristics of the object itself and on its original relation with each and all. This is how the set of means of production, in so far as they are the property of Others, gives the proletariat an original structure of seriality because it produces itself as an indefinite ensemble of objects whose exigencies themselves reflect the demand of the bourgeois class as the seriality of the Other. Conversely, however, it is possible for the investigation to consider the common objects which constitute by themselves, and in the practico-inert field, an approximation to a totality (as the totalisation of the multiple by the Other through matter) and to try to discover whether they too must con- + +stitute the multiple in question as seriality. + +2The Storming of the Bastille + +After 12 July 1789 the people of Paris were in a state of revolt. Their anger had deep causes, but as yet these had affected the people only in their common impotence. (Cold, hunger, etc., were all suffered either in resignation - serial behaviour falsely presenting itself as individual virtue - or in unorganised outbursts, riots, etc.). On the basis of what exterior circumstances were groups to be constituted? In the first place (in temporal order) the existence of an institutional, practical group, the electors of Paris, in so far as they had constituted themselves in accordance with royal decrees and in so far as they were in permanent session, in spite of, or contrary to these decrees, designated the inert gathering of Parisians as possessing, in the dimension of collective praxis, a practical reality. The electoral assembly was the active unity, as the + +being-outside-itself-in-freedom, of the inert gathering. + +But this totalisation was not enough: indeed representation consists in defining, by some procedure, an active group as a projection of the inert gathering in the inaccessible milieu of praxis. For example, in bourgeois democracies, elections are passive, serial processes. Each elector, of course, decides how to vote as Other and through Others; but instead of deciding in common and as a united praxis with the + +Others, he allows it to be defined inertly and in seriality by opinion. Thus an elected assembly represents the gathering as long as it has not met, as long as its members are the inert product of an inert alterity and as long as crude multiplicity, as a numerical relation between the parts, expresses the relations of impotence amongst collectives and power relations in so far as these forces are forces of inertia. But as soon as an assembly gets organised, as soon as it constitutes its hierarchy, and defines itself (by party alliances) as a definite group (characterised by the permanence of a majority, by a complex play around a shifting majority, by the complicity of all the parties against a single individual etc.), this real praxis (in which the passing of laws, votes of confidence, etc., now have only the formal aspect of the original election as an infinite alterity of isolations, but express numerically and symbolically the agreements, disagreements, alliances, etc., amongst the groups in the majority) presents itself both as the faithful representation of the gathering - which being organised, it cannot in any way be - and as its dialectical efficacity. But the very fact of penetrating the gathering with a false totalised unitys (,Frenchmen, your government ... etc.') relegates the gathering to its statute of impotence. France as a totality realises itself outside it through its government: as the free totalisation of the collective which is the nation, the government relieves individuals of the task of determining their inert sociality in a grouping. So in so far as class conflicts and social conflicts did not, through the struggles of new groups, set the gathering against the legislative body and the executive power, the existence of these bodies was necessarily a mystification which relegated the collective to inertia: powers were delegated through serial passivity, and the affirmation of our unity there, in the Council, condemned us in all cases to infinite alterity. In this sense, those 'electors of Paris' were not necessarily a factor of practical unification, indeed, they probably feared the violence of the people even more than that of the government. However, provided that circumstances indicate a unification elsewhere, they can become a representation, but this time as a unity which is to be reintegrated as a unifying praxis in the gathering itself and as a negation of impotence. The government constituted Paris as a totality from outside. As + +3. I am not considering the problem at the real historical level and there is no need at present to know whether the government is an organ of the dominant class. I am merely discussing its formal relation as a representing praxis with the + +early as 8 July, Mirabeau had reported to the National Assembly (and his speech immediately became known to the Parisians) that 35,000 men were divided between Paris and Versailles, and that 20,000 more were expected. And Louis XVI answered the deputies thus: 'I have to use my power to restore and maintain order in the capital. ... These are my reasons for assembling troops around Paris. ' And on the morning of Sunday 12 July, the city was full of posters 'by order "of the king' announcing that the concentration of troops around Paris was intended to protect the city against bandits. Through these notices the city was designated for and within itself. Thus the place, as the practico-inert tension and exis of the Parisian gathering, was constituted by an exterior praxis and organised as a totality. And this totality as an object of praxis (the city to be besieged, disturbances to be prevented) was by itself a determination of the practico-inert field; the city was both the place, in its totalised and totalising configuration (the threat of siege determining it " as a container) and the population designated in the form of materiality sealed by the military action which produced it as a confined crowd. The rumours, the posters, the news (especially that of Necker's departure) communicated their common designation to everyone: each. was a particle of sealed materiality. At this level, the totality of encirclement can be described as being lived in seriality. It was what is known as enthusiasm: people were running in the streets, shouting, forming gatherings, and burning down the gates of the toll houses. The bond between individuals was, in its various real forms, that of alterity as the immediate discovery of oneself in the Other. Imitation - which 1 have described elsewhere - is one manifestation of this alterity of quasi-reciprocity. This structure of alterity constitutes itself through the action of common flue as a totaliry4 (that is to say, as the practical objective of the royal armies6 - in this case it is a totality of destruction, in so far as individuals were designated by their identical + +4. Destiny as a common danger to the working class (in its structure of seriality) is not totalising because the class is not the object of one organised, totalising undertaking: exploitation is a process which occurs both as the deliberate practice of a particular group and through the dispersal of group antagonisms. S. Furthermore, the government does not seem to have had any very precise plans. It did not really know either what it wanted or what lay in its power. But this is not the important point: the deployment of troops and the beginning of the encirclement bore their objective meaning in themselves, that is to say, they designated the Parisian population as the unique object of a systematic and synthetic extermination campaign. It is pointless to say that no one at court wanted there to be anv killing: it became, of itself and in the relation between the general + +membership of the same city) on the basis of seriality as inert flight. By threatening to destroy seriality through the negative order of a massacre, the troops, as practical unities, provided the totality, which was experienced by everyone as a negation, or a possible negation, of seriality. This was how, through the coexistence of the two structures, the one being the possible and future negation of the other (and at the same time the negation of all in everyone), everyone continued to see himself in the Other, but saw himself there as himself, that is to say, in this case, as a totalisation in himself of the Parisian population, by the sabre blow or the rifle shot which would kill him. And this situation established what is sometimes, and improperly, called contagion or imitation, etc. : iu this behaviour everyone sees his own future in the Other and, on that basis, discovers his present action in that of the Other; but, in these still inert movements, imitation is also selfdiscovery through doing one's own action over there in the Other, and through doing the action of the Other here, in oneself, fleeing one's own flight and that of the Other,6 launching a single attack both through the Other and with one's own fists, without either understanding or agreement (it is exactly the opposite of an understanding), but realising and living alterity on the basis of the synthetic unity of an organised, future totalisation of the gathering by an outside group. This was followed by some incidents in Paris itself, at the barricades and in the Tuileries Gardens, between military detachments and imitation gatherings (rassemblements d'imitation). These resulted in a new wave of serial, defensive violence, and arsenals were looted. This revolutionary response to a constantly deteriorating situation has of course the historical significance of an organised common action. But that is just what it was not. It was a collective action: everyone was forced to arm himself by others' attempts to find arms, and everyone tried to get there before the Others because, in the context of this new scarcity, everyone's attempt to get a rifle became for the Others the risk of remaining unarmed. At the same time, this response was constituted by relations of imitation and contagion, everyone finding him- + +function of an army and this particular situation, an immediate possibility which + +no longer actually depended on the intentions of the leaders. + +6. A person runs when he sees someone running: this is not because he learns what he must do: he discovers what he is actually doing. And, of course, he discovers it only by doing it. We encounter the same law in the group relation but + +self in the Other in the very way he followed in his footsteps. These violettt, efficacious gatherings, however, were entirely inorganic. Certain unities were lost or rediscovered, but this had no effect on what one might - like Durkheim but in a quite different sense - call the 'mechanical solidarity' of their members. Besides, there was an imminent danger that they would fight among themselves (the collective breaking down into reciprocities of antagonism) over the possession of a rifle. If the meaning of this passive activity is revolutionary, this is mainly because, as a result of an exterior praxis, the unity of impotence (inertia) had, hy sheer weight of numbers, transformed itself into a massive force. For this crowd, which within itself was still structured in alterity, found, in its very disorganisation, an irresistible mechanical + +force for destroying sporadic resistance at the arsenals. + +But the other factor - which was soon to create the revolutionary praxis of a group - was that the individual act of arming oneself, in so far as it was in itself a complex process whose aim, for every individual, was the defence of his own life, but whose motive force was seriality, was reflected, both of itself and in its result, as a double signification of freedom. In so far as everyone wanted to defend himself against the dragoons - in other words, to the extent that the government was attempting a politics of force and that this attempt at organised practice determined the entire field as practice - both as what might help this policy and as what might oppose it - the result, in the field of praxis, was that the people of Paris armed themselves against the king. In other words, the political praxis of the government alienated the passive reactions of seriality to its own practical freedom: indeed, from the point of view of this praxis, the passive activity of the gathering was taken from it in its passivity and inert seriality reappeared on the other side of the process of alterity as a united group which had performed a concerted action. This applies not only to the army leaders, who were well aware of it, but also to the Parisian population, which re-interiorised this knowledge as a structure of unity. Here again, their unity was elsewhere, that is, it was both past and future. It was past in that the group had performed an action and that the collective had recognised this action with surprise as a moment of its own passive activity: it had been a group - and this group defined itself by a revolutionary action which made the process irreversible. And it was future in that the weapons themselves, in so far as they had been taken for the sake of opposing concerted action by soldiers, suggested in their very + +materiality the possibility of concerted resistance. + +The uneasiness of the electors was to create institutional groups inside gatherings, as negative unities. They actually decided to reestablish a militia of 48,000 citizens to be provided by the various districts. The avowed aim was to avoid disturbances. In this new moment, the future militia appeared both as raised from the gathering and as designed to fight it, whereas most of the population had no fear of 'disturbances' and, quite rightly, saw no real danger except in the deployment of troops around the capital. In so far as the districts did seriously try to form militias, these groups in formation, unlike the representative groups, helped to unify the gatherings. 'Representation', in fact, presented itself as the gathering itself in the dimension of organised praxis and therefore, as we have seen, tended to maintain it in its inertia. The militia, on the other hand, was an organised body designed to bring about the practical negation of the gathering: it would prevent public assemblies and disarm the citizens. In this way, it helped the gathering to perceive its reality as an organised being. For it had to forcibly prevent the development of the organised being which armed itself yesterday and which would defend itse/ftomorrow. Or, to express it differently, these pre-fabricated groups were anti-groups which appeared to the gathering as having the task of keeping it in its structure of serial impotence. Through them, something was manifested as that which was negated, and had to he prevented and every member of the gathering, in so far as he was imperatively designated in his inertia, ' saw profound unity both as an absence beneath seriality and as a fundamental possibility. At the same time, the militia, as prefabricated groups, themselves represented, though negatively, a synthetic determination of the gathering. And the fact that they had been defined within the gathering externally, by institutional or semiinstitutional organs, manifested itself - in so far as it was a negated negation - as what had to be destroyed by means of a unification produced internally by the gathering itself. The violent contradiction between the militia and the people, occurring within the people, produced the possibility of an internal unity as the negation of the external unity. In so far as the militia was still a seal applied to a multiplicity, it could contradict and dissolve itself only in a free organisa- + +tion. + +Freedom - as a simple posi rive determination of praxis organised on the basis of its real objectives (defence against the troops of the Prince de Lambesc) - was manifested as the necessity of dissolving necessity. On this basis, a dialectic established itself at the Hotel de Ville between the constituted authorities, which did not wish to hand out weapons, and which equivocated and found pretexts, and the crowd, which was increasingly threatening, and which, through the behaviour of the electors, of the provost of merchants, etc., revealed itself as a unity-exis. When rags were found in the boxes of arms promised by Flesselles, the crowd felt that it had been tricked - in other words, it interiorised Flesselles' actions and saw them, not in seriality, but in opposition to seriality as a sort of passive synthesis. The process of trickery, in fact, belongs in the context of an antagonistic relation of reciprocity. In tricking the crowd,8 Flesselles gave a sort of personal unity to the flight into alterity; and this personal unity was a necessary characteristic of the anger which expressed and, for the gathering itself, revealed it. Everyone reacted in a new way: not as an individual, nor as an Other, but as an individual incarnation of the common person. There was nothing magical in this new reaction: it merely expressed the re- + +interiorisation of a reciprocity. + +From this moment on, there is something which is neither group nor series, but what Malraux, in Days of Hope, 8a. called the Apocalypse that is to say, the dissolution of the series into a fused group. And this group, though still unstructured, that is to say, entirely amorphous, is characterised by being the direct opposite of alterity. In a serial relation, in fact, unity as the formula (Raison) of the series is always elsewhere, whereas in the Apocalypse, though seriality still exists at least as a process which is about to disappear, and although it always may reappear, synthetic unity is always here. Or, to put the same point in another way, throughout a city, at every moment, in each partial process, the part is entirely involved and the movement of the city is fulfilled and signified in it. 'By evening,' wrote Montjoye, 'Paris was a new city. Regular cannon shots reminded the people to be on their guard. And added to the noise of the cannon there were bells sounding a continuous alarm. The sixty churches where the residents had + +gathered were overflowing with people. Everyone there was an + +orator.' 9 + +The city was a fused group. We shall soon see how this differs from seriality. But first we must make it clear that it would congeal into a collective if it were not structured in a temporal development, the speed and duration of which obviously depend on the circumstances and situation. A fused group is in fact still a series, negating itself in re-interiorising exterior negations; in other words, in this moment there is no distinction between the positive itself (the group in formation) and this self-negating negation (the series in dissolution). It can be shown that the initial structuration (in so far as it comes from the group itself) affected one district, as a part of a fluid whole, with its practico-inert structure. The Saint-Antoine district had always lived in the shadow of the Bastille: that black fortress was a threat, not so much because it was a prison as because of its cannons. It was the symbol of repressive power, as the boundary of a poverty-stricken and unsettled district. Moreover, skirmishes and repressed uprisings - in particular the bloody repression in April (the Reveillon affair) - had remained inside the gathering itself as an em (a collective memory was passing into the common structure - a point to which we shall have to return) . For the moment, I am not even taking into account the explosiveness which this exis might derive from the energy released by the dissolution of bonds of impotence. The important point as far as the genesis of an active group is concerned, is that this exis actually structured a route; it was primarily a hodological determination of the lived space of the district. And this route was negative: it was the opportunity for troops to enter the district by coming from the west and the north-west in order to massacre people there (as iri April).lo In other words, the practico-inert unity of the field was determined at the + +9. In L' ami du Roi, third edition, p. 70. + +10. The Reveillon affair also proves that the different districts were opposed and already limited by a certain social tension, that is to say, by class conflicts. It was the practice of Reveillon, one of the precursors of the nineteenth-century French industrialists - a tough, rapacious, and arrogant man - that provoked disturbances among the workers. Conversely, newspapers owned by 'middle' bourgeois like Hardy show that the military isolation of the district (always liable to be cut off from the others and subjected to looting or massacre) was based on social isolation: 'The Parisians,' wrote Hardy, 'are frightened of some kind of popular insurrection, even to the point of shutting their shops in some areas ... A considerable portion of the so-called workers of this suburb, stirred up by bandits against a very rich manufacturer of furniture paper, named Reveillon •. . ' + +moment in which seriality was in the process of dissolution, as the possible act of penetration by the Other, that is to say, by free hostile organisation. At the same time, this possibility actualised the threat of the Bastille: it was the possibility that the district's inhabitants would be caught in the cross-fire. And this possibility refers back to its fundamental social separation (which I have mentioned in the last footnote), which was also its negative unity. of course, all this was still merely lived in anxiety during the first few days of July. But as soon as the news of the intervention of the troops at the Tuileries arrived in Saint-Antoine, it actualised the possibility of a special massacre in the district. In fact, the news, reported by Others and + +The configuration of the place was a perfect expression of the social condition of its inhabitants. However, the district was not constituted solely of the poor, for the structures of a great industrial city did not yet exist. But the workers (in so far as they were working in the first factories, and had therefore been uprooted from the craftsman class by the new conditions) were much more numerous there than elsewh�e and, generally speaking, most of the residents belonged to the less fortunate classes. · It should also be noted that the Reveillon riots are cases of serial violence. At the beginning, there was not even any violence and workers could be seen crossing Paris in companies of five or six hundred men. In these regiments of hunger, unity as a negative determination of the whole could already be detected. But at the same time they were still gatherings of inertia: there was no structuration (no differentiation of functions), and no common action. For the individual troop, the procession of workers involved neither some particular action, nor a determination of plurality as such: two hundred more or less would not make any difference. Their number was pure exteriority and was not defined by the group in accordance with its praxis, and it therefore remained in a state of absolute materiality: pure quantity. Naturally, the unity of the gathering on the march, in so far as it was its real reason, was seriality. Even if, from the depths of the initial and contagional march, negative unity as a future totality was already occasioning heing-together (Gtre-ensemhle) (that is to say, everyone's non-serial relation to the group as a milieu offreedom) as a possibility which was perceived in seriality and which presented itself as the negation of seriality, the ohjective of the mar.ch was still indeterminate: it appeared both as seriality itself as a reaction to the situation, and as an equally serial attempt at display. Everyone agreed that these groups were perfectly peaceful and that they never resorted to violence; yet every6ne carried a stick. The Other (the petty bourgeois who was made a comprehensive witness by this passive activity) was presented with the contradictory character of the condition of the working-class: when he saw the gathering go past, he could see both their poverty and their strength. But this strength, which still derived from their number, and this poverty (whose characteristic of repetition in identity, or alterity, will strike the Other), consequently make the gathering on the march, in its practico-inert structure, at best a sort of serial + +believed in so far as it was Other, had to be perceived, in the practicoinert, as the truth of the district as Other, that is to say, in so far as it presented itself through Others as an other event, affecting Others. But this very alterity was a sign: this clash in the middle of Paris was simply a determination to take repression to extremes in so far as it was a sign - that is to say, as the first action in the district least exposed to this kind of action. Thus the real (but future) meaning (signification) of the Tuileries affair was the destruction of the Quartier Saint-Antoine, defined by the recent schemata of the Reveillon affair. Or, to be more accurate from the serial point of view, the Quartier Saint-Antoine was + +exterminated in the future by the Prince de Lambesc. + +Of course, what we encounter here is, once again, the designation of the district by things and by its topographical configuration, as these would be used in the organised action of an exterior enemy, as the particularisation of a general development. However, there is a considerable difference. In so far as things, in this case, presented themselves as destiny (as instruments of the organised action which was going to destroy the district) and in so far as the individuals in the gathering were obliged to negate them as such, they defined themselves for everyone within this negation - violent, but still purely subjective (passionnel/e) - as an instrumentality capable of being turned against the Others by a free, organised praxis. This means that their instrumentality for the enemy, once negated, revealed itself as a counter-finality for the enemy. But this counter-finality, as a pure abstract possibility, required a free, common organisation in order to be actualised and developed. From the point of view of this still unactualised aspect of destiny, organised by the Other and negated, what is new in relation to the characteristics already discussed is that the practico-inert structure of the district, as a negated destiny, realises synthetically, and as a material exigency (which only practical freedom can bring out) an objective relation of differentiation within the fused group. In other words, the practico-inert structure not only makes the fused group, through everyone, the unity of all, but also makes it a �tructured unity; materially and in inertia it suggests an initial differentiation of functions, a division of labour; that is to say, it presents everyone with the condition necessary for preventing the fused group from relapsing into a gathering. In fact, suffered destiny shows us the gathering caught in cross-fire, that is to say, subjected to the comhined action of the two forces of extermination situated at either end of the district. Turned back into negativity, it points to the unity of this + +interiorised duality as a double movement of struggle within the unity of an organisation defined in its practice both by the place as passive activi ty and by hostile organisation in so far as it is negated. Armed men would be needed to defend the district against the royal troops, and others to defend it against the Bastille. And the Bastille, in turn, in the context of scarcity, revealed the primary exigency of common freedom: if the district was to be defended against the soldiers, they would have to get some arms; there were not enough in the district, but there were plenty in the Bastille. The Bastille became the common interest in so far as it both could be and h.ad to be not only disanned, but also made a source of supply of arms, and, perhaps, be turned against the enemies from the west - all in a single action. The urgency then was due to scarcity of time: the enemy was not there but he might arrive at any minute. The task defined itself for everyone as the pressing revelation of a frightening common freedom. Naturally, the action itself had its own weight, its schemes and even a model derived from the past: it appeared through the ambivalence of the relations between the Parisian population and the constituted bodies. The practice of the crowd in front of the Hotel de Ville during the past few days had been partly solicitous and partly threatening, and, to this extent, the objective to be attained (getting anns wherever they could be found) defined itself through a predetennined operation. Yet the social structure of the group in fonnation (and the character of the repression it had already suffered), in addition to that of the hostile group (soldiers, some of them foreigners, and commanded by a noble officer) helped to give the operation a more uncertain character; that is to say, these two structures, in their synthetic relation, defined a limited field of possibilities in which the explosion of the still passivised attitude (demandexigency) and the appearance of organised action as violence appeared + +as the probable future of the ambivalent task. + +This example shows a group being constituted by the liquidation of an inert seriality under the pressure of definite material circumstances, in so far as particular practico-inert structures of the environment were synthetically united to designate it, that is to say, in so far as its practice was inscribed in things as an inert idea. But in order that the city or section should become totalising totalities - when, in other circumstances, the same realities might be lived as. 'collectives' - they had to be constituted as such by the external action of another organised group. The population would constitute itself as a defensive organisation in so far as it was threatened through things by an organisation + +which aimed at its negative totalisation (through annihilation). Should we therefore say that groups in the process of constitution are determined as the liquidation of a serial structure in so far as this selfdetermination is conditioned by the transcendent (transcendante) action of one or more already constituted groups? The answer is both yes and no. The proposition is true - it conforms to practical experience in so far as it suggests a sort of serial conditioning of groups in the domain of the Other. And as we shall see, the moment of this infinite conditioning does exist. Of course, very often - as in the example we have been discussing - a collective derives its possibilities of selfdetermination into a group from its antagonistic relations with an already constituted group or with a person representing this group. Nevertheless, the unity of self-determination through all the relations described comes to the collective through the Other in alterity as an other structure (structure autre) of the gathering, and as needing to be realised hy self-determination. In fact, it was not the intention of the two reciprocal actions to constitute a group; the objective was always other and the antagonism was based on the conflict of needs, interests, etc. Thus the developing group is not constituted intentionally by the praxis of the Other and it is led to self-determination through this practice (which may, for example, be one of extermination) and through reorganisation of the environment by the Other, in so far as the unity of the other praxis conditions it as the negation of its own unity (or as totalisation through systematic destruction). In this sense, though the unity of the group is its own product and is always here, wherever its members act (at least abstractly and in theory), it is also characterised by a structure of flight, since the induction (l'occasion inductive) proceeds from the outside" inwards without being either necessarily or generally desired by other + +groups. + +But the structure of seriality, as one of the relations between groups, should not detain us any longer. It was only necessary to observe that synthetic self-determination is frequently the practical reinteriorisation, as the negation of the negation, of the unity constituted by the other praxis. The reason for using the example of the Fourteenth of July is that it shows how a new regroupment dissolves a habitual seriality into the homogeneity of a fused city: the constituted reality had ceased to exist long ago and for a time the violence of the danger and the pressure (what Jaures called a historical fever) overcame social heterogeneities. Nothing had been foreseen which might constitute the unity of the city (except as a feudal 'good city'), no organ of unification, no instrument + +had been left at the disposal of the future group. On the contrary, it was intended to prevent it from existing as such. The Versailles Assembly had to be put at the mercy of the aristocracy by being isolated from the city. But the very precautions taken against the possible unity became a future of projected and shunned unity for the gathering, and therefore a negative ferment. Unity proceeded from one to another as an alienation of necessity to freedom, that is to say, as Other than the enemy's project and as an other result (resultat autre) of his praxis. This type of group (a homogeneity of fusion) produces itself as its own idea (we shall see what this means later): it is (by totalising extension) the + +sovereign nation. + +In this conception of a fused totality, comhined with the old conception of electoral assemhlies (parasites of the electoral body as a practico-inert thing), we will find the origin of the contradictions which split the ideology of the Constituent Assembly and, particularly, of its theoretician Sieyes. But we might have explained the formation of other groups by self-determination, no longer as negatively defined by a praxis which, from the outside, makes them the antagonists of certain Other groups, but as induced to determine themselves by the marginal existence of a multiplicity of organised groups, whether institutional or not, as determinations of the practico-inert field by a common action. In this sense every group to constitute itself is singled out as a group through seriality by the synthetic relations amongst other groups, even if these relations do not affect it directly. Of course a group will constitute itself only on the basis of specific circumstances, directly or indirectly connected with the life or death of organisms. But the practical movement of organisation, in so far as it transcends its condi; tions towards its objectives, actualises an external determination, which the gathering has already interiorised as a fantom possibility of produc- + +ing itself in the field of freedom. + +JThe Third Party and the Group + +Thus groups usually come to gatherings from groups; they may also arise within a larger group, as the recapture of unity in a partial or generalised petrification. However, it should be observed that worked matter, in so far as it mediates between the most varied activities (individual, collective, or common), may spontaneously present itself + +in the practico-inert field as a counter-finality, with the appearances of a negative totalisation of human multiplicity, although no concerted praxis presided over the configuration. In this way, it defines the place and time of self-determination negatively and in multiplicity. In fact, it almost always happens like this, at least in part; for example, the characteristics of materiality (as topographical configuration, as sociality of inertia, as transcended past or as exis) did, as we have seen, amplify and divert the vacillating, dangerous policy of the government (that is to say, they gave a character of brutal force to what in reality could only be a policy of weakness - even if the objective was violent oppression). In other words, it is always possible for materiality, as a worked Thing, to posit itself as essential through the inessentiality of separated men, and, in the seriality of inert-men, to constitute an imperceptible and omnipresent structure of free practical unity. Basically this means that scarcity itself, as a tension of the polyvalent practical field, at the same time as constituting man as the other sp,ecies, determines, in the same field, an undifferentiated (valid for any kind of grouping) possibility of unifying synthesis. And, from this point of view, we encounter what we found before: there is one level of reality at which unity comes to the group through groups as the interiorisation of a practical process of revelation and of the serial unity of multiplicities of groupings; and there is another level at which the unity of the group is reflected to the gathering on the basis of the inert unity (or passive synthesis) of worked matter, that is to say, the level at which the unity of the individual praxis, joined with other unities in the object, is reinteriorised by the gathering as a possible structure of common unity. Of course, this possibility of the designation-exigency of a group by worked matter arises in specific conditions (which may, in tum, require the marginal co-existence of other groups). In other words, the historical problem of the priority of the group over the gathering (or of the gathering over the group) is, in this context, a metaphysical prob- + +lem, devoid of meaning. + +In fact, however, this is not the real problem. And, in order to determine whether the transition from a gathering to a group possesses a dialectical intelligibility, it is not necessary to know whether the group derives its unity of self-determination as its own possihility from the practico-inert synthesis as a conducting medium for other common actions, or as providing in itself a model of a practico-inert community of action on the basis of the dispersal of the individuals who transform it. We have established that a group only arises if it is designated + +through the field of passive activity. But this designation is received by a gathering, which can receive it only in seriality (that is to say, in the flight of the Other Elsewhere). The real problem of structural intelligibility, therefore, is this : what are the conditions for a series, on the basis of given circumstances, to actualise a structure of practical unity which, though really determining it, as a material meaning (signification) (or the unitary praxis of a group), must in principle elude it, in so far as milieux of seriality are structured so that they can refract unity only in the infinite flight of the facets of recurrence, as the absolute Elsewhere, that is to say, as the Other or as a series totalised in the abstract, by a passage to the limit? It is not enough that unity is possible: it is also necessary that the instruments for wresting it from recurrence should be present in the collective itself. And this is the + +second, and more important, point which we must examine. + +As we have seen in relation to class, it is possible for unity, as an empty, formal totality which negates identity, to enter, under certain conditions, into contradiction with the seriality of impotence. We are not talking about concepts here, and it must not be supposed that the concept of unity will, through its opposition to the concept of alterity, develop from being abstract and negatj.ve into a concrete notion of positive unification. This simply means that the exis of serial unity is lived through multiple relations of reciprocity (comradeship oflabour, bonds in the residential collective, the close links of small groups which are themselves thrown into seriality, families, societies, etc.), which tend through their own free development to produce it as a synthetic foundation of all concrete relations (labour, belonging to the same class, etc., form the basis of friendships; in this way, the unitary basis arises in these relations as the mirage of a free foundation for all choices) . But, at the same time, confronted by Destiny and the Exigencies of the practico-inert field, the same unity as a serial structure of alterity is revealed as fundamental impotence (assuming we can ignore synthetic organisations) and reciprocity is encountered again, as the fleeting, inert dependence of everyone on the series, and of everyone, in his place in the series, on everyone else. This contradiction cannot take us very far, since unity arises here only to dissolve as an illusion; in practice it does not much matter whether, at least as a moment of illusion, it has a place marked out for it in serial experience. Unity cannot present itself, at least initially, as the objective possibility of groupment (that is to say, as the possibility of negating itself as gathering) because, at the moment where reality is impossible, the inert + +gathering presents itself as a concrete truth whose unity is an abstract appearance. Apart from this, the structure of this unity is indeterminate, since it does not present itself in terms of a practical objective, but rather as fundamental class-being, in so far as individual relations of free reciprocity cause it to appear as the foundation of individual + +choices. + +The importance of the contradiction we are describing lies elsewhere : its function, in effect, is to lead us, in our dialectical investigation, back from the moment of the constitution of groups, to the ternary relations of free, individual action, of free reciprocity, and of the mediating third party. In other words, those relations which appeared to us as self-mystifying freedoms in the field of passive activity, are the only possibilities of making intelligible the appearance of a constituted praxis, in and against the passive field. Mystified, alienated, and cheated, these free, practical developments, the source of individual, serial impotence, are still actual synthetic actions, and are still capable of unifying - from the individual point of view, admittedly any multiplicity that appears in the practical field. And though I claim that the totalising totality of the environment indicates a possible unity as the self-determination of every individual, it is true that it indicates it in the milieu of seriality, but it does it for everyone's free, dialectical actions in so far as they are for themselves dialectical translucidities. But the fact of everyone being affected by the possibility of union with all would have very little importance if this designation affected people only in their isolation or their relations of reciprocity. Indeed, unity could not appear as the omnipresent reality of a seriality in the process of total liquidation unless it affected everyone in his third-party relations with Others, which constitute one of the structures of his existence in freedom. In fact, as we have seen, everyone is also a third party in relation to reciprocal relations between other individuals, and this means that he totalises this relation in his praxis on the basis of material meanings (significations) and indications, uniting the individual terms of the relation as instruments serving a partial end. The third party is submerged in seriality, being structured a priori as the Other, and therefore as Other than everyone and Other than us, so that his internal-external relation of free alterity in relation to reciprocity gets lost in serial alterity. Nevertheless, it does exist - it is every one of us - as alienated freedom revealing itself in lived alienation as in- + +common danger does not at first eliminate seriality, either at the level of the isolated individual, or at that of reciprocity: it tears everyone away from his Other-Being in so far as he is a third party in relation to a certain constellation of reciprocities ; in short, it frees the ternary relation as a free inter-individual reality, as an immediate human relation. Through the third party, in effect, practical unity, as the negation of a threatening organised praxis, reveals itself through the constellation of reciprocities. From a structural point of view, the third party is the human mediation through which the multiplicity of epicentres and ends (identical and separate) organises itself directly, as determined by a synthetic objective. However, according to circumstances, this object will either fall outside the practical ends of the third party, or partially overlap with them, or contradict them, or har .. monise with them, or subordinate them to itself, or subordinate itself to them. But if the practical unity of surrounding materiality constitutes the multiplicity, externally and negatively, as a totality, the objective of the third party produces itself for him as a common objective, and the plurality of epicentres reveals itself to him as unified by a common exigency (or common praxis), because it decodes serial multiplicity in terms of a community which is already inscrihed in things, in the manner of a passive idea or a totalising + +destiny. + +As the possibility of repression in the Quartier Saint-Antoine appeared increasingly probable, residents of this district, seen as third parties, were directly threatened. However, this threat did not apply to them as 'accidental individuals' : they were not being sought for their individual activities (like a criminal in hiding). On the other hand, no one wanted to kill or imprison them as Other, that is to say, as general individuals (in the way that price rises threaten every wageearner in a given category as a wage-earner of that category). Rather, they are threatened as a moment of a punitive campaign which will develop dialectically, as a free organised action, whose successive moments are foreseen by the enemy. In other words, it was their political and social activity, their condition, the location of their homes (in relation to the military exercise), the urgency, from the enemy's point of view, of beginning 'flushing out' somewhere, the importance of their neighbours, their activities, etc., which had been or would be synthetically united by a single totalising process which would be realised in its dialectical unity by realising the progressive and synthetic unity of the district by annihilating it. At this level, everyone, as a + +third party, became incapable of distinguishing his own safety from + +that of the Others. + +This was not an issue of altruism and egoism; such behaviour, in so far as it exists in this very schematic form, constitutes itself on the basis of existing circumstances and it preserves human relations which are engraved in the practico-inert field, in transcending them. It is easy to see how a neo-positivist might interpret the new statute of the third party: in a situation of looting, disturbances, and sporadic riots (he would say) the 'accidental ' , 'serial' (in pseudo-generality) or universal individual might still have a chance of defending himself on his own; but if he was concretely threatened as a certain moment of a repressive campaign which unified the district by the development of totalising action, he would no longer have any �uch opportunity. He would have to defend himself as a concrete part of the totalised totality, that �s to say, no one would have any hope apart from the totalising negation (through the union of all) of the destructive operation. But this kind of rationalism is not dialectical, and, though Marxists sometimes make use of it, its analytical, utilitarian origins are quite apparent. The truth is not that the campaign of repression linked individual risks to the risks run by everyone; it is that, for every third party, it constituted a statute (which we will define below), by producing his own possibility of being killed or imprisoned as a specification of the common danger, that is to say, as a foreseen and controlled element of + +the programme of extermination. + +We must be quite clear about this : the totalisation which the third party receives from outside determines him through a new contradiction. His original structure as a third party expresses, in effect, simply the practical power of unifying any multiplicity within his own field of action, that is to say, of totalising it through a transcendence towards his own ends. As such, it can therefore serve as one moment of the mediation we are looking for: in his own activity (as a shopkeeper, worker, etc.), every resident of the Quartier Saint-Antoine district totalised his district in principle (,the customers', 'the comrades ' , etc.). But, at the same time, his real memhership of the district was serial in character and ' manifested its inertia of alterity. In this connection, it is easy to make the mistake of believing in the homogeneity of their statutes on the ground that they concern the relations between one man and one multiplicity. He actually totalises the district in so far as he is not part of the totality, and the district serialises him in so far as he lives in it. But if the totalising power of the third party produces, as the + +followed by panic, flight, and regroupment (followed perhaps by an organised struggle). The panic was both the new practical incarnation of the Other and a practico-inert process realising itself through the alienation of free reciprocities . Everyone freely fled the flight of the Other, which means that the Other was embodied in everyone as + +imperative flight. + +But as well as being Other, everyone is also a third party: as a third party, he organises the constellation which surrounds him, he attributes a free, totalising meaning to flight, as the violence of inertia on the basis of the overall situation. In so far as he becomes a third party, he can no longer grasp the serial structure of flight: he perceives the panic as the adaptation of a totality to a total threat. For him, it is neither Others, nor a few individuals, who flee: instead, flight, conceived as a common praxis reacting to a common threat, becomes flight as an active totality. But this simple unification would only be abstract, external and theoretical, if, for example, he observed these events from his window. Here, seria'ity helps: at the moment in which the third party grasps the flight, from outside, as an organised reaction, he lives it through himself, in serial imitation and as alterity. The two contradictory aspects of the Other and of the third party are now directly opposed in the indissoluble unity of a praxis. And the materiality of his membership of the series and of his passive activity gives the individual a statute which prevents him from unifying the multiplicity from outside; the movement of practical integration as freedom returns to him, a human thing in flight, and signifies him; the synthetic movement which starts from him cannot really enclose him, but at any rate it designates his integration as a task to be done. In the context of this neW task, every third party as such will seek in himself the dissolution into free common activity of his serial being. The activity of the group turns back on his passive activity; for him, flight, which began as a contagious phenomenon, becomes a common, organised action, through his individual praxis, and in so far as he has unified the group . in his practical field, with its own objective and, therefore, having to regulate itself, to adjust the means to the end, etc. For example, it may become a limited retreat leading to an offensive comeback etc. And this transformation would not be a change in knowledge or perception; it would be a real change, in himself, of inert activity into collective action. At this moment, he is sovereign, that is to say, he becomes, through the change of praxis, the organiser of common praxis. It is not that he wishes it; he simply becomes it; his own flight, in effect, realises + +t + +he practical unity of all in him. This particular structure derives from the particular link which unites the third party to the gathering which is being destroyed, and it makes him both the transcendent synthetic unification (over which everyone is supreme in the practical field) and + +aterm which is signified in immanence by the c + +ircular movement of its + +own totalisation. Transcendent, because the unification of all by the agent does not come to an end with his real integration into the totality; and immanent because the serial contagion can dissolve in him only in favour of the unity of the whole. On the other hand, his praxis is no longer in him as that of an Other, any more than it is his own reality + +for Others : in so far as seriality as contagion is l + +iquidated in the + +resumption into freedom of the passive movement, his praxis is his own in himself, as the free development in a single individual of the action of the entire group which is in the process of formation (and, consequently, of everyone in so far as common unity serves as a mediation between everyone and the third party). It is on this basis that his own action as sovereign (simultaneously unique and shared) lays down its laws in him and in everyone merely by its development. Just now, he was fleeing because everyone else was fleeing. Now he shouts, 'Stop I', because he is stopping and because stopping and giving the order to stop are identical in that the action develops in him and in + +everyone through the imperat + +ive organisation of its moments. + +It must be understood that, at this instant, the third party unifies the gathered multiplicity and makes it a totality, as when he unifies the Others in his practical field, as, for example, to take a readily intelligible case, when, in my perceptual praxiS, I see the gathering of people + +wai t + +ing for the bus as a group, and consequently say to myself, 'There are too many of them, I'll take the underground.' (Thus this groupobject, seen in relation to my own aim - finding a way of getting to work - and defined in these terms, becomes in its turn an objective motivation, that is to say, in the unity of my immediate project, it tends to counteract the slight preference which I have always had for travelling by bus.) The difference is that the group of passengers appears to me as an object, as a totalised totality. In effect, my project totalises them through its transcendence: to notice roughly how many there are, or to estimate it according to the density of the gathering, is to define it in my practical temporalisation by its co-efficient of adversity, that is to say, to define it in terms of how long I would have to wait before getting a seat on a bus. Besides, as we have seen, I pass from the illusion of polyvalent unity, as an initial synthetic perception, to + +the discovery of seriality, because the serial order which will forcq me to join a queue and perhaps arrive late outlines itself within my very + +perception of the group. + +On the other hand, I have sometimes had the experience of groupsuhjects, which may be either terrifying or helpful, and for which I am an object to be preserved, or destroyed; and I have a sense of being transcended by their untranscendable transcendence (transcendance). This is what J:tappens to the soldier who suddenly finds himself alone in the midst of the enemy, or to a half-dead mountaineer being carried down the mountain on a stretcher by a rescue team. Here, the unification is effected in the same way and in my practical field. But this unification does not disappear when confronted with passive seriality: on the contr.ary, on the basis of the common action of the group, it has the effect of revealing to me a unifying unity which does not depend on my own unification and which, suddenly, by its numerical strength, invests, penetrates and metamorphoses my own practical field, to the point of putting my own freedom in question (not in its inalienable existence, but in its ever changing or alienable objectification). This group is not an object in any way and, in fact, I never see it; I totalise it in so for as it sees me, in so far as its praxis takes me as a + +means or an end. + +There are also some intermediate forms : an emperor's pretorian guard might, according to circumstances, be either his worked Thing, his human tool or, if he is afraid of being assassinated, a communitysubject concealed behind simulated objectivity. Any transition from one form to an other is possible. But the gathering transformed hy me into my group does not have either of these two forms ; nor does it have any of the intermediate ones. However, it is easy to see how it presents itself: as a sort of synthetic transcendence of the group-object and the group-subject of the practical field. If, on this basis, I perceive + +flig + +ht as a common activity, totalisation will take place: the immediate structure of membership of the fused group is the real totalisation of all these movements by the same which is in me. In simple terms of perception, I can see the flight of the group, which is my flight, because, in the dialectical development of my praxis, I unite and co-ordinate similar or reciprocal actions (people helping one another to flee or to defend themselves). There is, therefore, something resembling one object fleeing on these hundred pairs of legs. And it really would be an object if I did not flee from its flight. But in fact, to the extent that I discover it through our flight, it is necessary that my synthesis should, + +in the end, turn back on me and integrate me entirely as a part of it. But this is impossible, because a totalising praxis cannot totalise itself as a totalised element. Thus, through the group, I indicate myself as a necessary culmination of the totalising action; but this operational indication never actually has its effect. (We shall deal with this fundamental structure at greater length later.) Thus I am neither totally integrated into the group, which has been revealed and actualised through praxis, nor totally transcendent (transcendant). I am not a part of a totalityobject and, for me, there is no transcendent (transcend ant) totalityobject: the group is not in fact my object; it is the common structure of my action. In material terms, this is often expressed by the fact that I cannot really effect a total (for example, perceptual) synthesis of the group in so far as it is my environment: I can see my neighbours, or, turning my head, the people behind me, but I can never see them all at once, whereas I synthesise the marching of everyone, both behind and + +ahead of me, through my own marching. + +Thus one thing which the group has in common with the groupsubject of which we spoke earlier is that the synthetic totalisation which I effect in my field through my praxis reveals to me an interior unity independent of this totalisation itself, that is to say, a unity which has constituted (or is constituting) itself spontaneousiy and outside it. Flight, as the unity of the group, is a unity independent of an objectifying totalisation: it is simply revealed through it. But, conversely, I could not take the group as a community-subject of which I am the object (the means, for example) : I have discovered that its flight, in it and in me, is the same; in other words, the practical unity which my totalisation reveals and which negates the objectivity of the group thereby negates my own in relation to the group, since this practical unity is the same (not in me and it, but in us). In the same way, if the pure, formal totalisation of multiplicity in my perceptual field revealed nothing but a practical unity which eluded it, this would be because this unity was in fact based on some deeper praxis: I come to the group as its group activity, and constitute it as an activity in so far as the group comes to me as my group activity, as my own group existence. The characteristic of the tension of interiority between the group (apart from me) and myself inside it is that in reciprocity we are simultaneously both quasi-object and quasi-subject, for and through + +each other. + +4 The Mediation of Reciprocity: the Transcendence- + +Immanence Tension + +But it is a common error of many sociologists to stop at this point and treat the group as a binary relation (individual-community), whereas, in reality, it is a ternary relation. Indeed, this is something that no picture or sculpture could convey directly, in that the individual, as a third party, is connected, in the unity of a single praxis (and therefore of a single perceptual vista), with the unity of individuals as inseparable moments of a non-totalised totalisation, and with each of them as a third par�r, that is to say, through the mediation of the group. In terms of perception, I perceive the group as my common reality, and, simultaneously, as a mediation between me and every other third party. I say every third party deliberately: whatever relations of simple reciprocity (helping, training a new neighbour or comrade, etc.) there are within the common action, these relations, though transfigured by their being-in-a-group, are not constitutive. And I also say: the members of the group are third parties, which means that each of them totalises the reciprocities of others. And the relation of one third party to another has nothing to do with altedty: since the group is the practical milieu of this relation, it must be a human relation (with crucial importance for the differentiations of the group), which we shall call mediated reciprocity. And, as we shall see, this mediation i� dual, in that it is both the mediation of the group between third parti�s and the mediation of + +each third party between the group and the other third parties. + +First moment of mediation. - Consider a regroupment behind some shelter, after a flight. Some individuals will not take part in it: the action of the enemy will have cut them off completely from any synthetic community. For them, seriality itself, which began in panic, has culminated in molecular exteriority: the individual, alone, cut off from Others, continues his flight, loses his way, hides in a cellar, gives himself up, etc. But we should not suppose that he has revealed his cowardliness. Cowardliness is a serial feeling, and, in isolation, the absent Other still determines it. But in any case - and this is the important point - every one of the third parties who are regrouping knows that the group will be less numerous than the gathering. This knowledge might be derived from experience, and in any case with cer- + +tainry from his immediately preceding perception: the third parry has seen the practico-inert field from which he has torn himself away reforming itself at the horizon through the flight of certain Others who will never return. When he goes back to join those who are planning to resist, his fate depends on the number of the resisters and is revealed to him by a rough estimate of this number. It is in the same way - though, as we shall see, in an entirely different structure of being - that everyone calculates the duration of his wait by the density of the serial gathering waiting for the bus. At most, the praxis may negate itself: this is what happens, for example, if the resisting forces are objectively excessively inferior to the enemy forces. And the risk run by the third party in his organic, personal reality reveals itself in objectivity as directly connected to the risks of failure which threaten collective praxis, and as inversely proportional to its perceived density (as the initial estimate of + +the multiplicity as power). + +But, while I am on my way to join up with the central core of resisters, who are sheltering behind some building, I happen to be in the practical field of another third party, who is coming out of another street and approaching the same group with the same purpose . And the arrival of this third party at the group has real, objective links with my own approach: for me he increases the multiplicity of resisters, thereby increasing the chances of success and diminishing my personal risks. This is the joyful surprise which all the assembled demonstrators feel when, on the occasion of a demonstration which has been forbidden by the police, they see individuals and small groups converging from every direction, more numerous than they had expected, and representing hope to everyone. On the other hand, I amfor them exactly what they are for me. This newcomer joins a group of 100 through me in so far as the group which I join will have 100 through him. Serially (or, as we shall see, from the point of view of the organisers, if there are any), we arrive at the group as two units. Through us, there will be 100 rather than 98. But for each of us (both me and the other third party) we are, reciprocally, each by the other (and, as we shall see, by all the Others) the 99th. To put it another way, each of us is the looth of the Other. Thus it is clearly a matter of reciprocity. I see approaching me the number which I form by adding myself to the group and I see it through the arrival of the Other; at the same time, hecause of this, the group is increased in me and in the Other, by me and by the Other, in me through the Other and through me in the Other. And this reciprocity is mediated, because the action of each of us is the counterpart + +of that of the Other through his numerical objectification in the + +group. Thus the group is the mediation . + +We have already discussed certain mediations by an ohject: in work, there are reciprocities which are mediated by the tool and the object to be produced. My act takes on meaning, in inert materiality, only if the act of the Other has already informed this materiality, has given it some initial meanings. If, however, we have not emphasised the mediating character of the practico-inert field, this is because its mediation is passive: it is the pure milieu in which actions meet. But the mediation of the third party by the group is of a different kind : first, of course, the hond between the worker and the material field is univocal; my bond with the group (as the link of the other third party) is one of interiority. -When I approach it to join it, I am already part of it. We have seen in what sense: as a limit of totalisation, as an impracticable task which has to be done. And, from this point of view, the present multiplicity of the group (to the extent that it has been roughly estimated) constitutes me objectively as a member of a tiny group of desperate menu who will get themselves killed on the spot, either as members of a huge invincible demonstration, or as taking part (as is more usual) in some intermediate formation. This internal, synthetic constitution of me by the group is simply totalisation returning to me to give me my first common quality over the collapse of seriality. And it gives me this quality as power. Thus the third party comes to the group which already possesses him, as a constituent and constituted power; that is, he receives the power he gives, and he sees the other third party approaching him as his power. For, in the group, the other third party, in so far as I totalise him with the Others, is not for me a third-parry-object, that is to say, a third party transcendent (transcendam) to me. As an individual, he transcends (transcend e) me towards his projects in so far as I transcend him: this is simple reciprocity. Integrated into the group by totalisation, he is quasi-transcendent through the mediation of the group, since I am in fact to integrate myself with him into the community, and since the task is indicated and since I remain in tension, at the limit of immanence and trans- + +12. I am not c1aixning that numher alone makes me desperate: whether I am desperate depends on the total situation. It is simply that although I may behave with desperate tenaci ty in some circumstances, I will have neither the opportunity nor the time, nor even the desire, to behave like this in the event of a popular tidal wave effortlessly breaking down all resistance, such as, for example, an un- + +protected body of police. + +cendence. My link to him is therefore new: if we were to collaborate in the group in some action which would involve only the two of us, we would encounter strict relations of reciprocity-transcendence again; but in so far as he himself signifies in and through my totalisation my being-in-the-group as a task realised over there and not here by me, he is transcendent-immanent to me; or rather his immanence refers back to my (totalising) transcendence in so far as, as we shall see later, his transcendence can determine my immanence. Through the mediation of the group, he is neither the Other nor identical (identical with me) : but he comes to the group as I do; he is the same as me. The characteristic of this new. crucial structure of mediated reciprocity is this : that I see myselfcome to the group in him, and what I see is merely the objectification of what I realise at the same time as him; he is my lived objectivity. We know that up to now the objectivity of an act appeared to Others or was reflected for me in the object produced. In the fused group, the third party is my objectivity interiorised. I do not see it in him as Other, but as mine. Now, the reason for this new structure (which lies at the origin of all so-called 'projective' actions or actions 'of projection') resides precisely in the fundamental characteristics of mediation. For the mediator is not an object, but a praxis. The group which I go to is not the inert gathering of these hundred people. Its inertia is merely an appearance and one that does not even exist for me. It is, in fact, an action: we are waiting (to become sufficiently numerous, or for some information, or for the enemy to be off guard, etc.). And the truth is that I try to integrate my praxis into the common praxis (that is to say, the plan to counter-attack, for example). This praxis is immediately given as the comprehensible meaning of the regroupment, and if this meaning is comprehensible it is because it appears to me through my own praxis, which is already, in itself, a regroupment (of myself with Others), and is conditioned by the common regroupment. On the other hand, the group is constituted in its compact nucleus by several men huddled close to one another, but who, for me and for the third party who comes to the group, are simply third parties. The apparent exis of everyone (his being-there, immobile, in-the-midst-of-the-group) is revealed to me as my praxis both in me and in him: the dislocation of temporality makes no difference; being in the group, in effect, consists in having come to it, as I come to it, and in staying in it (that is to say, coming to it constantly) just as, for me, to come to the group is to be already in it, in that its structures and forces determine me in my very reality. Thus both the third party and myself are mediated by the + +action of every third party, in so far as this action produces multiplicity and makes each of us the hundredth for the Other - in other words, in so far as this unity of practical self-determination penetrates the freedom of our reciprocal actions and makes them the same for each of us in being common to all. There is nothing magical or irrational about this: on the contrary, the transformation of free action into common free action by the free praxis of the group is absolutely intelligible. The unity of the praxis is conditioned by circumstances: from the moment that I, as one of its members, unify the group which is in the process of unifying itself, the unification, in so far as it may be effected by any third party, inside the common movement, is not only conditioned, in its freedom, by free action, but also conditioning, as my own freedom (that is to say, as my own project) within my own praxis. And this conditioning of me by every third party, that is to say, by the same movement everywhere, whether it is manifested in my praxis positing itself as regulatory, or in the reciprocity of my action and of that of a partiCular third party, is precisely my own freedom recognising itself as common action in and through my individual action. It is this synthetic enrichment (apprehended in me here and in the third party over there) which makes my simple action, which comes to me as the same (and simultaneously as realised here), produce in reciprocity a common result (,There are a hundred of us ! Here's the hundredth !', etc.), which could not be envisaged in itself(at least not at the rudimentary level of the fused group) and which operates through me in + +objectivity as the inversion of alienation. + +We have already seen how, on the market, my mere presence is alienating, how I am already for myself the Other, and how bewitched quantity causes the stock-piling of precious metals in Spain, for example, to lead to devaluation - so that to appear is, in itself, at least in the abstract, to force up prices. In this example we can see seriality and alienation as the other objectivity of my objectification. But in the present case, by contrast, what I discover is action as human, and quantity as instrumentality. Within certain limits, to be more numerous is to be more powerful. My appearance in the group eludes me in so far as the number depends on everyone: but this objectivity of my objectification suddenly becomes my objectivity for me. Through me, the number is increased; I am no longer the Other who comes to Others, endangering myself by my mere material presence; I am now my own action in the praxis of the group in so far as its objectification belongs to me as a common result. A common result: it is new, but it is mine in + +so far as it is the multiple result of my action multiplied everywhere, and everywhere the same; at the same time, this multiplied action is a single praxis which overflows in everyone and into a totalising result. For the moment we can set aside the example of the regroupment: it was only meant to provide a graphic model. Of course, it is obvious that the relation of every third party to every Other in the group and through it is a mediated reciprocity. And reciprocity within the group produces the group as a container to precisely the extent that the group allows + +this reciprocity by becoming a mediation. + +But I mentioned a second mediation: every third party tends to become a mediation, as such, between the group and any other third party (or all of them). This is because I am not in fact alone in carrying out the totalising operation, that is to say, in integrating the ensemble of individuals into the group and in revealing, through my action, the unity of a praxis which I produce and which produces itself. This operation is the individual and common praxis of every third party in so far as (failing to effect his real integration) he designates himself as free, common action becoming regulatory through him. From this point of view, I am, for every third party, a free human agent, but engaged (with other third parties and inside the group) in a constellation of mediated reciprocities. I move from the position of totalising sovereign in relation to everyone to that of totalised sovereign. At other (more abstract) levels of our investigation (experience), this totality may be both the result and the source of violent conflicts. But this cannot be the case in this initial moment of the group, because the Other, by totalising the practical community through his regulatory action, effects for me the integration which I myself should have realised but was unable to. Through him, in fact, my being-in-thegroup becomes immanence; I am amongst third parties and I have no privileged statute. But this operation does not transform me into an object, because totalisation by the third party only reveals a free praxis as a common unity which is already there and which already qualifies + +him. + +In practice, this means that I am integrated into the common action when the common praxis of the third party posits itself as regulatory. I run with all the others ; I shout: 'Stop I'; everybody stops. Someone else shouts, 'Let's go I' or, 'To the left 1 To the right 1 To the Bastille I' And everyone moves off, following the regulatory third party, surrounding him and sweeping past him; then the group reabsorbs him as soon as another third party, by giving some order or by some action + +visible to all, constitutes himself as regulatory for a moment. But the order is not obeyed. Who would obey? And whom? It is simply the common praxis becoming, in some third party, regulatory of itself in me and in all the other third parties, in the movement of a totalisation which totalises me and everyone else. I can recognise this totalising regulation as such only in so far as my action is the same in the totalising third party. On the basis of the common future adumbrated by the common movement (flight, charge, etc.), that is to say, on the basis of my future as the common meaning of my regulatory and totalising praxis, the order gives me my common, future possibility. It reveals this possibility as a means within my project. In this way I can, as being-in-the-group, myself become a means of the common praxis, that is to say, an instrument of my own praxis. (,Get back, you lot ! Let the others move ahead !' - initial differentiations, almost immediately reabsorbed, according to the circumstances and the outcome.) I execute the 'command'; I am the 'order', in so far as, through the third party, it accomplishes the integration which I cannot accomplish myself. This integration is real (and as we shall see, it will become more real as the group becomes more differentiated). And it is really the constituent whole which achieves practical unification through the order. In the extreme case, no regulatory third party even appears: orders circulate. Of course, they Originated in some individual third party, or sometimes in several thir� parties at once. But distance, and the impossibility of grasping the group when one is inside it, and many other reasons all mean that it is only the word which reaches my ears and that I hear it in so far as it comes from afar (in so far as my neighbour repeats it "\yithout changing it). The words circulate from mouth to mouth, it might be said, like a coin from hand to hand. And, in fact, discourse is a sound-object, a materiality. Furthermore, as they 'circulate', the words take on an inorganic hardness, and become a worked Thing. But this is far from meaning that we are going back to collectives. This thing is the vehicle of sovereignty: in short, it does not circulate. Even if it 'comes from afar', it is produced here as new, in so far as wherever it is, every place in the group is the same here. This object which is apprehended, understood, and reproduced in the immediate transcendence of praxis is merely totalisation itself in everyone, in so far as it can be achieved only by a sign. I decode the sign by my action, by conforming to the maxim produced; and the absence of the first signifier (of the third party who was the first to shout the words) makes no difference to the structure of my praxis: the authorless words, + +repeated by a hundred mouths (including my own) do not appear to me as the product of the group (in the sense in which this might be a hyper-organism or a closed totality) but, in the act which comprehends it by actualising its meaning, I apprehend it as the pure totalising and regulatory presence of the third party (as the same as me) in so far as it accomplishes my integration where I am and through my freedom. But it should be noted that this regulatory totalisation realises my immanence in the group in the quasi-transcendence (transcendance) of the totalising third party; for the latter, as the creator of objectives or organiser of means, stands in a tense and contradictory relation of transcendence-immanence, so that my integration, though real in the here and now which define me, remains somewhere incomplete, in the here and now which characterise the regulatory third party. We see here the re-emergence of an element of alterity proper to the statute of the group, but which here is still formal: the third party is certainly the same, the praxis is certainly common everywhere; but a shifting dislocation makes it totalising when I am the totalised means of the group, and conversely. In other words, everyone has, for each and for all, a possible dimension of escape or of tyranny, in so far as integration, though a free, practical unity, refers everyone who has been integrated back to an 'immanence-transcendence' tension which is in danger of breaking into transcendence (or into a false immanence which conceals a dominating transcendence). In any case, we shall call the individual's being-in-the-group, in so far as it is mediated by the common praxis of a regulatory third party, his 'interiority' or 'bond of interiority' in + +relation to the group. + +This alternation of statutes (everyone passing from interiority to quasi-exteriority) must appear as the very law of the fused group. Everyone is distanced from all, as the transcendent (transcend ant) agent of the union and as merged with everyone by a totalising third party; this alternation is characteristic of temporal actualisation, but it temporalises a basic structure, or in other words, a set of structural determinations. In historical reality the event conditions the actualisation. In fact the number of regulatory third parties, even if it is fairly high, is always limited, and concrete circumstances select them, or lead each of them to select himself from the group as its spokesman. At the Palais-Royal in I789, the first person to have got himself heard, on some historic day, was probably one who happened to be close to a bench or chair and who could therefore get higher than the Others, in the spatial rnaterialisation of all the dialectical characteristics which we + +have enumerated, within the group, but separating from it in order to totalise it and therefore establishing a dialectical relationship with the crowd and then being reabsorbed by it and reintegrated by the speeches of some other orator emerging a little further on. At this level, there is no longer any leader. In other words, the crowd in situation produces and dissolves within itself its own temporary leaders, the regulatory third parties. But a dialectical inversion can already be detected here. For we have seen practical community coming to individual action and structuring it in the movement of disintegration of seriality. But we can now see in this orator, addressing the upturned faces and shouting, 'To the Bastille I', a common individual (that is to say, one whose praxis is common) who gives the entire crowd the biological and practical unity of its organism as the rule of common unification: and in fact we shall see below how common unity, as a developing totalisation, attempts to + +realise itself as individuality. + +5 The Intelligihility of the Fused Group + +We have now observed the formation of a fused group and described its stluctures. Now we must define the mode of intelligibility of this new praxis. I must remark to the reader that this appearance of the group as an undifferentiated totality does not correspond, at least not necessarily, to a historical anteriority of the Apocalypse. (On the contrary, for me, the Apocalypse presupposes the existence of serial gatherings and institutionalised groups). We are discussing it first because its historical reality is undeniable: in certain circumstances, a group emerges 'hot' (a chaud) and acts where previously there were only gatherings and, through this ephemeral, superficial formation, everyone glimpses new, deeper, but yet to be created statutes (the Third Estate as a group from the standpoint of the nation, the class as a group in so far as it produces its apparatuses of unification, etc.). Sieyes' question1 3 about the Third Estate, which was nothing (and therefore a pure + +13 .. '\Vhat is the third estate? Everything! Up to now, what has it been in the political system? Nothing ! What does it seek? To become something in it !' See + +multiplicity of inertia, since it existed as nothing) but could be everything (that is to say - as certain people then thought, including Sieyes himself, by an abstraction from which, as a liberal bourgeois, he soon recovered - the nation, as a totality perpetually reshaping itself, the nation as permanent revolution) shows clearly how through the troubles of 1:;88-9 and the groups which formed sporadically (which up to that .time were called riots) the bourgeois even more than the worker in the cities (though work was really done by the workers) glimpsed the transition from an ossified, cold world to an Apocalypse. This Apocalypse terrified them; in order to avoid it, the members of the Constituent Assembly would willingly have become accomplices of the aristocracy if only it had been possible. But it was France as the Apocalypse that they discovered through the storming of the Bastille. And through this people's battle, they learnt not only what the inert words of this speech suggested to them: its 'power', the contradictory 'necessity' of governing both through it and against it etc. ; they sensed + +that History itself was revealing new realities. + +This was not highly significant; but what is important is that this form constitutes itself in reality at certain moments of the historical experience and that it then forms itself as new - irreducible to the gathering, to the mass statute, etc., and also to organised, semiorganised, or institutionalised groups, and that its novelty is of itself an allusion to a more radical and deeper novelty: free praxis becoming through society as a whole and through the conflicts of antagonistic groups the developing statute of all the social structures of inertia. For our purposes, this is enough: its real, dialectical existence and its emergence from the liquidation of petrified forms are sufficient reasons for taking such a historical reality as our starting point. Indeed, from the point of view of critical knowledge - that is to say, from our point of view - this formation is more absolutely simple than any other (since groups develop by differentiating themselves) and, therefore, more legible. I shall now go back over my earlier descriptions and examine them from the point of view of practical dialectical rationality. Is there an intelligihility of the fused group? And what intelligibility? And what can intelligibility mean in this conext? These are the + +questions which we have to turn to now. + +The centre of the problem is the question of the shifting unity of syntheses, of the multiplicity of the unifications, etc. It is at this level that we must ask ourselves: can several syntheses produce one syn- + +What we have seen emerging, at the expense of the collective, and under the pressure of circumstances and through a hostile praxis which expressed its project of totalising destruction through the synthetic significations of the practico-inert field, is not an actual totality, but a shifting and ceaselessly developing totalisation. But this group did not constitute itself for itself; whatever enthusiasm and joy may have been felt by the petty bourgeois who ran through Paris, addressing complete strangers and exhorting one another, the deep motivation was Terror; that is to say, as project and motivation are one, it characterised the project in so far as it was transcended and preserved; and union was created on the hasis 0/ a numher 0/ objectives which gradually became more definite and converged into a single one: the defence of Paris (and, in the case of the Quartier Saint-Antoine, the defence of the district). Furthermore, to precisely the extent that the structure of the group anticipates differentiation, it comes to the group, as we have seen, precisely from the gradual definition of the objective (for example, the need to defend the district by fighting on two fronts). It will be said that the same applies to an organism, and this is true - with two crucial reservations. The possibility of an action, whether individual or common, arises at a certain stage in the development of organisms and through their organised structure; the organism which has satisfied a need by some practical activity survives the disappearance of this activity: it survives as an organism, that is to say, through the unified variety of its functions. Although the group, as an evolved and differentiated reality, is also characterised by a hierarchised and unified plurality of functions, the completed action (local - that is to say, entrusted to a group or common organ) refers the group to a certain type of practico-inert being which we shall describe later. In short, the organism is both totalisation and totality; whereas the group must be a developing totalisation whose totality lies outside it in its object, that is to say, in the material totality which designates it and which it attempts to appropriate and turn back into instrumentality. In this sense, the objective and the danger are two stages of a single process which designates the developing totalisation from the outside: objectification (or the conquest of the objective) becomes the transcendence and domination of the common danger through transforming material destiny (topographical configuration, etc.) into an instrument. But to precisely the extent that the totalised totalisation achieved by the surrounding matter (occasioned, for example, by an other praxis on the part of some other group) is reappropriated by the group and re- + +interiorised as its internal and univocal relation to a particular instrumentality, this totalising totality, within the group, and as an instrument in use, becomes the very condition of all structural transformations. It is chiefly in this sense that we should understand the intelligibility of Marxist descriptions which show the object at the basis of the group as conditioning its internal turbulences and the overthrow of its relations with the others. In one sense, therefore, and provided one remembers that work - not only as a free organic dialectic, but also as wear and tear, as expenditure of energy, and as real but particularised efficacity (which, as such, is stolen or integrated into an active group) is a material, concrete reality a� a process, as a transformation of energy, only at the level of individual praxis, it can be said that the praxis of the group is constantly to reorganise itself, that is to say, to interiorise its obj ective totalisation through the things produced and the results attained, to make of it its new differentiations and its new structures, and thereby to transcend this rearrangement towards new objectives or rather, to make this internal rearrangement, as structures which have to be transcended (because attained) the transcendence of old objectives and of interiorised instrumentality. In this sense, a group might define itself from the outside on the basis of the common objective imposed on men by a totalising structure of the surrounding materiali ty (and perhaps of another praxis examined in its objectivity). If the group happens to posit itself for itselfin its most differentiated forms (and, for example, with antagonistic bonds with some other group) ; even if the group happens to be able in itself to present itself as the real, total meaning of each and every individual life, as is the case 'whenever a national community (which, as we shall see, is a complex ensemble of antagonistic groups, of provisional alliances and of serialities) goes through a crisis of nationalism; and if, finally, being-in-the-group becomes, as a regulatory objective, a structure of the human relations which are to be constructed out of the liquidation of bourgeois atomism, the fact remains that the concrete group, in its elementary forms, is a practical organisation required by certain situations through every third party. In other words, it constitutes itself as a means: but this in no way implies that it must remain a means. Here, in fact, the dialectical investigation (experience) shows us at once that it is a means of the third party to the extent that he is a means of the group. In particular, because it is free, practical relations between individuals which produce the group, it must be recognised that the group undergoes a dialectical evolution of which we must provide an account. The point is to show + +the (dialectical rather than historical) basis of all groups (including ones which posit themselves as essential through the inessentiality of their members), that is to say, to display their practical instrumental reality. Certain situations pose urgent questions to individuals, as multiplicities in the practical field - questions which already transform them in their reciprocal relations and which can be resolved only by a rearrangement of their relations, that is to say, by the interiorisation of + +multiplicity and the liquidation of alterity. + +From this point of view, the danger of the organicist illusion having been finally removed, it should be noted that this reshaping of human (and non-human) relations takes place in the same mode as the transformations of an organism: individual action is perpetual adaptation to the objective, that is to say, to the material configuration; the body interiorises the surrounding materiality in its attitudes and postures and, less noticeably, in its internal reactions and even in its metabolism. In this sense, the basis of intelligibility, for the fused group, is that the structure of certain objectives (communised or communising through the praxis of the Others, of enemies, of competitors, etc.) is revealed through the praxis of the individual as demanding the common unity of a praxis which is everyone's. The structure of synthetic unity is, therefore, even at the level of the univocal relation of interiority, directly derived from the grasp of a unitary (and passive) structure of the surrounding materiality through the synthetic unity of a dialectical, individual praxis. Unity is reactualised practically by the individual, both over there as the community of the objective, and in his own action, here, in its present moment either as the exigency of being common praxis or as the first realisation in him and in every third party of this community. On the other hand, if the urgency of common action appears (whether rightly or wrongly, that is to say, whether in accordance with a real actualisation of objective exigency or in accordance with mistaken calculations) only to one individual, or to several members of the gathering, then this intelligibility relates only to a possibility which is negated as soon as it is posited. If the 'order' is not followed, if the individual who advances towards the enemy remains alone (either because there has been no liquidation of seriality, or because the group has constituted itself against him and by another praxis suggested by Others) , then the constitution of the common praxis manifests itself in this individual praxis as a negated possibility. Of itself it liquidates itself in favour of isolated action or, on the other hand, of immediate reintegration into the gathering. The individual + +who no one follows may, in case of extreme anger, throw stones at the attacker or the police, alone. Alternatively, he may suddenly turn + +round and seek refuge in the infinite milieu of circular seriality. + +The reality of the praxis of a (fused) group depends on the liquidation (either simultaneous or subject to temporal dislocations which can be ignored) of the serial, both in everyone and by everyone in everyone, and its replacement by community. This reality (which sometimes produces itself and sometimes does not) must therefore be comprehended in its intelligibility. But this intelligibility is defined precisely by the practical relation of the hostile praxis (through the material object) to the free action by which the third party unveils this praxis by opposing it. It is through the individual discovery of common action as the sole means of reaching the common objective, in fact, that the historian demonstrates and evaluates the urgency, the imperious clarity, and the totalising force of the ohjective (that is to say, of the danger which has to be avoided, of the common means which has to be found). Since every action, here, is the same, we must concentrate our attention primarily on the praxis of the third party, wherever it may be, in so far as it is conditioned in its free development by a common future (either to be realised or to be avoided). It is the tension of this future in the practical present, and the progressive and regressive decoding of this fundamental relation, which furnish the first elements of intelligibility. We must investigate not only how the threat - or the real action, already begun - of the enemy affects the third party, but also how this developing future transforms his statute, and with what urgency it appears (an urgency which, as an objective relation between the enemy action and that of the third party, may turn out to be very different from real urgency, that is to say, from the urgency which the historian will be able to demonstrate after the event as a meaning of the entire process). And conversely, on the basis of a common action adumbrated by the third party, we must investigate what possibilities are defined through and for this action, and what chances of success reveal themselves in the object itself through the adumbration of the praxis, etc. From this point of view, it may be that the problem is not to understand why a given initiative accompanied by a particular order was not taken up (in a historical reconstruction, the explanation might be, for example, that the group would have run into disaster if it had followed the order, and that it must have known this, given the material configuration of the place and all the other circumstances) but, rather, to interpret intelligibly the fact that in such circumstances a few + +individuals might have believed they could dissolve the gathering by + +inventing a common praxis. + +This problem - though a negative one - concerns certain secondary disciplines within anthropology (in particular those which deal with the individual as such) and it refers us back to the abstract statute which we went through in the first moment of our dialectical investigation (experience). The failure of this attempt relegates the individual to isolation and is to be explained in terms of his negative relation to the third party, that is to say, of a relative non-integration (or maladjustment, the word does not matter) which in turn is to be explained, in the context of the totalising movement and of History, in terms of the circumstances of his personal life. Precisely because of this, the transformation of the gathering into a group, wherever it occurs, includes, for the historian, its own intelligibility: that is to say, it is to be interpreted positively as the most concrete relation of the third party to circumstances and to circumstantial objectives, in so far as this relation manifests itself without being either obscured or determined by the specific behaviour of every individual as such. But it is obvious that such individual circumstances (which, as we have seen, may be his position; or which may also be his personal qualities - intelligence, courage, initiative there are plenty of these rather vague words) will produce one individual rather than an Other as the first regulatory third party. But these circumstances are 'general particularities' : they determine the third party in relation to the group and the group in relation to the third party without telling us anything about the past or the transcended-being of the individual, and indeed, even without our really knowing14 whether this rapidity of initiative was produced in him by his free praxis as one of his group qualities, that is to say, as an + +14. I say, 'even without our knowing', not because, a priori, there can be no means to settle the question, but because, in fact, most of the spontaneous regulations, directly emerging and directly absorbed, elude the observer and moreover the historian who, in any case, is seldom obliged to study them. He would, however, if, for example, he was dealing with the event known as the 'September Massacres', simply because, ever since the first meetings of the Convention, the Girondins brought up the problem of responsibility in relation to this very subject. But it is clear that later historians will seek for the action of an anonymous Third Party only if they are trying to establish the responsibility of particular organised bodies (the Commune) or politicians. The Third Party in so far as he is the same, a little ahead of the same, is not their concern: only the Third Party as a group (simple totalised-totalisation, immanence-transcendence relation) can be + +of interest to them. + +o'r the same men. The fused group should therefore be characterised as. an irreversible and limited process: the reshaping of human relations by man had temporalised itself in the practical context of a particular + +aim and as such would not survive its objectification. IS + +In this sense, a group defines its own temporality, that is to say, its practical speed and the speed with which the future comes to it (on the bases of a threat, for example, which itself externally defines an urgency, that is to say, which makes time an objective exigency and a scarcity; the practical speed of the group is the reinteriorisation and embracing of urgency). Joseph Le Bon, a member of the Convention and representative of the people at Arras, said, from his prison, after Thermidor, that no one - not even himself - could really understand or judge events and actions which had occurred at an other speed. But this problem of temporalisation refers us back precisely to the real structure of the group, that is to say, to its own type of reality. The problem is to understand what, in a fused group, is signified by unity (which the description immediately confers on it: the group does this or that, etc.) + +as a synthetic unification of the diverse. + +What is really involved, as we have seen, is in fact a synthetic relation which unites men for and by an action, and not those vague interpenetrations which an idealist sociology sometimes tries to resuscitate in some form or other. But - and this is where the question of structural intelligibility arises - our comprehension of the individual dialectic has made us see synthesis as the unifying unity of a unique praxis which integrated diversity through work. The univocal relation or interiority linked inertia as diversity to action as the unifying negation of this diversity. Within the group, as we have seen, diversitY arises not at the level of the individual agent, or even at that of relations of reciprocity: it appears at the level of the syntheses. In other words, every third party, in so far as he is himself and not another, effects the unification of all, and by the mere actualisation and practical interiorisation of the totalising designations through which other groups single out the inert gathering as a negated totality (or a totality to be negated) indicates that his integration is a task to be done. Is this not just another example of serial commutativity? It would seem that alterity + +I', . I shall deal with institutional groups and groups of repetition later, It is obvious that their structure is more complex, since they define themselves both by the dissolution of serial inertia and as materiality sustained by the passive + +is to be found quite simply at the level of totalisations and that every totalisation is, for everyone, that of the Other, in him and in the Other. These questions at least have the advantage of defining the problem: if there is any doubt as to the intelligibility of the group, this is not because of any lack (that is to say, the question is not, and never has been, as some have believed, how separate particles could constitute a totality) . On the contrary, it is because of an excess: the difficulty is due to the fact that we are acquainted with praxis as a synthetic activity, that we have observed every third party in action liquidating seriality and unifying the gathering into a group; thus we seem to be faced with an excess of unifications. Can we call this reality with a thousand centres a unity, when we have already discovered, in the case of reciprocity, a relation with several epicentres, which, for this very reason, was + +unable to unify its terms? + +But, in fact, the question has been badly formulated. We are not really trying to find out whether the group, as a multiplicity of individuals, possesses an inert statute of unity, whether the men who compose it can be stuck together as organisms by some kind of gelatinous glue, or whether some 'collective consciousness', a totality irreducible to its parts, imposes itself externally on each and every consciousness, as the Kantian categories impose themselves on the multiplicity of sensations. We have seen, in fact, that the unity of the group was praxis (when it was hot; we shall observe other possibilities later) . The important thing, therefore, is to find out how far the multiplicity of individual syntheses can, as such, be the basis for a community of + +objectives and of actions. + +But these syntheses themselves, as we saw when we discussed them above, realise the substantial unity not of men, but of actions. In effect, every synthesis is hoth the practical constitution of common action, subject to reciprocal conditioning, and the revelation of this action as already existing. And in effect we have taken the third party at the moment when he was still in the gathering, and engaged in a passive, disordered activity. And we have seen how, by dissolving his seriality, he is able to see the original contagion disappear and how he constitutes not only his behaviour as free activity (by giving it a meaning), but also serial violence as common action, through his own activity (which he constitutes as the rule and meaning (signification) of the common praxis) . This 'discovery', in fact, is itself an action: at first, as we have seen, the third party, by his exhortations, his orders, etc., acts on passive activity and helps to transform it in Others into a praxis; + +and thus he makes himself a free rule for the liquidation of passivity in all. On the other hand, on the basis of existing circumstances (in particular, on the basis of the negative unity signified by a hostile praxis through the passive syntheses of the environment), this movement of actualisation of the common praxis occurs at about the same time in all the third parties as such. It is the moment in which orders circulate. Now, in this moment - for example, in the moment already mentioned, where a gathering, broken up by the police, regroups against it and becomes a demonstration - the multiplicity of individuals is still not transformed into substantial unity. Yet a regroupment does occur: something exists as a totality. But this totality is quite simply the demonstrators' attack on the police. And this is the first thing for us to explain. Now, it is obvious that, in the case of gatherings which, as in 1789, are unorganised, the transition from flight to regroupment does not originate in any particular order, issued by any particular individual; or at least, such an order was not very important. If the first order was 'obeyed', this was actually because everyone gave it. But here, it seems, we have that plurality of syntheses which would seem to be incapable of constituting a true unity. However, let us look at it more closely: in the moment where the demonstrators regroup, everyone rediscovers his praxis in the Other emerging from the other street and joining the group in formation; but, in so far as each of them was the free origin of his new behaviour, he would find it in the Other, not as his Other-Being, but as his own freedom. Here we encounter once more the mediated reciprocity which will turn out to be the essential structure of the organised group. But we can now see that this regroupment in formation, towards which everyone is advancing, and seeing himself advance in the person of his neighbour, serves as a mediation between third parties: this means that for everyone it is an ensemble · to be totalised and a group to be expanded by his own presence; and through him, in fact, everyone perceives the movement of the third party who confronts him as his own movement and as the spontaneous expansion of the group of which he is about to become a part. Thus my praxis appears to me not only as myself, here, now, but also as myself approaching me through my neighbour, and as sustained by its own totalised effect on my neighbour and myself. (By acting in the same way and by making myself the same as him, I encounter him in the group as a totalising increase of its strength, which by totalisation determines me through the group itself: his individual action which is mine gives me, through the expansion of the + +whole, a greater security). Now, from the beginning of the regroupment, and during the ensuing fight, the plurality of totalisations by third parties does not cease to exist; there is nothing but hundreds of individual syntheses. However this multiplicity negates itself in every one of the acts which constitute it. Indeed, in so far as each of them constitutes the whole as common praxis, he presents himself as the regulator, that is to say, as the praxis of the whole in himself. And in so far as he recognises himself in each individual praxis, he sees each of them as the presence in a third party of the total praxis. But, at the same time, by liquidating seriality, he has produced his own praxis as a free, dialectical determination. Thus when he tries to attack the police, he carries out an action which only the existence and practice of the group make possible; but, at the same time, he produces it as his free practical activity. Thus the action of the group as total praxis is not initially other action (action autre) , in him, or alienation from the totality; it is the action of the whole in so far as it is freely itself, in him + +and in any third party. + +This requires further explanation. We must show in what way every praxis is a free individual development and in what way it could only be what it is as the praxis of a totalised multiplicity. The second point can be easily established by means of an example: alone or with a few comrades, a particular demonstrator would never even have tried to attack the police - simply because the impossibility of such an attempt would have been inscribed in the facts. His behaviour was therefore determined in itself as collective, that is to say, as an action which could be carried out only by a multiplicity of individuals. But for the first time we are encountering this multiplicity in the form of a means, that is to say, as a reinteriorised multiplicity. We have seen how the mass, by its sheer quantity, is weight, efficacity. But it is also clear that the efficacity of masses as such produces the other e./fect (I' e./fet autre) ; that is to say, the effect necessarily produced by inorganic materiality in the practical field. Here, in contrast, the individual joins the struggle as a multiple, that is to say, multiplicity is already in his action as a means which has been integrated by a free praxis. He joins in the attack neither as isolated nor as a hundredth, but as the free utilisation of the power he gets from heing, here and everywhere, the material strength of the number one hundred. Number, as a structure of the action - that is to say, as an element in everyone of the decision of the third party - is merely an elementary kind of weapon. Everyone possesses it in its entirety, just as everyone can possess a pick or a + +pistol (that is to say, tile pick or the pistol). But, at the same time, everyone sees it around him, and finds himself in it, just as several soldiers may find themselves together in some military machine and manoeuvre it together. For instance, as well as being his own guarantee, it may be his protection (or, in other circumstances, a negative element - people separate and divide; but this will become clear later). In this sense, number in this particular third party and in others does not appear as an other-being (etre-autre), but as the interiorised reality which multiplies individual effectiveness a hundredfold (not by giving the third party a hundred times his own strength, but by allowing him, for example, to disintegrate the hostile group by fighting against one of the individuals who compose it, instead of suffering their undivided action in separation). Addition, therefore, instead of being a mere inert summation of the units, becomes a synthetic act for everyone: everyone joins the group in order to be more numerous and hence the increase of + +the group becomes everyone's practice. + +The other question can now be answered directly: free totalising praxis allows itself to be conditioned in reality and in practice by the totalisation it has just brought about. Its dialectical rationality has revealed the threat to it, in totalisation, as the negative unity of the group and of itself as totalised by the enemy; again, its dialectical rationality, by transforming the passive totality of the future victims of the repression into the active totalisation of resistance, has, in and through the group, appropriated a practical structure of interiorised multiplicity. In and by his praxis, the third party affirms in the group the lack of distinction between the individual and the common action. Earlier we said that the series was nowhere, that it is always elsewhere; the group, in contrast, is always here and in so far as we know it to be elsewhere too, it constitutes this elsewhere as the same here. This is how its circularity is to be understood. The circularity of the series is a circularity of flight; it destructures every here-and-now by disqualifying it through the Others here-and-now. The circularity of the group comes from everywhere into this here-and-now so as to constitute it as the same everywhere, and, at the same time, as free, real activity. My praxis is in itself the praxis of the group totalised here by me in so far as every other myself totalises it in another here, which is the same, in the course of the development of its free ubiquity. Here there appears the first 'us', which is practical but not substantial, as the free ubiquity of the me as an interiorised multiplicity. It is not that I am myself in the Other: it is that inpraxis there is no Other, there are only + +(actualised by some designation but already materially present in the structure of the common environment), but by the time the other third parties realise that the little wall is a possible shelter, they are already regrouping behind it. The sovereign third party who freely designates is no different - precisely because he is everyone's own freedom - from a mere sign-post bearing a practico-inert message (signification) which is to be transcended by praxis. To say: 'Let's shelter behind this wall' is to make oneself a free meaning freely transcended everywhere including here, since for the third party who points + +it out, indicating it and running are the same thing. + +We should notice here that, in a case of panic, the mere fact of the Other's running reveals my action to me in the milieu of the Other, and that running to hide behind the wall emerges as a contagious propagation. In any case, in so far as the group is in the process of constituting itself by liquidating seriality in all, where seriality does remain it may help the common action by caricaturing it, simply by local panics. The basic difference between serial activity, which though counter-finalised and passive -.does have its teleological reason, and group praxis, in this case and wherever it occurs, is not the freedom of individual praxis, since contagious panic, as much as a deliberate attack, realises itself through everyone's praxis; it is that in the first case, freedom posits itself only to reveal its alienation in the passive activity of impotence (I discover myself in the Other as hunted, and the alienation culminates by transforming itself and passing from the discovery of necessity to the submission by the other to the reign of necessity), while in the second case, in the group in the process of constitution, the leader is always me, there are no others, I am sovereign and 1 discover in my own praxis the orders which come from the other third parties. When demonstrators are questioned about the origin of this or that common praxis (either when their ae:tion was 'wild' or, quite simply, when it took place on a local scale and without being foreseen), they often cannot decide whether someone (that is to say, anyone) gave a practical sign to direct the common activity or whether, as they all say, in fact: 'We did this because it was the obvious thing to do, because there was nothing else to be done', etc. They have especially if they are questioned in a trial, by hostile judges - a clear, active awareness of their solidarity with a'V' of the demonstrators: if someone actually did shout, attack or fire first, etc., they will not give his name or, if someone has been caught in the act and is shown to them, they will say (and this is an active praxis of a militant group) + +that they do riot know, that they are all responsible. Thus, at this first stage, there is no leader, or, in other words, the situation may hy accident be such that a single third party designates, signifies and adumbrates the initial action; but after that for one reason or another, and in any case because of the circumstances of the struggle, there was no longer any common signification, the developments of the skirmish forced every individual or small group to adapt to the praxis of the enemy without being able to co-ordinate with the other parts of the original group - but with each individual still fighting as the free + +totalisation in action of the demonstration. + +But it is remarkable, too, that when he is questioned, the demonstrator does not relate to the group, either as to a transcendent (transcendante) synthesis or as to a single quality in everyone's action. Whether he is responding in a hostile way to the representatives of an oppressive government or establishing the facts for themselves, he will interpret the action as a free development, the objectives and means as free, practical certainties (evidences). And this means that he presents the situation as revealing itself to praxis as it does in simple, individual activity. Quite simply, the accounts (and the emergence of the dangers which themselves designated their demonstrations, or of objectives which produced their risks and their finality, as each individual describes them to us in his evidence) necessarily presuppose that every participant was the same praxis as the totalisation here of the free, common development by and through the free totalisation of the practical field by an individual praxis. Thus, in contrast to the rout as seriality, this flight - which already projects itself obscurely as a means of regroupment - has everyone as its sovereign agent here in so far as it is common; and everyone produces the common meanings (significations) which come to him from everywhere either as certainties, by transcending them, or as free choices of means and ends. Of course, in the fight itself, the offensive or defensive activity may involve certain beginnings of differentiation which constitute a structure of alterity (some - others). But since this alterity is a means (some people are to attack the soldiers or police from the street behind, while others charge them head on), it is produced in the free development of praxis as invention. For everyone, of course, this involves reinteriorising a given (in fact this 'given' will turn out to be simply the earlier statute of seriality). But, for precisely this reason, he is subordinated to the ,common unity of the praxis and every 'same' hecomes other, both here and over there, in so far as he is the same everywhere (that is to say, in + +so far as the elementary, spontaneous organisation is half-produced by, and half-imposed on, every third party by objective circumstances and by the tactics of the enemy) . Similarly, the interiorised numher remains a quantity; but in so far as it conditions (as a means) the development of action, this quantity without parts presents itself in everyone as an intensity, that is to say, as the same degree of power (in all third parties) against the enemy. In this sense, the relation to the neighbour is both interchangeability :;I.TId unicity (of me and him) as the absolute presence of the entire praxis everywhere: everyone is a hundredth in so far as + +everyone freely hecomes a hundred. + +In the methodologically simplest case (that of victory; for example, the taking of the Bastille), the unity of the result (as in individual praxis) becomes the objective reality of the group, that is to say its being, in so far as it can produce itself only in inert materiality. It may be objected that the result is not always inert: but this objection is based on regarding the inorganic as a certain statute which defines a particular kind of materiality, rather than, as would be correct, as a condition which, in particular circumstances, may characterise any kind of material entity. If, for example, the prisoners taken by the crowd, on 14 July, are a material and inorganic result of the common action, this is because they represent the objectification of the people's victory as the destruction of an organised fighting group and as its replacement by a multiplicity of impotence (by re-exteriorised quantity as the only possible relation amongst the prisoners). It goes without saying, of course, that the result - as a group objectified in its practice - is in itself capable of being alienated. This problem must be studied quite closely and we shall return to it. But this alienation - even if it is a new encounter with necessity - does not necessarily appear in the moment of victory; it may continue only much later, through thousands of different circumstances and practices. Indeed, in this respect, collective practice resembles individual practice: everyone can, now or later, discover his alienation as necessity, dependent on activities and circumstances. However, as we have seen, this alienation shows through in every moment of daily life, in that, for example, every attempt by the exploited to escape their condition individually inflexibly confirms their class-being in objectivity. The action of the group is necessarily new in so far as the group is a new reality and its + +The people have taken the Bastille. This public fact cannot be interpreted in the same way as the significations which it has just over- + +thrown. This is why alienation - if it occurs - generally reveals itself much later and through confrontations. Thus the moment of victory presents itself to the victorious group - except in exceptional circumstances - as the pure objectification of freedom as praxis; and its character of irreducible novelty reflects for the group the novelty of its unity. And no doubt everyone sees the objectification as the result of his free praxis, in so far as it is the whole developing here through free individual action; but it is striking that this perception by everyone of total objectivity occurs in the milieu of third parties, as common behaviour. It is the constant procession of Parisians in the passages, halls and staircases of the Bastille which is the real actualisation of the people's victory. For isolated individuals (such as an armed bourgeois on guard at night) the common objectification has now become simply an abstract signification an"d their exultation - if they experience it in isolation - is a spiritual exercise rather than a way of living victory. (Besides - as we know from contemporary accounts - the dominant feeling amongst the bourgeois guards was fear. Absorbed by a worked thing which was too large for them, the common action transcended and crushed them, and manifested itself - wrongly - with its counterfinalities, and perhaps even, in an illusory way, as alienation. In the absence of all, it became the Other Action (l' Acte Autre), which might lead to catastrophes, merciless repression, etc.) In short, as long as the victory was still alive, the total object appeared to everyone only through a total practice, that is to say, in so far as everyone was with everyone else and realised here the actual presence of this totality. Thus its inorganic materiality, as the first alteration of the objective praxis, remained temporarily concealed: in so far as every visitor to the captured Bastille interiorised the multiplicity in his 'public visit' the synthetic unity of the object as a practical organisation revealed itself and the plurality of inertia was itself subjected, in this ohject, to unity. The unity of a group had, to some extent, come to the gathering from the hostile object which designated it as the unity of a process of annihilation (in so far as a group praxis actualised this threat). At present, the common action of everyone in the milieu of all expresses the victory by producing the total unity of the enemy object, and reduced to impotence. What, from a certain point of view, is already no more than a historic chateau, a ruin, produces itself through the group as hostility + +crushed and bound, but still dangerous. + +In short, the multiplicity of syntheses cannot be defined in the practical group (or the fused group) as the inert co-existence of + +identical processes, connected by mere relations of exteriority. Nor can it be described as a serial link of alterity uniting the syntheses as others. Yet it does exist, since everyone acts and develops his actions on the basis of circumstances which condition him. It is also true that there is no synthetic unity of the multiplicity of totalisations, in the sense of a hypersynthesis which would become, in transcendence (la transcendance), a synthesis of syntheses. What actually happens is that the unity of the all is, within each actual synthesis, its bond of reciprocal interiori ty with any other synthesis of the same group, in so far as it is also the interiority of this other synthesis. In short, unity is the unification from within of the plurality of totalisations, it is from within that it negates this plurality as the co-existence of distinct actions and affirms the existence of the collective activity as unified (unique). From within: from the inside of each synthesis in so far as it affirms itself here, in freedom, as the developing totalisation and constitutes all the others, through practice, as itself( either by positing itself as regulatory, or by accepting its rule from some third party, that is to say, by produc- + +ing it freely here as the same and unified). + +On the other hand, the interiorisation of practical unity involves, as we have seen, that of the multiplicity which becomes the means of the common action, and, therefore, the means of unification from the point of view of total objectification. This reinteriorisation of multiplicity, as a transition from discontinuous quantity to intensity, results in the dissolution of numher as a relation of exteriority between discrete elements (between individual totalisations). Being a hundred, heing a thousand, as much for the group as in the eyes of the enemy himself (,There are too many of them, we'd better leave them alone,' etc.), is a possibility of counting or being counted which immediately reverts to being a free unity-means. Thus, in so far as it reabsorbs number, the group is a non-quantifiable multiplicity. This does not mean that its quantity is eliminated as inorganic materiality; it means that its quantity must be conceived in it as instrumentality. And, of course, this also applies to the characteristics of masses (weight, etc.), in so far as, in the elementary fight we are considering, they are all interiorised and controlled exteriority. Here, the inorganic characteristics of the group are means of acting in the practico-inert field, just as the practical organism in its individual action acts as a source for transforming energy in the physico-chemical field of exteriority (that is to say, in so far as it uses and controls its being-in-exteriority as an inorganic + +.structure transcended and preserved �y organic structures). + +Now it is clear that the intelligibility of this new (and possibly unexpected) structure, that is to say, of unity as ubiquity within each and every synthesis, depends entirely on the two following characteristics : this ubiquity is practical: it is not that of a being or of a state, but that of a developing action; and it can be conceived only as the ubiquity of freedom positing itself as such. I have already stressed the first characteristic: if the problem were to place the unity of the group in its substance, everything we have just said would be pure logomachy or sophistry, for the substantial unity of a totality exists in every part only in so far as the whole is distinct from each part and produces itself as a transcendent (transcend ante) totalisation of them all. But we are dealing with a praxis, and we must realise that here, in contrast, all the synthetic determinations we have described really create the common action in so far as each of them makes it exist both in itself and everywhere (for example, the order which springs from any mouth and which is executed by a hundred arms is a real process of totalisation). Besides, the substantial being of such a common action lies outside it and in the future, in the common objective (which is the first designation of the group by the enemy in so far as the group constitutes itself as the negation of this negation); and it objectifies itself as common by the common realisation of the objective which itself and by itself (outside it) has already constituted itself as common. For example, the flight of the adversary is common in itself (and not only as produced by the common effort), in so far as the common practice of the enemy appears as turned back but still common. Even the prisoners, as the destruction of a threatening unity which has been reduced to passive multiplicity, have meaning only by reference to a previous meaning (to the negative common praxis which has been destroyed). But the essential characteristic of the fused group is the sudden resurrection of freedom. Not that freedom ever ceased to be the very condition of acts and the mask which conceals alienation, but we have seen how, in the practico-inert field, it became the mode in which alienated man has to live his servitude in perpetuity and, finally, his only way of discovering the necessity of his alienations and impotences. The explosion of revolt, as the liquidation of the collective, does not have its direct sources either in alienation revealed by freedom, or in freedom suffered as impotence; there has to be a conjunction of historical circumstances, + +a definite change in the situation, the danger of death, violence. + +The silk-weavers of Lyon did not unite against alienation and exploitation: they fought in order to prevent the constant lowering of + +wages, that is to say, basically, for the restoration of the status quo. (But of course, their very practice prevented this restoration in any case. After the revolt, society was no longer the same, the pre-history of the French proletariat had given way to its history.) But against the common danger, freedom frees itself from alienation and affirms itself as common efficacity. Now, it is precisely this characteristic of freedom which produces in each third party the perception of the Other (the former Other) as the same: freedom is both my individuality and my ubiquity. In the Other, who acts with me, my freedom is recognisable only as the same, that is to say, as individuality and ubiquity. It is freedom, therefore, as the dialectical structure of action, which prevents the third party from letting himself be determined by the third parties as Others: in fact, in our example of running away and regrouping, freedom dissolved alterity by positing itself, simultaneously, as a first synthesis, in the third party and in everyone, and as a transformation of passive activity into freely directed action for a common objective. And the totality as praxis came to "V' freedom through the totalisation of all (that is to say, through the transformation of the gathering into a group unified by action). Thus, through the presence of the free actions of which it made itself regulatory, my own action took on a dimension of interiorised multiplicity. But if this interiorisation of the inorganic did not reintroduce alterity into the agent in the form of an inertia of the totality, or of an infinitesimal distance between the practical totality and the individual praxis, this was just because the interiorisation was only an instrument chosen by my free action in so far as it was chosen every- + +where by the free praxis of all. + +Thus the common praxis, as the totalisation and struggle against a common praxis of the enemy, realises itself in everyone as the new, free efficacity of his praxis, as the free intensification of his effort; every freedom creates itself laterally as the totalisation of all freedoms, and totalisation comes to it through the others as a lateral dimension of its individuality, in so far as it is freely individual for them. This has nothing to do with the radical transformation of freedom as individual praxis, since the statute of this freedom is to live the very totality of the group as a practical dimension to be realised in and by its individuality. But it is true that there is a new relation between freedoms here, since in every totalisation of the group, the freedoms acknowledge themselves to be the same. This relation, which differs from ternary relations of reciprocity and from third-party relations, is a reciprocal recognition between third parties in so far as it is mediated + +by the developing totalisation of all the reciprocities; and this recognition is neither contemplative nor static: it is simply the means required by a common emergency. It is for this reason that common action, at the elementary level, is not essentially different from individual action, at least in its practical aspects, except in its results, which are obviously greater. A single individual freedom, inflated by a totalised multiplicity, and emerging anywhere, identical, always controls, in a plurality in action, from here, from the centre, wherever it manifests itself, a first use of the multiple and of its strength, a first differentiation of functions. And the unity of this freedom beneath the shifting multiplicity of the syntheses is itself, and fundamentally, the relation between a negative unity of all (totalisation through annihilation by the enemy) and the negation of this negation to the extent that it is occasioned as totalising and that it produces itself freely on this basis. Of course, this theoretical description is never completely . applicable: it is not true that freedom, emerging everywhere and everywhere the same, communicates the common project through everyone to all and through all to everyone. Conflicts occur precisely to the extent that the liquidation of seriality is a temporal process which may be late here and early there; the remnants of alterity represent, for the freedoms themselves, as totalising, a threat of seriality. The group must act on itself in order to hasten these liquidations: we shall come back to such common, internal action. Moreover, we have supposed for convenience that the individuals who compose it are homogeneous, or (to put it differently) we have considered them only from the point of view of the threat which hangs over them. In fact, each comes to the group with apassive character (that is to say, with a complex conditioning which individualises him in his materiality); and this passivity - in which we should include biological as well as social determinations contributes to the creation, even apart from seriality, of a hysteresis which is capable of occasioning a new series. For these and other reasons, the theoretical schema which I have sketched does not apply in reality: there are procrastinators, oppositionists, orders and counterorders, conflicts, temporary leaders who are quickly re-absorbed and replaced by other leaders. But the essential point remains, through this l�{e of the fused group (which is in fact only its struggle against death through passivisation): namely, if the group is really to constitute itself by an effective praxis, it will liquidate alterities within it, and it will eliminate procrastinators and oppositionists. This means that the common freedom will create itself in everyone against them until in the + +end the orders which circulate really are the orders which everyone gives himself in himself and in all, until the homogeneity of anger, courage, and the determination to fight to the end, manifesting itself everywhere, reassures every demonstrator, and shows him that the danger of defeat or indecision will no longer create, over there, as an anxiety, the possibility of an Elsewhere and instead constitutes him from everywhere as the practical reality of the group here. This is the heart of the matter: I depend on everyone, but through freedom as practical recognition I am guaranteed against this dependence. They will fight my fight, with my determination; over there is no more than a here; I am no more in danger 'over there' than they are here; I expect nothing from them (alterity), since everyone gives everything both here and 'over there'; thus my own action - even when the conditions of struggle prevent me from seeing them - is regulatory of theirs; it is practical freedom in me which sets its own limits in them; thus in driving my tenacity to the limit, I produce this tenacity everywhere.1s + +16. In fact, aggravating surprises, stampedes, and routs do occur. But for the moment we are discussing the group without taking into account the hostile praxis (if the hostile group decides to throw in all its strength at a particular point, it will break down the homogeneity of the group from the outside). But for the moment, this does not concern us: in effect, the group is not a metaphysical reality, but a definite practical relation of men to an objective and to each other. If certain circumstances of struggle lead to stampede and if this stampede is not followed by regroupment, the group is simply dead, and contagious panic re- + +stores the domination of the practico-inert. + +praxis. It is, in effect, not only a practice of defensive violence against the violence of the enemy but also, as sovereignty, violence against necessity, that is to say, violence against the practico-inert field in so far as it is constituted by Thing-destinies and by enslaved men. Just as, as the investigation has shown, in this field of alteration, necessity is an imperative limit which imposes itself on freedom from within (in so far as it is expropriated by the outside), so the reversal of the practical movement and its reappearance as a negation of necessity constitute themselves as the violent destiny of necessity itself, in so far as it + +produces itself for man through men and things. + +But, at the same time, this violence, always ready to attack any reemergence of inertia within the group, dissolves itself in pure, unanimous sovereignty, in so far as, through the active member of the group, sovereign freedom is always here and now. However, as violence is always going on, whether against an external enemy or against insidious alterity within, the behaviour of a revolutionary, on 14 July as on 10 August, appears contradictory: he not only fights for freedom (that is to say, for the practical realisation of a concrete objective), but also realises sovereign freedom in himself as unity and ubiquity; at the same time, however, he commits violence on the enemy (in fact this is simply counter-violence) and he uses perpetual violence in order to reorganise himself, even going so far as to kill some of his fellow members. But there is not really any contradiction here: this common freedom gets its violence not only from the violent negation which occasioned it, but also from the reign of necessity, which it transcended but preserved in itself, and which constantly threatens to be reborn as a disguised petrification, that is to say, as a collapse into the inertia of the gathering. Freedom as the sovereignty of individual praxis is not violence: it is simply the dialectical reorganisation of the environment. Freedom as alienation unmasked becomes the structure of its own impossibility in the form of necessity; finally, necessity as confined and self-confining freedom in passivity becomes the qualification of the practical negation which transcends it in so far as this practical negation has to destroy a dimension of freedom in it. As ruthless destruction of freedoms buried in practico-inert necessity (and which, as slaves, exhaust themselves in imparting to it its movement of infinite flight), this freedom constitutes itself a priori as violence. The only contradiction between the characteristics which are so often opposed to one another by reactionary writers - Hope and Terror, sovereign Freedom in everyone and Violence against the Other, both outside and inside + +the group - is a dialectical one. And indeed, these are the essential structures of a revolutionary group (not only in its most undifferentiated reality but also, and to an even greater degree, as we shall see, in its most complex forms) . And it will be easy to show that these supposedly incompatible characteristics are indissolubly and synthetically united in every action and declaration of the revolutionary demonstrators. I mention them in passing here in order to show, as I have done in previous chapters for other levels of the investigation, that the practical and ideological determinations of a fused group are a single structure dependent on its morphology and the dialectical laws of its movement. But this definition of the fused group in terms of common praxis does not determine the structural relations which hold between third parties in primary interiority, in so far as the group is a means of common action. We have seen that the ontological relations of the group ' s members cannot be characterised in terms of common membership of a totalised totality. But at this level of our investigation we can in fact define the group as a perpetual reshaping of itself, in accordance with objectives, with exterior exchanges and with internal imbalances. We have still not established anything about History, or whether it is really a totalisation of totalisations. But - apart from the dialectical syntheses which constitute individual action and which totalise the whole of the practical field rather than the organism - fused groups have presented us with the (methodologically) most simple form of totalisation. A group is not (or at least it dries up and ossifies, the more being or inert materiality it contains): it constantly totalises itself and disappears either by fragmentation (dispersal) or by ossification (inertia) . This totalisation does not produce itself - in the simple case I have discussed - through differentiated organs : it occurs everywhere and through everyone; wherever one is, it happens here. So we must now define the relation between individuals (as totalising and totalised, rather than as the presence here of the total praxis). In short, does common activity not condition a heing-in-the-group for everyone? And + +how should this term be interpreted? + +We have already observed that totalising syntheses have two moments : in the first, I produce myself as the third party by effecting the totalisation of the gathering; and indeed, I produce this totalisation in so far as 1 form part of it and in so far as the inertia tends to dissolve in me, along with my bonds of alterity. Yet, as I have pointed out, I cannot effect a real integration of myself into the group. To the extent that I produce the synthetic unity, this unification cannot figure in the + +totality as a unified unity. But this does not in any way mean that the unified individuals are passive objects in the synthesis: the unification is practical and I can recognise my own action in the common action. But the common action, which is free in so far as it is common, this flight, for example, is constituted by my unifying praxis as a grouped fligllt, that is to say, as a unification of the diverse in one praxis; and the movement which reveals this group to me in its action refers me back to the same action, performed by me in the group, and as a member of the group; but at this moment the movement stops and designates me as needing to be integrated in my organic reality into the ensemble which I have just constituted. In short, my integration becomes a task to be done; in so far as I am designated abstractly in my membership of the group (as one of its members) and in so far as I am really unified by my praxis as common praxis here, I become a regulatory third party, that is to say, my action presents itself as the same in the very slight dislocation which derives from the non-realisation of membership; and as it is freedom, this infinitesimal (but impassable) distance produces it as the free reflection here of the common action, that is to say, as the possibility for all of grasping the common action in myself and of consciously regulating it. But, conversely, in so far as every third party does the same and issues some order, he becomes the rule of my freedom in me and therefore really integrates me into the totalisation, which returns to him without closing. Through him, an interiority creates itself as a new type of milieu (a milieu of freedom) and I am in this interiority: if he stands on a chair, or on the podium of a statue, or if he harangues the crowd, then I am inside; and if! in turn climb onto the podium which he chose, I am, again, inside but my interiority is stretched to the limit, and the slightest jolt could make it into an exteriority (for example, if ! make a mistake about the common action, if ! propose to the group an object different from its own). Thus, in the simple case of the fused group, my being-in-the-group is my integration into it through all the regulatory third parties in so far as it is the same free support of a common action within the interiorised multiplicity; and at the same time, or alternatively, it is my belonging to the totalisation which I effect, and which is the same, in so far as I cannot totalise myself. It is this presence-absence, this belonging which is always realised for the Other who is myself but un realisable for me, who am nothing other than him, it is this contradiction, this abstract separation within the concrete which characterises me in the individual tension of my being-in-the-group. Of course, this + +tension exists in everyone as a third party. But we should be quite clear about this: the group is not a reality which exists in itself in spite of the 'transcendence-immanence' tension which characterises the third party in relation to it. On the contrary, the 'transcendence-immanence' of its members creates the possibility of the group as common action. Pure immanence, indeed, would eliminate the practical organism in favour of a hyper-organism. Or, quite simply, if it were possible for everyone to effect his own integration, every action, in so far as it was common, would lose any possibility of or reason for positing itself as a regulatory action and the group would no longer conceive itself in its praxis through innumerable refractions of the same operation. In other words, the action would be blind, or would become inertia. Pure transcendence, however, would shatter the practical community into molecules related only by bonds of exteriority and no one would recognise himself in the action or signal of some atomisecl individual . Altogether, these observations enable us to attempt a critical assessment of rationality (as a rule of understanding) at the level of the group. Common praxis is dialectical, from the most basic level on (that of the fused group) : it totalises the object, pursues some total aim, unifies the practico-inert field and dissolves it in the synthesis of the common practical field. If common praxis is to be a form of rationality, it must be dialectical rationality. And, since it is always intelligible, we are compelled to recognise the existence of this form of rationality. Moreover, it should be noted that in itself it does not display the specific characteristics of the individual dialectic as the free development of a practical organism. Although - as we have seen, and as will soon become clearer - a dialectical relation may insert itself between a common praxis and an individual's praxis, a common praxis is not in itself a mere amplification of the praxis of an individual. As we have seen, the interiorisation of multiplicity is one of its essential characteristics. And the organism is undoubtedly comparable in some ways with interiorised inertia. But, when applied to the organic individual, these words have only a metaphysical and uncertain meaning in relation to its biological being, in so far as it eludes apodictic, dialectical investigation and manifests itself, beyond reach, in the milieu of the transcendental (transcendentale) dialectic. In fact, dialectical investigation shows us the action of the individual as unifying itself in the unifying synthesis and in the transcendence of the practical field , but it neyer reveals it to us as unified. The practical organism is the unifying unity of unification; thus the investigation refers us (as if to its first, most + +abstract intuition, and as if to its limit) to man as the hiological unit on which every praxis is based (and which every immediate praxis realises as a temporalisation towards an end). The interiorisation of multiplicity, however, is a moment of collective action and the group constitutes itself hy it (as by the other factors already mentioned) as the means of the common praxis. In this simple form (the fused group), we are in fact forced to admit that the group is initially a means, in + +which the organism is agent, end and means all at once. + +In our example, the grouping, still in a primitive state, is the invention of everyone in so far as everyone is personally threatened by a danger which presents itself as common. And everyone can invent this new instrument in so far as the practical organism can already totalise multiplicities in a practical field, recognise the praxis of developing common totalisations and create a group as a reinteriorisation and practical inversion of a totalising signification of negation (the praxis of total annihilation). Thus the practical creation of means of defence is a resumption in freedom, as a new relation with men, of an exterior unity, or a dissolution of the serial relation of impotence by the free affirmation (through circumstances) of freedom as a human relation in a new praxis (which comes to the same thing). This does not mean, however, that either the interiorisation of the multiplicity in me, or the affirmation here of my freedom as a recognition of all our freedoms, or totalisation as the constitution of a means for praxis, or the synthetic and common character of the original urgency and of our objectification in the victory, are capable of constituting a new statute of hyperorganic existence, as heing-in-the-group - any more than the specific characteristics of common action (in particular, the utilisation of multiplicity and the differentiation of functions) succeed in making it a hyper-dialectic whose intelligibility lies in its synthetic transcendence + +of individual dialectics. + +We have shown in fact that the unity of the group is immanent in the multiplicity of syntheses, every one of which is an individual praxis, and we have emphasised the fact that this unity has never been that of a created totality, but rather that of a totalisation which is carried on by everyone everywhere. Thus the intelligibility of the group as praxis depends on the intelligibility of individual praxis, in so far as individual praxis is lost and then rediscovered in the practico-inert field. A rupture occurred, as we saw, at the stage of alienation (and not the creation of a new moment of the dialectic) and the groups we have described are a new determination of every praxis, heyond impossibility, in so far as + +depends on the enemy, the place, etc., is, through and for me, the common action; it is so in so far as the activities of Others, by individualising themselves under the pressure of circumstances, help to render mine possible and, to this extent, require it. In a way, each individual holds down part of the hostile forces by his struggle. Mediated reciprocity is the basis for the intelligibility of the differentiation which arises in the context of the struggle and as a response to the hostile praxis. The action of the other third party remains the same as mine (whether what we are combating is a natural scourge or an enemy), beneath a differentiation which produces itself as purely circumstantial, in that the common praxis is defined in and through the regroupment with its common objective, which remains the same in every individual praxis. But in a fused group, a mere means to common security, these differentiations, however advanced they may be, do not survive action. Even if they are free adaptations to enemy action, they are nevertheless originally induced by it. Any spontaneous innovation (such as that of the combatants who try to scale a wall in order to lower the draw-bridge of the Bastille) is - as in individual praxis - a transformation of a practico-inert structure into practical activity; or, to put it differently, it is the practical reading of a possibility inscribed in matter, and which reveals itself (or constitutes itself as a means) on the basis of the total project. Once the total result is achieved, the group can read its unity as a totalitarian synthesis in its ohjectification. Thus it can, in principle, relapse into non-differentiation. IS The differentiation of functions - as a very general structure of which the division of labour is a concrete particularisatiol1 - appears as the statutory reality of the group only in so far as the group itself becomes the object of its + +totalising praxis. + +In particular, whatever the origin of the group may be, the permanence of the dangers may require it to persist between the moments of real activity, as a permanent means of resisting the enemy. I take this example (the enemy have withdrawn, they may attack tomorrow) because it is an extension of those we have just examined : but I must repeat that we are not trying to reconstruct a genesis. The new exigency comes to the group to the extent that the third party reveals it, or in other words, in so far as individual praxis interiorises the + +18. In fact, memory, roles one has played, successes won, etc., create a particular exis for certain individuals as members of the group. And this is already a first + +objective permanence of the common danger in the form of a common exigency. But this new state of the group (which manifests itself historically in every revolutionary situation) is defined by new characteristics, conditioned by new circumstances. The unity of the fused group lay quite simply in real common action, that is to say, in its own undertaking as much as in that of the enemy, and in the violent, dangerous, and sometimes fatal attempt to destroy the common danger. There was nothing ideal about the totalisation of the group: it was done by sweat and blood. It objectified itself in destruction, and perhaps in the slaughter of enemies (for example the summary executions after the taking of the Bastille). At the same time, though constituting itself as a means of acting, the group did not posit itself for itself: it posited the objective and it hecame praxis. If, however, the grouped multiplicity is to survive the realisation of its immediate objectives, the urgency diminishes. Of course, the offensive return of the enemy troops is always possible; in some cases, it is probable, even highly prohahle. Faced with this threat, extending from the possible to the virtually certain, the common watch (the refusal to sleep, or to yield to fatigue), continually being armed, etc. , cannot be regarded as belonging to what I called exis; these are really actions - especially as these actions (whose development we shall examine later) transform themselves into organised and organising behaviour. But the imminence of the danger should not be allowed to conceal its absence from us . This absence of the enemy is not a non-being: it is a relation to the group which fears its return. And this relation - at least as far as we are concerned - manifests itself as practical deconditioning. The differentiations of the group, during the skirmish, its transformations and its real intentions, occurred under the almost unbearable pressure of the enemy group and were determined as negations of this pressure. It is in this sense that they can be called 'adaptive behaviour' : the structure of the fighting group is also that of the enemy taken negatiyely (saisie en creux). In absence, the new differentiations are, of course, determined in close relation to the totality of objective circumstances. Nevertheless, the group determines itself in accordance with a future unification (unification through the return of the enemy) and a past unity (its group-being as transcended past, or, in other words, its practical reality in so far as it has heen, and in so far as it has objectified itself in materiality). This means that it has no way of acting on the enemy, tomorrow or even tonight, other than by immediately acting + +This structure of common action was already implicit in the fusion, since the initial differentiations were, in effect, internal transformations of the group. However, the active and the passive were so closely intertwined that it was often impossible to tell whether the group differentiated itself through its struggle or whether it was differentiated by an enemy manoeuvre. 19 On the other hand, when the enemy does not realise itself as a controlling force, differentiation becomes, within the group, an action of the group on itself. In other words, by becoming its own immediate objective, the group becomes a means of future action. We may speak here of reflection, in the strictly practical sense: the group, waiting for the attack, looks for positions to occupy, divides itself so as to man all of them, distributes weapons, assigns patrol duties to some, and scouting or guard duties to others, establishes communications - even of the crudest sort, a mere warning shout - and in this way, in the free exploitation of places and resources, it constitutes itself for itself as a group. Its objective is indeed a new statute, in which individuals and sub-groups take on various functions in, by and for it, and so intensify its power, and strengthen its unity. It is impossible to deny that it posits itself for itself once it has survived its victory. Or, to put it another way, there is a new structure to be explained : group consciousness as the transcendence by every third party of his heing-in-the-group towards a new integration. We must examine the dialectical problem of unity and differentiation in this light. Are these two practices initially incompatible? Or does one arise as a + +transcendence and strengthening of the other? + +Furthermore, the problem of the sur"i"ing group (for it begins by surviving its original praxis) suddenly becomes connected for us with the problem of heing, that is to say, of permanence. So far we have seen only two sorts of permanence, the first being the inert synthesis of the inorganic, the second, biological integration. Can the group transcend both? Or will it be constructed on the model of one or other of them? From the moment in which the pressure drops, the chances of dispersive massification increase: every third party can see behind him his common action, and can also perceive it ahead of him in a produced object (or in the ruins of a destroyed object); and, as we have seen, this + +19. Or by tactical mistakes: in thoughtlessly attacking one part of the group, without seeing the other elements emerging from other streets, the body of soldiers or police will constitute these new arrivals as encirclers or define them by + +perception of common objectification is a group structure (the crowd visits its conquest, the Bastille). But as the urgency disappears, group behaviour may also be broken. For the common perception of objectification is neither necessary (for every third party) nor urgent: besides, all it does is relate the group's past-being to its present totalising practice as its sole reason. The group comes in order to see itselfin its past victory; that is to say, it takes itself as its own end, first of all implicitly (seeing the Bastille conquered, the fortress finally reduced to impotence) and then explicitly (the lowered draw-bridges, the prisoners, the free movement in the courtyards and halls, all reflecting, in the practico-inert, the action which changed their statute) . To this extent, then, reflexivity comes to the group from its past praxis, in so far as the produced object designates the group to itself as a group - to precisely the extent that this object appears only to an unfolding group praxis. But this object designates it to every third party in a synthetic opposition of two "Statutes : outside, past, inert, inscribed in things, the group is already made of marble and steel; its object-being (the Bastille) is the real preservation of its past-being (practical struggle and victory) in so far as this past being is in itself inertia (transcended being). + +20 + +But in so far as its praxis of disclosure is common, and in so far as the common object refers of itself to this community, the practical link appears as developing disintegration. Indeed, from one point of view, the only reason for the regroupment here is the common object, in so far as it has to be perceived in common. Thus the immense pressures which caused the liquidation of seriality have temporarily disappeared; in this way, the regulatory third party has practically nothing left to regulate: the 'order' no longer has any meaning simply because there is very little left to do apart from reactulising the common objectification. The people may be united to one another by an immense + +20. It would be impossible to devise a theory of individual and group memory here. This problem is central in any study of groups, whatever its purpose. But it lies beyond the range of the present investigation. It should however be observed that the structure of inertia of the past (as transcended being) is not its only determination: it derives a practical structure from the transcendence itself in so far as it preserves it in its movement. It would also be necessary to describe the past as exis both in the practical organism and in the group. Organic exis is itself the object of a transcendence (there is no habit which is not also an adaptation to the present on the basis of the future); the exis of organisation, as we shall see, can be transcended, but need not necessarily be so. In any case, it is sufficient here to note that I consider the group in its relations to a certain structure of the past rather + +collective pride (or any other common conduct), but this is not very relevant: the behaviour of the third party always manifests itself as the same Izere as anywhere else in the group, but it no longer has practical efficacity. Multiplicity remains interiorised (we visit the site of our struggle), but it does not have any real effect. (Though it may have an effect on the group itself: we come in large numbers to inspect our victory, therefore we still hold fast. Or again: we can feel confident, etc. This is an example of what I shall call propaganda as immediacy: a finality without an agent and without a project.) Certain actions can be regarded as true regulations: someone dares to push open a door and go into a dark room; then some other daredevils follow on his heels: but the real aim - such as free access to the conquered Bastille - is not directly connected to these initiatives; even if the door had not been pushed open, the crowd would still have enjoyed its great victory. And even at the time there is no way of telling for certain whether these unnecessary (si peu exigees) actions, which are already dispersing, are totalising and common actions, or whether they are contagious or quasi-serial. In short, the being-of-the-group is the unity of all outside themselves in the produced object and the group praxis is weakened by the very movement by which it tries to appropriate the object. + +Total disintegration (which would mean the disappearance of the common object as such) does not actually ever occur, because everyone is still linked to the object by other practices of appropriation unfolding through other third parties as the same: one person climbs on to the battlements, and another plants a flag. All these slightly differentiated practices run through the common object (like shivers), and so it is revealed to me by them too and therefore appears to me - illusorily - as a still developing objectification of the common action. No matter: this tension within survival expresses for every third party the double danger which threatens the group: being incorporated into a passive synthesis of the practico-inert field (a 'monument to the dead') or dissolving into a new serial gathering. This tension, lived by the third party, is in fact a sudden flash of awareness, to the extent that it reveals the group in danger and that it transcends itself - by revealing itself towards a new end, that is to say, towards the preservation of the group, as a free practical unity, against this double danger. In particular, this aim will appear in urgency, when struggles threaten to begin again, or when a surprise attack is expected. The group becomes the common objective in everyone: its permanence must be secured. But the tension which we have just explained posits a common exigency: + +the permanence of the group cannot be either the loosening of the common bond, threatening to tip the group back into seriality (either suddenly or gradually), or the practico-inert inertia of objectification, which is simply a being-outside-oneself, and which by its very structure contradicts freedom itself as a common violation of necessity.21 In other words, the group as surviyal, between a completed action and an imminence in absence, posits itself for itself as an immediate objective, both from the point of view of its practical structure (differentiation and unity) and from the point of view of its ontological statute. Of course, it is still a mere means; but it is a means to be worked on - in the same way that a tool must be an immediate aim to the extent that + +essential ends depend on its manufacture. + +2The Pledge + +It will be immediately obvious that initially the ontological statute is the most important: in a first moment of the dialectic, in fact, the relation of unity to differentiation depends on permanence. If the existence of the group in itself resists the forces of dissolution, divisions into sub-groups according to the needs of the struggle and of work will not pose any threat to its unity. But in a second moment, as we shall see, unity as praxis will become the very foundation of the + +ontological statute. + +In the first moment, the group, positing itself for itself through the third party and by the reflection of transcendent unity as inertia onto totalisation in interiority as praxis in the process of dispersal, requires a contradictory statute, because the group desires permanence in the form in which it derives it from inertia and from free totalising praxis or, to put it differently, because it desires that totalisation in its very freedom should be subject to the ontological statute of inert synthesis. + +21. This practico-inert being-outside-itself effectively threatens to subject the common action in its objective result to a new alienation: the alienation of the group itself as a group in the alienated world. We shall see that it cannot avoid it. But the spontaneous movement is to ayoid it: simply because it perpetuates itself + +It is the actual conditions of survival which drive it back into this contradiction: the common praxis is freedom itself doing violence to necessity. But if circumstances demand the persistence of the group (as an organ of defence, of vigilance, etc.), while people's hearts are untouched by any urgency or hostile violence, which might occasion common praxis; if its praxis, turning back upon itself, in the form of organisation and differentiation, demands the unity of its members as the pre-existing foundation of all its transformations, then this unity can exist only as an inert synthesis within freedom itself. This moment of the fused group, in which everyone is the same, here, in some exhausting and dangerous action, which itself becomes the universal measure of everyone's action, must perpetuate itself for everyone in separation and in waiting and perhaps in isolation (in the case of a guard, for example); any particular sub-group must be able to retain in itself, in so far as it becomes regulatory, a free but given link with every other third party as regulatory and as totalised. This opaque elsewhere, which congeals around it and isolates it (night, silence, the special dangers of the situation), retains the fundamental structure of a here, despite all the appearances of alterity; in short, the really other action of the sub-group (which is on patrol, while the others are behind the barricades or at the windows of houses) is designated from its very foundation as the same, here and everywhere. But since in fact its alterity is real, this determination of unity can come to it only from the group as a lived permanence which imposes itself through dispersal. This ontological structure of the group therefore involves an inversion. Of course, it is always a means in relation to the final objective (which is complete victory). But in relation to the praxis of differentiated waiting, it has to posit itself as a pre-existing agent. Praxis is the only real unity of the fused group : it is praxis which creates the group, and which maintains it and introduces its first internal changes into it. In the moment of the praxis of organisation and anticipation, it is the group which guarantees that every separate action is a common action or, to put it differently, it is the group as a reality which produces the unity of the common praxis. My courage and endurance, during my lonely watch, will be proportional to the permanence within me of the + +group as a common reality. + +The dialectical exigency which I have just explained reveals itself to everyone, in the moment of survival, as a practical exigency: in fact, to the extent that the distribution of tasks determines itself on the basis of a near future, it entails mistrust of the future; it is in it, as a possibility + +of dispersal, that the dissolving action of separation and of inactive activity first come to be feared. Suspicion appears within the group not as a characteristic of human nature, but as the behaviour appropriate to this contradictory structure of survival: it is simply the interiorisation of the dangers of seriality. (Interiorised multiplicity was really present in everyone as an immediately given power in the earlier skirmish; and this multiplicity remains; it is always instrumentalised, and it is what makes it possible to post guards, patrols and combat groups everywhere. But, at the same time, it passes over to a sta tute which is more concrete, in that it is diversified and structured, but less immediately understood, since it coins itself in isolation. Separation as the rational use of number is an inversion of immediate union, or a mechanical use of quantity. One does indeed turn out to be multiple, but in a situation which appears to have all the characteristics of the isolation of impotence). Besides, the possibility of free secession manifests itself as a structural possibility of every individual praxis; and this possibility reveals itself in every other third party as the same in so far + +as this particular third party, here, reveals it in them. + +Thus the ontological statute of the surviving group appears at first as the practical contrivance of a free, inert permanence of common unity in everyone. When freedom becomes common praxis and grounds the permanence of the group by producing its own inertia through itself and in mediated reciprocity, this new statute is called tlle pledge (Ie serment). It goes without saying that pledges can take very different forms, from the explicit act of swearing an oath (for example, the Tennis Court oath; an oath as the synthetic link between members of a medieval commune) to the implicit assumption of a pledge as the already existing reality of the group (for example, by those who are born into the group and who grow up among its members). In other words, the historical act of making a pledge in common, though it is universal and always corresponds to a surviving group's resistance to the divisive tendency of (spatio-temporal) distance and differentiation, is not the only possible form of the common pledge, in so far as the pledge is a guarantee against the future, inertia produced in immanence and by freedom, and the foundation of all differentiation. If we examine it in its explicit reality as a historical act - for example, the communal bond in the Middle Ages - this is only because this posits itself as such + +A pledge is mediated reciprocity. All its derivative forms - for example a witness's oath in law, an individual swearing on the Bible, + +etc. - derive their meaning from this basic form of pledge. But we must be careful not to confuse this with a social contract. We are not trying to describe the basis of particular societies - which, as we shall see, would be absurd; we are trying to explain the necessary transition from an immediate form of group which is in danger of dissolution to + +another form, which is reflexive but permanent. + +A pledge is a practical device. It cannot be presented as a possibility for the individual, unless it is assumed that the possibility is social and that it appears only on the basis of groups which are already bound by a pledge. As we have seen, the abstract experience of the practical organism, in so far as its praxis is a constituent dialectic, can give us only the translucidity of an action which is defined by its objective and which exhausts itself in its objectification. But, in so far as it is the group itself as praxis, this invention is the negation of some exterior circumstance which defines it negatively (en creux). In other words, it is the affirmation by the third party of the permanence of the group as the negation of its exterior negation. And exterior negation must not be confused with the danger of extermination by the enemy (or by a cataclysm) ; it only involves the possibility that certain tasks involve the re-emergence of the multiplicity of alterity or of exteriority, and this re-emergence does not directly imply the annihilation of the individuals as such. In this sense, the pledge is art inert determination of the future: that is to say, this inertia is above all a negation of dialectic inside the dialectic. Regardless of subsequent developments of praxis, of the event, or of the developing totalisation (up to and including the level of historical totalisation), one element will remain non-dialectical : every member's common membership of the group. The group will enter into new dialectical combinations which will transform it as such, but this will not affect its common unity, that is to say, its interior statute as a group.22 The act of swearing an oath therefore consists in freely presenting the dispersal of the group in the future as an inert impossibility (as a permanent negation of certain possibilities within the field of possibilities) and, conversely, in bringing the future group to the present community as the limit to all possible transcendence. Here again we encounter the dialectical law which we met at the beginning of this investigation: the re-exteriorisation of inorganic inertia is the basis of instrumentality, that is, of the struggle against the + +inertia of matter within the practical field. The group tries to make itself its own tool against the seriality which threatens to dissolve it; it creates a factitious inertia to protect it against the threats of the + +practico-inert. + +The device itself, that is to say, behaviour as immediate praxis, appears in the schema of intelligibility elucidated earlier. There is mediated reciprocity; whether or not it is spoken, the order: 'swear' certainly represents the invention as the regulatory action of the third party in the existing group. But it should be observed that in the milieu of the same, the third party fears dispersive dissolution in the other third party as much as in himself: the possibility of his being isolated may come to him from the third party, but only to the extent that it can come to the third party from him, or even, to the extent that it can come to him through himself. This negative possibility is therefore in everyone and here the same, and the reverse of the praxis of the fused group as uhiquity. And it is the possibility in everyone of becoming other through the other third party, and for him, through himself and for himself. Thus, in the order: 'Let us swear', he claims an objective guarantee from the other third party that he will never become Other : whoever gives me this guarantee therehy protects me, as far as he is concerned, from the danger that Being-Other may come to me from the Other. But equally, if he were to swear alone (or if everyone swore except me), then I alone would thereby take responsibility for bringing alterity to the group. But in fact the act of making a pledge cannot be anything but common: the order is 'Let us swear'. This means that I also make myself, both in and for him, a guarantee that alterity cannot come to him through me (either directly, as would happen if! were to abandon him in the middle of a joint action on behalf of the group, or through the mediation of all, as would happen if, within the majority, I + +abandoned the struggle with them and fled or surrendered). + +This reciprocity is mediated: I give my pledge to all the third parties, as forming the group of which I am a member, and it is the group which enables everyone to guarantee the statute of permanence to everyone. A given third party can pledge the permanence of the group against alterity only in so far as this permanence depends on him, that is to say, in so far as the other third parties have assured him, on their account, of future unchangingness. For how could he guarantee that he will never be the Other, if he does not begin with the assurance that alterity will not come to him from outside and in spite of him (or unknown to him)? Indeed, it is characteristic of alterity to come to + +everyone through the Other. Thus my pledge to the third party receives at its source a dimension of commwzity; it comes to touch everyone directly and through all. This common action of the third party realises itself as an objective structure of interiority and characterises the group as such. The pledge is not a subjective or merely verbal determination: it is a real modification of the group by my regulatory action. The inert negation of certain future possibilities is my bond of interiority with the sworn group to which I belong, in the sense that for everyone the same negation is conditioned by mine, in so far as it is his behaviour. Of course, it must be added that my own behaviour is itself conditioned by everyone else's. But this is not the most important point to emphasise: what appears at first, indeed, is that the guarantee of permanence provided by the oath of the Others produces itself in me as the objective impossibility (in interiority) that alterity should come to me from outside; but, at the same time, it is the possibility that I should make myself Other (by betraying, fleeing, etc.) which is underlined as a possible future coming from me to the Others. Now, this possibility may realise itself in the free development of my action: I may freely decide to abandon my post or to go over to the enemy. It goes without saying that the word 'freely' - here and elsewhere in this work - refers to the dialectical development of an individual praxis, born of need and transcending material conditions towards a definite objective. Betrayal and desertion, brought about by fear and suffering, are, therefore, from this point of view, free praxes in that they are organised behaviour in response to exterior threats. It is also clear that the fear of being afraid for example, of letting the side down, of being the one through whom the group changes through panic into an inert mass - may be important for an inexperienced young combatant. He is afraid of this fear as an irresistible impulse and, at the same time, he rejects it as a free preference for his own safety over that of all. In this sense, my pledge becomes my surety for myself in that it is me offering myself, in every third party, as everyone's guarantee of not relapsing, in my person or through my conduct, into serial alterity. Thus, in making a pledge, the first movement is to swear so as to make the Others swear, through mediated reciprocity, that is to say, so as to guarantee oneself against the possibility that they will disperse. The second moment of the operation is to swear in order to protect oneself against oneself in the Others. It should also be noted that the second moment cannot be that of the totalising action of a regulatory third party: when I make a pledge, in fact, or when I swear or perform some equivalent act, I + +form of unpredictability (that is to say, the opposite form from that of the pledge: if circumstances were to change in some way or other I would be unable to predict sincerely what I would do), since praxis is the transcendence of conditions, it is adaptation to transformations of the practical field. This does not mean, of course, that we are uncertain, that we lack basic projects, acquired structures of predictables: quite + +the reverse. + +But even if these conditions, transcended and preserved by freedom, did enable us to predict everything (as with an agent who is completely contained within the practico-inert field), they are exactly the opposite of a pledge: through a pledge, freedom gives itself a practical certainty for cases in which (because circumstances vary) future behaviour is unpredictable. This is possible only in so far as freedom is other for itself - that is to say, in so far as it is no longer simply the transparency of an urgent adaptation to the exigencies of need and to the dangers of the field. And this alterity can come to freedom only from the Other. If, however, we do not relapse (at least not yet) into seriality, this is because the Other is being regarded here in his practice, that is to say, as power and as freedom; and this activity affects me as a hardening against the world of impotence and seriality. In short, the third party remains the same for me (he freely does what I do, when I do it: his pledge, like mine, is regulatory in mediated reciprocity); but through the practical activity of the third party, in so for as it is tile same, I come back to myself as the unshakable common condition of his possibility. The deep reason for this completely formal, negative alterity is that the group takes itself as its own objective. Thus every action of every third party must have every other third party (and all) as its objective, and as its means and agent (in so far as he takes it up or transcends it and organises it for Others); and, instead of transcending itself towards the object, every action turns out to be in an object which manifests itself as homogeneous. Thus, by appearing as an aim and revealing itself as a common praxis which has to be sustained, the group reveals every praxis, in formalism (if not in inaction, since there is such a thing as an activity of surviving communities), as the condition and means of every Other, in so far as this Other is the same. In practical reflection, everyone returns to himself in so far as he positively conditions the free action of every third party by negatively limiting his own. But the project of limitation returns to him (through a freedom which makes a pledge) as an exigency in him for everyone's freedom, that is to say, both as his freedom as an Other and as the freedom of the Others. The + +moment of making the pledge is - in spite of the words that are spoken - only a project which announces itself with an urgency and affirmative force which are conditioned by the real organism, by need, by danger, etc.; or rather it would be, if it could be separated, for one individual, from the common pledge. But if this moment is, also, that of all the pledges returning upon mine, I become in everyone the transcended condition of free praxis (sure of myself and of the Others, no one need concern himself with anything outside his specialised task) and, in so far as this free common praxis returns to me as a condition of my own freedom (I, too, must rely on them in performing my task, either on my own or in a sub-group), it constitutes the untranscendability of + +being-in-the-group as an exigency. + +EXigency, as we saw in our discussion of the practico-inert, is a claim made on some praxis by an inorganic materiality (and, of course, through some oilier praxis). Exigency, in this context, has the same characteristics, but it is the agents themselves that are inorganic inertia. To the extent that the permanence of my membership of the group is my own free project, this permanence is for my action an objective situated in the future, and coming to me on the basis of future dangers. But this project of itself makes a claim on every member of the group, in that it can be carried out for and by everyone only in and through the permanence of the group, everywhere. In so far as the same project becomes, through my free pledge, a complete response, deliberately given by me, to this claim in the third party, it returns to me through the third party: as faith sworn to the Other - and in the Other - it is, therefore, a limitation on my freedom. Now this limitation conditions the possibility of his free pledge, that is to say, of that free limitation which I need in order to be free. Thus my project returns to me as its own negative, inert condition: for me to be able to rely on the group in separation, everyone must be able to rely upon me; I can claim that they will sustain the limitation of their own possibilities (of betraying, of disbanding, of slackening their activity, their work, etc.) as an impossibility of changing only if! yield to their claim on my freedom, for example, as the necessary condition of the calm with which they will carry out a dangerous task, certain that everyone everywhere is doing everything to guarantee their maximum security. Yes, in this dangerous mission which may save us, or save me in the totality, I exist in everyone as his trust and courage, that is to say, as the immutability of all the Others; through every concrete action performed elsewhere, the future negative therefore appears in my action as my exigency upon + +the order 'Let us swear' - that is to say, in the common decision to swear. At the moment of the decision, the pledge still lies in the future, but its signification - as an immediate objective of the group and as a means of maintaining the permanence required by certain more distant objectives - presents it to everyone as a common operation, or, in other words, as the group acting on itself through every memoer. Thus even if the pledge of one third party is given before that of others (for example, in the serial order of signing), it can never fail: it temporalises itself in an already limited temporality which contains in advance the pledges of all. In a sense, to say 'Let us swear' is to swear: the possibility of a disagreement about this is in fact normally purely formal. If the pledge is recreated, this is because objective circumstances already constitute it as the group's only reflexive means of preserving its unity. It should be defined as everyone's freedom guaranteeing the security of all so that this security can return to everyone as his other-freedom so as to ground his free, practical membership of the group as an untranscendable exigency. Indeed, after the pledge, as before, the third party makes himself a member of the group through his common praxis, and therefore in freedom: this means that his very action develops in dialectical freedom, either within a sub-group or as the common praxis of an isolated individual. The pledge is simply the coincidence, at the source of his practice, of the security of the absent third parties (which he guarantees) and of his own security (guaranteed by the third parties). Exigency and un transcend able permanence as an inert negation of possibilities reveal themselves under the influence of definite conditions (actions of the enemy, for example, such as terror, torture, + +or separate offers to negotiate, etc.) . + +.3 Fraternity and Fear + +At this level of description, it is at last possible to pose the question of intelligibility. In fact, we shall discover the intelligibility proper to the pledge if we can solve two problems. First, since the pledge comes to the surviving group through third parties and in mediated reciprocity, our investigation must grasp the dialectical continuity (that is to say, the free development) which always constitutes the re-creation of sworn faith. In other words, the individual project and the common + +praxis of the fused group are comprehensible realities; our investigation must establish whether the re-creation of the pledge is a dialectical process, capable of being understood on the basis of concrete circumstances. Secondly, the structures of the common pledge, as elucidated here, at first appear to have a sort of abstract ideality: the reason for this is that the pledge as an action of the group on itself does not at first appear as a modification by the effort (by work and combat) of the material statute of the group, but as an immobile contraction of its bonds. Of course, language is materiality, action is effort. But neither the repetition of orders by a hundred mouths, nor the raising of hands, can be compared with the exhausting work of construction or of combat. In our descriptions of the fused group, meanings (significations) corresponded to the creation of a common praxis both as a real consumption of energy and as a directed modification of the environment. Thus the group really constructed itself as a whole produced by work, through sweat and toil, to precisely the extent that its common effort inscribed it in Being. Compared with this enormous dialectical event, which can also be seen simply in terms of energy transformations, the moment of the pledge appears as a moment of ideality. Moreover, the unity of the fused group derived its materiality from the intolerable pressure of the enemy group; it was the interiorisation and inversion of this pressure (of this totalising destruction). The unity of the pledged group, by way of contrast, in so far as it comes from it alone and from a possible but not yet actual attack, seems to be a mere play of signs and meanings; nothing material really unites me to the third parties. And if the pledge were simply a reciprocal determination of discourse, it would not explain the adhesive force which causes me, while isolated and under enemy pressure, to have the feeling of being a member of the group. In the case of differentiated dispersal, in fact, the action of the enemy tends (directly or indirectly, and whether deliberately or not) to accentuate isolation (in contrast to what happens in a fused group). In the face of death or torture, common interest is in danger of giving way to immediate necessity (avoidance of death or pain): it would be almost impossible to believe that the operation described above could, on its own, constitute the untranscendability of the group in these + +circumstances as an irresistible force of inertia. + +These two problems are really identical; we will solve them together and through each other. For, though we have described the internal structures of the pledged group, we have not grasped the true, immediate meaning of the pledge as freely re-created by the third party. + +The origin of the pledge, in effect, is fear (both of the third party and of myself). The common object exists; indeed it is common interest in so far as it negates a community of destiny. But a reduction of enemy pressure while the threat persists, entails the unveiling of a new danger for everyone: that of the gradual disappearance of the common interest and the reappearance of individual antagonisms or of serial impotence. This reflexive fear is born of a real contradiction: the danger still exists (it may even be objectively more serious - the enemy may have obtained reinforcements), but it becomes distant, and moves to the level of signification, and does not arouse enough fear. Reflexive fear, for the third party, is horn when no one - not even him - is sufficiently afraid. The change of state which characterises the surviving group is its very vulnerability: assuming it does not disintegrate, there is no guarantee that attack would give it back its statute as a fused group. Reflexive fear is lived entirely in the concrete, through real facts: one man being exhausted, another wounded, and a third asleep, myself having an argument with a fourth, and so on. And the transcendence of this developing dissolution by the third party can occur only through the negation of the circumstances which condition it, that is to say, by the + +negation of the absence of fear. + +The fundamental re-creation, within the pledge, is the project of substituting a real fear, produced by the group itself, for the retreating external fear, whose very distance is deceptive. And we have already encountered this fear as a free product of the group, and as a coercive action of freedom against serial dissolution; we have seen it appear momentarily during the action itself; and it is called Terror. Terror, we said, is common freedom violating necessity, in so far as necessity exists only through the alienation of some freedom. Through the third party who reveals the group as threatened by death in his own person and in that of the Others, transcendence reaffirms the group as a threat of immediate death for any praxis which tried to become individual again and relapse into seriality. The group as action upon itself, at the level of survival, can only be coercive. The regulatory third party reveals that the diminishing fear of danger is the real threat, and that it must be counteracted by an increasing fear of destroying the group itself. The aim is the same: to protect the common interest. But, in the absence of any material pressure, the group must produce itself as a pressure on its members. And this re-creation is in no way idealist, for it presents itself concretely as a set of real means (accepted for everyone by all) of establishing in the group a reign of absolute violence over its + +members. It does not matter much whether statutes are laid down, and organs of supervision and policing created (as in some developed groups) or whether the pledge simply gives everyone, as a member of the group, the right of life and death over everyone, either as an individual or as a member of a series. The essential point is that the transformation lies in the risk of death which, as a possible agent of dispersal, everyone runs within the group. On the other hand, this violence is free: for present purposes, it is irrelevant that, historically and in particular circumstances, some elements of the community may have usurped it for their own advantage: we shall return to this point. What matters is that no usurpation of violence (or conquest of power) can be intelligible unless violence is initially a particular, real, practical bond between freedoms within common action - in other words, unless this violence is the kind of action on itself of the pledged group, in so far as this action is re-created, carried out and accepted by all. But this is precisely what a pledge is: namely the common production, through mediated reciprocity, of a statute of violence; once the pledge has been made, in fact, the group has to guarantee everyone's freedom against necessity, even at the cost of his life and in the name of freely sworn faith. Everyone's freedom demands the violence of all against it and against that of any third party as its defence against itself (as a free power of secession and alienation). To swear is to say, as a common individual: you must kill me if I secede. And this demand has no other aim than to install Terror within myself as a free defence against the fear of the enemy (at the same time as reassuring me about the third party who will be confirmed by the same Terror). At this level, the pledge becomes a material operation. The first moment, 'Let us swear', corresponds to the practical transformation of the common statute: the common freedom constitutes itself as Terror. The second moment - the successive or simultaneous giving of pledges - is a materialisation of Terror, its embodiment in a material object (swearing on the sword; signing the text of the common pledge or creating organs of coercion). Thus the intelligibility of the pledge derives from the fact that it is a rediscovery and an affirmation of violence as a diffuse structure of the fused group and that it transforms it reflexively into a statutory structure of common relations. In fact, to precisely the extent that the relations of the third parties are mediated, that is to say, to the extent that they pass through all, the character of violence cannot be detected in them: they are the free common relations of members of the group as such. But as soon as the danger of disintegration .appears, + +is betrayed, divine sanctions in no way prevent the group from e..'{ecuting the traitor: the right of life and death - however linked to the + +transcendent - is the very statute of the group. + +A free attempt to substitute the fear of all for the fear of oneself and of the Other in and through everyone, in so far as it suddenly reactualises violence as the intelligible transcendence of individual alienation by common freedom: that is what pledges are. They are completely intelligible because they are the free transcendence of already given elements towards an already posited objective in so far as this transcendence is conditioned by concrete circumstances which prefigure it negatively (en creux) (a destiny to be negated). But the structUl,"es of freedom and reciprocity which we examined at the beginning, far from disappearing, take on their full meaning when they manifest themselves in the practical material movement of terror. It is still true that my pledge is a guarantee for the other third party; but the meaning of this guarantee is precisely violence. The third party is guaranteed against my free betrayal by the right which I have granted everyone (including him) to eliminate me in the event of my failure, and by the Terror which the common right establishes within me and which I have demanded; and this guarantee - which deprives him of any excuse in the event of dispersal or betrayal - means that he can freely guarantee + +his own solidarity (freely demand Terror for himself). + +Thus I encounter Terror within myself as exigency. In other words, the fundamental statute of the pledged group is Terror; but, if circumstances are not specially restrictive, I can remain at the level of exigency and untranscendability. For the pledge is a free relation of free commitments. At this level, I perceive the exigency only as my committed freedom in the other and as the exigency of myself towards the Other. If the pressure increases, the same relation reveals itself in its fundamental structure: I have freely consented to the liquidation of my person as free constituent praxis, and this free consent returns to me as the free primacy of the Other's freedom over my own, that is to say, as the right of the group over my praxis. Here again, it does not matter whether this right is conceived as a duty towards the group (that is to say, concretely as an imperative negation of a possibility: this obviously has nothing to do with morals or even with codes) or whether it is conceived as a power of the group, consented to by me, of taking my life if I do not act in accordance with a given directive. For us, and in this moment of our investigation, this makes no difference: these different forms of behaviour are in fact conditioned by circumstances and they + +constitute themselves in their situation. The important point is that within itself, and implicitly, the concrete duty contains death as a possible destiny for me; or, conversely, that the right of the group + +determines me, in so far as it is agreed. + +This statute of the pledged group is, in any case, crucial: indeed, it might be said that our dialectical investigation has led us to elucidate the original practical, and created (and constantly re-created) relation between active men within an active community. The group as permanence is, in effect, an instrument constructed in concrete circumstances, on the basis of a fused group (or at least, this is how it appears in our dialectical investigation). And this construction, which is common, or effected by every third party as a common individual, can never be reduced to 'natural', 'spontaneous' or 'immediate' relations. It occurs, in effect, when external conditions have occasioned a reflexive praxis within a surviving group : the nature of the danger and of the task implies that the group - in so far as it is threatened with dissolution - posits itself as a means of its praxis and a means to be consolidated. Thus the relations between members of the group establish themselves in a community which is acting on itself; they are pierced by this subjective praxis and conditioned by it. However, we have already seen that the coercive character of the group derives from the fact that it does not have existence (like an organism) or being (like a material totality). At this level, the group, as a reality, is initially no more than the impossibility for everyone of abandoning the common praxis. To put it differently, its being is for everyone a pledge of death as the inert + +negation of any possibility of strictly -individual action. + +This being is, as we have seen, an Other-Being for every free praxis. But still we do not relapse into seriality, since, for each third party, this Other-Being is the same Other-Being as for his neighbour. In this sense, violence is everywhere Terror as the first common statute. But this Terror, as long as unity has not been destroyed by circumstances, is a terror which unites rather than a terror which separates. Indeed, in so far as these men have constituted themselves by their pledges as common individuals, they find their own Terror, in one another, as the same; here and everywhere they live their grounded (that is to say, limited) freedom as their being-in-the-group, and their being-in-thegroup as the being of their freedom. In this sense, Terror is their primary unity in so far as it is the power of freedom over necessity in everyone. In other words, being-in-the-group is, for everyone, an intermediary between free common praxis (for simplicity, we assume tha.t the action + +has not yet begun) and the statute of serial impotence. It is the statutory guarantee, freely demanded, that no one will relapse into the practicoinert field and that individual action, in so far as it becomes common, as such escapes from alienation (even if the total praxis of the group relapses into it). As a reflexive construction, this guarantee is everyone ' s solicitude for everyone, but this solicitude is a bearer of death. But still, it is through this mortal solicitude that man as a common individual is created, in and by everyone (and by himself), as a new entity; and the + +• + +violent negation of certain future possibilities is, for him, indistinguishable from this statute of created novelty. In the pledged group, the fundamental relation between all the third parties is that they created themselves together from the clay of necessity. It is on this basis that their immediate relations of reciprocity established themselves . Everyone recognises violence in the other third party as the agreed impossibility of turning back, of reverting to the statute of sub -humanity23 and as the perpetuation of the violent movement which created him as a common individual. But, of course, this recognition is both practical and concrete. It is concrete because every third party recognises the members of the group not as abstract men (or abstract instances of the genus), but as sworn members of a particular species - a species which is connected with concrete circums tances, with objectives, and with the pledge. It is practical because it is the pledge itself renewing itself through some particular act of reciprocity (he helps me, does me a good turn, etc . ) and presenting itself as its fundamental structure. This is particularly evident in the case of public or clandestine mutual aid groups, but this case is more complex than those we are examining here. And as every pledge is conditioned by that of all, since ultimately it is that of all which provides the basis in everyone, in his inert-being, of the freedom of the common individual, recognition is simultaneously recognition in everyone of his freedom (in a double form: committed freedom and the freedom of free practical development following commitment) through the freedom of the other, and an affirmation of + +membership of the group. + +T otalisation, in this context, is simply the reactualisation of the statute everywhere (that is to say, in everything here and now). It presents itself both as having been performed once and for all and as + +23. I use this term without giving it any definite content and because it seems to me to mark, at every stage, the relation between a group which posits itself for + +having to be constantly reactualised. In the act of constructing the pledge, in fact, an object is created (in the 'historic' moment in which the decision was taken): this material object retains in its materiality the historical pledge as an untranscendable past. The objectification of the fused group (a fortress taken and dismantled, etc.) is not abandoned; on the contrary, it becomes the material realisation of an archaic unity, the moment of common rising. But it is another, earlier mode of reality: the signed agreement and the actual place where the pledge was made appear, at the level of the pledged group, as the group's force oj'inertia, as the perseverance of the being-in-the-group in its. being against internal and external threats. It is the indissoluble reciprocity of significations between, on the one hand, the inorganic materiality of the fact, revealing here and now, on the basis of every future-project (avenir-projet), its present-heing as a constitutive structure, and, on the other, past human fact as the immediate link with the future (the fact of swearing was, in both its immediate and its profound reality, a precaution against the future), but as an untranscendahle link, and so as the eternity oj' presence in the future. The pledged group produces its objectification as a particular material product in it (the written pact, and the very hall in which it was signed, which was formerly a container, become, after dispersal, an interiorised product, a material mediation between the members). But this interior objectivity (which produces itself for everyone as an impossibility of going back beyond a certain past date, as an irreversibility of temporalisation) is not the objectification of the group as heing; it is the eternal, frozen preservation of its rising (of the reflexive, statutory rising through the + +pledge). It is the origin of humanity. 24 + +In becoming for everyone an imperative nature (by virtue of its character as an untranscendable permanence in the future), this beginning therefore directs recognition to the reciprocal affirmation of these two common characteristics: we are the same because we emerged from + +24. Let there be no misunderstanding: I am not talking about those few great revolutionary moments in which contemporaries actually have the feeling of prodUcing, and being subjected to, man as a new reality. Every organisation which has the reciprocity of the pledge is a new beginning, since it is always the victory of man as common freedom over seriality, whatever it may be. In fact, this victory is already won at the level of the fused group, but it is through the pledge that the group posits itself for itself, no longer as the implicit means of a common praxis, both produced and absorbed by it, but as a means of attaining a more or less distant objective, and therefore as its own immediate objective. + +the clay at the same date, through each other and through all the others; and so we are, as it were, an individual species, which has emerged at a particular moment through a sudden mutation; but our specific nature unites us in so far as it is freedom. In other words, our common being is not an identical nature in everyone. On the contrary, it is a mediated reciprocity of conditionings: in approaching a third party, I do not recognise my inert essence as manifested in some other instance; instead I recognise my necessary accomplice in the act which removes us from the soil: my brother, whose existence is not other than mine ap ;:roaches me as my existence and yet depends on mine as mine depends on his (through everyone) in the irreversibility of free agreement. Indeed, everyone lives group-being as a nature: he is 'proud' to belong to it, he becomes the material referent (signifie) of the uniforms of the group (if there are any) - but as the nature offreedom (it is its frightening force of inertia, in so far as it comes to me as exigency). Thus the relations of common individuals within the group are ambivalent links of reciprocity (unless they are governed by the resumption of the struggle and the total objective): he and I are brothers. And this fraternity is not based, as is sometimes stupidly supposed, on physical resemblance expressing some deep identity of natures. If it were, why should not a pea in a can be described as the brother of another pea in the same can? We are brothers in so far as, following the creative act of the pledge, we are our own sons, our common creation. And, as in real families, fraternity is expressed in the group by a set of reciprocal and individual obligations, defined by the whole group on the basis of circumstances and objectives (obligations to help one another in general or in the particular and fully determinate case of an action or a concrete task). But as we have just seen, these obligations in turn express only the community of fundamental exigency and, in addition, past self-creation as an irrevocable mortgage of practical temporalisation. From this point of view, fraternity is the real bond between common individuals, in so far as everyone lives his being and that of the Other (whether in simply being there, close to the Other, or in the resemblance-solidarity of black rebels, or of whites on the defensive) in the form of un transcendable reciprocal obligations. Indeed : the colour of their skin, taken as a pure, reciprocal obligation by the black rebels of San Domingo, and, at the same time, as everyone's material, inert guarantee against the possibility of being alienated, the colour of their skin being taken, in and by everyone, not as a universal physiological characteristic, but as a historical characteristic based on the past unity of a free promotion - + +this is fraternity, that is to say the fundamental, practical structure of all the reciprocal relations between the members of a group. What is later called comradeship, friendship, love - and even fraternity, using the term in a vaguely affective sense - arises on the basis of particular circumstances and within f'. particular perspective, for a given reciprocity as a dialectical, practical enrichment, as a free specification of this original structure, that is to say, of the practical, living statute of the sworn members. The constituted group is produced in and by everyone as his own birth as a common individual and, at the same time, everyone can grasp, in fraternity, his own birth as a common individual + +as having been produced in and by the group. + +Furthermore, this fraternity is the right of all through everyone and over everyone. It is not enough to recall that it is also violence, or that it originated in violence: it is violence itself affirming itself as a bond of immanence through positive reciprocities. This means that the practical power of the bond of fraternity is simply (in immanence25) the free transformation of the fused group by everyone, for himself and for the other third party, into a group of constraint. This lack of distinction is particularly evident when the sworn group proceeds to the summary execution or lynching of one of its members (suspected, rightly or wrongly, of betraying the group). The traitor is not excluded from the group; indeed he himself cannot extricate himself from it. He remains a member of the group in so far as the group - threatened by betrayal reconstitutes itself by annihilating the guilty member, that is to say, by discharging all its violence onto him. But this exterminating violence is still a link of fraternity between the lynchers and the lynched in that the liquidation of the traitor is grounded on the positive affirmation that he is one of the group; right up to the end, he is abused in the name of his own pledge and of the right over him which he acknowledged in the Others. On the other hand, lynching is a praxis of common violence for the lynchers in so far as its objective is the annihilation of the traitor. It is a bond of fraternity aroused and accentuated amongst the lynchers, in so far as it is a brutal reactualisation of the pledge itself and in so far as every stone that is thrown, every blow delivered, is a new affirmation of the pledge: whoever participates in the execution of the traitor reaffirms the untranscendability of group-being as a limit of his freedom + +l.s. Indeed, it goes without saying that, down to its last member, the group is characterised by its transcendent relation to the other group, that is to say, to the + +and as his new birth, and he reaffirms it in a bloody sacrifice which, moreover, constitutes an explicit recognition of the coercive right of all over every individual and everyone's threat to all. Furthermore, in the developing praxis (that is to say, during the execution) everyone feels at one with everyone in the practical solidarity of the risks run and of the common violence. I am a brother in violence to all my neighbours: and it is clear that anyone who shunned this fraternity would be suspect. In other words, anger and violence are lived both as Terror against the traitor and (if circumstances have produced this feeling) as a practical bond of love between the lynchers. 26 Violence is + +the very power of this lateral reciprocity of love. + +This enables us to understand how the intensity of the group's actions arises from the intensity of the external threats, that is to say, from danger; and if this intensity no longer manifests itself as a real pressure but the danger itself still exists, then it is replaced by the artificial substitute of Terror. Terror is a real product of men in groups, but it still depends, in itself and for its degree of intensity, on hostile violence (that is to say, both on suffered violence surviving in people's memories, and on expected violence, as in the case, for example, of a counter-attack). The creation of Terror as a counter-violence engendered by the group itself and applied by common individuals to every particular agent (in so far as he contains a threat of seriality) is, therefore, a use of common strength, hitherto used against the enemy, in order to reshape the group itself. And all the internal behaviour of common individuals (fraternity, love, friendship, as well as anger and lynching) derives its terrible power from Terror itself. In this sense, everyone is, for everyone, the same in the unity of a common praxis; but, precisely because reciprocity is not integration, and because the epicentres, though dissimulated, are still in mediated reciprocity, and because I cannot be both a totalising and a totalised third party, and because the Other me who approaches me also exists in me as myself become Other (and limiting my freedom), the possibility of constraint or extermination is given simultaneously in every reciprocal relation. This has nothing to do with mistrust: mistrustful behaviour occurs in groups of constraint when they are already eroded by divisions, and therefore at a quite different moment of the common temporalisation + +26. I am of course referring to the execution of traitors rather than to the kind of racist lynching which, in America, provides recreation for a member of another + +and in different circumstances. The possibility of loving a traitor is given in fraternity itself and as a condition of it: and this means that any concrete and practical relation within the group is necessarily addressed through the common individual to the organic individual, and thereby helps to give him a real existence which common solidarity must either negate or pass over in silence. And this possibility that fraternity with a given person may suddenly change, through the betrayal of the brother, into lynching and extermination, is given in fraternity itself as its source and limit: we fraternise because we have made the same pledge, because everyone has limited his freedom by the other; and the limit of this fraternity (which also determines its intensity) is everyone's right of violence over the other, that is to say, precisely the common, reciprocal limit of our freedoms. However, as can still be observed today in authoritarian parties, fraternity is the most immediate and constant form of Terror: traitors, in fact, are by definition the minority. It is really the reciprocal translucidity of common individuals (which is capable of leading organic individuals into friendship): no 'milieu' is warmer than an authoritarian party which is constantly subject to external threats (and which is authoritarian hecause it is threatened). But, whatever the fraternity, in the event of deviation, heresy, or betrayal, it cannot survive violence (except in the form described above: the link between the executioner and the condemned man); and it cannot oppose it either; not, as has too often been said, because it would be weak and ineffective against Terror, but quite simply because it is violence itself lived as violence-friendship (as a violent force within relations of friendship). This violence, born in opposition to the dissolution of the group, creates a new reality, the act of treason; and this act defines itself precisely as that which transforms fraternity (as positive violence) into Terror (negative violence). Thus, if I am a member of a constraining group, the violence of my fraternisation rests on the practical certainty (which is not, or need not be, explicit) that this fraternisation will become either a lynching, in its own name, or a pitiless condemnation, if my brother behaves as an + +Other and if the group sees in him a threat of dissolution. + +The immediate bond of freedom and constraint has produced a new reality, a synthetic product of the group as such. My application of the term 'right' to this reality may seem premature, since, ultimately, all institutions are grounded on the pledge, which is not in itself institutional. It would be better to say that this reality, in this abstract moment of our investigation of the group, is simply the diffuse power of + +jurisdiction. But we must be quite clear about this: I use the word diff use only to make a contrast with specialised organs; in fact, the common individual's pledge gives him juridical power over the organic individual (in himself and Others). Freedom which has been freely limited forever by his other-being is each person's power over all in so far as it is in everyone an accepted mutilation. It is impossible to derive juridical power either from individual freedom, which has no power over reciprocal freedom, or from a social contract uniting several entities, or from the constraint imposed on the group by some differentiated organ, or from the customs of a community in so far as they appear to involve an exis. As for the circumstances which explain the particular content of this power (that it is exerted as a particular prohibition, as a particular exigency, etc.), they may show us, in fact, that a given risk run by a given group in particular circumstances gave birth in this group to a given common decision, but by themselves they cannot explain repressive power as a practical form of the decision in + +question. + +However, we are not in any way attempting to describe the historical genesis of the power of jurisdiction: and we shall see below that such an undertaking does not even have any sense. But our dialectical investigation involves us in the re-creation of this power in a surviving group which is attempting to become a statutory group. Juridical power appears here as the creation of a community which realises that it neither is nor ever will be a totalised (and totalising) totality; it is therefore a new form of totalisation intended to compensate for the impossibility of completing the totalisation, that is to say, of its appearing as a form, a Gestalt, a collective consciousness above all the members, and, therefore a guarantee of their permanent integration. This new statute of totalisation is Terror, and Terror is jurisdiction: through the mediation of all, everyone agrees with everyone else that the permanent foundation of every freedom should be the violent negation of necessity, that is to say, that, in everyone, freedom as a common structure is the permanent violence of the individual freedom of alienation. And everyone demands that everyone should both guarantee him the inert structure of common freedom and make himself, as violence and terror, the inert negation of certain possibilities. It would be dangerous to assimilate this diffuse juridical power to the simplest form of the sacred: this would take us too far and the examination of these matters is not part of our task. It will be sufficient to note that in our investigation and at this level of abstraction, for groups + +which have defined themselves in combat and by the liquidation of the old seriality of impotence, the Sacred constitutes the fundamental structure of Terror as juridical power. The Sacred is manifested through things; it is freedom producing itself in worked matter, both as absolute sovereignty and as thing. It is, so to speak, freedom returning to man as a superhuman, petrified power. This has nothing to do with the exigencies of the practico-inert field, which, although they do indeed express the freedom of the Other, absorb it entirely and do not show it, so that an inert thing could of itself be an exigency. In the case of the Sacred, freedom manifests itself in a thing, upon its very destruction (through explosive disintegration)27, but by affirming itself in opposition to the thing it becomes an inert-power over man. And reyelation, prayer and other practices in relation to this power constitute it as sacred in its very contradiction: freedom, in human relations, does not intimidate; it is the same in the agents of a relation of reciprocity; it defines itself for everyone by its homogeneity. In the present case, however, it manifests itself to individuals oyer the total submission of matter (disintegrated or pierced by rays or directly modified, without labour, by mere sovereign will), but it does so as heterogeneity, that is to say, as an untranscendable negation of their possibilities. In this sense, its power has the possibilities which are negated in everyone as its fundamental structure, as the inertia of every freedom. To put it differently, it constitutes everyone, within his freedom, as received (and accepted) passivity. And worship consists precisely in free praxis which recognises the inert limitation in it of its possibilities as an absolute gift and a creation which proceeds from inert freedom as a sacred power. This simply means that any pledged group, as a diffuse power of jurisdiction, manifests itself for every third party, and in the totalisation performed by the other third party, as a sacred power. It serves no purpose if the sacred assumes a specifically religious or cultural form: it is (at least in general: circumstances determine cases) simply a character proper to Terror as inert freedom and negative power and its relation to everyone's other-freedom in so far as it negates certain possibilities. This relation manifests itself as sacred when a coercive and unanimous totalisation reveals itself through the common object. This is the origin of ceremonies, to the extent that materiality (vestments, stereotyped actions, objects of veneration, the + +inert commemoration of the past, the inflexible and invariable order of actions etc.) expresses inertia in them, and also that their conventional and teleological aspect embodies freedom-power. And the Sacred, with its rituals and its ceremonies, derives, like juridical power, from a non-being of the group, that is to say, from the fact that any real community is a totalisation or, to put it differently, a totality which is perpetually detotalised. It is through a fundamental contradiction, in fact, that the act of totalising, in so far as it is performed by everyone, is + +also the essential factor of detotalisation. + +However, as we have already noted, the possibilities of dissolution, for the group, even when enemy pressure is relaxed, would be less close and less threatening if its members could remain united, in one place, in the square, etc. For unity in everyone, as a synthetic determination of multiplicity, would be the interiorisation of the real, visible and tangible promiscuity of the people in the group. We have seen that the group posits itself for itself in a reflexive practice and becomes its own immediate objective not only when circumstances require it to be permanent, but also when the diversity of its tasks requires that differentiation take the place of the fluid homogeneity of fusion. In this way, in fact, a risk is incurred that distance will make everyone isolated and separate, · or that new conflicts, arising from the differentiation itself, will produce new antagonisms in the community. Through the pledge, the group ensures an ontological statute which will mitigate the dangers of differentiation. As I have already said, this pledge is not necessarily a real operation or an explicit decision: in reality, when the group posits itself as its own end in and by every third party, and when this practical reflexivity defines, if only implicitly, the common reception of Terror, it is enough that violence, both in its negative forms (the liquidation of the uncommitted, and the suspect) and in its positive forms (fraternisations) manifests itself in such a way that the statute of permanence becomes an immediate certainty for every totalising third party. So, whether or not a pledge was really made, the organisation of the group becomes the immediate objective. It was this organisation, as an ulterior objective, which necessitated the creation of permanence; and again it is this organisation which the permanent group now sets itself as its immediate aim. And the unity of the group + +This pledge, whether implicit or explicit, defines everyone as a common indiyidual, not only because it concerns his being-in-the-group, but also because it is only through the mediation of all that it can take + +place in everyone. But this has nothing to do with inorganic products or with an inertia of exteriority: in this sense, Terror does not inflexibly define the permanent limits of freedom for everyone. In fact, it merely raises the threshold at which untranscendability will become transcendable; or, to put it differently, it makes it less prohahle that one will abandon one's post, go over to the enemy, etc. Treason, as a new form of human action, is nevertheless always a concrete possibility for everyone; its probability is a function of the synthetic complex of historical circumstances (including everyone's individual history). This means that the group is also - negatively - the totalisation of its points of possible rupture, and that for each point there is a certain threshold "l-,ove which the rupture may occur; and these thresholds are extremely + +variable. 28 + +28. This does not in any way mean that for certain individuals their being-inthe-group is really untranscendahle. But this has nothing to do with either courage or fidelity: the best may fall into a trap, the most devoted may become the unwitting instrument of the enemy. It is therefore perfectly legitimate to consider the group also as a multiplicity of points of rupture; the more so the more differentiated it is. However, we shall see that from another point of view differ- + +entiation is a unifying link. + +3 + +The Organisation + +1 Organised Praxis and Function + +In so far as organisation, as the action on itself of the statutory group, is directly relevant to a critique of dialectical Reason (whether it is a matter of differentiation in combat, or of the division of labour in a particular case), there is no need for a formal enumeration of its possible forms (or for tracing the historical movement of the division of labour or of the transformations of the army on the basis of weapons and of combat techniques). Our sole problem is dialectical rationality. We are acquainted with two types of intelligible actions: the translucid (but abstract) praxis of the individual, and the rudimentary praxis of the fused group. To the extent that the second is relatively undifferentiated and that action in it is everywhere the same, everywhere common, everywhere governed by orders coming from all sides, but which a single third party might have uttered one after the other, we can take it that non-differentiated praxis retains the characteristics of individual action and amplifies them. It is alive in so far as it is, in everyone, both total and the same; no doubt it multiplies, but we have seen that an individual becomes a member of a group by interiorising multiplicity. Through the relation of mediated reciprocity, he spontaneously and concretely benefits in his own activity from the activity of the Others. Inertia, control, and complex organisations are nowhere to be found : this means that praxis is everywhere plenary, that it is everything it can be everywhere and that, ultimately, reciprocal conditioning manifests itself through the object and through objectification, but that the operation, in so far as it is very close to the operations of a practical organism - though separated from individual praxis by the whole practico-inert field - retains a sort of translucidity. Organised action, however, involves a system of relations, and of relations between relations, such as to make one wonder what type of praxis manifests + +itself in it - comparing these combined structures with the constitutive dialectic of individual action - and whether this praxis is still dialectical, and what kind of objective it sets itself, what kind of reshaping of the practical field it performs, what internal development characterises it, and, finally, how far it is really praxis (that is to say, freedom) and how + +far a constituted instrument. + +The word 'organisation' refers both to the internal action by which a group defines its structures and to the group itself as a structured activity in the practical field, either on worked matter or on other groups. People say both: 'We have failed because the organisation (distribution of tasks) left a lot to be desired' and 'Our organisation has decided that .. .', etc. This ambiguity is important. It expresses a complex reality which might be described in the following terms: the group can act on a transcendent (transcend ant) object only through the mediation of its individual members: but the individual agent performs his action only in the definite context of the organisation, that is to say, in so far as his practical relation with the thing is directly conditioned by his functional relation to the other members of the group, as already estahlished either by the group (as a plenary meeting of its members) or + +by its representatives (however they have been chosen). + +Organisation, then, is a distribution of tasks. And it is the common objective (common interest, common danger, common need assigning a common aim) which defines praxis negatively and lies at the origin of this differentiation. Organisation, then, is both the discovery of practical exigencies in the object and a distribution of tasks amongst individuals on the basis of this dialectical discovery. In other words, the organising movement settles the relation between men on the basis of the fundamental relation between group and thing. Depending on the nature of the circumstances and on the characteristics of the praxis (in fact, according to the whole historical conjuncture), this can lead either to a voluntarism which defines the task of the individual on the basis of the exigencies of the aim without reference to everyone's individual possibilities, or to an unprincipled opportunism which reduces the common praxis (common in its aims, intensity, and complex organisation), in accordance with empirically given limits of individual praxis (limits which, on closer examination, might show themselves capable of being pushed back by some action of the group upon itself, without the workers, combatants, etc. suffering it in their individual organisms). Depending on the ensemble, one can equally well find organisations (generally very close to the simple pledged + +group) in which function is always (or sometimes) defined in terms of the task to be carried out and of the particular capacities of each person (in so far as he is known by Others: for example, in a very small combat unit, a particular mission will be assigned to a particular soldier + +because of his exceptional strength). + +I have presented these various possibilities not because they occur historically in disorder or in an arbitrary order, but because, as far as our problem is concerned, they are strictly equivalent: voluntarism and opportunism are characterised, in the organisation, as the action of the group on its members. The group acts on the object, indirectly, only in so far as it acts upon itself; and its action upon itself - which as we shall see is its only action as a group - defines itself on the basis of a praxis (which is either already estahlished or gradually revealing itself). The group defines, directs, controls and constantly corrects the common praxis; it may even, in some cases, produce the common individuals who will realise it (through technical education, for example, etc.). But this set of operations presupposes differentiation: for example, the distribution of tasks (or of weapons or supplies) presupposes an earlier distribution, that is to say, the creation within the group of specialised apparatuses (misleadingly called organs: directive organs, groups for co-ordinating, mediating or distributing, or regulating exchanges, administration, etc. ). This first moment of differentiation - which has nothing in common with the appearance of command, although, as we shall see, it is the basis of it - is, therefore, fundamentally an action of the group upon itself. And, to precisely the extent that this differentiation remains very abstract (there is the service which prepares the work and the other common individuals), it corresponds to a still very abstract conception of praxis: the group, united in a common, but still inadequately determined project (a combatant community, a vigilance committee, a team of technicians or an association for buying and selling property on the moon) produces its first differentiation in order to give itself the means of proceeding to this determination. And there should be nothing to surprise us in this differentiation, in itself, since it is simply a pledged statutory group acting on itself - a group, that is, whose internal relations have been explicitly constituted so as to respond to the demands of the situation and to make differentiations possible. In other words, our problem is not to explain any particular division: the internal praxis of the pledged group or (and this comes to the same thing) the possibilities which reveal themselves to the action of every third party in the + +group, are simply the unveiling of its tasks tkrougk its morphology. The establishment of any particular differentiation is only a concrete modality of a more general structure: through the pledge, the statutory group becomes capable of differentiation; to put it differently, it makes itself such that not only do differentiations not destroy its unity, but also practical problems can reveal themselves to it through differential problems. And since the thought of the group, that is to say, its practical idea of the Universe, is simply the transcendence (depassement) of the practical idea which it has of itself towards the transcendent (transcendant) object; and since the practical idea which a group has of itself the schema which it uses to resolve its internal problems - cannot be separated from its internal constitution (both as its action on itself and as its objective structure), differentiation, which is the abstract thought of the statutory group, becomes the concrete thought of the organised group: it appears, in fact, as the creation by third parties of an increasingly precise differentiation and thus the thought of the transcendent object expresses the increasingly concrete and differentiated structure of + +unified multiplicity. (I shall return to this point shortly.) + +Thus individual differentiation is of little importance, at least for our purposes, and its appearance, though new, is immediately intelligible. But the intelligibility of organised action is a completely different matter: the problem is what type of unity and reality can be attributed to praxis in its new form of organised praxis, and what meaning it can have. What we are interested in, therefore, is the relation between the action + +of the group on itself and tke action of its members on the object. + +We shall study the different moments of this relation step by step and by deepening our investigation (experience). We must first specify what the task is when it appears in the group as the objective of a process of organisation; this will lead us to a new definition of the common individual, since his statute in the organised group is of itself a determination (and therefore a limitation) and a concrete enrichment of the statute of the pledged member (inertia in freedom, right, etc.). Then, having explained function, as the statute of the common individual, and its two aspects (a practical task in relation to the object, and a human relation in so far as it characterises the being-in-the-group of the third party), we shall have to examine the foundations of a logistics of organised systems (as the multiplicity and unity of inverted and mediated reciprocities) and describe the structures as such, that is to say, as they arise in the group in opposition to the passive activities of the practico-inert; and then we shall find in them a new human and social + +product: active passivity. Only then can we approach our two essential questions: in fact we shall have to rearrange all our conclusions into a synthetic movement which will itself produce the intelligibility of organised praxis and reveal in it a new apodicticity - that is to say, a radically different necessity from the first. This will enable us to examine the ontological statute of the organised group as a concrete reality given in the dialectical investigation (experience) or, in other words, we shall discover whether the organisation should be regarded + +as practical existence or as being. + +At the level of the fused group, the common individual appeared to us as an organic individual in so far as he interiorised the multiplicity of the third parties and unified it through his praxis, that is to say, in so far as unity determined multiplicity through him as an instrument, a force. This characteristic of synthetic unity posits itself for itself in the statutory group when the situation demands separations which endanger the community for everyone in the person of every third party and in the possibility of his breaking the unity, and relapsing into the statute of massified isolation. The common characteristic of the individual (or his being-in-the-group) becomes everyone's juridical power over organic individuality in himself and in every third party. But this power is still abstract: its abstraction is a measure of that of the group and of the common praxis. At the level of organisation, this abstract and fundamentally negative power (as the free inertia of freedom) is concre�ised and changes sign: in fact, it defines itself for everyone, in the context of the distribution of tasks, by a positive content. It is function. As such, it remains an inert limit of the freedom of the third party, and, therefore, its basis is still Terror. And Terror can always re-emerge as a relation between pledged members when the conjuncture and the particular history of the organisation compromise the functions of the third party (or render them useless or parasitical) and reveal, from below, the danger of dislocation. The organisation then reverts to the less differentiated stage of the statutory group; and functions appear as little more than abstract significations with no reality. That is why, in certain historical conditions, Terror can appear + +as a regression and simplification. + +But in the normal exercise of organised activity,Junction is a positive definition of the common individual: either the group as a whole or some already differentiated 'organ' assigns it to him. It is a determination of individual praxis: an individual belongs to the group in so far as he carries out a certain task and only that task. In simple Terror, + +however, the inert limit of possibilities remains abstract and purely negative : it is freedom freely renouncing the right to dissolve the group relation in any case of separation. Function is both negative and positive : in the practical movement, a prohihition (do not do anything else) is perceived as a positive determination, as a creative imperative: do precisely that. But in the milieu of the pledge, doing that is the right of each over all, just as it is a right of all over each: the definition of power, in so far as a concrete function particularises it, is that for everyone it is the right to carry out his particular duty. Thus, he must actualise everything that predetermines his function (the common objective, practical problems, the conjuncture, the state of techniques and instruments) in inertia (as an inert possibility defined by discourse, for example, and which it realises in repetition), in the milieu of sovereignty over things (the dialectical freedom of organic praxis) and of power over men (social freedom as a synthetic relation based on the + +pledge), in short, in freedom. + +If a football team is being formed, the function of goalkeeper, or forward, etc. , appears as a predetermination for a new young player. He will be recruited by one of these functions; it will select him on the basis of his physical qualities (weight, height, strength, speed, etc.): but in so far as it designates him in his free praxis, that is to say, in so far as it produces a determination of inertia at the basis of his freedom, it is already power, and he lives it as exigency: the exigency of training, for example. The team in which he has been signified by this function is then obliged to raise him to a (physical and technical) level at which he will be capable of performing the actions which the group requires. This may also signify his right to refuse excessive training, badly organised and exhausting travel, matches played in bad conditions, etc. And it is as a common individual that he has these negative rights: in other words, his praxis freely reappropriates the exigencies of his + +function. + +At this level, there is no difference between rights and duties. The classical distinction - which tends to make duty into a right of other third parties over me, and to make right into the duty of other third parties towards me - was still valid at the previous level; but once the positive content of function has been defined, the distinction ceases to exist. There is no ground for stating a priori that the diet involved in the training of a particular sportsman is either a right of the Other (of the other members of the team) or his own right. If, as an organic individual, he were to resist following the diet, the Others would + +impose it on him (either because he needs to lose weight, or because he has a wrong attitude to his 'job', or because he eats tbo much, or eats indigestible food) because each of them, as a function, in the praxis, requires every member of the team to reduce himself to his own function. On the other hand, if he adopts the prescribed diet without qualification, then, for the administration of the sport group (the 'organisers') this is simply their duty to keep it for him as long as necessary; as a function of the group, he will require his fellow team members not to deflect him from his duty, or even help him to carry it out, and if necessary to force him to do so. It is clear that each formulation indicates only more clearly the increasing inextricability of right and duty. If one member of the team makes this exigency (to keep fit, to persevere with the training) into a power over another player or over the group, then it acquires a juridical and dialectical structure which is + +the complex organisation of all forms of imperative. + +Suppose that I am integrated into a group, and that there is another common individual, M, defined by a certain function. I require that M should receive from the group the necessary subsistence and training, etc., to enable him completely to fulfil the requirements of his job. Now, I require this not only for the group (that is to say, from the point of view of the common praxis), but also from the group (since it is the group which distributes the functions).28a. I require it for my own function, that is to say, for the guarantee which each and every member must freely offer me, and I also require it for everyone as a particular third party, and for anyone (both because member N or Z as such will require that I require this guarantee for him: it is he, for example, who has most to lose in his functions through the failings ofM - and because, for example, I am more seriously threatened through Nor Z by these failings); lastly, I require it because M himself, in the name of the pledge, requires of me (as a limit-power) that I require it of him. Now, all these abstract moments of concrete exigency are given together in my way of acting, of realising my function through my action and of basing my action on my powers: the right which the group has through me over all, and the duty towards the group as defined by all, the reciprocity of right (I have the right that you should assert your rights), + +28a. Of course, the group requires it of the group through me in so far as it has provided itself with a representative (team captain, manager, etc.). When conflicts are stiII masked or undeveloped, therefore, the group as a milieu of regulated heterogeneity realises itself through tension between functions; its + +that of duty (my duty is to remind you of yours), that of right and duty (I have the right that you should allow me to do my duty), that of duty and right (I have the duty to respect your rights) - the infinite complication of these reciprocities (in the context of the complex reciprocities which we shall examine shortly), all these lines of force constitute the web of what might be called power as reality lived in and through praxis. According to circumstances, one or other of these lines of force may appear, as a form, against the synthetic background of all the + +others; but if they are not all present, the group will break up. + +For the sake of simplicity, let us consider the abstract case of an organisation which is not directly conditioned in its internal structure by exploitation (it may constitute itself either for the exploitation of Others or against the exploitation of its members by Others, but there will be no relations of exploitation between the third parties who comprise it) and a particular function of which consists in a certain operation performed with a particular tool and with some definite technique. The technique and the tool define the moment of the historical process in so far as it produces, penetrates, sustains and totalises this particular group within this developing totalisation. But the common individual perceives techniques and tools as his sovereignty in the practical field, that is to say, as an extension of his individual praxis. In this sense, tools and techniques (which are really one and the same object) are the group itself in so far as the common individual perceives it as his own social power over things. In other words, acting with tools reveals his dated historicity to him (it can also be defined as an inert negation - but from the abstract point of view of a diachronic totalisation) as practical sovereignty (over inorganic matter). It is at this level that the tool is a practical unveiling of the world to precisely the extent that the practical organism is a tool. By this I mean both that it changes the world by a reorganising transcendence, and that in this very transcendence it reveals it to be a world in the process + +of being reshaped. + +These themes have been discussed many times by many different authors: I shall only refer to the first technical agent to grasp, and fix in experience, the social moment of unveiling the world by a praxis involving tools: Saint-Exupery and his book Terre des Hommes. 29 The astringent power of the aeroplane (as an instrument which reduces travelling time) is not only produced by a technician using an object + +which 'has already been worked by men, but also, and inseparably, revealed as a real movement of contracting space. But this real movement in itself is revealed as a means of control, and can never be a matter of contemplative perception (except for the inert passenger who is being transported from one city to another). It also determines the speed of the operations to be carried out (including thoughts, as hypothetical actions and as constantly corrected syntheses of the practical field). In the context of the practico-inert, we saw how worked matter produces its own idea. Here, it is the other way round: activity involving tools defines itself through the instrument of society as a practical power (structured by the tool which it uses and transcends) of thinking the aevelopment of the world. This power comes to the third party through the group which produces (or acquires) the tool and defines the function. But though this enriching limitation may limit possibilities - as abstract determinations of the social future - it must also concretise them, that is to say, multiply the practical options by creating, through the task and the tool, differentiated structures amongst the possibilities or in other words, by defining sub-possibilities. It is obvious that the options do in fact impose themselves on the basis of real objectivity, or of the developing process; but the instrument, as practical perception, creates the permanent possibility that certain subpossibilities will inscribe themselves in praxis from the outside, and require an immediate option. The speed of the danger and of the defensive action, for example, are just as much a function of the speed of the plane, as of the nature of the possible dangers. But these imperative options present themselves to the agent (the pilot, for example) in terms of the world soliciting his own power; and the final choice30 + +expresses his sovereignty. + +Here we encounter the organic individual as an isolated agent in the first moment of his concrete truth. It will be recalled that he was presented, in his pure abstraction, at the beginning of our dialectical investigation; we find him now iIi his complex relations with the + +30. It would be completely wrong to give the word 'choice' here an existential interpretation, It is really a matter of the concrete choices which present themselves to, for example, an airline pilot trying to save the passengers in his plane, two of whose four engines are out of action, which is losing fuel, etc. It would be taking Pavlovian obstinacy to the point of total blindness if one denied the specificity and irreducibility of these choices, The part played by routine is undeniable, but in cases of danger it is not sufficient; it is necessary to innovate or + +to take risks. + +common individual. He loses himself through the pledge so that the common individual may exist (as an enriching limitation of the field of possibilities) and then he finds himself again at the level of concrete praxis, in relation to the common individual, that is to say, to the task (with the available instruments). And by 'organic individual', here, I do not mean some given individuality which distinguishes everyone from everyone else (individualities, as we have seen, are historical individualisations of material conditions; and in any case they do not concern us here); I mean free constituent praxis in so far as it is finally only signified by function; in fact, to the extent that the determination of the sub-possibilities becomes richer and richer in the context of function under the influence of tools, functional predetermination appears as a schematic adumbration of a sector of activity: in this sense the common individual, as function, remains mostly undetermined. To be a pilot, of course, is to he nothing hut a pilot. But, in the course of the job, the variety of exigencies (revealed by the tool and in action) is so great, their urgency so evident, that it would be impossible to realise one's heing-a-pilot as a totalised ensemble of practices confined within strict limits. A praxis, however, though completely unintelligible unless defined in terms of tools and techniques, of the common objective and the material circumstances, is only a free organisation of the practical field on the hasis of the enriching limitations which have produced us. Of course, the individual action of a practical organism no longer has anything in common with that of another practical organism which possesses rudimentary tools and less developed techniques: it is true that the conditions of sovereignty are social. 31 Everyone knows that the power of the plane is not that of the pilot. On the other hand, in so far as this power can be practically realised only through the specialised praxis of the pilot, that is to say, through the transcendence of inertia and the use of forces of exteriority, everybody also knows the opposite - that airline pilots, though identical as common individuals, are at the same time differentiated, for the group itself, by what is stupidly called their individual qualities, which is, in fact, simply the history of their technical choices as free dialectical agents. For an airline pilot in mortal ,danger, what is excluded is a set of possibilities, which are in any case completely unserviceable (to negate the common individual in him, the responsible individual, the + +sale master on board, all of whose initiatives must be aimed at saving the plane, and to relapse into fear, isolation and the irresponsibility which is characteristic of isolation located beneath any groupbeing). What is required, meanwhile, is to transcend the pure inertia of common-being by some action (if action is still possible) or to choose between two techniques, both tested, both of which have their defenders: thus, in function, the practical individual (as a constituent dialectic) reasserts himself by transcending common inertia in a praxis which preserves it by using it (which, as I have said, amounts to transcending the inertia of the instrument). The individual as organic praxis is helow the common individual in so far as he grounds him with a pledge, and beyond him in so far as he is his practical individualisation. But in this new moment of his reality (still abstract, because we have not yet run through the moments of alienation and of the practicoinert in the reverse order), he is no more than the common praxis, in so far as it has to be actualised through individual acts which transcend it. It goes without saying that the common individual, in so far as he is produced hy the group, is something more and something different than he at first appeared. For his function is a technical bond with a particular instrument. And of course the technique is the instrument itself in so far as it ha ; been invested with meanings (significations) (mediations between tI le agent and the thing) by the labour of Others. But, of course, it is also the becoming-instrument of the specialised agent. Through training, professional instruction, etc., the instrument exists as an exis in the practical organism of anyone whose function makes him use it. Or, in other words, the exis of the specialist must correspond to the signifying inter-connections of the parts of a machine (or tool), as an inter-connection of assemblies. However, we are not at the level of alienation here: the group constituted itself in opposition to it and has not yet relapsed into it. And this inter-connection should not be seen as an inert instrumentality of man tied to the inert humanity of the machine. In fact, praxis is the t�mporalisation of exis in a situation which is always individual (or rather which always threatens to he so); this means that action defines itself here as the simultaneous transcendence of assemblies by the tool, of the tool by assemblies, and of the whole by a directed process which future possibilities have occasioned in the distant future. There can be no exis, no habit without practical vigilance, that is to say, without a concrete objective to determine them in their essential indetermination, and without a project to actualise them by specifying them. Thus exis, as an enriching + +limitation of the common individual, manifests itself concretely only in and through a free practical temporalisation. Routine opposes initiative, of course, but this contradiction occurs at another level: it has meaning, in fact, only in the context of a complex historical conflict which opposes new means of production to old ones, forces of production to relations of production, etc. As such, routine corresponds to a total situation and expresses the overall attitude of particular groups and milieus (that is to say, it manifests itself in terms of a political and social alliance between these milieux and the conservative class). But, to take a routine practice (that of a Tennessee peasant in 1939 who refused to use electricity) as a particular action and in its positive relation to a specific objective (ploughing, sowing, breeding etc.), there is no difference between its structure and what we have just been describing: regardless of whether he uses electricity, votes for the Democrats or Republicans, and of whether (because of his lack of technical education) he is hostile to elementary forms of co-operation, the peasant, with his work tools, defines his practice in terms of a few concrete and constantly renewed objectives; he effects a real transformation of the practical field by adapting himself to difficulties with + +the means at his disposal. + +The main purpose of my examples was to show how the common is transcended in work itself. They were not intended to take us back to the simple groups which we were studying before. In effect, these were characterised not only by their integration, but also by the strictly common character of their objective and, consequently, of their praxis. However else they may differ, a football team and a group of armed rebels have one thing in common, from the present point of view: that the real objectification of the action of each member lies in the movement of common objectification. In the case of a football team, the action of every player is predetermined as an indefinite possibility by function, that is to say, in relation to a future objective which can realise itself only through an organised multiplicity of technical activities. Thus, function is for every member a relation to the objective as a totality to be totalised. In the match, every common individual will, in the light of the group's objective, effect a practical synthesis (orientation, schematic determination of possibilities, of difficulties, etc.) of the field in its present particularities (mud, perhaps, or wind, etc.); in this way, he tries to make himself generally prepared for the specific characteristics of the match. But he will realise this practical synthesis - which, ultimately, is a kind of mapping, a sort of + +totalising survey - not only for the group and on the basis of the group's objective but also on the basis of his own position, that is to say, in this case, of his function. From the moment when the real struggle begins, his individual actions (though they require initiative, daring, skill and speed, as well as discipline) no longer appear meaningful apart from those of the other members of his team (in so far, of course, as each team is also defined by the other) - not only in the abstract, in so far as each function presupposes the organisation of all functions, but also in the very contingency of the concrete, in so far as a particular player's slip or clumsiness at a particular point strictly conditions the movement of another player (or, of all the others) and gives it a teleological meaning which can be understood by the other + +players (and, though this is incidental here, by the spectators). + +Thus no particular movement, pass, or feint, is entailed by the function itself: function only defines the abstract possibility of making particular feints, and performing particular actions in a situation which is both limited and indeterminate. The action is irreducible: one cannot comprehend it unless one knows the rules of the game (that is to say, the organisation of the group on the basis of its objective), but it can never be reduced to these rules; it cannot even be understood on the basis of them unless one can also see the whole field. Thus, this particular act is contradictory. In itself it is in fact a complete individual action (it has a partial aim: to pass the ball; an assessment of the developing situation in terms of the future, a calculation of chances and a decision - which may be modified by new developments), which can either fail or succeed and whose success defines it as a self-sufficient dialectical process. In other words, if we assume that this particular individual had this particular objective (to pass the ball to the member of his team whom he thinks best placed to use it for the benefit for the entire group), the action, as a constituent praxis, irreducible to function, is completely intelligible. But in fact the impossibility of stopping at this partial objective is revealed to us in our investigation by the fact that the permanent reorganisation of the group continues (in accordance with general rules and with the particular exigencies of the situation) and that it absorbs every particular moment which conditions it. Thus the meaning of the particular undertaking - even if, as such, it is successful - lies in the use made of it elsewhere in the undertakings of other members of the team. And it may be worth remarking the practical justification of this past activity lies in the future: only the opening, the try, and possibly the goal will provide a definite justifica- + +tion of the daring with which a particular individual tactic was adopted at a given moment. Thus individual praxis, as its transcends the common individual through its concrete temporalisation, is retrospectively modified by every other praxis in so far as they are all integrated into the development of the match as a common process. But is this a case + +of alienation? + +It will of course be noticed that the individual practice of the player integrates and objectifies itself in the real, living development of a common tactic (or in some cases, strategy); every practice, solicited by a moment of the common development, becomes engulfed in the moment which it helps to produce on the basis of the first. As we have seen, its justification and truth lie in the completed process. But as this validation is produced through successive mediations, that is to say, through successive suppressions of third parties in favour of the practical totalisation (one initiative is justified by another which it has enabled another player to take, but this initiative, in turn, will be mediated, in relation to the whole, by other initiatives), the objectification, as a mediation by the other and the mediation of this mediation etc., could be seen as a process of serial alienation. In this way we would come back to the schema of the moment of necessity: the action of the practical organism in objectifying itself is revealed as other both + +in its practical essence and in its results. + +But in fact, this alienation (at least at this level) is only apparent: my action develops, on the basis of a common power, towards a common objective; the fundamental moment which is characteristic of the actualisation of the power and the objectification of the praxis is that of free individual practice. But it determines itself as an ephemeral mediation between the common power and the common objective; in realising itself in the object, not only does it annul itself as an organic action, in favour of the common objectification which is in the process of completion, hut also this annulment-towards-the-objective reveals the common praxis to it - not in it, as the ontological structure of the constituent project (in which case we would be back with some organicist magic), but outside it, as something whose developing objectification dissolves all individual work (that is to say, every individual objectification). But this common objectification is, in fact, simply the reaiisation of the objective: the group temporalises itself in an objectification which eliminates it32 as an active organisation in 32. Either definitively (they separate) or tcmporarily (the winning team re- + +mains compact until the next match, but in an other way). + +favour of the result as a produced reality. And this totalising elimination towards and in favour of the common objective is the common undertaking of every third party, in so far as it is lived as the indissoluble unity of right and duty. This common undertaking manifests itself in the individual act which actualises function on the basis of concrete circumstances and it is through this act that the undertaking advances to its end. Thus, the individual praxis is a self-suppressing mediation, or a mediation which negates itself for the sake of being transcended by a third party. But its unique and total aim is to produce a particular result as a means which has to be transcended towards the common end. He therefore produces his action in the light of the common objective, mediated by the future actions of the other members of the team, and, inseparable from the long term end, so as to dissolve in the common objectification. In fact - in a football match, for example his action has a common past - namely the perpetual reorganisation of the field by the players - and this common field is precisely what, at a certain moment of common temporalisation, rouses him in turn, as a common individual, to action (indicating the common danger, the common possibilities, the weaknesses of the present organisation, etc.). This common individual, with his powers, his tools, and his acquired abilities suffers, in praxis itself, an alienation to freedom: he cannot, in fact, set himself a common aim without it immediately metamorphosing into the individual aim of a free constituent praxis (passing the ball, conceived in terms of the whole organised field and as a means of offensive reorganisation, becomes the occasion for combining the positions and movements of the individual organism in his individual relations with the ball, in terms of the individual tactics of an opponent who is trying to intercept him; the essential moment of the action becomes that of individual struggle. Even before passing the ball to another member of his team and seeing the outcome of his decision gradually emerging, the individual must have triumphed, through his personal qualities, over another individual, in the other team; who has the same function and who has therefore benefited, in principle, from the same training, etc.) . But this transformation of practical power into isolated freedom is only a moment of the metamorphosis which leads up to the disclosure of common objectification; and this culmination is precisely the meaning of the transition to isolated freedom; this freedom is expressly designated as a mediation between the common individual (who is nevertheless defined fundamentally by an inert limit, to be reactualised + +in freedom) and the common objectification which realises itself at the same time as the individual action (a reorganisation around the passing of the ball) and reflects the common objective back to the common individual. Through the mediation of everyone' s individual praxis, the common individual objectifies himself as a common individual in the common objectification which produces him and which is produced by him. The moment of freedom has to be passed over in silence, since + +it would negate the team if it were to posit itself for itself. + +This indeed is what happens if one has no 'team spirit' - which is rare in sport, work or research, but frequent in some contradictory activities such as theatre. The 'great' actor, the sacred beast, has no team spirit: this does not mean that he relapses into his own individuality (that he arrives late, that he rehearses when it pleases him, or that he refuses to perform and pretends to be ill, etc.), or rather, since this does sometimes happen, it does not necessarily mean this. But it must mean that his free praxis posits itself for itself as an individuality from beyond. On the basis of the common aim, the common undertaking, the common organisation (every character being a function defined by actions, and speeches, which are strictly conditioned by the reciprocal organisation of times and places), he affirms himself alone. This already gives a hint of what is, as we shall soon see, usurpation: it changes the fixed places, the times of speeches, the order. Now, in individuality as power-beyond, this is not a return to seriality, but a confiscation of power for the sake of a single individual. He is not back in isolation; he is the group's actual unity. And in serving the common undertaking (Macbeth or Lear) everyone turns out to be serving him. + +We shall dwell on this point later. + +However, it should not be supposed that 'team spirit', that is to say, the strict interdependence of powers in connection with the common objective, results in the concrete agent being reduced to his function. This could not occur unless the situation - by its everyday banality could itself be assimilated to an abstract generality (the weather is fine, not too hot, the wind has dropped, the local team is playing at home against another team from the same region, a team which it knows and which is clearly inferior). As soon as unexpected emergencies arise (which, in a sense, is normal) individual initiative takes on considerable importance; in the final objectification, that is to say, in the totalisation of the undertaking by its result, the group as a past totality defines itself not by the order of its functions, but by the real integration of individual actions into the common praxis and by the hierarchy of + +individual initiatives in the context of the 'general' struggle. However, every third party appreciates the importance of a particular third party ('It's lucky you were there . . .', 'If you hadn't been fast enough to .• .' , etc.) in the total objectivity, that is to say, on the basis of the match as a totalisation which was developing and which has eliminated itself in an object (victory). This transcended totalisation (totality-in-the-past) is the concrete reality of organised praxis in all its contingencies and material accidents (due to accidental features of the environment), that + +is to say, of its historical temporalisation. + +By way of contrast, function (at the beginning of a match, for example) is, for everyone, a common and partially indeterminate signification of p ossibilities. So after his action, the individual manifests himself to the group as a concrete moment of the past totality, as a structure of irreversibility in its temporalisation, and therefore as a common individual. But this common individual is defined as a historical and concrete individual in so far as his action was an unforeseen (and, on the basis of function, unforseeable) moment of the common undertaking - or, to put it differently, of the reshaping of the group by the group. What is revealed as common by the group is the individual particularity of his action (in so far as his initiative was justified by subsequent developments). In him, the group becomes aware of having saved its common undertaking by a risky but successful manoeuvre. In other words, every third party becomes aware through him of practical freedom (the constituent freedom of praxis) as creative freedom in the common individual. This retrospective illusion is nevertheless a common structure: the group-totalisation turns back on itself as a transcended totality and, in this transcended totality, it perceives the free praxis of a given third party as the practical superiority of a given common individual. So-and-so, for example, is a good goalkeeper: he is good because on several occasions he has saved his team by his individual actions, that is to say by a transcendence of his powers in a creative practice. But if it is possible to speak of class-being, for example, in the practico-inert field, the reason is not hard to see : the complex system of alienations means that individual praxis realises its being in trying to transcend it. But it must be emphasised that in this case the opposite applies: the individual transcends his common-being in order to realise it; and being a goalkeeper or half-back is not like being a wage-earner. Function, as common-being, is an indeterminate determination which temporalises itself as a positive enrichment in circumstances which present themselves as concrete imperatives + +reqUlnng concrete choices; so, as soon as the common individual 'makes' one of these choices, he transcends himself as a common individual in order to lose himself in the common objectification. What will later be called the goalkeeper, the centre-forward, etc., in the organised group ('We have an excellent goalkeeper, but our backs are not that good', etc.), that is to say, the common individual in so for as his function is determined by his past acts (and, therefore, is characterised by his future possibilities: the team will count on the goalkeeper, will rely on him for a particular operation) possesses only past heing. This being, who is the object of a non-temporal designation (even though the process is temporalised), reveals himself to the practical, retrospective perception of the common undertaking; but in the moment of temporalisation, he is not: he is free organic praxis transcending function so as to become annulled in the common objectification but who, in particular circumstances, appears as an irreducible signification of the transcended, structured totality. Function is abstract imitation, inertia transcended and preserved by the action, in the moment of temporalisation; or it is, so to speak, the particularity of common individuality in so far as the action, in the past, is confined within the limits it prescribes (not so as to have been incapable of realising anything but its own power, but so as to have deliberately set itself this realisation as an objective). In the organised group, in moments where the practical tension relaxes (though the group does not dissolve), the common individual perceives his function as his common individuality: the past meaning of his present is both his task as a prescription-pledge and his actions as actualisations of his task, transcended in the course of earlier undertakings; the future meaning of this same functional present is· the determination of his power (in future undertakings) by concrete possibilities which define themselves simply as the projective transcendence of past actions and their metamorphosis into a future beyond of the right-duty couple: a good goalkeeper is individualised as a common individual in so far as he produces himself in the future through his past actions as capable of doing more than is expected of everyone at the normal level of organisation. He becomes capacity. Now, this capacity as determination of the possible future is simply the practical, constituent freedom of the organic individual lived as the free future individuality of the common individual; it is past, transcended praxis in so far as the member of the organised group lives it as the individualisation of his being-in-the-group; lived as future exis, it is past freedom. By allowing his free praxis to be absorbed by the common + +threat, the danger and means of defence (or attack) are always otner and vary according to spatial and temporal determinations. But the source of the differentiation may be internal : precisely to the extent that the instrumental complex which characterises a group (in its evolution) can be regarded as the immanent common object of this community; in this case, the objective of the distribution of tasks is either a better use of technical equipment or else a response to the pressure of new inventions and new tools. In any case, the important point is that the group reinteriorises alterity the better to struggle against it: either to dominate the complexities of an immanent object; or to confront a transcendent (transcend ante) diversity. In the organised group, the alterity of the members is both induced and created. Following the pledge, in effect, every third party remains the same as the other third parties, even though the pledge is made with a view to a differentiation (still abstractly foreseen). In other words, the third party undertakes, by means of his pledge, to commit himself to negating any possibility of alterity, arising either from his own action as a practical individual, or from any exis whatever. (The young pledged member of a combat group is given a new exis by the situation: for example, he is the one who has never fought before, who has not known war, etc. That which, in the moment of civil peace, was only an abstract and purely logical determination, in praxis, through enemy pressure and through the common objectives, becomes an exis - a complex of negative possibilities, of being unable to shoot, of being afraid, etc. - and this exis distinguishes him from, for example, the old soldier who is making the pledge next to him; he is otner than the old soldier. But by his pledge, the young fighter swears to put this alterity in brackets, and to + +render it accidental and negligible). + +But, in the dialectical development of a statutory group and in its transition to an organised group, it is clear that the function of the pledge (to exercise terror over the Other and, making a clean start, to establish the dictatorship of the Same in everyone) is to serve as the basis for the reintroduction of alterity. As Levi-Strauss would say, it is suppressed as Nature, and reinteriorised as Culture. Alterity-Culture becomes a creation of man and a free means of preserving the free group when the group is able to make an indissoluble connection between the following two approaches: both affirming the radical lack of differentiation and strict equivalence of its members as common individuals (through the pledge); and itself producing functional alterities on the basis of this perfect equivalence - producing, that is, + +alterities which define the Other in the Same by his task.33 Thus, to the extent that the group has so decided, everyone is Other in the group, just in so far as this alterity is a relation defined by a rule, in conformity with a praxis and in so far as this relation, to the extent that it has been estahlished, is capable of being the object of practical understanding. As a member of a series, I do not understand why my neighbour is other; serial alteration reinforces accidental alterity (birth, organism) and renders it unintelligible; as a member of a living organisation, I understand that the Other is a practical and signifying creation of us-as-thesame (nous-les-memes). From this point of view, another team-member's relation to me is entirely comprehensible: he is, so to speak, the means, the object, and the principle of all practical understanding in the organised group. He is other hecause it is necessary (from the point of view of the common objective and of the common praxis which he indicates at the horizon) that this or that should be done, to allow the completion of some other task, which conditions the possibility of me + +carrying out mine. + +And the teleological link between these functions is immediately given in the functional action: there is no need to explain it in words or to take a contemplative view of it (which would in any case be impossible). Action and comprehension are one. In comprehending my own aim, I comprehend3" the aim of the Other, and I understand both and those of all the Others - in terms of the common objective. And, + +33. In fact, as we have seen, the real process is often more complicated than this, because the statutory group, when it is incomplete, develops and organises itself by creating functions in accordance with nature-alterities. 'The strongest person will do this,' etc. But it is sufficient simply to note this fact. Beneath the surface, the process is the same: it is just that in this new case, the common use of a natural difference suppresses it as nature (accident, chance, the negative and serialising influence of the individual past or of individual organic characteristics) and consecrates it as culture. A particular strong man becomes function and his power is his strength: the group consecrates it in him; and this is the original meaning of: 'Give away everything and everything will be rendered unto you.' This imperative is typical of the group, and means: negate negative alterity in yourself, cast it off to the common benefit of positive alterity (negate your youth, your fear; give away your vigour and agility), and you will be reborn as a common individual produced by the group without negative alterity; as for positive alterity, it is a power which the group has created and consecrated in you and, as such, it can be amplified (physical strength by training, by weapons, etc.). I note this in passing, but concentrate on simpler facts in order to grasp their intelli- + +to precisely the extent that the group restores individual 'qualities' as a consecrated power, differences of training or physical strength which benefit some Other receive, so to speak, a statute of intelligibility: it is as if the group had at some point produced the strength and the brains it required. Hence my relation to this brain or these muscles will be primarily social, based on the ubiquity of the pledge and the equivalence of everyone who is the same (des memes). He is not primarily a stronger man than me; he is primarily a reinforcement of the common defences in a particular place which is more liable to attack than any other. But the express condition of this practical reinforcement is egalitarian fraternity; it is merely a special form of it: the pledged relation of fraternity is channelled by a functional relation. In fact, in small organised groups (without any direct relation to the appearance of command), the limits of everyone's powers, what falls within the competence of one third party and what into that of another, is always carefully and exactly determined. Conflicts within the group frequently arise because competences have remained indeterminate in some respect or other, or because some new circumstance, by creating a new problem, produces a provisional indeterminacy in certain functions (and + +therefore in the relation between men). + +Thus freedom, as common praxis, initially produced the bond of sociality in the form of the pledge; and now, it creates concrete forms of human relationship. Every function, as a relation between me and a particular Other or all the Others, defines itself negatively as a reciprocal (direct or indirect) limit of competences, and positively as the action which makes my action both necessary and possible. But function is the common individual, or everyone's being-in-the-group. At the level of the organisation, being-in-the-group is no longer an abstract, polyvalent determination of human relations; it is the organised relation which unites me to each and all. But this human relation, by concretely expressing a heing, receives an inert rigidity from it. In fact it involves reciprocities of powers based on the pledge, that is to say, on the free negation of certain possibilities. In fact, the relations between common individuals, in so far as these relations present themselves as a tem- + +which, within a particular group, the common individual no longer understands the function of the others, or fails to understand that a particular function is fulfilled by an Other rather than by him. I would ask the reader to be patient, and recall that a dialectical investigation is circular. We shall get to it when the in- + +poralisation of their 'being' within definite limits, aim to leave nothing indeterminate. (This is clear when, for example, the first meetings of a society establish its office, secretaries, treasurer, committees, etc. ; and still clearer when the relations are hierarchical). The determination of competences, being a distribution of tasks, implies that a given functional individual can never have a certain type of relation with another: + +this is the negative meaning of all 'rules'. + +In the organised group, human relations involve their own freely accepted limits. But, as we saw above in connection with the task, the concrete limitation of statutary relations corresponds to a positive enrichment: within the limits of hierarchical relations, for example, numerous sub-possibilities differentiate themselves, whereas in a pledged group, the only possibility, in its total abstraction and complete indeterminacy, was for everyone to preserve the group from all kinds of external and internal threats. It was the same thing (in a negative sense). But the hierarchical relation of superior to inferior, for example, consists precisely in avoiding internal ruptures (insubordination or slackness) by positive and adapted actions (a joint rejection of voluntarism and obedience, etc.). The aim of the parties to the pledge, on the other hand, was urgent but still vague: the Tennis Court oath is an example of this. Faced with a still imprecise threat, but with an increasing hostility from the aristocracy and court, the deputies of the Third Estate swore not to allow themselves to become divided. They did not know what their tactics should be. And in fact it was the people of Paris who resolved the problem. The unification of an organised group, in contrast, is always defined by its objective, which is concrete. The relations between common individuals must, therefore, I:e constantly created within the limits laid down by a concrete task and + +solely with a view to the successful completion of this task. + +Now, this relation is no longer the simple, indeterminate relation of each to each, with and through all : it is primarily a particular mediated reciprocity which unites an X to a Y (or to several Ys); the mediation is effected by the whole group as a developing totalisation (rather than as a complex of units), that is to say, as a common praxis laying down its own laws; and it is through the mediation of new reciprocities - this time uniting the Ys to the Ms, and thereby the Ms to the Ns, etc. - that the common term X relates to each and to all. Thus every common individual is specified, and his direct and indirect relations within the group are necessarily specific and established with specified other individuals. Furthermore, in this concatenation of specific relations + +which unite an X to the Y s, then, through the Ys, to the Ms, and through the Ms to Ns, etc., the group intervenes, as a totalisingpraxis defined by its objective, in every new relation, in order to perform the mediation. However, the structure described here is too simple; and in fact, it complicates itself of itself. In fact, it should be noted that there is always a concrete possibility that the mediated relation between X and N will arise, at the same time and in the same connection, both by an indirect chain of specific relations and directly. If this possibility were realised, two sub-possibilities would remain: either the direct and the indirect relations between X and the Ns will not differ in their specification (the general has his orders transmitted to soldiers through the hierarchy, but in certain circumstances he may be in direct contact with a fighting unit and give them orders personally), or the specifications of the direct and indirect relations are different. (In principle - and setting aside for the moment the question of what actually happens the hierarchical and indirect relation of a Soviet manager with 'bluecollar' and 'white-collar' workers is mirrored within the Party, of which the manager and many of the workers will certainly be members, by a direct relation in which the hierarchy is dissolved and replaced by another hierarchy. It is possible - though this is a purely logical hypothesis, and never actually happens - that the manager might indirectly command a local leader of the Party and, as a member, directly obey him, and find himself directly under his orders.) In fact it often happens that the two cases occur together and define the same power in relation to two different sub-groups. An X has direct and indirect relations of identical specification with Ms; and direct and indirect relations of different specifications with Ns. These various relations may be established with the distribution of tasks; and it is not rare for them to be specified in the course of common action. And it should be added that, if the group is numerous and relatively dispersed, indirect relations tend to disperse into indefiniteness; or else the limitation of competences may, for a whole interior zone, fail to determine the common relation which is to unite common individuals to specified powers : in either of these cases the original 'Terror-Fraternity' relation reappears in all its starkness, generally in its positive form; the common individuals whose existence I am aware of, who work in the common praxis, and whom I cannot touch directly, are my hrothers. But fraternity, as the affirmation that every Other is the Same, does not eliminate heterogeneity. Each of the workers, of the sportsmen or combatants is my brother in so far as hy his differentiated function he + +commands me and enables me to fulfil n'!Y Junction. Fraternity reveals itself as the immediate and fundamental relation which subsists in its abstract starkness between heterogeneous individuals in the absence of any specified relation. In direct or indirect functional relations this fundamental link subsists, as the synthetic bedrock on which all relations are built; but it does not allow itself to be grasped in its abstract strength, precisely because it is there to serve as a basis for differentiations. Thus two common individuals within a sub-group may well abstractly designate the bond between them as fraternity: but in fact - except when the historical conjuncture dissolves all specifications without breaking up the group - this is only a verbal determination. It is in their reciprocal action, in their function, in their specific relation as mediated, that they actualise the fundamental bond and transform it by affirming it. But at this level of praxis, discourse is practical and concrete: it is used to give orders or to name everyone's + +respective function. + +Furthermore, in arbitrarily considering 'an X' in his relation with the Y s, I have, for brevity, presupposed an absolute beginning. This has no importance provided we re-establish the true procedures of dialectical investigation, but it would be a mistake to stop at this way of classifying or of thinking: indeed, if it were necessary to begin arbitrarily with the sub-group of the Xs or the Ys or with any other subgroup in order to conceive the ensemble of mediated relations, one would have to admit that there was at least one case in which all functions are independent of each other: the case in which the group and its structures are explained in terms of any one of them. In fact, the relations of X to the sub-groups ofYs, Zs, etc., have meaning only in tre true milieu of the organisation, that is to say in circularity. For the possibility of beginning the explanation of specific relations anywhere and everywhere really means that every relation is double: X has afunctional link with Y and Z only in so far as the specific relations, both direct and indirect, of all the individuated powers of the group turn back on him and specify his power. In other words, I can, a priori, determine the powers of X on the basis of Y as well as those of Y on the basis of X. Of course this is a logical determination : actual praxis emphasises subordinations and co-ordinations, either temporarily or definitively. But if the practical structure of an organised group has an orientation, and if, practically, it is this orientation which I have to find (,Who is responsible?', 'Who must I speak to ?', etc.), this vectoral reading does not destroy the circular structure: this structure, in effect, + +is simply the determination of the milieu of 'Fraternity-Terror' by + +mediated reciprocity. + +In our investigation we have discovered that, whatever the organised group may be concretely, it is a complex circularity of mediated reciprocities, both direct and indirect. In this respect, it merely determines and enriches the reciprocity which we have seen to constitute the original bond of the fused group. But we cannot go any further unless we examine this new type of reciprocity - which is born of fundamental reciprocity, and is a construction of the group, and, in fact, a + +product of its work on the original relation. + +Now, the first effect of this work is that it inverts the fundamental relation. In the fused group, mediated reciprocity emerges from praxis itself as a relation of convergence between two third parties who come together in the generating movement of the group: I see the advent of myself in the other (the same) in so far as the other sees the advent of himself in me, and, through this very movement of regroupment, everyone becomes in turn a constituent and a constituted third party. Reciprocity is a direct, convergent, lived relation. As we have seen, the vicissitudes of action and the transformations of the situation gradually produce the diversity of tasks. Even at the level of the fused group (elfewhere is always here; but elsewhere, the enemy is other and behaves otherwise), this diversity is interiorised; and it is as a defence against the dangers of differentiation that the group recreates its unity in the freedom of the pledge. But the pledge itself, as a fundamental relation between agents, is reciprocity. Only reciprocity can produce in me a free limitation of my freedom: as I have already shown, I rediscover myself in myself as Other-Freedom in so far as, for the Other, I am his guarantee of always being the Same as myself; and in so far as the Other's pledge is for me a guarantee of being the Same as him. There is reciprocity here but, in so far as it allows practical freedom to be affected by inertia, it is already a worked reciprocity. The pledged member uses mediation by the group so as to entirely transform the free spontaneous relation which appeared at the beginning of our investigation. As soon as the pledge is given, reciprocity becomes centrifugal: instead of being a lived, concrete bond, produced by the presence of two men (with or without mediation), it becomes the bond of their absence. In his isolation, or in the milieu of the sub-group, everyone derives his guarantees and imperatives from the inertia which affects common individuals whom he no longer sees. In this sense, reciprocity is no longer the living creation of bonds; it is, on the + +contrary, reciprocal inertia. Through the pledge, man rebels against the separating power of inert materiality (spatio-temporal distances, obstacles, etc.), but at the same time, he interiorises it; and reciprocity, as an inert limit of freedom, comes to man from outside, as exteriority against exteriority, and it exists in him as worked matter. This very inertia, still in a crude state, is what is refined in everyone by functions, and transformed into precise tasks, into practical relations with instru- + +ments, with places, with enemies or with things. + +Since this inert reciprocity is established to serve as a basis for powers as alterity reappearing inside freedom, it is important to understand an apparent paradox: the heterogeneity of functions (even in a hierarchy) is simply a determination of inert reciprocity. I call this an apparent paradox because, at least from the point of view of positivist logic, relations which unite two heterogeneous terms and refer to them in their heterogeneity seem vectoral, that is to say univocal, relations, Between one common individual and another, it is possible to establish a double system of directed relations (in opposite directions). But their differences of function apparently make it impossible to merge the two systems into a single, two-directional system. A doctor treats the deputy mayor; and he votes for him in the municipal elections. Thus there is a set of relations proceeding from the doctor to the patient (treatment, the practical knowledge of his body and its deficiencies), and of others proceeding from the patient to the doctor (trust, fees, etc.). Now we can add another relational system: administrator -+ administered, elector -+ elected. Of course these circumstances all interact and the relations condition one another. Nevertheless, reciprocity seems to be excluded a priori: it would be absurd to say that the doctor is to the patient what the patient is to the doctor, and perhaps even more absurd to say that the doctor is to the patient what the + +administered is to the administrator. + +But this is because we have deliberately taken our example from a social situation which is not characterised (at least not necessarily) by the individuals belonging to the same organised group. Thus heterogeneity is to some extent (we shall see later how much) based on suffered, serial alterity. It may be that the doctor is treating the deputy mayor because they belong to the same political group (they met during an electoral campaign, etc.), but it is not true that he became a doctor in order that the other should become deputy mayor - nor conversely. In an organised group, however, heterogeneity derives from thp. needs of praxis; it is created on the basis of reciprocal sureties + +and is a determination of mediated reciprocity. Sometimes it is incorrectly called interdependence. But interdependence, as we have seen, can be suffered in serial alterity: in an inert gathering, everyone depends on the others in so far as they are Others and in so far as he is himself an Other. But here, interdependence is a free overthrow of serial interdependence: everyone depends on the Other in so far as they are both the same. The mediation of functions is the common praxis: the group produces me as the power to realise a certain detail of the common praxis so that this praxis can be realised in its totality and differentiate itself (se dltailler) in objectifying itself; by performing this function, and through the development of the common action, I allow every particular function to differentiate itself, and to realise itself + +as another detail of the objectification. + +Thus the reciprocity of two radically heterogeneous functions remains unintelligible as long as they are not mediated by the practical group, but its full intelligibility emerges as soon as both functions are understood in terms of the common praxis. But this should not be taken to mean that every organised group, or every agent, is indispensable; This obviously depends on the objective and on the circumstances: indeed the common individual has, as it were, a marginal utility, because, according to circumstances (lack of finances, of weapons, or of men), functions are eliminated in a certain order, which varies according to the praxis and its aim. But though such a reorganisation is always possible, in accordance with some scarcity, it is in fact the creation of some other group, with other means and, often, a more limited objective. The problem is not to determine who is and who is not indispensable to the common action; or rather this problem is practical rather than critical. The important point, for us, is that in a group in action, the organisation of powers and tasks creates a concrete internal milieu with its own structures, tensions, and immanent relations; and this internal milieu, in so far as it defines itself in relation to a transcendent objective, is the practical reality of the group, its physiognomy and internal objectivity. In so far as every function maintains this objective reality through particular events, and for a given multiplicity (and in fixed or only slightly variable conditions: budget, means of communication, etc.), it is the reciprocal counterpart of the others. That any particular function may atrophy or disappear when the situation is transformed is obvious : but this will only occur if the group proceeds to a rearrangement and modifies the internal relations of its members, and therefore its structure. Functions are reciprocal in + +that all of them, in reciprocity, help preserve a particular internal physiognomy of the group in activity, that is to say, in so far as they have been defined by a practical plan which is the guiding schema of + +the action. + +A political group which undergoes a purge and survives it thereby demonstrates that the purged members were not indispensable to it: but, at the same time, it becomes other and the new statute which it gives itself defines it irreversibly. But most of the time, all functions are initially all equally indispensable : this is because they are established on the basis of certain techniques and instruments which themselves helped to define a particular type of action. Later, this action may appear wasteful and ineffective, but only from the point of view of other techniques and instruments. It is therefore impossible ever to make an absolute hierarchy of functions (which define themselves in a dated temporalisation). On the contrary, the fundamental character of an organised group is that all these functions are conditioned and guaranteed by the mediation of the developing common praxis. Hence every function becomes the signification of the other in so far as it is itself signified by the praxis; and every function contains the other in its practical activity. This is particularly evident in small, highly disciplined groups, like sports teams, in which every movement of a fellow member, seen in its Junctional differentiation, is decoded in the very movement which it occasions in another fellow member, as a differentiated function, through the practical field defined by the action of the group and as a function of all the other movements. 35 Mediation, for a given goalkeeper or centre-forward, is the pitch itself in so far as their common praxis has made it a common practical reality to be occupied or traversed with a variable co-efficient of instrumentality and adversity; and every developing reorganisation of the team on the field constitutes it through the pitc1z itself as Junctionally situated (in relation to the ball, to a particular opponent ahead of him, etc.). But as soon as he takes up this spatio-temporal situation and transcends it by his praxis (in accordance with his function), the common situation of the whole team is reciprocally modified. For a spectator, to understand a match is precisely to decode the functional and individualised + +35. In fact, in a football match, everything is complicated by the presence of the opposite team. The positive reciprocity between members of a team is closely connected with a negative and antagonistic reciprocity. But this complication + +particularisations of mediated reciprocity as a perpetual totalisation on + +the basis of a known objective. + +But inert reciprocity as reciprocal inertia cannot be reduced to the simple forms just described. Of course, it is and remains centrifugal, and affirms itself in opposition to the void and to separation. But we have just seen its original structure: it is necessary for A to do what he does for the common praxis in order that B can do what he does, and conversely. This structure becomes complicated under the pressure of circumstances simply because it becomes a sort of inorganic materiality of freedom. Thus, in a way, through inert reciprocity, inorganic materiality again becomes the mediation between practical agents, like the worked thing (precious metal, etc.) in the practico-inert field. This means that the group acts constantly on itself in order to modify its possible counter-finalities and that it can act only by creating new reciprocities. In fact, organisation, as internal praxis, can neither produce nor preserve itself in the milieu of reciprocity unless it becomes a determination of this reciprocity as a free, inert relation of synthetic + +interiority. + +So far, we have always described organised groups as if they were composed of relatively homogeneous individuals or of ones who differed only in respect of some qualities whose very diversity corresponded h armoniously to the differentiation of their functions. But this would hardly apply even to selective groups, carrying out their own enrolment according to definite rules. But the organised group is a very broad genus of which the selective group is only a small species. In fact, organisation takes place on the spot, with whatever means and men are available (at least in most cases and in the living moment of constitutive activity). Thus the synthetic bond of unity and the rule of reciprocity - which distinguish the group from other multiplicities, into a particular, hitherto inert, multiplicity - positively reveal, within the resulting interiority, as a function of these bonds of interiority, differentiations which, outside the group, were simply inert relations of exteriority, and inside the group become involuntary reciprocities. An example may make this clearer: throughout this investigation we have maintained that a nation is not a group. Consequently the proportion of young and old in a nation depends on complex processes (which, as we shall see, alone represent the absolute concrete - that is to say, the perpetual conflict between group praxis and practico-inert processes, the presence of common structures even in seriality and of seriality even in organised groups) which, taken as a whole, cannot + +correspond to any praxis. Amongst these processes, in fact, the demographer will attempt to designate, as immediate factors, sexual behaviour in the different classes of a particular society, progress of domestic hygiene and of medicine - in other words, medical technique in relation to the infant and old age mortality rates. And these data will be taken from a society which is already defined by the relation of its children to its old people, that is, a society which bequeathes to its new generation a certain demographic structure on the basis of which the demographic tendencies arising from new conditions will partially modify this inheritance. Of course, as Marx indicated in a passage quoted in The Prohletn of Method36 'population' is an abstraction: its variations refer us to all the material conditions and to the historical process. Thus the rise in the French birth rate after the Second W orId War is a process whose development can be studied without any complete understanding of its signification. (At first it was thought to be a temporary phenomenon, common to all post-war periods. But it has persisted and stabilised, which is somewhat paradoxical since it + +is, at least in some respects, peculiar to France.) + +But as soon as economic (or social, technical, or political) research turns to French production - or the redistribution of national income or the demographic demands of economic progress, etc. - and, using some constantly revised working hypothesis, decides to treat the active population, or various groups of workers (defined as primary, secondary or tertiary, or by class, or according to any other synthetic project) as a unified group, the relations of pure exterior contingency which apparently unite an Alsatian adult, living and working in Paris, to some old man born in Paris and to a fourteen-year-old boy from Nantes who passes them in the street, suddenly appear as structured in reciprocity. Within the group of producers, in effect, the old man and the boy become non-productive elements who have to be fed. However, for society, the child is an investment: society spends money to make him a worker. The old man is more or less a dead weight (it goes without saying that I am looking at these relations strictly from the point of view of contemporary economists and demographers). On this basis, we can see how adults (who, even in primitive society, + +36. The Problem of Method, p. 49. 'The population is an abstraction if I leave out, for example, the classes of which it is composed. These classes in turn are an empty phrase if ! am not familiar with the elements on which they rest. E.g. wage labour, capital, etc.' See Marx, Grundrisse, trans. Nicolaus, Penguin Books, 1973, + +confuse death and birth, childhood and old age: not primarily in the name of mysterious intuitions, but because they are useless mouths) are engaged in a double reciprocity: regardless of the social system, part of their product will in fact go to the child, and part to the old man. In the case of the child, the reciprocity is that of capital invested with interest: he is maintained so that one day he can take over and maintain others in turn; and he allows himself to be kept, controlled, and produced with a view to this future. The other reciprocity refers back to the past; it is a temporal reciprocity. The contract or pledge, without ever having given rise to any particular act, goes back to the period when the old man was an adult at the height of his powers and the adult of today a c:!ild. Thus we encounter the original situation again, though we live it in its consequences and thirty years later; and this shows that functions, as reciprocity, can succeed one another, the second appearing when the first no longer exists. But this is not what concerns us here. The important point is that if one totalises, then differences will be interiorised and lived as special characteristics of the common praxis, that is to say, as the internal physiognomy of the group. The French community considered as a productive group has its present structure, and a different future, because of the proportion of the young (under IS, for example) to the old (over 60), that is to say, because of the proportion in it of useful work (production of goods, of future workers) to sacred work (pledged reciprocity, the maintenance of old workers). In reality, for the sake of simplicity, demographers, sociologists and economists choose to treat the active community as if it were an organised group : and this is quite justified as long as they see it merely as a heuristic hypothesis or a method of exposition and do not allow + +themselves to be taken in by it. + +But this example shows clearly to what extent, in the common act of pledged association and through the synthetic structure of reciprocity (the only fundamental structural bond of the group), the practical unification of a multiplicity into a group gives rise to heterogeneities which produce themselves in serial inertia as non-reciprocal but which, in the common praxis, have to be lived as reciprocities. This means that in the milieu of mediated reciprocity nothing can happen except in the form of reciprocity; but this means too that the heterogeneity constructed and sustained by the pledge reveals non-constructed and non-functional or pseudo-functional heterogeneities (that is to say, heterogeneities which determine themselves in this functional unity as functions or as counter-functions). Mediated reciprocity, as a free + +determination of the common praxis, is constantly traversed and is always in danger of being modified by secondary reactions of reciprocity developing from the distribution of tasks. These secondary reciprocities have the same structures as primary ones: they are mediated by the common praxis and through this mediation every individual characteristic becomes functional. In the case under consideration, for example, the totalisation of productive forces makes age a characteristic of the common individual. In this way, it helps give the group its physiognomy; praxis would be different if the proportion of old and young varied. But though these secondary reactions may be favourable to the common activity (it is not logically impossible), the fact thaJ they arise from the pledge does not mean that their origin does not lie in the practico-inert. Thus, the possibility that they may impede, or slow down, or divert praxis is also present a priori. Besides, it is not out of the question that they will endanger the group even + +when they constitute an internal factor of acceleration. + +It is well known that Rakosi set out to liquidate the Hungarian petty bourgeoisie and proletarianise it. But a number of workers in Budapest were former members of the petty bourgeoisie, and as petty hourgeois they were deeply opposed to the regime. At the time of the rising, when the workers organised demonstrations, this group, through its common action, developed in reciprocity its internal contradiction. The proletarianised petty bourgeoisie accelerated the insurrectional movement and, in certain places and in certain cases, gave it a counter-revolutionary aspect. This did not in any way correspond to the action of the true workers (that is to say, workers of working-class or peasant origin), but it was used later as a pretext for justifying Soviet intervention.37 In so far as factory work could not escape the practico-inert, it was incapable of opposing the two groups of workers to each other. In short, these two groups did not exist and, given the temporary impossibility of even imagining an insurrection, the origin of a worker remained an accidental matter for the Others. In the unity of a praxis, however, the workers - who as alienated producers were all really members of the working class - grouped themselves as a class and + +37. I did not take account of this in my article Le Fantome de Staline (Les Temps Modernes 129-30 [1956-7]; reprinted in Situations VII; trans. The Spectre of Stalin, London, 1969. [Ed.]), because I was unaware of it. It was later - some weeks afterwards - that I learned of it from reliable wi tnesses. Need I say that this correction makes absolutely no difference to my conclusions and my position? + +thereby caused class conflicts to reappear inside their practical community. The majority remained working-class, but the minority revealed itself to be petty bourgeois and demoralised. The violence of the hatred and despair produced a ferment; it triumphed, in so far as it was lived in reciprocity. But it also denatured. It is known tha t the insurrectional committees arose partly in order to struggle against this denaturing. Nevertheless the whole group had to live the contradiction of its minority, in which the condition of the workers opposed the class-being of the petty bourgeoisie. In other words, the group could not exclude by violence pledged members who were pursuing the common aim or at least seemed to be doing so, and perhaps believed they were too; but it was too late to do any effective rearrangement or reorganisation: there was not enough time, and the second intervention inter- + +rupted the reorganisation when it began. + +For a group which is organising itself in the reflexive awareness ofits practical unity, the problem is not so much the neutralisation or elimination through violence of reactive reciprocities, as their reappropriation and their retrieyal in the light of a consciously pursued objective. But although the abstract possibility cannot be ruled out a priori, and many examples of it could be cited, such reciprocities are not usually dissolved in freedom; as a rule, freedom tries, through the action of all common individuals, including those through whom a reciprocal counter-finality is manifested, to provide them with a foundation as free, created functions. Indeed, at this level, Freedom-Terror itself comes to be respected as a free, diversifying integration: when counter-finality presents itself as a movement towards some more total integration, it is respected for showing the face of unity. This is why - particularly in combat groupings - sectarianism and all forms of violence initially manifest themselves in the form of respect, and then get the upper hand (for the point of view of a totally adapted praxis imposes itself only gradually). On the other hand, in so far as secondary reciprocities appear to threaten praxis with paralysis (or to threaten the group with serial dissolution), Terror, as the liquidation of interiorised differences, attempts the exclusion of third parties and the liquidation of pseudo-functions. In any case, these abstract considerations can only be meaningful in the context of a historical study of a particular group. I refer to them here simply in order to indicate the nature of the perpetual work which the group must perform upon itself. In fact, in so far as this work tends to transform interiorised alterities into functions, which is the usual case and the one which concerns us at present, it is + +bound to effect this integration on the basis of the aim and of the primary reciprocities. But this immediately shows not only that the true work of organisation is the synthetic production and the distribution of tasks, but also that it must constantly effect the synthesis of the mediated reciprocities which arise in different layers of the common reality. The organised group cannot be practical and alive except as a progressive synthesis of a plurality of reciprocal fields. In other words, all common organisations are pluridimensional. In fact, as the task becomes more complicated and the volume of the group increases, systems of simple reciprocities are replaced by systems of composite reciprocities. In particular, the appearance of commutation (which is often destined to compensate for reactional alterity) introduces a successive system of temporalised reciprocities the function of each of whose intermediary relations is simply to mediate mediations between the initial and the terminal relation. This is not the place for an abstract logistical study of reciprocities, though such a project might tempt a mathematician . A calculus of reciprocals would obviously leave out of consideration practical totalisation as the mediation and foundation of this original, social relation; but, on the other hand, it would provide a rigorous elucidation of the typical organisations of the reciprocal, of their developments and interactions - and of substitutions of terms and transformations of elements in so far as these modifications of indivi- + +duals leave the structures of the system intact. + +But if it really is possible to devise a theory of reciprocal multiplicities in organised groups,38 independently of all concrete, historical ends and of any particular circumstances, do we not immediately collapse in the face of an inert ossature of the organisation? And do we not abandon the terrain of liberatingpraxis and the dialectic and revert + +to some kind of inorganic necessity? + +3 Structures: the Work of Levi-Strauss + +The entire question of the intelligibility of organised praxis arises at this leyel: There can in fact be no doubt that reciprocal relations can be + +treated by the 'exact sciences' : and they are already present, as a foundation, in the administration of a school when it decides the timetable for a particular class or in the strict arrangement (by the management of French Railways for example) of the train timetable of a particular network for the winter or summer period. But, on the other hand, it should be noticed that these calculated determinations nevertheless refer to actions (in railways, for example, they involve not only finished, 'crystallised' work - machinery, rails, etc. - but also the actual work of the railwaymen, from engine drivers to ticket-collectors). Thus the peculiarity of this 'ossature' seems to be that it is both an inert relation and a living praxis. It should also be added that the permanence of the relation as such does not in any way imply the immutability of the terms or of their positions; there may be considerable changes, provided they take place in such a way that the specific determination of reciprocity is preserved. This has been explained admirably by Levi-Strauss in his work on The Elementary Structures of Kinship. We should note in particular how his study of matrimonial classes led him to this crucial conclusion: 'These classes are much less conceived of in extension, as groups of objectively designated individuals, than as a system of positions whose structure alone remains constant, and in which individuals may change position, and even exchange their respective positions, provided that the relationships between them are maintained.'39 But above all Levi-Strauss's work makes an important contribution to the study of those strange internal realities which are both organised and organising, both synthetic products of a practical totalisation and objects always susceptible of rigorous analytical study, both the lines of force of a praxis for every common individual and the fixed links between this individual and the group, through perpetual changes of both of them, both inorganic ossature and everyone's definite powers over everyone else, in short, both fact and right, mechanical elements and, at the same time, expressions of a living integration into a unitary praxis of those contradictory tensions of freedom and inertia which are known as structures. Function as lived praxis appears in the study of the group as ohjectivity in the ohjectified form of structure. And we shall not understand anything of the intelligibility of organised praxis as long as we do not raise the question of the intelligibility of structures. + +39. C. Levi-Strauss, Les Structures Elementaires de la Parenti, Paris, 1 949, trans. von Sturmer The Elementary Structures of Kinship, London andBoston, + +But let us quote Levi-Strauss, one of whose examples will be helpful + +to us: + +'Suppose there are two patrilineal and patrilocal family groups, A and B, united by the marriage of a b girl and an a man. From the viewpoint of group A, the b woman represents an acquisition, while for group B, she represents a loss. Thus, for group A, which benefits, the marriage is expressed by a change to a debit position, and for group B, which is decreased by the loss of one female member to the profi t of group A, by the acquiring of a credit. Similarly, the marriage of each of the men of group B and of group A represents a gain for his respective group, and thus places the group in general, and the family involved in particular, in the position of debtor. By contrast, the marriage of each of the a or b women represents a loss, and thus opens up a right to compensation .... Each family descended from these marriages thus bears a sign, which is determined, for the initial group, by whether the children's mother is a daughter or a daughter-in-law .... The sign changes in passing from the brother to the sister, since the brother gains a wife, while the sister is lost to her own family. But the sign also changes in passing from one generation to the next. It depends upon whether, from the initial group's point of view, the father has received a wife, or the mother has been transferred outside, whether the sons + +have the right to a woman or owe a sister .... + +'Each couple bears a ( + ) or ( -) sign, according to whether it results from a woman being lost to or acquired by line A or B. The sign cha�ges in the following generation, the members of which are all cousins to one another .... It is now only necessary to look at the cousins' generation to establish that all those in the relationship ( + + ) or (- -) are parallel to one another, while all those in the relationship (+ -) or ( - +) are cross. Thus, the notion of reciprocity allows the dichotomy of cousins to be immediately deduced. In other words, two male cousins who are both in the credit position towards their father's group (and in the debit position with regard to their mother's group) cannot exchange their sisters, any more than could two male cousins in a credit position with regard to their mothers' group .... This intimate arrangement would leave somewhere outside not only groups which did not make restitution, but also groups which did not receive any- + +abstract summary of several concrete studies, is that it displays the structure as a complex reciprocity of credits and debts. These credits and debts, of course, depend on a basic dichotomy: they are reciprocities which unite two groups. But, from our point of view, there is no difference between groups-united-by-a-system-of-matrimonialrelations and sub-groups.41 Now, we can also see that a debt presupposes a power, a right acknowledged by the individual or the family and appropriated by some individual or family of the other sub-group, the system being a mediation hetween the two parties. Of course, this is a mediated reciprocity and, in a sense, a concrete relation between a demand (in the name of the common pledge) and a free will which has freely deprived itself of the freedom to refuse. In short, the debt of family group A (which has just acquired a daughter h by marriage) is a debt which is lived, created hy actions, and accepted or even undertaken, though certain complex circumstances of family histories may cause it to be cancelled (hence violent conflicts between groups). In spite of this, the debt is capable of being represented by an algebraic sign associated with a symbolic designation of the group (A) or of the individual (a), and the same applies to the credit which corresponds to it. And their mutual, symmetrical relation can be expressed by an exact proposition: in the matrimonial system of 'cross-cousins', no individuals who (as a result of the system of filiation) possess the characters (+ +) and (- -) can be united; marriages can take place + +41. The abstract point of view of critique can obviously never be that of the sociologist or the ethnographer. It is not that we are denying or ignoring the concrete distinctions (the only real ones) which they establish: it is simply that we are at a level of abstraction at which they have no place. In order to connect with them, one would need the set of mediations which transform a critique into a logic and which, by specification and dialectical concretisation, redescend from logic to the real problems, that is to say, to the level at which real History, through the inversion which is to be expected of this abstract quest, becomes the developing totalisation which carries, occasions, and justifies the partial totalisation of critical intellectuals. In the very moment in which the ideologue (as we shall see) recognises his investigation as dated (1957, here and not elsewhere or at any other time), History takes back and transcends, but does not remove, the dialectical schemata which it has always had, but which he has only signified, and which designate him as a moment, as their passed signifier, and then allow him to sink into Being, while they become dialectical schemata, the intelligibility and objective rationality of the totalising movement, that is to say, the rational foundation and rule of development which illuminates CO'lcrete processes, but appears in them only in the form of the poorest and most removed layer of signifi- + +cation. + +of sisters and of the marriage of cross-cousins can be defined in these terms: 'A is to B as B is to A; or again, if A is to D as B is to C, C must be to D as B is to A. '44 Here we encounter some well known aporias (but ones which lack real consistency, and which the sociologist is right to ignore): right cannot be deduced from fact, fact cantlot produce right, and right (as the ensemble of juridical practices, whether codified or not) is fact (it is a foct that one gets married in a particular society in one way rather than another), fact engenders right (in the organised community and when it takes place in accordance with juridical laws: a particular marriage between a man from group A and a woman from group B is a foct; they did get married, yesterday or last year; but this fact is lived by group A, for example, in the form of a complex of obligations, that is to say, of exigencies which come to it from the future). But in the perspective which the work of Levi-Strauss has opened up, these superficial aporias are merely characteristics which are indissolubly linked and which constitute the intelligibility of the structure. Let us try to see them in their true relations. + +(i) Structure and Function + +The persuasiveness of Levi-Strauss's rigorous demonstrations is due to more than the necessity of their conclusion; as a determination of our knowledge this necessity can have no basis except in a practical necessity, the necessity which makes a man from group A who marries a woman from B, for familial or personal reasons, into a debtor of B and which constitutes through him the whole of group A as debtor. We have already anticipated that in organisations we would encounter an apodictic experience on the part of the agent and that this would, at first sight, resemble that of alienation. The married man from group A constitutes himself as an other in relation to group B - and not as any other, but as a common individual designated by a new function (his debt). And we must go further, since the act of marriage will have the effect of constituting every child in a 'creditor-debtor' relation to the groups in question, and because, through him, this relation will strictly determine his future marriage possibilities (but in common, leaving his individual possibility undetermined). The son is born with an untrans- + +cendable future, that is to say, with an untranscendable limit to some of his possibilities: he is designated on the basis of a free action of the previous generation (the father chose one woman or another from among the b women), and as a result of a concatenation of determinations + +which can be treated by a sort of ordinal algebra. + +Is this really alienation? Obviously not: the free choice of a wife, in the first generation, effectively involves, as a freely accepted condition, the inert negation of certain possibilities (in other words, the acceptance of the inert necessity of exogamy in some form or other) and this negation is itself based on the free production of a particular kind of mediated reciprocity. Obviously these characteristics (inert negation, i!'�rt possibility, lived reciprocity) are not, or need not be, explicit. In the very freedom of choosing a wife, they are reactualised and sustained. And debt, as a relation which constitutes a man a in relation to B, is the free production, through this choice, of a mediating function between A and B. Through a, A and B - debtors and creditors - are linked, and to some extent, the power of B over a is the power of a over A. Thus he has the right to require the group to keep the undertaking given by the common individual who, in his person, married + +a B woman. + +Thus these are genuinely free human relations (undertakings, pledges, powers, rights and duties, etc.). And if the son of an ab marriage is constituted with a double character even before being bom and regardless of who he may be, this is because, even before his mother becomes pregnant, he is primarily a determinate possibility of the father and mother - that is to say, a limit which is as yet still only their limit, and which will remain theirs as long as the future child is no more than their own possibility. From birth onwards, the arrival of the child in the milieu of the pledge is the equivalent for him of making a pledge; anyone who arrives within a pledged group finds himself to be pledged - not as a passive object receiving his statute from outside, but as a free common agent who has been granted his freedom (the real function of baptisms, initiations, etc., is to reinteriorise the pledged function as a free pledge(5). Later, we shall discuss this point at length: for this + +45. This explains the strange attitude which is current amongst many lukewarm or sceptical Catholics (or even free-thinkers). I call them Catholics because of their origin rather than their faith; but if a married couple in this category has children, they will have them baptised as a result of the following line of reasoning: 'They must be left free: they can make their own choice when they come of age.' For a long time I was surprised by this; I thought it concealed some + +second pledge has special characteristics which need to be elucidated and, most importantly, is infinitely more widespread than the first. + +What is certain is that birth is a pledge to precisely the extent that the pledge is a birth. If birth is reproduced artificially (in an initiation, the group takes responsibility for it) then the young initiate will no longer distinguish between his social birth, his bodily birth, his powers and his pledge: in fact, initiations were originally associated with trials and ordeals; and at the same time, were expected and promised. The organic individual freely bore the expected ordeals in order to achieve the statute of the common individual (that is to say, in order to have and to exercise practical powers); and this undertaking - manifested by + +sort of conformist timidity, some fear. But in fact, from tile point of view of the group, the reasoning is valid. As someone who had been baptised., but who had no real links with the Catholic group, it seemed to me that baptism was a mortgage of future freedom (especially as these same arguments often lead to the child being given a religious upbringing, going to his first communion, etc.). I thought that total indeterminacy was the true basis of choice. But from the point of view of the group (to which the lukewarm or unbelieving but respectful Catholics still belong, the cousin possibly being a seminarist, the maternal aunts being pious, etc.), the opposite is true: baptism is a way of creating freedom in the common individual at the same time as qualifying him by his function and his reciprocal relation to everyone; he interiorises common freedom as the true power of his individual freedom. He is, as it were, moved to a higher potential of efficacity and capacity. Thus the parents wish to place him at this higher level so that he can, with all his power and in complete knowledge, decide whether to remain in the group, whether to change his function (lukewarmness) in it, or whether to withdraw. It seems to the Christian non-believer that 'the born atheist' is only an individual and that he is unable to rise to the level of faith as common freedom, so as either to choose or criticise it, whereas the believer will have both the experience of religious power in the Christian community and also, through his doubts, if he has any, the experience of the lower level of isolation. I now realise that neither my own reasonings nor those of the respectful freethinker were correct. Whatever one does, in fact, one prejudges: in the eyes of Christians, atheists are isolated, and characterised by a simple negation; but atheists also form a group (with different statutes, looser bonds, etc.) and a child must submit either to the baptism of atheism or to that of Christianity. The truth, which is very hard for liberals - but then any truth is hard for tender liberal souls - is that it is necessary to decide the meaning of faith (that is to say, of the history of the world, of mankind) on behalf of the child, and without being able to consult him, and that whatever one does, and whatever precautions one takes, he will bear the weight of this decision throughout his life. But it is also true that it can mark him only to the extent that he has freely interiorised it and that it becomes the free self-limitation of his freedom rather than an inert limit assigned to him by + +his very endurance - is precisely the second pledge. There can be no doubt that the individual lives it as an acquisition of merit: but it is equally certain that adults see it as an indication of commitment. It is as if, on the basis of this commitment, they were reserving the right to punish him if he should wish to leave the group - on the basis of this commitment; as if they wanted to be able to say to him: 'Your impatience for the initiation, your courage during the ceremony committed us to you, and you had the right to ask us to install you as a common individual in the community. But, reciprocally, in committing us so wholeheartedly, you were committing yourself to us: your enthusiasm was a free determination of your future and you took upon yourself the burdens (exogamy, etc.) which have weighed upon you ever since your parents' marriage.' Thus rites of passage, like marriage, are bi-Iateral, symmetrical ceremonies: they actualise a reciprocity. It is therefore impossible for the child not to interiorise this future anterior which has been constituted for him a priori and not to interiorise it through pos i tive acts (initiation procedures, choice of a wife, military prowess or, where appropriate, the struggle for power). This is still the meaning of the very true and constantly repeated sentence, 'No adult can say, "I did not ask to be born" '. Thus, ultimately, the organic individual grasps his contingency in every movement of his life. This means that he is not his own product; but as a common individual, his birth is indistinguishable from the arrival of his freedom and its determination by itself. To be born is to produce oneself as a specification of the group and as a complex of functions (burdens and powers, debts and credit, right and duty). The common individual produces himself as a new + +pledge within the group.46 + +But in the case both of the original pledge and of the secondary one, (in fact it is always, except in emergencies, a matter of secondary pledges), function depends on a veiled inertia, on what I just called the inorganic materiality of freedom. And the aim of the common individual within the group is to preserve the permanence of relations through changes in the position of individual terms; which means that + +46. It goes without saying that what we are considering here is the abstract case (or the elementary group) in which problems of exploitation or class struggle do not appear. We are proceeding slowly, and at the end of the journey we shall encounter the concrete, that is to say, the complex collection of practical organisations interfering with the practico-inert and the alienation of common action taken up by the passivity of the series. Only at this level will class struggle, + +exploitation, etc., take on their true meaning. + +he modifies his praxis (and acquires new characteristics) in so (ar as other third parties (or all of them) are themselves led to change either by praxis or by the pressure of external circumstances. Thus the relation remains fixed in so far as it is preserved. And if, through a directed action, a system in movement is invoked, that is to say relations which produce one another, then these relations will arise as mathematical relations rather than as the moments of a dialectical praxis. As functions, in fact, they are still the condition for the praxis (of the common individual and of the totalising group), but they are not the praxis itself; on the contrary, it is their inert instrumentality (as the limitation of their possibilities) which conditions everyone's efficacity. This is how the efficacity of a goalkeeper, as well as his personal possibility of being good, very good, or excellent, depend on the set of prescriptions and prohibitions which define his role. The match would no longer have any meaning, and would become a formless scufHe if the goalkeeper could, as he wished, also play the role of half-back or centre-forward (and conversely). Once functions have been distributed, therefore, it is not a matter of them dialectically modifying themselves simply through belonging to the same whole (which is, however, the characteristic of actions in so far as they are produced by individuals - within certain limits, as we shall see). In fact, the creation of the functions was dialectical, although it was produced in the light of the multiplicity of agents and exigencies. But, although always capable of being rearranged, the functional organisation has to be put in question by the whole group, either through a reflexive attitude of each of its members, or by some specially differentiated organ, in order to realise the co-ordinations, modifications, adaptations, etc. , when + +they come to be necessitated by the totalisingpraxis.47 + +47. What is deceptive today is the acceleration of History, due, as we know, to the internal contradictions of the capitalist system. The need to reduce costs in order constantly to create new outlets entails the constant transformation of the means of production; industry, from this point of view, is in a permanent state of revolution, which leads to a constant rearrangement of capitalist organisations and, rather more slowly, a perpetual transformation of trade-union organisations and of their praxis. But these transformations take place in spite of everything on the basis of reflexive totalisations (coming either from the base or from the summit), that is to say, on the basis of the questioning of the whole of praxis by the common individual (the unions will be described as 'failing to adapt to the new directives of the employers' policy'), rather than by a sort of interpenetration of activities, or, to put it differently, by a spontaneous reorganisation of all detailed action by all the others, under the pressure of new circumstances and beyond + +We shall therefore call these structures, in so far as their inorganic materiality has been freely interiorised and reworked by the group, the necessity of freedom. This means that the inert (that is to say, different reciprocal limitations) comes into contact with itself in the group, and through the profound relations of interiority which unite each to all in mediated reciprocity, but that this contact of inertia with itself necessarily takes place according to the laws and the intelligibility proper to this sector of materiality; and this means that the conditioning of functions by each other (once their synthetic, reflexive determination is complete) takes place in exteriority, as in the physical world. However, it is important to recognise that this skeleton is sustained by all the common individuals and that it is always possible for the group, as totalising action, under the pressure of new circumstances, to dissolve it entirely. It should therefore be noted both that it is the free attachment of each individual to the community in so far as it is the inorganicbeing of each member and that this necessity, as exteriority structuring interiority, is simply the obverse of the practico-inert: the latter effectively appeared as passive activity, whereas the former constitutes itself as active passivity. Everyone's inorganic-heing, as we have seen, involves a considerable measure of indeterminacy: it is the foundation of my praxis, and it frames it and circumscribes it, it channels it and gives it everyone's guarantee along with the instrumental spring board it needs. But praxis itself, when completed, cannot be reduced to this skeleton: it is more and it is different; it is the free concrete realisation + +of a particular task. + +We should not be surprised by the opposition of these two necessities: the second is the interiorisation of the first and its negation by organising labour. We have seen how the group acquires inertia in order to struggle against inertia; it absorbs the passivity which enables matter + +reflexive questioning. In other words, an organisation (whatever it may be) will, given an acceleration of the historical process, live its inertia as a perpetual dislocation which must always be compensated. But these rearrangements can occur only in the light of new functions which also owe their efficacity to the exact determination of their limits. In short, the action of reorganisation is praxis in so far as it redistributes tasks with a view to achieving the same total objective in varying circumstances. The same applies to the organic action of each common individual. But even if function were modified every day, it would, as a statute defined by the reflexive attitude and assumed by the effective action of the worker or fighter, remain a structure of inertia, and an object of logical analysis, and, as + +such, capable of being studied as a mechanical system. + +to sustain the passive syntheses which it needs in order to suryiYe; but it is precisely not, in itself, a passive synthesis, and its passivity sustains the active synthesis which is praxis. The practical comprehension of active passivity is given to everyone - regardless of his group - in the behaviour known as 'freely agreeing to discipline' . The only error which in any case is not so frequent as one might suppose - is due to language: there is a danger that the words will give the impression that the only effect of free consen.t is to bring behaviour into line with prescriptions. But in fact everyone discovers in his action that discipline affects him in his very freedom with a kind of being, that is to say, with a certain form of exteriority which, paradoxically, sustains his bonds of interiority with everyone else. But this means that exteriority as such, as the foundation of the action, is always external, or rather that it is at the extreme boundary which separates transcendence (Ia transcendance) from immanence : in the heat of battle, a soldier obeys the order of a superior in freedom, because he recognises its importance, because he transcends it towards the common aim; in a sense, therefore, this is a free reciprocity. Yet the hierarchical bond between the lieutenant and the private is entirely contained in this relation; in other words, the inert reciprocity of command underlies concrete action. The complex structure of this organised connection actually comprises three signifying layers which it is necessary to describe: the first is concrete praxis; this includes the second, which is power (freedom-terror) and function (right-duty); and this in turn includes the third, which is an inert skeleton. And the inert skeleton is in fact the most abstract of the three layers. The organising sub-group could not determine it - as a set of elements in a symbolic calculation - except �n the concrete basis of a differentiated pledge, of rights-duties, of functions and of everyone's relation to the common objective. From the moment when, for example, an organisation selects its 'cadres', a problem immediately arises, one of whose aspects is purely quantitative - namely that of the numerical relation of cadres to militants (of officers and NCO's to privates) in a particular situation, in the light of specific objectives and on the basis of quite definite instrumental and technical resources (for example, in a state of international tension in which, as at present, there is an opposition between 'blocs' each characterised by a given level of armaments, presupposing a certain industrial capacity). And calculation enters into this quantitative problem as if all the relations involved were relations of exteriority. It should also be added that the creation of these cadres, if it takes place, + +may lead to a qualitative change in relations of interiority (for example, atightening of authority). But there would be no sense in working on the inertia of the group if it were simply a matter of rearranging inertia which has already been produced, as interiorised exteriority, in so far, that is, as it is sustained by relations of power, of rights, etc., which were differentiated through the pledge and which perpetuate the + +pledge which produced it. + +(ii) Structure and System + +In this sense, we can describe structure as having two sides: it is both an analytical necessity and a synthetic power. Power certainly constitutes itself by producing in everyone the inertia which is the basis of necessity. But, conversely, necessity is only the external appearance of this freely created inertia; it is, in other words, the index of this inertia seen in exteriority, either by an observer who does not belong to the group, or by a specialised sub-group which uses analytical methods and symbols for dealing with certain problems of apportionment and distribution, because the multiplicity which they treat (the group as plurality in circumstances of scarcity, scarcity of cadres or provisions, etc.) is only the external appearance of an interiority which alone makes the problem possible (not in its solution, but in its very formulation). Even to think of regarding individuals as organisms which have to be fed, in order to enumerate them, to establish the relation between provisions and the number of mouths to be fed, to establish provision centres or to bring the existing ones closer to the front etc., the army must already be a practical totalisation, a combat. But even this is not sufficient; certain functional relations and powers and discipline must be presupposed, so that, at a particular practical level, execution can be relied on. To say that the bases are too far away means that the Quarter-master is doing everything possible, and is not to be blamed. To say that they can be brought nearer (by a certain distance) means: we are increasing the power of the supply services; their efficacity will therefore increase accordingly - in short, they are entirely devoted to + +The other aspect of structure is, in effect, that of a mediated reciprocity. Furthermore, we have seen that this mediation is quite simply that of the totalising group. Thus, while structure is revealed, in + +exteriority, as a mere skeleton which can be examined and reworked in itself on the mere tacit presupposition of the whole - that is to say, by silently ignoring the practical totalisation as the support and reason for the inertia at the moment of the combination of terms - it is, in interiority, an immediate relation to the totalisation. In fact the totalisation is closer, at each term of the reciprocity, than everyone is to each other, since everyone is linked to the other through it. Pouillon is right in saying: 'The idea of structure is ... profoundly different from that of order. Only structure makes it possible to transform the vicious circle of which Pascal accuses Cartesian knowledge into, so to speak, a true circle. In a structure, each element is the particular expression of the totality immediately and totally reflected in it, rather than an intermediate stage in the constitution of the whole. There is no other way of avoiding the paradox of the simultaneous autonomy and dependence of an element in relation to the whole or of con- + +ceiving the synthesis of the heterogeneous.'48 + +But it is important to realise that what we are dealing with here is not a totality but a totalisation, that is to say, a multiplicity which totalises itself in order to totalise the practical field from a certain perspective, and that its common action, through each organic praxis, is revealed to every common individual as a developing objectification. In other words, the mediating group is already, in itself, a complex dialectic of praxis and inertia, of totalisations and already totalised elements. In fact, this is where the reflexive structure which is characteristic of the organised group as such needs to be more securely defined. It does not mean that a particular, collective illumination inhabits the group (a consciousness of collective consciousness), but only that every common individual (already common: through the pledge or the first action of the fused group) adopts practical behaviour which takes the group as its immediate objective on the basis of some distant objective. These practices produce the group as a quasi-object for its members. (For non-members, not only contemporaries, both enemies and allies, but also, subsequently, historians and sociologists, it is an object in any case and whatever its structure, hut it is a practical and signifying object, which produces its own instrumentality around certain instruments.) The group has an internal ohjectivity; that is to say, the group exists through every common individual in two + +radically distinct forms: prior to any functional determination, it is, for everyone, the security of each and all, which is once again present in + +him as the Other-Being of his own freedom. + +We have seen that, as the organisation becomes formed and constituted, this inertia, which can affect freedom only by using other freedoms, appears decreasingly as a negative limit and increasingly as the basis of powers. But obviously this unity of inertias will not of itself produce change in anyone except through someone's real, free praxis. The group as a totality or an objective reality does not exist; on this level it is simply the fact that the free production of inertia is the same and determines itself as such intentionally or, to put it differently, that there is a single pledge. And this does not mean that this pledge on its own is the transcendent unity of the pledged agents; on the contrary, it means that, in each common individual, there is no principle of individuation for the act of swearing: thus the individuals are diverse but their pledges - however distinct as spatio-temporal acts - are, through everyone, the pledge, an individual act of the common individual (in that it consolidates or produces this individual). But in the common decision to swear there is a presentiment of the exigencies of differentiation; and it is precisely the unfolding of these exigencies before the pledged individual which shows him the group as a means, and therefore as an end and an object. Every means is an end in the practical moment in which it has to be found or produced so that another means, and thereby the end, can be accomplished. And the group-means is revealed through circumstances: they indicate certain possibilities in the multiplicity in so far as it is subjected to and controlled by unity + +through each individual unification. + +Thus the creation of forms of differentiation treats the group as a transition from homogeneity to a calculated heterogeneity or, more commonly, from a less differentiated state to a more differentiated one. And, in so far as it reveals itself to the practical action of the organising third party, the group appears as a developing (or still to be achieved) totalisation, rather than as a completed totality. Nevertheless, it is an object; and this means that its instrumentality can be modified by work; through organisation, tlle organising third party produces or maintains tools (like a worker who whets or repairs his tool). And once again, for everyone, this practical object cannot be any more than a quasi-object, since it is both the matter which is to be differentiated by functions and the unity of the pledge which founds heterogeneity as the free, controlled use of multiplicity, and allows it to be reintroduced. + +In other words, through the individuated practice of the common agent, the group is an object in one form and the foundation of the act (as pledged inertia) in another form. And this produces reflexivity as quasi-objectivity. (Individual reflexion also involves a single consciousness, but in so far as its relation to itself never allows it to be either one or two.) But it should be noted that once the organisation already exists and needs to be rearranged (possibly from top to bottom), the relative autonomy of functions (that is to say, of the limits of competence), by threatening to posit itself for itself in the individual function, accentuates the object character of the unified multiplicity and tends (without ever wholly succeeding) to simulate + +the impossibility of a total objectifying duality. + +In any case, radical duality is still out of the question: it is the same (the pledge as non-individuated in the common individual) which recurs practically as the still undifferentiated unity of this multiplicity. Even if he belongs to a specialised group, the organiser derives his power to organise from this relation of the group to itself (and to its end); if he tends to conceal his membership of the group in his behaviour, this is precisely to the extent that his work makes him treat structures and common individuals in exteriority (that is to say, as a numerical multiplicity and a relational skeleton which have to be rearranged). But in an organised group, the act of organising is only a means - often entrusted to specialists - of efficacity; and the essential practical relation is that of the individual agent fulfilling his task with the external object in which he realises the common objectification. It is at this level that function, as a relation to a given sub-group or directly or indirectly - to all, is mediated by the group. And it is clear what group must mean here: a practical relation between the pledge as the same in everyone and the already unified multiplicity which it allows to become differentiated. This reflexivity determines every common individual in so far as he understands the utility of his task and the necessity of his being organised. This means that every functional differentiation, regardless of which individual or sub-group chose it, is reaffirmed in pledged freedom; in short it is adopted (assumle). In this sense, although every common individual may be transformed, disqualified, requalified, silenced, or displaced by new reorganisations according to the common objective, he can never produce himself, in his actions and his active passivity, as purely and simply an object of the group. It may in fact be true that the group treats him (or can treat him) as an object: his activity may be chosen + +(and subsequently changed) according to a strict calculation. But, in so far as every pledged member is always the same, the organiser makes his decisions in so far as he is the same as the organised, and the organised adopts the decision in so far as he is the same as the organiser; this means that he sees his own common decision as a moment in a + +common, already differentiated process. + +A given activist, sent into a particular factory or collective farm, in order to explain a decision of the Soviet government to a group of workers must treat himself both as the inert object of a choice (his deployment does not necessarily take his capacities into consideration), and as an element in an immense process which realises itself in divergence (at the same moment thousands of activists are spreading out in order to go and perform the same act everywhere) and whose deep convergence of praxis will temporalise itself in the common objectification (the unification of reactions in all milieux everywhere). But he cannot grasp himself in his inertia and in his being as a discrete element of an objective process unless, hy himself and in free, individual praxis he realises all the moments which affect him in this process (from the moment when he presents himself by some prescribed means of communication at his place of work to the moment when, on the basis of a set of principles, explanations, and unchanging evaluations, he produces the individual reply which he must give to a particular individual question). And it is precisely the free realisation of the common process which refers him back to the other free realisations of different propagandists and which reveal his localised action to him (he has persuaded people here, in a given town or province) as the common objective of a common praxis. In other words, structure as the exteriority of interiority is reinteriorised by functional activity without heing dissolved by it. The agent conceives it, in his very activity, as the intersection of two planes: on the one hand, the work ofinstrumentalisation which the group performs on its multiplicity and, on the other hand, his own inertia as a free pledge and as a free adoption of his character as a discrete quantity on the basis of an indissoluble common unity. For him, exteriority signifies interiority and the multiplicity of inert relations is simply the practical determination of the common unity. + +This example still does not get us to structure, since essentially it concerns a very rapid event which is quickly reabsorbed into its objective: the propaganda which accompanies and follows a policy change. Nevertheless, if it is examined more closely, it becomes evident that it presupposes structure as an expression of the totalisation and as + +the inorganic skeleton of organisation. It should be noted, in fact, both that any young activist, taken individually (that is to say every one of them) was produced by the Party, or by certain specialised organisations, to perform tasks of agitation and propaganda and, at the same time, that this productive action, performed by a sub-group (as an expression of the whole) over very young boys can temporalise itself only in reciprocity, that is to say, it must also be adopted and interiorised by the individual. He is the product of a given administrative group in so far as he is his own product and vice versa. If his mission is to train a group of workers and to increase output (as a team leader and Stakhanovite) he still has to make himself capable of raising norms by his own work. Conversely, if the administration selected him, this is for a set of aptitudes, linked to his loyalty to the regime and revealed through his praxis; and in any case, his selection can always be revoked. These two indissoluble actions, which together require that the product of the free, common organisation shOl.\ld, as a common individual, make himself his own product, eventually, in their reciprocal development, achieve the double, equally reciprocal result of producing the activist as an inert determination of multiplicity and as an individual expression of the developing totalisation. Then a particular mission will constitute him as a power-object, that is to say, as a unit which has to be transported to a particular place by a particular means of transport in order to make contact with specific sub-groups and as a real right-duty who may require of the local authorities or of certain individuals the means to carry out his duty. It is therefore the exercise oj a Junction which develops in this particular event: and this function is structure in so far as it is seen as the potential and power of the group of activists. On the other hand, in this relatively simple case, and other things being equal, everyone is the same as everyone, and since every propagandist is conditioned in his very power by the interiorised multiplicity of his subgroup,49 and, finally, since the group does not possess the metaphysical existence of a form or a Gestalt, of a collective consciousness or a + +49. The size of the regions to be covered, the number of meetings to be held, and, ultimately, the very efficacity of his work - as determined by his own fatigue as well as by the slowness of communications - are determined (at a variable level of the organisation, sometimes at the apex, from the outset, sometimes at the base, in the course of the operation) on the basis of the simultaneously quantitative and reciprocal relation (in definite circumstances and with definite instruments) of the multiplicity of the sU:b-group of activists and of the social ensemble which is to be + +'agitated' or persuaded. + +created totality, each individual, as a common individual, is in himself the propaganda sub-group as a statutory unit of the interiorised multi� plicity and his own activity is an expression of the totalising organisation. (The 'totalising organisation' here means the synthetic ensemble of governmental and administrative services which have created these 'organs' of agitation in the light of a certain objective, of certain mediations between the apex and the base, and of certain relations with + +the masses.) + +It is obvious - and we will come back to this at length, later in our investigation - that suffered inertia has infiltrated this ensemble, which includes a regime, in the form of revived seriality. But, at the present abstract level of our investigation, this inertia does not yet appear: it will emerge later, in dialectical circularity. The important point is to define the moments of the investigation in their purity, even if it is only logical, so as to avoid the danger of attributing to constituted realities characteristics which confused and hasty observation reveals to us, but which really belong to another moment of the dialectical process. It is therefore particularly dangerous to speak here of bureaucratic seriality, although it is obvious that in our example it affects everything, and primarily the creation of propaganda sub-groups. We shall also see that this seriality transforms, but certainly does not eliminate the character of practical expression which is concealed by function in the common individual: it extends this transformed expressiveness and produces the common as a signifier-signified in relation to society as a + +whole. + +At present, taking the sub-group and the totalising organisation in their pure state (that is to say, in the concrete struggle against a given, particularised threat of serial dissolution), there can be no doubt that tltis particular young activist, in his individual way of realising his powers, is not only autonomous, as Pouillon noted, but also a simple, detailed, practical expression of the total operation (and of the complex organisation which has foreseen and planned this kind of operation for a long time). He is autonomous simply to the extent that concrete circumstances (he is speaking to an audience defined by particular interests and jobs, by a particular culture and particular hahits - in the sense of exis) are the other side of untranscendable inertia, that is to say, in so far as they always require him to mediate between the abstract determinations of his task and the particular difficulties he encounters. He is expression in so far as his whole undertaking is incomprehensible except from the point of view of a certain transcendent relation + +between the leaders and the masses, which involves the social and political system of the USSR as a whole. From this point of view, tactical differences are themselves expressive since they never cast doubt on the basis. A kind of authoritarianism (which we need not define here) lies at the basis of their mission and their common-being (in so far as these products of the organised group produced themselves). And from the structural point of view it does not matter whether this authoritarianism manifests itself as a structured characteristic of the individual (which is sometimes incorrectly called a character trait) or whether it appears through a tactic which is apparently flexible and conciliatory but which really has no other aim than to realise the centralised authority while concealing it. Or rather, tactical differences do not reflect differences in the structure unless they arise at two different moments as two attitudes of the sub-group (rather than as individual variations). If the operations of the activists, as a unified multiplicity, are carried out in voluntaristic arrogance, they will, in one way or another, simply express the activities of the government and + +administration. 50 + +We shall therefore refer to the function of the sub-group or of a member of the sub-group as structure, in so far as its concrete exercise through the free praxis of the agent reveals it as a specification of the totalising rearrangement of the whole by itself. It should be clear that the word expression here refers to a fundamentaliy practical relation, that is to say, a reciprocity of constitution: free, individual praxis realises the previous totalisation as a positing of limits; it pursues the totalising operation by concretely objectifying itself in a concrete result which signifies the totalisation of results which are in the process of being objectified. Meanwhile the organised totalisation designates and solicits individual action, as function, as its inevitable concretisation; it constitutes a power and an instrumentality for it. Structure is this double oonstituent designation, in its two simultaneous and opposite orienta- + +50. This does not mean that the arrogance of the activists necessarily signifies a return of central organisations to some form of dictatorship at any particular tnoment. On the contrary, it may - in concrete circumstances - signify a lack of coordination between organisations or a stubborn resistance to new policies from the structured past amongst the young activists . The ensemble determines the signification, as an expression of the totalising and totalised totality. My point is simply that this expression - which always appears in experience - is a necessary presence of the totalisation in the totalised part since the totalisation for this part + +is no more than function, that is to say, structure. + +tions, either at the level of mere abstract potentiality (the level of power acknowledged by common individuals), or at the level of actualisation. It is obvious that this relation between the individual and the group (as an interiorised multiplicity in each and all) existed even in the fused group where, indeed, we laid stress on it. But one cannot yet speak of a structured relation, for the simple reason that the reciprocal bond has not yet been specified. Structure is a specific relation of the terms of a reciprocal relation to the whole and to each other through the mediation of the whole. And the whole, as a developing totalisation, exists in everyone in the form of a unity of the interiorised multiplicity and + +nowhere else. + +(iii) Structure and the Group's Idea of Itself + +In the reflexive context of the group, however, this structural relation must also arise as reflexive knowledge: in other words, the individual action of the common agent cannot realise itself as a determination of the indeterminate without conceiving function negatively in the transcendent object as exigency and as a negative adumbration (esquisse en creux) of behaviour and, positively, in interiority, as duty and power. The moment of mediation through organic praxis is also that ofknowledge, that is to say, of the co-presence of all reciprocal implications; but of course this does not mean that this knowledge is explicit or thematised. But, if we consider all the characteristics, already enumerated, of knowledge in the organised group, we can immediately see that the organic individual produces and is aware of himself as a common individual: first, in so far as the object reflects the group to him as practice and as practical knowledge, that is to say, both on the basis of the common objective as the future revealing the present situation in the practical field and on the basis of conceiving one's work on the object as a particular detail of the common objectification; and, secondly, in so far as the whole, as a practical totalisation which is also performed by him, forces him, in functional determination, practically to conceive the transcendent object as common and the practical field as a common situation to be modified. Thus structure, considered, by way of abstraction, as knowledge, is simply the idea which the group produces of itself (and of the universe in so far as it is practically determined as a field of objectification). And the content and foundation of this reflexive idea is simply the common organisation as an objective + +system of relations; or rather, the organisation conditions it and becomes its internal norm. At this level of abstraction and purity (that is to say, in the absence of serial determination) the idea of the group is without alterity: it is the same everywhere as a pure expression of the here and now; and there is nothing surprising in this since it is a particular actualisation, under the pressure of specific exigencies, of structure as a relation of reciprocal expression between the part and the whole. But, at the same time, at this level of non-differentiation, it remains purely practical, that is to say, it is still both an organising reflexion and a pledge; or in other words, both the truth of the group as practical experience and its ethic, as the constitution of common individuals by imperatives and rights based on pledged inertia, are absolutely not differentiated and, indeed, the principle of their indissoluble unity lies in the very urgency of the common tasks. The idea of man, in an organised group, is simply the idea of the group, that is to say, of the common individual, and fraternity-terror, in so far as it is expressed by specific norms, derives this particular colouring from the real objective, that is to say, from needs or dangers. The material organisation of the group is indistinguishable from the organisation of its thoughts; the system of logical relations which constitutes the untranscendable principles of every mental operation for everyone is indistinguishable from the system of inert worked relations which characterises functions in exteriority. Invention and ideational discovery - as individual praxis - occur as free, reflexive action on tlte hasis of an organised specification of freely adopted inertia; and it is one and the same thing to be unable to transcend a given practical organisation, or a given system of values or a given system of 'guiding. principles'. However, the idea of man which is produced by the group as an idea of itself cannot be compared to the idea which is produced by the gold coin in the practico-inert field. 51 This in fact supports the ideas of the Other by its fundamental inertia; and so it cannot change. The idea of the group, on the other hand, as a structural determination of the indeterminate, must be invented, and remains infinitely variable + +within certain limits. + +But the double character of structure (an inert object of calculation when seen as ossature without taking account of totalisation, or an effective power actualised by the praxis of each and all) implies a double character in the idea. In one sense, it is the free comprehension every- + +where of functional activity in everyone in so far as its heterogeneity relates to the homogeneity of pledges on the one hand, and to the synthetic unity of the transcendent end on the other. It is at th: s still practical level that the group has a silent knowledge of itself through each common individual: but this understanding (evidence) is not available to those who do not share its objectives. As practical individuals, they may perceive these ends in the common action as it unfolds before them, and carry out a correct reconstruction of the praxis: but they will never perceive the common relation to the end concretely as an inter-individual relation, that is to say, as a milieu specified by organisation. It is at this level that complex knowledges may disconcert a sociologist or ethnographer who encounters them in underdeveloped societies, because they conceive them as theoretical knowledges derived from observation of an object, whereas they are really practical structures which are themselves lived in the interiority of a common action. Ethnographers have stressed the logical flexibility of primitive thought. Deacon has written about a matrimonial system: 'The native is capable of pretty advanced abstract thought .' 52 But this is not a good way of formulating the question; the point is not to discover whether they are capable of abstract thought in general, as if this thought were a universal capacity which everyone possesses to a greater or lesser degree, but to show within the investigation whether or not they are capable of comprehending the abstract structures of their matrimonial or kinship systems, which is perfectly clear today. In other words, we should avoid putting the cart before the horse by claiming that primitive people understand the abstract relations which constitute the organisation of their group because they are capable of abstract thought; on the contrary, we should say that their capacity for abstract thought is determined by the abstract relations which structure their society, that it is simply these relations themselves in so far as every common individual has to live them all in order practically to realise his relation to all in the unity of a common objective. In fact, functional relations determine not only the level of abstraction of thought but also the limits of its application: this relational system as the instrument and limit of ideational power constitutes itself as a generalised system of logical relations, which means + +p. A. B. Deacon, Malekula: A Vanishing People in the New Hehrides, ed. C. H. Wedgewood, London, 1934 (George Routledge and Sons), p. 132.. Quoted + +hath that it can be applied to a certain number of similar cases, well defined and forming part of the social, everyday life of the natives, and that its existence - as inertia - is by itself a sometimes invincible resistance to the elaboration of any other system. In this sense, in effect, truth is normative because fidelity to logical 'principles' is only a form + +of fidelity to the pledge. + +But, apart from this implicit understanding - which is simply a structure of power - there is, at least for certain specialised organs, a knowledge which is equally practical and reflexive, but which is of a logistical and combinatory kind, directed at function as inorganic inertia, that is to say, the relational system as ossature. I shall not dwell on this since I discussed it above: it is clear that totalisation as a pledged milieu which sustains this inertia is passed over in silence in the moment of calculation. But it should be noted that, although the totalisation is invisible, it occurs at the level of the organisers and calculators in that they know and acknowledge their right and power to calculate only to the extent that it is their specialised function: the basis for the calculation of discrete elements is, therefore, the lived comprehension of Structure as the reciprocity of the whole and of the part (that is to say, the comprehension we have just been describing) in so far as it arises in the praxis of the organisers and in so far as it gives meaning to this praxis. The organiser therefore has an immediate, practical comprehension of the structures in all their complexity and this is the basis of the abstract analysis which he then performs on these structures as skeletons. In fact, the natives of Ambrym 'gave Deacon demonstrations, using diagrams'. 53 They drew lines on the ground, and these, according to their length and position, represented one or other of the spouses, their sons, their daughters, etc., seen, of course, from the point of view of a complex matrimonial system. In this case, it is important to realise that in producing these relations in the domain of the absolute inert (earth or sand) and of perfect exteriority, they were not copying some model which they carried in their heads; and it would be equally incorrect to say that they project their synthetic practical consciousness of themselves and of everyone into the analytical milieu of the inanimate: such a projection, in fact, is impossible, since it would involve - roughly speaking - two distinct orders of + +integrated by synthetic rationality, but it is also clear that the opposite is not true: a dialectical proposition would lose its meaning and dissol ve into relations of exteriority if it were 'projected' into the milieu of logical or mathematical calculation. In fact, the decision to make the kinship system into a fabricated, inorganic object (lines made on the ground) corresponds, for the native, to a practical attempt to win the support of inorganic materiality in order to produce the structures in the form of inert abstract schemata. The reason for this is that he is explaining them to a stranger who is situated in the exterior, and who therefore thinks in terms of exteriority: he therefore expresses pledged inertia not as an interiorised exteriority, but as a pure determination of universal exteriority. But in establishing this minimum schema, that is to say, in reducing structure to ossature, he is guided by the synthetic understanding which defines his membership of the group. Thus his task is not a matter of projection or transposition: he is simply creating an inert object which presents in exteriority, to a man from the exterior, a set of passive characteristics which retain only the inertia of these structures and which, indeed, falsify this inertia by presenting it as an elementary, suffered condition (whereas in fact it is produced by + +the pledge). + +It is obvious that this construction is not a thought: it is a piece of manual work controlled by a synthetic knowledge which it does not express. But this example enables us to understand the other work in exterioriry, performed by a specialised sub-group on pledged inertia as an exteriority of structure, in and for the group. This work is also guided by a dialectical thematic and a comprehension of the whole which it does not seek to project or 'render', and it cannot, in the first instance, be regarded as a thought. It becomes one only through practice: the organiser creates analytical thought (and the rationalism which corresponds to it) with his hands; it is born within his hands because every praxis explains itself in terms of the objective and the object. Thus, at the level of calculation and redistribution, the 'transformations of ossature' which are performed on the basis of a functional and totalising power develop a set of guiding schemata which are simply the laws of inertia transformed into practical laws of organisation. Practical knowledge unfolds simultaneously on two planes and according to two types of rationality; and this is not surprising, especially in modern societies, where it is almost impossible to find the solution to a practical problem if the question is not treated at several levels simultaneously (in fact, as we shall see, the practico-inert field + +reintroduces itself at the moment of the true concrete so producing a new complexity) . But this does not constitute an unintelligibility or a split in thought, since dialectical Reason sustains, controls, and justifies all other forms of thought, because it explains them, puts them in their proper place and integrates them as non-dialectical moments which, + +in it, regain a d ialectical value. + +4 + +The Constituted Dialectic + +Individual and Common Praxis: the Manhunt + +In the course of these preliminary observations we have not encountered any major difficulties. This is because we are trying to determine the meaning and scope of dialectical Reason. Now, at the level of these first approximations, we have not encountered any critical problems which are really new. True, the new necessity produced and sustained by organising freedom had to be analysed and elucidated; and the relation between the two aspects of structure (system and function) has had to be discussed in some detail. But, on the one hand, this has, on the whole, involved a very simple dialectical progression, which merely united into new syntheses factors which had already been discussed (the pledge, terror, inertia, reciprocity, objectification, refiexion, etc.) and, on the other hand, at the level we were occupying we rediscovered constituent organic praxis as the indispensable mediation between the common individual and the common objectification of the praxis of the group. So since praxis, when considered at the level of each function, is still individual action and, as such, a moment of the constituent dialectic - regardless of readjustments and the relation of common individuals elsewhere; and since the organised group acts only upon itself (in order to make everyone better able to carry out his share of the common task), and since this very action is done through the mediation of individual praxis, the real new modifications which have arisen before us have not raised the question of constituted intelligibility. In other words, the kind of dialectical intelligibility which we explained at the beginning of our critical investigation was sufficient to explain the practical relations of individual functions within the organised group. But this is because we ourselves were taking an insufficiently synthetic view of such groups. This was necessary in + +order to explain its structures, but it meant postponing the real critical question: what type of existence or being characterises the common action of the organised group in so for as it is common (rather than in so far as it can be resolved into a multiplicity of f unctions)? What kind of intelligibility does this action define? What is a constituted dialectic? What we have been studying, in fact, is the conditions of common action, rather than common action itsel£ This action can in fact be referred to by certain determinations of language: the people of Paris have taken the Bastille; the rebels have seized the radio building; the team has won a match; we have put a new locomotive into production, etc. In all these sentences, the subject is plural (or unified but multiple) and the action is singular, seen either as a temporalisation ('They took, they are taking') or in its common result: The storming of the Bastille, the people have taken . . . , etc. Now, we have explained the interiorisation of plurality, but this gives us no guide to praxis as a common temporalisation or common objectification of the group. We have seen, in effect, that through the organisation it is realised through the mediation of organic individuals and of the individual dialectic. But, in opposition to this, it has a concrete unity, which implies an organisation of means in the light of the end and a realisation of the synthetic end through labour. Everything would be simple if, corresponding to praxis as the concrete, living temporalisation of the group, there was a living, concrete group - in short, a Gestalt or an organism or a hyperconsciousness - which temporalised and objectified itself. In fact, it is clear that the group, 'united' around an instrumentality or 'contained' in appropriate locations, does not exist anywhere except everywhere, that is to say, it belongs to every individual praxis as an interiorised unity of multiplicity. And the ubiquity of the heres corresponds to the real practice of negating plurality. This totality does not circulate, it is not elsewhere; it is always and entirely both here and the same. But if we abandon every magical or mythical interpretation, then it is clear that this ubiquity does not mean in any way that a new reality is incarnated in every common individual, like a Platonic Idea in individuated objects; on the contrary, it means that there is a practical determination of everyone by everyone, by all and by oneself from the point of view of a common praxis. The proof is that this unified multiplicity re-emerges as inert exteriority within the group itself, that is to say, as ossature. However, the action is one as individual action, the objective is one, and the temporalisation and the rule it gives itself �re {me; so everything is as it would be if a hyperorganism had tem- + +poralised and objectified itself in a practical end, by unifying and unified labour of which every common individual with his constituent mediation would be a completely inessential moment. The thing seems even more paradoxical at the real level of action, that is to say when it is split, within the group itself, by deep conflicts of interest, by local (or generalised) revivals of seriality, or by accidents. Through all the well known incidents, disorders, accidents and misunderstandings the Parisian crowd stormed the Bastille. But though we are still only at the level of abstract purity, this synthetic signification of praxis at first appears paradoxical: the praxis is not in fact the temporalisation of an organic unity, but a negated and instrumentalised multiplicity which temporalises and unifies itself in the common praxis through the mediation of individual temporalisations. In other words, the only unity is practical unification, that is to say, the unity of every particular labour with all the Others. But then what is this unity of local, heterogeneous temporalisations? What kind of reality does it have? And what kind of intelligibility? Of course, everything is already organised; but is the common praxis, as a synthetic temporalisation of this organisation, organised or organic? And since its signification (its temporalisation as diachronic signification, and its final objective as synchronic signification) is and can only he one,54 should its unity be regarded as homogeneous with the significations of individual, organic praxis or should we recognise that a signifying synthesis performed by the organised group is absolutely of a different order than an individual synthesis? If it is of the same order, how are we to explain the fact that the group produces a praxis which is individual and organic in character (even if it is distinct from individual actions in scope and power)? And if it is of a different order, shall we have to accept a hyper-dialectic, which means either regarding the group as a hyper-organism, or making the dialectic into a transcendent law imposed on the object? In fact how does it come about that I understand the meaning of a group action? Of course, I may be mistaken or mystified: but the existence of historical science is sufficient to convince me that it is possible, in the long term and given sufficient information, to understand a common signification in the course of individual research. The historian, as a solitary worker, can grasp the precise aim of some political action, that + +H. Of course, I am speaking from the abstract level of purity. I do not yet have the means which, later, will enable us to reveal a new alienation as a new + +is to say, the end pursued by a given organised group, even if this end was not realised. Scholars debate and disagree about the declaration of war in 1792 and about the behaviour of the Girondins. Sociologists like Levi-Strauss grasp the functional signification of the incest taboo in certain societies, although this signification is normally hidden. Is there, therefore, any homogeneity of knowledge between the moment of individual praxis and that of the common project as a temporalisation which unifies the organised multiplicity? And what if there are structures and practical sub-reactions whose teleological signification must, a priori, escape me because the practical thought of the individual researcher is of a different order and, a priori, of a lower degree of complexity than the signifying action of the group? All these secondary problems are simply special ways of formulating the fundamental + +question of the constituted dialectic and its rationality. + +Now there is a false aporia which can be quickly disposed of: if I have a real understanding of the common activity of a group of which I am not a part, this must be because it does not transcend my possibilities as apractical individual; but, conversely, it is also because I approach it with the powers and in the function of a common individual. I mean by this that the historian is a product of a group, that his instruments, techniques and powers, as well as his knowledge, define him as a member of a research community and that he will understand the common undertaking of a historical group in so far as he himself belongs to a historical group which is defined by a particular common undertaking. And if he were a solitary researcher - which is really senseless unless it simply means that he is not a member of a university or does not have a degree - he would still be integrated into other groups (economic, cultural, political, religious, etc.) and would therefore be a common individual, capable of understanding any common + +praxIs. + +But the reciprocity between historical knowledge and its object postpones the problem rather than solving it. Since organic constituent praxis is an indispensable mediation between the common individual (as a limitation of possibilities in the light of a common objective and as the unification of a multiplicity by mediated reciprocity) and the practical exercise of a common function, how can this moment of pure practical individuality carry within itself a comprehension of the common scope of that which is realised by the individual organism? This can also be expressed from the point of view of historical research: the historian, of course, is function, power, and ability; but all this has to be + +reactualised by a synthetic invention, that is to say, by and in a synthetic, individual decoding of the practical field: now, the practical field, in this case, is constituted by certain documents and monuments through which a common signification must be rediscovered. Thus it is clear that the historian would not have the capacities necessary for comprehending a common historical action ifhe were not the social product of an organised group. This implies that his experimental invention, as an individual mediation between his function and the object (the past group which he is reconstructing), must involve a double comprehension : that of the common function of the scholar and that of the common praxis of the past group. These observations point to the following conclusion: there is always a permanent possibility, even if it can occur only in the context of organised functions and powers, of the practical + +organism comprehending the praxis of an organisation. + +But as I showed in The Problem of Method, comprehension is not a faculty, or some kind of contemplative intuition: it is reducible to praxis itself to the extent that it is homogeneous with every other individual praxis and that it is situated by reference to any action performed in the practical field, and therefore in an immediate practical relation to it. This implies, therefore, that common action and individual praxis exhibit a real homogeneity. The individual would be unable to understand either his own common action in terms of the totalising praxis of the group, or that of a group external to himself, if the structures of common praxis were of a different order than those of individual praxis. If the objectives of the group had a hyper-individual character, then the individual would never be able to grasp them. This does not mean that the common action is an organic synthesis of the members of the group but, on the contrary, that the group, far from having hyper-individuality in its action, sets itself objectives of an individualised structure and can achieve them only through common + +operations which are individual in character. + +But there is a danger of very serious confusions if we do not explain these conclusions at once. The common aim is in fact always doubly common: it is the aim of everyone as a member of the group, and its signifying content is necessarily common. In a1o/ case, there is an interest which defines the group itself, which is valid only for the group and which is accessible only through it, and this is equally true for a group of rebels organising to resist government forces and for employers reaching an agreement against the workers' unions, etc. Indeed, a group is often established as a last resort on the basis of individual recognition + +of impotence: the history of industrialisation in France shows a bitter resistance by family capitalism to all forms of capitalist association. In particular, the first mining companies appeared when it became absolutely impossible for landowners to exploit the sub-soil individually. In the same way, the common means, that is to say, the distribution of tasks and powers, the division of labour, the organisation of functions, are constituted by the transcendence of seriality, massification, individual antagonisms and isolations. And, as we have seen, it is circumstances, external pressures, which dissolve seriality in third parties and make it emerge in the group, that is to say, in a milieu of freedom and terror which they were unable even to conceive. In this sense, the group statute is indeed a metamorphosis of the individual. And the practical moment of the actualisation of the powers constitutes him, in himself, as fundamentally different from what he was on his own: adopted inertia, function, power, rights and duties, structure, violence and fraternity - he actualises all these reciprocal relations as his new being, his sociality. His existence is not, or is no longer, simply the temporalisation of organic need in a project: it arises in a field of violent but non-antagonistic tensions, that is to say, through a web of synthetic relations by which it is profoundly and fundamentally constituted as a mediated relation, that is to say, as terror and fraternity for all and for itself. Thus sociality comes to the individual through common totalisation and initially determines him through the curva- + +ture of internal social space here. + +But these essential reservations only serve to underline the fact that the formal structure of the objective and of the operations is still typically individual, in the original sense of the term, that is, in the sense in which the organic individual is characterised as a constitutive praxis and rearrangement of the practical field by an individual totalisation. If the objective of the group is, by definition, incapable of being realised by an isolated individual, then it can be posited by such an individual (on the basis of need, of danger, or of more complex forms). Although groups founded in this way seldom have much historical importance, it is quite common for an individual to conceive a common aim, and thereby to discover a community which ought to be formed and try to constitute a group because he also realises that he is unable to realise his undertaking on his own. Such isolated cases occur naturally in complex societies which present inert serialities, collectives, various groups, etc., alongside one another; and the very project of founding a group is conditioned by the real existence of + +similar groups. But the fact remains that practical action in this case is the individual's determination of a group which ought to be constituted for a common objective which he discovered on his own. 55 It may be added that he already belongs in some way to other organised groups: this is certainly not false. But though he may be a common individual in these groups, he discovers the end as an isolated or serial individual. If an individual senses the need to start an international health organisation, then it can in fact be said that it is in his sociality, that is to say, in his relation to the society in which he lives, that he is affected by the external imperative. But he goes beyond this sociality towards a larger integration, because his membership of a given national community cannot by itself show him an international objective. On the contrary, this practical movement of disclosure can occur only in connection with his attempt to de-situate himself (to remove himself from a restricted situation and enter a broader one). This does not mean that everyone is always capable of grasping every common objective : that would be absurd. On the contrary, the problems arise in terms of objective contradictions. And, as we have seen, they can appear to all the Others in a series in the dissolution of this alterity. But here too what matters is that, through mediated reciprocities, through the play of the regulatory third party and of immanence-transcendence, the movement of comprehension appears in everyone as the individual transcendence of seriality towards community. There is no common aim that an individual cannot set himself, provided that, in the unity of the + +project, he tries to constitute a group to realise it. + +And precisely because the decision to group or to regroup is occasioned by the common objective as the exigency that it should be pursued and realised in common, it also appears that the constitution of a group is a means which is accessible to individual praxis. In fact, it is clear that the abstract individual whom we encountered in the first moment of our investigation perceives the Others as a multiplicity in his practical field. And we have also seen that his sovereign praxis, as a perpetual reorganisation of the field in the light of needs, realises the + +55. Obviously this objective must answer some need of the society under consideration and appear as an exigency in the historical circumstances which define the moment. Normally, there are individuals in different plat:es who are unaware of one another but who are pursuing the same aim. But this does not mean that they are not individually subjected to a common exigency; and even if, as often happens, they eventually unite, they do not discover the social object as + +common individuals. + +practical unity of this objective multiplicity. This unity may appear as mere serial alterity; but if there is an exterior group then, as we have seen, it reveals itself as a group to the extent that unification by the individual, though effected from outside, turns out to display an internal unification, realised in practical autonomy. But above all the practical agent performs totalising actions in relation to organic individuals as well as to inanimate objects: to flee from a marching crowd is to totalise it, to turn it into a group when it may have been only a series. Thus the action offorming a real group is already given in organic praxis, and given precisely to the extent that there has always been a possibility of unifying a discrete multiplicity, whatever it may be (whether inert or constituted by organisms). This possibility contains an indeterminacy because it is not yet settled whether the group is to be constituted from the outside (this can occur in the construction of a trap as the totalisation of an already constituted group as well as in a practice which defines a seriality - children, the sick, etc. as a unified, receptive group which can be the object of my generosity) or whether it is to be constituted as a wrapping produced by the agent in order to envelop both himself and the others. But clearly this indeterminacy is logical rather than real. Practical priority is initially given to the group-object which is totalised from outside, since the primary movement is the sovereign reorganisation of the objective structures of the practical field. And anyone who tries to constitute a group in order to realise a common objective, useful to all, sees it initially, in the abstract moment in which he begins the undertaking, as his means of achieving his objective. It is only the progressive constitution of the community which gradually reveals to him that he is necessarily integrated into it. But this makes his comprehension of multiple activity even clearer and more obvious to us: in the moment in which he is still staying outside the group (which is as yet unconstituted or in the course of being constituted), he already grasps the unity of an interiorised multiplicity as a specific means from the point of view of an individual praxis. In fact, he also organises material objects: in the dialectical unity of his praxis, he creates material quasitotalities whose elements interact in such a way that, for example, they can transmit and amplify a movement which he makes at one point of the system to the intended objects. The transcendent, organisational movement is not in principle different when it is men who are being grouped; the difference emerges in the undertaking itself (and, in fact, there is no need for it really to begin: the abstract schema of the + +synthetic movement is sufficient) in that the projected unity immediately appears as perpetuating itself through everyone's activity. This initial disclosure reveals two contradictory characteristics: the passivity of the inert object maintains the unity that has been forged, but it also covers up an infinite dispersal. On the other hand, the activity of a group in formation realises true unity as praxis, but thereby emphasises the real multiplicity of the pledged members as a multiplicity which is constantly being overcome by a produced inertia. On the other hand, the original difference between a group which is united from outside and a controlled mechanical system is not basically a matter of complexity and simplicity; the human system is a practical arrangement which produces its effects through itself. Thus, when the sovereign individual undertakes to rearrange the human multiplicities of his practical field as a group, he tries to produce an instrumental system whose elements are united and governed in accordance with a practical rule, and whose organisation differs from inert systematisation in one essential respect: autonomy as productive of passivity and of specifications. And the complexity of organised groups is generally connected with the complexity of the mechanical arrangements which the agents + +are capable of at that historical moment. + +These remarks are, of course, not intended to emphasise the individual as the producer of the group (this accidental case is of limited interest). They are only intended to show that the organic individual, simply in his movement to organise the practical field, develops a comprehension of the group-object as an instrumental construction. Anyone who can shelter behind rocks can also shelter behind those other masses - men. On this basis, if these men, for some reason, assume the task of protecting him, he will be able to comprehend that these new kinds of rocks make themselves into rocks by their reciprocal pledges and that they arrange their gathering as rocks by means of a reciprocity of functions. This means that they behave as though they were animated by his own will, and at the same time, that his will branches through them and produces innumerable divergencies, so as to converge, and that, complete everywhere, it opposes itself everywhere in order to recognise itself as the same. But these constantly resolved oppositions do not disconcert him from outside. Neither the ensemhle (the group-object, integrated into his personal undertaking as a specific means and, consequently, illuminated by the objective itself), nor detailed rearrangements (the transformation of a simple musical notation into a chord, the amplification of the plan and its + +plural realisation) can disconcert him. When danger threatens, the Pretorian guard arranges itself around the sovereign; but the danger threatens him, and the group-object, which is simply the means of avoiding the danger, is to be decoded in terms of the fears of the exalted personage, and it provides reassurance in so far as it rules them out as impossible; the sovereign 'fears' doors, windows, and everything that opens onto the outside world; his fears, diversified by the diversity of the practical field, are embodied in one instant as precautions in the diversity of the guards who go and position themselves at every possible entrance. In this moment, they become active and functional (inertia as active passivity, power in so far as it is defined by the objective constitution of the entrance to be guarded, etc.); and the individual who is being protected understands them as, for example, the simultaneous realisation of the actions which are required by the object and which, if he had been on his own, he would have had to perform + +successively. + +It is here, in fact, that the novelty of the group-object resides for the individual - here rather than in the praxis (of each and all) as such, for praxis is in fact always understood through praxis, at least as regards its formal reality (since what is involved here is precisely the comprehensibility of certain material supports). In its origin, the transformation lies in the possibility of realising in simultaneity, on the basis of reciprocal relations, what the individual would have to realise successively. But, apart from the fact that the basis for comprehending this simultaneity is given in the praxis of the organism itself (the simplest operation,jor the individual, is the organisation of simultaneities: I hold the handle of one lever and push it with my right hand; and I pull another with my left hand; at the same time I bend or reach out, etc.), and apart from the fact that an adumbration of a practical redistribution of the group, in its objective interiority, is schematically provided by the organic posture and that this involves a comprehension of every practical, spontaneous metamorphosis of an object in response to a situation, the most important point to emphasise is that the arrangement of an instrumental (and inert) ensemble by one person involves, as an essential aim, the compression of a given practical temporalisation into simultaneity, so that the agent can transcend this flattened duration + +This is what is called 'making time', and it is an exigency of time itselfin that, in the world of scarcity, everyone's time is scarce (although it is no more than practical temporalisation). In this way, one puts the + +auxiliary tool 'within reach', another tool, to be used later, a little further away, near the object on which it will be used; and in this way, as I have said, inert interdependencies are constructed so that individual practical movements can be absorbed, divided, and distributed in several directions at once. In short, there is no visible contradiction at least in elementary forms of sociality - between the group-instrument and the inert instrument. To the person who gives it its tasks, the main characteristic of the group-object (slaves, for example) appears to be its ability to absorb the praxis of the individual and to make it into its temporal and practical unity. For primitive societies and techniques, the inert instrument retains a magical, double residue of individual praxis: the past labour of the tool-maker and the past labour of its user coincide in the tool; and it has been established that in such societies, the maker and the user of the tool are generally the same person. For the primitive, therefore, this magical character derives from the fact [hat his own future praxis appears to him as a power inscribed in inertia and as an already given transcendence of this passivity towards the future. (Obviously the two moments - creation and use - interpenetrate in the indifferentiation of passivity.) Now, the instrument itself is not an indeterminateJorce: it is an organised reality (for example, it has a blade and a handle). So at this elementary level there is a homogeneity between, on the one hand, the group-object as it reinteriorises an individual's project and praxis and so becomes, as a means, his relation to the objective, and, on the other, the inert instrument as it absorbs a praxis which produces and constitutes it as a mediation between its owner and his aim. This is illustrated by the native's magical tendency to attribute mana to his weapons or tools (that is to say, a power as potential praxis and a mortgage against the future) and by the opposite tendency, in the outsider, to treat the organised group as a material object endowed with powers. In the extreme case, in the practico-inert field, the sanctified instrument and the totalised group + +are equivalent. + +Conversely, an individual who is tracked down in the practical field by a group organised for a man-hunt - and, specifically, for a hunt for him - experiences this organised praxis as the free project of an individuality which is wider, more flexible, and more powerful than his concrete individuality, but homogeneous with it. The practical field appears to him to be undermined by this freedom; it becomes the other meaning of every object in the field. And this other meaning becomes practical truth: the truth of a given exit (a gate or path) is no longer that + +of an exit, but that of a trap set by the group. The individual cannot attempt to break out of the circle unless he manages to reinteriorise his objectivity for the group, that is to say, to decipher his own acts in terms of the common freedom of his enemies: the action I am about to perform is precisely what they expect of the object that I am for them, etc. Thus he is immediately given an understanding of the common aim, since this common aim is himelf. And on the basis of the objective that he is, he can reconstruct in practice and in prospect the operations of the group (of which he is the negative and totalising unity)56 and thereby assess his own action objectively from the practical point of view of escape or flight. Dialogue (in the sense of rational antagonism) is possible between the individual and the group that surrounds him. And both of them - he in his isolation, and the other either through each and all or through differentiated organs - can foresee, with some variable margin of error, how the other will act by treating for his own + +part his own acts as objects. + +We need to go beyond this and note that the hunted man realises in practice the truth of the group : except in the special case where he knows the names and characters of all his hunters (which can only apply in a very restricted multiplicity), he realises the group not as a hyper-organism, but as ubiquity in each structure and in everyone's praxis. Meanwhile the hunted man sees or guesses at human presences behind a door or trees and regards these presences as all the same; he sees their ruthless ferocity as transforming every elsewhere into a here. For him, the differentiation will depend entirely on the practical situation: the group is up there on an eminence so that it controls a whole region; the group is down there, behind some trees whose function it is to hide it, but which may also, by way of counter-finality, conceal certain presences from it. Thus, through the practical interiorisation of his objectivity for the group as practical freedom, he + +56. We have already seen how either a hostile extermination group or a 'natural' danger can constitute themselves as the negative totalisation of a given group, via the destructive process which unites all the members in a common (and non-serial) extermination. But here the negative totalisation is different: by discovering himself as an ohjective and reinteriorising this objectivity, the individual becomes the outside-being (etre-dehors) of the group which is pursuing him and, in so far as he is threatened with the danger of being killed, he sees death approaching him as a possibility which belongs to the enemy group and as the possibility that the success of the group will be realised (the annihilation of the individual) as a negative objectification (the result is an inert disappearance) and as a + +reveals the truth of the function. By deciding to go behind the curtain of trees rather than cross the field without cover, he differentiates these sames (les memes) by means of the real situation, that is to say, through function: in these common individuals, behind the trees, the group is closer to him, but not so well placed to see him; in the person of those lying in wait on the hill, the group is further away but it can see further by means of an instrument (the hill is being used). And this differentiation of functions does not by any means prevent the fugitive from being trapped: and therefore function, reciprocity and structure are also revealed by the flight of the hunted man as the physiognomy of a freedom which is organised for extermination. In other words the hunted man, in the tension of being surrounded, sees those behind the trees as the same as those up on the hill in so far as both of them deprive him of the possibility of escape by their reciprocal positions; and the common praxis appears to him as a here in both places to the extent that the danger up there and the danger down there are a function of one another. But in the deliberate action of the man-hunt he sees this reciprocity everywhere as an intentional structure of the common praxis in every member of every sub-group. He acts, in fact, in the light of the ubiquity of the enemy's co-ordination: those up there are directly connected with those down there. If he is seen by those on the hill, they will force him towards the sub-groups who are concealed in + +the plain, etc. + +It is not necessary to develop this example any further. It must be admitted that, as moments of the dialectical investigation, these examples still do not show that the formal structure of the common praxis is the synthetic unity of the individual praxis - and this formulation is inaccurate anyway. But they do at least prove that an individual's understanding of praxis can remain of the same kind whether applied to the praxis of a group-object, to that of a group-subject or to that of a practical organism. In each case, the common end is practically conceived as that towards which the group transcends what is given; and this practical perception is itself an individual transcendence (depassement); and in each case, the actions are decoded in a movement from the future to the present and each of them reveals itself in this regressive unity as a means, unified by the common + +There is nothing surprising about this: it is true that the objective of the group is common in so far as it appears only through each common, that is to say pledged and structured, individual; but it is also + +true that the practical moment is realised through organic praxis and that this constitutes itself as the comprehension of its individual task in so far as the common task objectifies itself in it. This shows that the final, common objective can manifest itself only through individual action and as its common beyond, and that structure, as a relation to the totality, is lived as the deep meaning (signification) of the task being performed. Certain determinations of action in effect come to the individual from the group, as a new statute which, in his individual isolation, he could not have produced or even understood - in particular, and fundamentally, the pledge as a free limit of freedom. We have seen, in fact, that a praxis reduced to its individual translucidity cannot in any way commit an indeterminate future (that is to say, a future in which all the conditions of praxis are different); my own freedom turns against me as Other in so far as it is other for the Others. Thus the modality of action, its normative aspect, often eludes those who are not grouped, even if they live it themselves as members, + +in different circumstances, of another group. + +What people calI fanaticism, blindness, etc. , is really fraternity-terror as experienced in another group and in so far as we, as individuals, treat it as an emotional occurrence in individuals. But, on the one hand, a pledge is not produced by a hyper-dialectic; it is an incarnation of the inter-individual relation of reciprocity. And on the other hand, even if the modality of action eludes the non-grouped individual externally, it is still lived in the group through the mediation of individual praxis; and this means that power and the imperative, far from producing and qualifying this praxis, are adopted and interiorised by it in so far as they occasion it. In the process of concretely unfolding and adapting to circumstances, free praxis produces its own inertia, its own limitations, and keeps these determinations in Being. Moreover, individual praxis is immediately reciprocal, as we saw at the beginning of this investigation. And this reciprocity is the basis of the worked product of freedom interiorising multiplicity - which we have called the pledge. The pledge is the practical comprehension of reciprocity as a means of constituting a group inertia in the same way that pledged praxis implies a common understanding of the group objective and of the pledge. From this point of view, apart from modality (it is still necessary to establish dialectically the formal conditions in which a nonmember of the group can recognise it in the group member), there is always a possible reciprocity between the member of the group and the non-member; it may be difficult for the first to explain the conditions of + +common life to the second (but this difficulty appears a posteriori; the soldier will find it easy or difficult to explain the interior milieu of his unit to the non-soldier, depending on what type of war he is fighting), but he can always reveal his aim to him. In other words, they can communicate in so far as there is a formal homogeneity between the following three comprehensions: the comprehension of the groupobject by the subject who is not grouped (in the sense of being a subject of the individual, grouping action); the comprehension of the group-subject by the non-grouped as an object (that is to say, by the very process which interiorises its objectivity), and the comprehension of the group-praxis by each of its members, as a mediation of function + +and objectification. + +2 Spontaneity and Command + +But, far from making our task easier, the homogeneity of individual praxis and common praxis at first presents us with difficulties; it involves a kind of aporia, or impotence of the dialectic. Given that the group as an interiorised multiplicity is so profoundly different from the organic individual, that, in other words, we have avoided treating the group as an organism, except metaphorically, how can the group produce, in common, actions whose fundamental structure is the same as that of individual actions? It might be said that a limit is given a priori. Not a limitation adopted as pledged inertia, nor for that matter a limitation experienced and suffered as the insurmountable resistance of some inert materiality to a given undertaking: but rather a kind of breathlessness of the dialectic reproducing its original movement, regardless of the internal constitution of the agent who realises it. This involves a new kind of untranscendability, and it is necessary to explain it. In order to do this, we must make a closer examination of the process of organisation, not as a real constitution of a being -in-the-group based + +on the pledge, but as a distribution of tasks. + +It is common - for example, in periods of revolution - to contrast a centralising, authoritarian tendency coming from above, that is to say, from the elements who hold power for the time being, with a democratic, spontaneous tendency which grows from the base. The first is supposed to realise the organisation of the masses into hierarchised + +action groups from outside or, at least, on the basis of a frozen immanence-transcendence; and the second is supposed to realise groups through the free, common action of the multiplicity upon itself, and as such to represent true democratic self-determination in interiority. The difference hetween these kinds of organisation is supposed to he qualitative and radical; they are treated as two essentially opposed realities, only the second of which can really constitute the group as common self-creation. The implication of this fundamental contrast is that truly common objectives, operations and thoughts are produced in the autonomous process of the demassification of the masses by them- + +selves and of their spontaneous organisation. + +This conception has political and ideological foundations which cannot be discussed here. I am not denying that politically it is of the greatest importance whether organisation is imposed from above or produced from below. Similarly, I admit that the social, ideological, ethical (and, primarily, material) consequences of a movement will be completely different depending on whether the popular movement produces its leaders as a temporary expression of its praxis and reabsorbs and transcends them through the development of this praxis or whether, on the contrary, a group detaches itself from the masses, specialises in the exercise of power and arranges the tasks in an authoritarian manner in the light of its own conception of the people's objectives. Of course it is obvious that the regime itself will be different in the two cases, as well as the relations of reciprocity between individuals. But the important point here is, quite apart from any political considerations, that the mode of regroupment and organisation is not fundamentally different according to whether it depends on centralisation from above or on a spontaneous liquidation of seriality within the series itself and on the common organisation which follows. In short, this is not and cannot be an issue about Blanqui, Jaures, Lenin, Rosa Luxemburg, Stalin or Trotsky. And, just as a premeditated crime and an act of justified defence may, in spite of all the practical and legal differences between them, involve the same muscles and be realised in the same basic actions (the differences emerging at a higher level and from the point of view of a different praxis - that of a police investigation or a trial, for example), so, in the same way, the type of formal intelligibility and rationality can be the same with organisation from + +It should in fact be recognised that the habit of speaking of dialectical transformations of the masses is always metaphorical. For + +example, when Trotsky emphasises the qualitative transformation (especially from the point of view of revolutionary potential) caused by the first meetings of workers and soldiers, he is perfectly right. And today, when other writers take up these remarks and develop them in order to show the revolutionary character of the Hungarian rebels, showing that a truly revolutionary situation is characterised both by specific circumstances and by the constitution of insurrectional groups including workers, students and soldiers, they may be right historically, that is to say, at a level whose concrete determinations no longer fall within the area of our research. But we should avoid following certain historians or Marxists (whether Trotskyists or not) when, before or after the event, they give what is really a 'Gestaltist' description of these 'typically revolutionary' meetings, as if an organic synthesis arose spontaneously out of them - based, of course on the quantitative relations of the three social groups involved, but transcending the quantitative relation towards a new qualitative differentiation. (For, as we have seen, Engels permitted every consistent Marxist to reveal the transformation of quantity into quality in the name of the external dialectic.) In fact, even if soldiers and workers do constitute the first organising committees of the rebellion (not only in Paris in 1789, with the encounter of the residents of the Quartier Saint-Antoine and the French guards, but also in Germany in 1918 and Russia in 1917), these relations are too universal and have to be specified in each case: univer- + +sality is hard to find and define in a dialectical process. + +Whereas for analytical Reason this is concrete reality, as a relation which is indifferent to its terms, in a dialectical investigation it appears, as we shall see, either as an immediate, abstract appearance, as the first delusion to be dissolved, or else as the concrete, hidden conclusion of the entire investigation, and, as it were, as the totalising but ultimate foundation of rational development. And if, without prejudging the nature of a 'typically revolutionary' organisation, one imagines the se groups in a particular concrete historical situation, for example, either St Petersburg in 1917 or Berlin in 1918, but not in both cities at once, then a concrete relation of reciprocity will re-establish itsel£ For the workers, given the situation in the country and the city at the time, and the special characteristics of the Navy and the Army, here and always, either the soldiers or the sailors (and each case must be examined separately - Kronstadt is not St Petersburg, etc.) are practical, irrefutable evidence against the government, and a defence against its attempts to smash the rebellion, a direct or indirect relation to other classes (in + +particular, to the peasant class in so far as the peasants who had been mobilised outnumbered the rest, and also in so far as these war-weary, discontented servicemen were a mediation between the workers, the ex-peasants, and the countryside, of which the fighters in fact represented the most advanced section) and a proof of the collapse of the regime, a beginning of universalisation: these other exploited men appeared to them as representatives of all exploited people. But above all 'the soldiers are with us' took on, for and in everyone, a special meaning because ever since 1905 (not to mention earlier times) the soldiers had been, in spite of themselves, instruments of repression. Conversely, for a soldier who rejected external discipline, the workers represented the only possibility of integration and of fightingdiscipline; the workers, indeed, unlike the soldiers, knew that insurrec- + +tions required practical organisation even more than strikes. + +These relations of reciprocity are exactly the reverse of the suggested 'Gestaltist' syntheses: they establish themselves through a practical recognition within action, on the tacit basis of the pledge. And the giyen heterogeneity, which presides over the encounter, becomes a pledged homogeneity which guarantees a created heterogeneity. On the other hand, it would be absurd to deny the practical end of such organised groups: in each case there is a danger, and it is necessary to secure defences, to maintain vigilance, etc. And above all, whether one likes it or not, one has to go back to the truths established by the historians: the organisation selects its organisers. It may reject or reabsorb them, but it is undeniable that, generally speaking, it preserves them in their role by means of the pledge which supports function by adopting passivity. Historians of the French Revolution have established, for example, that there was a category of popular agitators, some of whom have been identified and traced, who, between 1789 and 1794, were present at every important event, and whom the 'common individuals' of the sections regarded as their organisers and whose function, preserved by reciprocal inertia between the popular 'days', maintained a kind of passive organisational ossature in the everyday dispersal: the organisation would reform around them in moments of tension. These popular agitators were not leaders: it is primarily in this respect that their power differed from that of the actual leaders. They did not issue orders: but the group reconstituted itself around them, exalted them and communicated its power to them; it gave itself orders through them. They were in fact simply regulatory third parties whose regulatory activity became function on the tacit basis of the pledge. For this + +reason it would be absurd to use them as an argument against the + +democracy of the popular organisation. + +But two important points should be noted. On the one hand this democracy is really fraternity-terror, that is to say, it is actually based on violence. For this reason Guerin is wrong to contrast it with the violence of authoritarianism from above. Although circumstances may, in fact, produce violent contradictions between the base and the apex, the only possible basis for violence from above is violence from below. But as we shall see, violence tends to become purer as it moves away from its origins, and what disappears is fraternity. On the other hand and this is what is most important for us - by virtue of the pledged inertia of function, the organiser-agitator will remain, for some time, the means through which the group defines its praxis, and creates its own organisation. This does not mean that the organiser can impose a particular action or forbid another: he would immediately lose his power if he tried to issue orders. He is a medium and he knows it; and if he acts (some of them are corrupted) it is through the group, and in secret. But since the orders of the people issue from his mouth, since the reorganisation has to be carried out through his individual praxis, and since his exhortations and gestures indicate the common objective, we have to conclude that popular praxis is essentially capable of being created, understood and organised hy an individual; which means, in other words, that the group can define its common action only through the mediation of an individual designation. In the tension ofimmanencetranscendence, the 'leader' proceeds to the reorganisation of the group as a quasi-object and distributes quasi-objective functions in accordance with the objective which he thereby defines. In this way, he constructs a practical device in quasi-objectivity which will preserve itself as it is through assumed inertia, just as an instrumental system in the inorganic world is given an organisation by individual praxis and supports it with its passivity. Of course, things are not really so simple: he is interrupted or warned, his invention is anticipated by someone else, a few people organise spontaneously in connection with everyone, and others suggest some rearrangement to him, etc. As I have said, he is, in a sense, a mediation. But the important point is that this mediation is necessary as long as the group itself, because of this mediation, is not finally constituted along with its organs of control, distribution, etc. And clearly, even then, whatever the system of self-administration (Soviets, revolutionary committees, etc.), the mediation of the individual will simply have been institutionalised. For example, if one votes + +one will be voting for one motion and against another, for one amendment and against another, in short, for an individual, practical deter- + +mination of discourse. + +The difference between a regulatory third party and a leader is that one is in charge and the other is not. We will come to the question of command shortly. But - except when contradictions become acute - it should not be supposed that the 'transcendence-immanence' tension disappears. In fact, what distinguishes the leader from the agitator apart from the coercive nature of his power - is, frequently, the number of mediations which separate him from the group. But in each case we come up against a strange limit of the dialectic: the organised group obtains results which no individual could achieve alone, even if his strength and skill were doubled; moreover, organisation as practical being is normally constituted in a more complex and better adapted way than any organism. To resemble a guard in a square formation, one would have to have eyes all round one's head, and arms in one's back; to resemble a combat unit which is protected by guards at night, one would have to be able to sleep and watch at the same time. Thus an organisation does not reproduce an organism, but is meant to be an improvement on it by means of human invention. It takes the practical unity of the organism as its ideal (though as we shall see it does not achieve it), but it dissolves the facticity of the living being. But these transformations do not extricate it from the inflexible necessity of being situated, that is to say, regardless of its instruments, of being designated as a practical point of view, as an anchorage defined by the very world it is trying to modi(v. And in order finally to achieve these supraindividual results, it must allow itself to be determined by the unifyin"g unity of an individual praxis. Thus the individual cannot achieve the common objective on his own, but he can conceive it, signify it, and, through it, signify the reorganisation of the group, in the same way as he would carry out a rearrangement of his individual practical field. The individual integrates himself into the group and the group has its + +practical limit in the individual. + +groups entrust planning, the distribution of tasks, supervision and administration not to individuals but to specific sub-groups. In such communities, everything is a common task and the individual as such apparently dissolves in a small sub-group; and then reciprocities exist only between sub-groups. But if the individuals of the organising subgroup sink into anonymity, the sub-group still does not transcend the framework of an individual conception in its common praxis. In other words, it is still impossible to determine a priori, that is to say, on simple inspection, whether the plan adopted is the work of one person + +or several: for, in order to construct it, several became one. + +Of course, disagreements within the organising group are inevitable and may even be violent. And the plan gets organised through these disagreements. In the most complex groups, rent by class struggles, by conflicts of interest or of point of view, and partly infected with seriality, it will no doubt be claimed that the several organisers, if they have been carefully selected, represent the diversity of tendencies - which no individual could do. But, apart from the fact that a synthesis is not usually achieved and that compromise proposals reflect in some form the deep impotence which results from divisions, such decaying or disunited groups do not belong to the present level of our investigation. People in a technical office or managerial department, etc., normally belong to the same class and milieu, share the same interests and have had the same technical training: however violent their disagreements may be, they are not a direct result of social conflicts and it would be ridiculous psychologistic scepticism to attribute them to personality conflicts or secret rivalries, although, of course, such conflicts and rivalries may be expressed in the contradictions which divide them. In fact, these contradictions are really just objective structures of the practical problem that has to be resolved. And when experts are trying to find a solution to a problem like traffic in a city, they are faced with a set of given, material incompatibilities, whose origins may be extremely varied : the constantly rising number of cars, the insufficient number of garages, the relative narrowness of most of the main roads, the necessity for car owners to use their cars for getting about and to have parking places, which is in itself contradictory since the number of cars lining the streets necessarily limits the speed and volume of traffic. The solution, if there is one, obviously has to transcend and resolve all these material conflicts; and it must emerge in a framework of scarcity, since the budget of the city (or state) does not permit any large expenditure. Any conflict between the members of the group will, in + +fact, be due to the fact that in trying to transcend the objective contradictions everyone is, unintentionally, simply favouring one of the terms of the contradictory proposition in a false synthesis. One solution ignores the interests of traffic flow; another makes parking in the city impossible, and so makes the car useless and threatens to impede the expansion of the motor industry; and another, which revives an old plan of building wider roads, simply ignores the limitations of available resources. Each of these solutions is individual: by which I mean not only that it was proposed by an individual, but also that it determines and defines an individual in the group; if he favours one solution rather than another, it is not impossible that this is the result of certain pressures, or ifhe has discovered this solution amongst all the others, this may be because his fundamental project cleaves to certain possibilities and rejects all the others. But such practical 'predispositions' can do no more here than define an approach to the problem: the contradiction is in the object; it manifests itself spontaneously and it explodes in the final synthesis all the more violently if the synthesis neglects one term in favour of an other. Of course the contradiction may strike other experts, especially ones who are themselves proposing a partial synthesis, that is to say unintentionally expressing one contradiction while meaning to transcend others. Each of the solutions is an individual reality - an objective, individual failure - in so far as the mistake has to be attributed to individual limitations: a part was mistaken for the whole. But the limitations are themselves individual: by this I mean that people are limited here in relation to other individuals, better equipped than themselves, rather than in relation to the group or to mankind. However, this individual reality (in the ancient sense in which the individual is characterised by the degree of nothingness which he has interiorised) reveals, through false discourse, an objective, material contradiction which produced the false synthesis which favoured one term and neglected another. In other words, it represents the objective possibility of serving some interests while neglecting others (possibly in the same person); and this possibility is a structure of the problem in so far as it is really already expressed in the practice of certain groups of car users, garage owners or traffic police. Through them, one term attempts to destroy the other and impose itself; by lending the support of its common strength, the municipal authority may allow the attempted solution to 'hold', at least for a while. But since the contradiction would remain, with one term being favoured, it would reappear even more violently in some + +other form and the whole problem would recur. Thus, what a particular individual becomes responsible for is the contradiction as it exists in the practico-inert field: it is in this field that the increasing number of cars (a strictly serial phenomenon) comes up against the rigidity of urban structures (inorganic and serial inertias); and this contradiction, by becoming a structure of a technical problem, detaches itself from the milieu of seriality: it is at the centre of the practical + +field. + +But it should also be noticed that, as an individual, the expert serves a purpose, in that his own solution becomes his ideological interest, his being-outside-himself which he defends in the same way as he would defend himself, and because it is himself. Thus the conflicts between different solutions reactualise the contradictions as a permanent conflict, outside, of material forces. Every solution is really just a veiled attempt to make one term dominate the other. And the inter-individual violence of the conflict is inconceivable outside an organised group. In the milieu of the pledge, the Others must become the same again, for otherwise the calculated alterity of functions becomes a suffered alterity. Thus, above all from the practical point of view of finding a solution, the conflict between two individuals (a reciprocal antagonism) occurs as having to end with the destruction of one in favour of the other, or of both in favour of a third or of their reabsorption by the group. For these serene experts, of course, there is no threat of physical liquidation or of brain washing; but though their individual lives are not in danger, their social heing may perfectly well be annihilated (either in the form of this individual solution, or, less determinately, as their reputation with others, both of which define their being-outside-themselves-inthe-group. And this being-outside-themselves is not to be confused with the constitutive relation of the common individual: reputation is really the specification of power in so far as this specification arises as a common result in the interiority of the group and is functionally connected with the concrete exercise of this power). Thus the mediation of the individual was necessary in order to carry the objective contradiction into the group; but the common-being-in-the-group was necessary in order to restore the virulence of the contradiction through personal conflict. In fact, it is obvious that everyone has been aware of all the givens of the problem for a long time and that, in the course of a given session, the first reports will once again enumerate the difficulties, aporias, objective conflicts, etc. But these oppositions cannot manifest themselves in their truth as long as they are the object of a pure + +enumeration or of a strictly verbal description (I include diagrams, statistics, etc., under this heading). This is because the organising subgroup stands in a relation of immanence-transcendence to the surrounding group: a quasi-separation (or quasi-negation) conditions the relations between them in inertia (we shall return to this shortly) as long as the lived contradictions of the surrounding group (in the relations of its members in so far as they need to remain the same but are in danger of being disunited by the object) cannot be reinteriorised by the organising sub-group and lived at a level of abstraction and specialisa- + +tion which is precisely that of the sub-group. + +Thus any expert, if he is a car-owner, can experience for himself the contradictions suffered by every member of the seriated-group (the meaning of this term will become clear when we examine it concretely) which is the Parisian population (in so far as some of its members are car-owners). But at this leyel, he either suffers or avoids the problem by some special expedient which is incapable of being generalised. In short, his own misfortunes determine his reactions as a Parisian, but they have practically no effect on his attitude as an expert (an individual 9efined by his power), though he may use them as examples or illustrations in his arguments. But his practical point of view is formed within a community of experts (or else in isolation, but only in so far as this isolation is simply one mode of being-in-the-group: for example, when working on his report in his office). Thus car accidents, impassable streets, traffic jams, etc., are reproduced in all their violence within the specialised sub-group when conflicts of material interest are taken up by individuals in the form of ideological interests. As a mediation of an antagonistic reciprocity, the sub-group controls its tension and defines the urgency of transcendence. Thanks to the fact that individuals are endangered in their being-in-the�group, and that the subgroup makes their conflict both possible and inevitable, the objective problem develops (or can develop) all its contradictions at the level where it ought to be possible to find a solution (of course there may not be any solution in present conditions). Besides, these inter-individual conflicts may become common conflicts, in so far as the individuals who suggest the solution become, for others, the regulatory third parties of an organising action which they had already guessed at though without + +But what purpose is served by this virulence? - To raise the question in all its forms and in all its complexity, or, in other words, to effect the becoming-question (Ie deyenir-question) of the sub-group. The + +maximum tension will be realised when the group, at its own level and in accordance wi.:h its functions, becomes the traffic of Paris. Now this complexity bristles with contradictions and cannot sustain itself as such: it is a way of interiorising the problem, but as long as they remain divided, the common individuals will be paralysed; the moment of the interiorisation of the contradiction, in so far as it transforms those who are the same into others, must be transcended towards synthetic unity. The more integrated the sub-group, the more sensitive it is to the profound contradiction of the same and the other through all its members, and the more tempted it is to reach a solution through terror, that is to say, through requiring support for one of the proposed theses. In this case, it is not important whether or not a vote is taken: what matters is the elimination of the minority as such. And, ahove all, it must be made clear which thesis is being supported ; if, as often happens, this is a thesis which has already been proposed, one which has just been explained, then, if one refuses to submit to the law of alterity, one is bound to give an arbitrary advantage to one or more of the terms of the objective contradictions, to the detriment of the others. There is no thought, in the sense of an 'organising practice', which selects a best (if not actually good) solution by a synthetic transcen- + +dence of the contradictions. + +The common action (or power to determine a reorganisation) therefore becomes defined as a common adoption of an individual proposal (made by a common individual). If thought does take place, however that is to say, if someone proposes a best, if only temporary, solution then it will ohviously manifest itself as a regulatory praxis and through the regulatory third party. (It does not matter here whether there is one third party or several, or whether the solution is 'found' by several people at the same time; what is important is that everyone, in so far as he is a common individual mediated by organic practice, produces it as a free dialectical movement of his thought). What is involved, in fact, is a dialectical transcendence through a practical project: and it therefore presupposes a synthetic grasp of all contradictions, in short, a living reunification of the [sub-]group by the third party, taking the dissensions themselves as an instrument of reunification. The sub-group then becomes simply the synthetic unity of its own divisions, that is to say, it realises, through its dissensions, the objective contradictions which the whole group derives from its situation. And, by finding a solution, the individual posits himself as a regulatory third party, that is to say, he exhibits his solution as the opening to a possible future and + +to a field of action which is conditio�ed by a new objective (in the short term, since the fundamental objective remains unchanged). And this solution presents itself both as an objective transcendence of objective contradictions and as a possible reorganisation of the sub-group itself in interiority. When the solution is adopted, factional divisions (in the most general sense) organise themselves into a structure of positive reciprocity: within the new unity, the contradictory terms are preserved as indissoluble elements of the new arrangement, and their + +mediated contradiction becomes an adopted heterogeneity. + +It does not matter in the least whether the solution was found in the course of meetings of the sub-group or through isolated work, since, as we have just seen, isolation is a particular functional relation between the individual and a sub-group to which he belongs. What is important, on the other hand, is that the practical development of the contradictions can and must take place through the regulatory third party: in so far as these contradictions realise themselves in the unity of the divided sub-group, he grasps them both within himself, and outside himself, in the common field, and in so far as he is a common individual (just as a footballer perceives the moving organisation of the practical field as it conditions and transforms him and so realises itself through him); and since these internal contradictions are the interiorisation of objective contradictions, he perceives them in the indissoluble unity of praxis as a problem of the objective organisation of the whole group in so far as the solution of this problem must effect a reorganisation of the organising sub-group. In other words, he not only sees the solution as necessarily involving a reorganisation of the sub-group, but also sees the reorganisation of the sub-group as having to be effected on the basis of + +a possible solution. + +And the practical conception is thought: which specifically means that it is a practical transcendence of the group's relations to the world and to itself and of the sub-group's relations to itself and to the group, in so far as these relations are the inert, pledged ossature of the community or, in other words, capable of being seen as the inert exteriority of interiority. Its thought is based on these relations, even if it has to modify some of them in the name of the whole; it is structured by them, and it preserves them by synthesising them through a project which transcends and uses them. At the same time, they lie before it in quasi-objectivity as the inert matter of an ordinal mathematics. Thus the structure and instruments of thought are common, but thought as praxis is a mediation of the practical organism and of the free, con- + +stituent dialectic between these inert relations and the final objectification. Finding a solution is the synthetic, individual relation between structures brought together in living syntheses and the structural relations rearranged in response to this synthesis, in a practical field rent by contradictory exigencies. Since the discovery of a solution arises as a regulatory praxis of the third party, and since comprehension is this discovery in so far as it occurs in the other third party as regulated praxis, the action, as the unity of the reorganisation of the subgroup and of the new organisation of the group, occurs everywhere as + +the same, here, now. + +This is the crucial point: what we are touching on here is that essential structure of communities which epistemological idealism calls an agreement of minds. There are no such things as minds - any more than there are souls. This is already established. But the word 'agreement' is also misleading. Agreement presupposes, in effect, that different individuals or groups, with different horizons, and with characters and habits of totally different kinds, realise a contractual agreement in reciprocity on a minimum basis. Idealist optimism may then claim that this minimum will rise to a higher minimum, this minimum to another, so that, finally, agreement will reign in the whole of human knowledge or activity: but this is a philosophy of History. It is still always the case that the new agreement is the minimum for the given situation, even if it is based on previous agreements. At a given moment of its history, science can bring about the agreement of individuals who differ in age, sex, social condition, interests, language, nation, etc. (We shall come back to this later.) And these individuals will agree, for example, on Fresnel's theory or on the laws of thermodynamics and their proofs. At the same time, the object of the agreement becomes external to each of them: a communist physicist and an anti-communist physicist can agree on some experimental results and their interpretation, without any change in their sociality or organic + +individuality. + +And, in a way, this is what actually appears to happen; but this is because it involves a more complex structure than what we are examining at present: but what is really involved is a resurrection of unity through seriality and the creation of groups in the serial milieu without the dissolution of alterity. In fact, such induced unity is the degraded product of small, active groups whose activity, as we shall see, is refracted in seriality. The contradiction in the idealist conception is due to its assumption that truth can be the same in the other as Other. And + +it would be impossible to claim that scientific agreement between two others is an example of basic human reciprocity (and that, consequently, alterity in its social and political forms, etc., is merely a secondary modality which will ultimately dissolve) without making an a priori judgement on the whole of History and, for example, simply rejecting class struggle and exploitation. For intellectual agreement about a scientific truth is always possible between an employer and one of his workers (all that is necessary is that both of them should have the desire and the opportunity to learn, which depends mainly on circumstances). But if a welder and the owner of a shipyard are both convinced of the truth of Archimedes' principle, each of their convictions is an other conviction, because it exists in a divided society and, as it were, at the two ends of an exploitative system. Here, an agreement about science is quite unimportant (just like an equally real agreement about the weather or the temperature). One might even say that it has no concrete reality, simply because the two individuals are such that a confrontation in knowledge is extremely unlikely, and would, in any case, be pointless. They are in fact two individuals whose concrete relations are governed by the mode and the relations of production and who, each for himself within a homogeneous group, reproduce the movement of thought of a given strict proof. In short, when individuals or groups are fundamentally other (and therefore inevitably opposed), 'an agreement of minds' as a permanent possibility of reciprocity remains abstract and quite inessential: after all, the artillery of two enemy armies will be in complete agreement about ballistics. On the other hand, both in organising and in heuristic groups (which includes active groups of scientists concretely working to� gether), the appearance of a solution commits everyone much more totally and much more concretely than any 'agreement'. An agreement, in effect, realises at one point the exterieJr unity of the Others as Others and thereby decomposes into a dust of identities: all the Others are identical at this particular point. When a solution is produced as the practical conduct of a regulatory third party (for this is what primarily it is: a determination of discourse, graphic proofs, the reproduction of experiments, etc.) and when it also reproduces itself through the praxis of every other third party, then it is in fact the temporalisation of everyone as the same in the ubiquity of a here. This means that comprehension is creation (and amongst such scientists or experts, it may happen that, as soon as the first words have been spoken the field of possibilities becomes illuminated, that the future immediately appears, + +even more clearly than the regulatory action had intended to determine it); but it also means that the free creation does not occur in an Other as such but in a common individual who, momentarily altered (by the contradictory divisions) reconstitutes himself as the same by his practical activity in so far as this is one and the same thing for the whole of this + +interiorised multiplicity. + +Thus we have two descriptions of the act in question (a third party explaining a solution to his peers); and both of them are inadequate. The first is implicitly organicist: it presupposes that there is a synthetic act (the demonstration by the proposer) and that this single act realises itself through the audience as the unity of integration. This interpretation amounts to submerging all but one of the people involved into indistinct inessentiality and to constituting the originator as a totalising hyper-consciousness; it is based on superficial syntheses of perception which make the ensemble of listeners appear as a background from which the author stands out. The second interpretation, by contrast, is based on analytical rationality: it eliminates the group, replacing it by its multiplicity of exteriority, and resolves the act of understanding into a definite number of identical processes occurring in different organisms. The proposer's demonstration is then itself a process every term of which is governed by the preceding one and it serves as the inducer + +of identical reactions in external units (listeners, spectators). + +The concrete truth is much simpler than the two mistaken interpretations between which we constantly vacillate : the actual process of discovering the solution - even if it slightly precedes that of the exposition - still belongs to the process of common division: in fact it is, inevitably, primarily the appearance of one solution amongst others; and each of the false contradictory solutions has really been lived as a totalising reorganisation and has been realised as a new internal contradiction, dividing the group and signifying its author in his individuality. When it comes to trials, the truly synthetic solution realises itself as a restructuring of the group. The trial may be experiment or calculation - as isolated work - or, in different circumstances, it may consist in the explanation of the solution. In any case, an isolated trial, however severe, is still inadequate: the truth is hoth a controlled, practical decoding of objectivity and a determination of sociality in interiority. 57 57. There is no reason to expect these two operations to occur together or to follow one another in quick succession. Nevertheless, the first fixes certain abstract conditions for an integration which is the only possible source of its concrete + +Thus the operation is not the property of the regulatory third party any more than the storming of the Bastille was the responsibility of the first individual to shout: 'To the Bastille 1 Run I' It is performed by everyone, in three ways: a practical chain of abstract arguments (that is to say, of inert necessary relations whose necessity appears to everyone in all its persuasiveness, in so far as it is understood through the same relations united in the living structure); liquidation, through a totalising rearrangement, of their ideological separatism; and the realisation of the common practical field by and around them and by all in a strict and novel operation. This constructive liquidation takes place through three temporal ex-stases: past and future are mutually determining and the practical present, already illuminated by a global understanding (that is to say, by the future already prefigured as signification) occurs as a regressive determination of the mediations which unite this future to the past. It can therefore be said that the operation takes place everywhere, that the only way in which explaining is superior to comprehending is that it has the abstract privilege of regulatory action over regulated actions, that this operation - explaining and comprehending - is an individual praxis of the liquidation of practical contradictions on the basis of common structures: and that this individual praxis can never reproduce itself in the form of identical processes in each third party since it actually presupposes two mediated reciprocities: that between each comprehension and explanation through the medium of the developing totalisation (that is to say, of the rearrangement as everywhere) and that between everyone and everyone else and between everyone and all through the regulation of the third party (the + +solution being explained). + +But the synthetic bonds of reciprocity are here reduced to their simplest expression: reciprocity designates the comprehension of the other as the same as mine in so far as mine is the same as his. The abstract link simply amounts to a reinteriorisation of multiplicity and to its strict subordination to the different forms of synthetic unity. In fact - and this structure was explained above - there is not one comprehension, or ten, or thirty: this comprehension, everywhere the same, has no numerical determination. It is neither the explanation by the third party realising the group in the form of a totality-unity, nor a numerical plurality of acts. It is not the synthetic action of a hyperorganism; nor is it the individual, localised action of a particular practical organism: it is the action of a practical organism without any determination of individuality, to the extent that it mediates between + +function and objectification and tlta t it arises as uhiquity in the organised milieu. My comprehension is mine only in so far as it is that of my neighbour: and the multiplicity of identity disappears in so far as every understanding implies all the others and realises them; ubiquity is the reciprocity of unity as, with a single movement, it excludes both the multiple and the identical. This double exclusion is perfectly conveyed by language with the first person plural, when it expresses the interiorisation of the multiple: in the we, in fact, the multiple is not so much eliminated as disqualified; it is preserved in the form of ubiquity. True, one can say, 'We are two' , just as one says, 'They are two'; but in the second case, the enumeration is real, and expresses commutativity (either may be the second unit) whereas, in the first case, this com- + +mutativity is the non-explicit content of reciprocity. + +Thus before becoming an objective reorganisation, the discovery of the solution is an individual moment whose here is everywhere and which determines itself reciprocally by its reciprocal presence in every here. Of course, this is an abstract interpretation: as soon as seriality enters the group - however slightly - multiplicity tends to reappear. But there are intermediaries between the non-multiple or ubiquity and numerical multiplicity, and the latter really exists as such only when the group is completely dead: and then there will not even be any comprehensive construction of a solution, or if there is, it will no longer have the power to break the serial inertia. But for us the most important point is that the moment of synthesis is still that of individual performance; quite unlike a universal objective realising an agreement of minds while preserving their diversity, the individual performance realises nothing, but everyone realises himself as the same hy realising it. The truth in its original sense, therefore, as sociality and within an integrated group, is the elimination of all alterity; it realises integration through the mediation of a regulatory third party. But this leads to an absolute impossibility of distinguishing between the truth as an individual performance and as a common one. This lack of differentiation through ubiquity between one and all finds expression in the fact that science will both name a law or principle after its discoverer - Ohm, Joule, Carnor, etc. - and also allow constructive work to develop anonymously. Not only is it impossible for common operations to transcend individual operations in their practical structure; in addition, as we shall see, the individual operation appears to the group as a + +practical ideal which it can never entirely achieve. + +that a schematic solution to its problem has been found. A solution has been outlined, and it is now necessary to consider matters of detail, concrete modalities of application, etc. At this level we encounter the heterogeneity of freedom once again: and it is based, in effect, on the common adoption of the regulatory plan of the solution, which has now assumed a new character: common structure. On the one hand, it is a comprehensible and pledged inertia; it is obeyed, and no one should try to question it. Thus, in itself, it represents a synthetic relation of omnipresent inertia. In everyone it is entirely the same, as a common basis, and it does not reside in anybody in particular, or even have any special position in its originator. On the other hand, as an organising schema (which controls the new organisation of the group through the sub-group), it defines the limits and powers of organising praxis: precisely because they are integrated, because everyone is the same and bases his own activities on the same overall plan, it is possible for any individual to create his own heterogeneity by means of a detailed proposal which presupposes, and contains, as its ossature, the inert relations of the overall plan. In the extreme case, everyone will make himself heterogeneous through his free, enriching proposal, while constituting this invention in the object as a moment of the totalising objectification which will have to be transcended. The progressive work of adapting the schema to the concrete therefore develops under the control of the plan, through heterogeneous moments each of which + +preserves and transcends the previous one. + +At this level (at least in theory, that is to say, at the level of abstract purity which we are now occupying), the contradictions do not affect the group itself; they are temporalised and surmounted in the light of a possible future unity, of the common praxis and the group itself. But, from the point of view of intelligibility, it should be recognised that the harmonious development of heterogeneity on a basis of unity again refers us to the practical unity of the organism. Even if the entire process were the product of different operations, performed by different individuals, every proposal that was suggested, contradicted, transcended along with its contradiction, and preserved, might, a priori, be a position that was transcended and preserved in the free, dialectical praxis of the organism. The only difference is that the constituted dialectic rests on a non-dialectical moment: that of adopted inertia. This inertia, in fact, makes common praxis possible in so far as it lays down untranscendable limits to the constituent dialectic. And of course every practical organism contains a structure of inertia - this is + +why it can be the instrument of any instrumentality - but this has nothing in common with the inertia of freedom. In fact, free, organic transcendence is always a transcendence of material conditions; but the limits of action are prescribed by historical circumstances as a whole, + +rather than by a pledged inertia produced by praxis itself. + +This inert negation, however, is the necessary condition of common action: it is through it that the common individual exists as power, function, and structure; and dialectical praxis, as the mediation between the common individual and the object to be worked, itself differs from the free isolated praxis of an organism, in so far as it transcends, preserves, and actualises inertia, power and function - in short, the common individual. There is a synthetic, constitutive relation which, in the group itself, is the definition of each individual (in relation to everyone and to all); and the common individual, actualising himself through individual praxis, arises in a field of incredibly violent forces which form and deform him and involve him everywhere. In this sense, the concrete individual in the group is radically different from the organic individual and the common individual. At first sight, this makes it even more paradoxical when the group in action 'relapses' into its common praxis at the level of individual praxis, if not as regards the power and the efficacity of its action, at least in its formal structure. But the paradox disappears when one remembers that the group is an 'antiphysis', that is to say, an undertaking, a systematic operation on the fundamental relations which unite men, and that the overall plan of this operation could only be the dialectical movement which produced it. In other words, the practical aim is not the group, but the common objective; the group organises itself in order to achieve the objective in common, but organisation constitutes it dialectically as an amplifier of dialectical praxis - in fact not only as a very powerful organism, but also as an organism which eliminates the contingencies of its constitution by a careful division of labour and a systematic differentiation of + +functions. + +Now these new characteristics do not prevent it from being situated and, consequently, they do not prevent external transformations from giving rise to contingency in its organisation (that is, to contingent limitations of its foresight). Nor do they mean that the plan of action cannot be the same for the group as a product of human labour and for the labour which produced it, except that the group as an object of labour must retain its determinations, as a worked thing, by a certain inertia, or that the only unity which a group can give itself - since the + +hyper-organism is an illusion of idealism - does not oscillate between the false unity of worked matter (a coin which has been struck) and the synthetic, living unity of the organism. So we are now in a position to assert that the dialectical rationality of common praxis does not transcend (ne transcende pas) the rationality of individual praxis. On the contrary, individual praxis goes beyond it. And its special complexities, its knotted relations, and the formal concatenation of its structures derive precisely from the fact that the second rationality is constituted, that is to say, from the fact that the group is a product. In other words, the group constitutes and organises itself in response to the pressure of necessity in order to produce a dialectical action. And if it succeeded in hecoming an organism, the organic unity of its action (assuming a hyper-conscious unity, etc.) would be different in kind and would have a different intelligibility: each organism might have some comprehension of the hyper-organism as a structure connected to the whole, but this would be very different from ours, which, in the organised group, aims at totalisation. In any case, the conjecture is so vague that it is impossible to settle whether this comprehension would apply to the hyper-organic whole, or to its hyper-action (which is itself a rearrangement), or to the one through the other, or whether there might be no comprehension at all. But precisely because it fails to become a totality, that is to say, to transcend individual praxis by a practical hyper-dialectic, it falls short of the level of the praxis which alone could provide it with a model of active unity, just as the organism itself provides its totalisation with a model and schema of ontological unity (a point to which we shall return). And the paradoxical tension which constitutes the praxis of a group is that it is in itself a metamorphosis conceived as the ubiquity of the individual through all the others, and therefore, in a way, a new statute of existence (power and 'violence-fraternity') and that its actio,n - which is the very reason and law of its constitution - does not differ from what can be projected by an organic individual who uses a group-object in order to carry out the project. But this factual untranscendability (which is not a necessity, but a permanent certainty of the investigation) necessarily refers to the impossibility of being a hyper-organism, which is the limitation of the group; and this impossibility itself is primarily simply the impossibility of acquiring an organic unity. The untranscendable connection between the group and the practical organism as Idea (Idea not in the sense of a determination of discourse, but as an unrealisable task which becomes regulatory by constantly positing itself as capable of being realised the + +next day) is the changing signification of a perpetually rearranged and + +perpetually unsuccessful totalisation. + +The group is haunted by organicist significations because it is subject to this rigid law: if it were to achieve organic unity (which is impossible) it would therefore be a hyper-organism (because it would be an organism which produced itself in accordance with a practical law which excluded contingency); but since it is strictly forbidden this statute, it remains a totalisation, and a being which is subsidiary to the practical organism, and one of its products. In short, since the organic level cannot be transcended, it cannot be attained; and the organic state, as a threshold which would have to be crossed in order to reach hyper-organic unity, remains as the ontological and practical statute which serves to regulate the group. Similarly, the group constitutes itself through labour as a tool for producing a dialectical praxis, though this dialectic, forged through organisation, is constituted by the free dialectical actions of the organic individual and is modelled on them. The result is not only that the common action is capable of being recreated by a single individual (the leader, the 'organisation-man', etc.), but also that the intelligibility of the constituted dialectic is weighed down and degraded in comparison to the full intelligibility of + +the constituent dialectic. + +4 Praxis as Process + +We must now seek to explain why, though - as we shall see - it is still intelligible, common praxis lacks the translucidity of individual praxis. First of all, it is obvious that the fundamental reason is its adopted inertia: however extensively adopted it is, it will still come to everyone as his other freedom and consequently from the third party as Other, even though alterity arises here in its formal purity. HI run up against my own limits, against certain untranscendabilities (the fact that I have one function in the group rather than another), then I can obviously provide practical interpretations of them (recognising the reason for my function in circumstances and my abilities) and, rediscovering my original pledge, whether it was implicit or explicit, I can reproduce it in the urgency of the resuscitated past, and on this basis run through + +the dialectical sequence which leads to this present, to this task. But negation and limitation as such cannot be dissolved even if I comprehend them, as I must, in terms of their instrumental function. And I can always rediscover the dialectical movement within the group, which produces all the determinations which are based on these - rights and duties, powers and structures - though they do not have the translucidity of my own pure organic praxis. Both my right and my duty appear with a dimension of alterity. Of course, these are relations with others, but still, trans lucid human relations do exist, and I spoke of them at the beginning of this work: I mean immediate reciprocities. What we have here is worked reciprocities. Right and duty, in their non-transparent certainty, appear to dialectical investigation, and to practical consciousness, as my free alienation from freedom. But, in fact, we know the aims of the pledge: the problem was to struggle against our multiplicity by interiorising it, that is to say, by constantly subjecting it to unity. Thus the problem of dialectical rationality as constituted Reason arises at the most basic level of integration, that of + +common action against multiplicity. + +Taking our investigation to a lower level of abstraction and purity (though it is still wholly abstract), we can immediately observe that the interiorisation of multiplicity constantly has to be redone, and is never successfully completed: this is due primarily to the actual circumstances of struggle and action, that is to say, not only to the totalising historical process, but also to the objective and the instruments. To begin with the latter, it is striking that, provided the group is not itself the whole of society (that is to say, practically always), the other intervenes in so far as the instrument of the group is the product of his labour. And worked matter, from within the group which is constituted upon it, thereby impregnates all interior organisations with a certain alterity. Whichever group is considered today, it takes no more than a strike affecting the post office (or telecommunications) for practical unity to be temporarily broken. Now, this unity has meaning only in the movement of action and in the urgency of the situation: if it is disrupted, this will not break a pledged fidelity between common individuals; it will simply force everyone to carry out his task in very unfamiliar circumstances, since he will be deprived of the information, instructions and orders which the group normally provides. The common individual subsists; he is the pledge and habits in everyone; but in the new situation he tends to reduce himself to a purely negative determination, a handicap of inertia: the organic individual is no longer a mediation + +between, on the one hand, a common-being which is alive (that is, sustained and nourished by the common milieu, by the given and maintained powers), though limited by inertia, and, on the other, the objectification of common praxis. Isolated, he identifies himself as a practical organism with the group, that is to say, he gives the group the statute of dialectical spontaneity which characterises hi s own organism. (As we shall see, this sudden isolation as rupture is not lived in the same way as those continuous functions which characterise the being-in-thegroup of the individual as isolation and which, consequently, produce isolated individuals as useful, necessary members who live their isola- + +tion as their practical community statute.) + +But it is obvious that this identification of the group with oneself contains two specific and opposed possibilities: sacrifice to the group, in spite of the unreliability of orders and information, and the use of the group by the individual. The danger that common individuals will dissolve, in this case, is not prior to the pledge (fear, 'private interest', etc., in so far as they threaten a group with disintegration), but subsequent to it: the group dissolves in the individual when he keeps the powers of the group and, in the absence of links, embodies the group in himself alone. Thus the problem of links (liaisons) is inseparable from that of organisation; or rather, it is a special aspect of it: the problem of the links of organisation is inseparable from that of the organisation of links. And if the developing organisation, through the general form it assumes, determines the general type of links, then conversely these links, depending on the difficulties they present (cost, relative slowness, scarcity of men, danger, etc.), act on the organisers and make them alter their plans. The connection between forms of government and administration and the possibilities of communication (that is to say, the real techniques and means of communicating) is revealed to us in + +its inflexible rigidity by the whole historical reconstruction. + +But, for us, the problem has two aspects: this dependence really gives the group, whatever it is, the depth of the world; which means that it is united to the serialities of the society in which it was engendered through the mediation of worked matter. It may be said that the individual also depends entirely on the social ensemble, that is to say, on the social circumstances of his materiality. This is true. And, ultimately, his class situation and, for example, the state of medical techniques, in so far as they reflect production as a whole, and affect him through the refractive index of his class, determine his practical possibilities in so far as they condition his organism from inside. But + +this is only a superficial analogy, just because biological reality is one. Certainly, there are linking organs (nerves, blood, endocrine secretions, etc.): and illnesses - occupational or other - may destroy some of these links while certain medicines may re-establish them and even, in certain cases, improve them. The differences must lie elsewhere, even if one imagines progress in medical techniques making it possible gradually to transform the organism. It is in this respect that the biological links are established through and between biological functions and in the biological milieu. The organism produces its own ways and these ways are themselves functions; the inorganic appears in it either as a substance which has been integrated into the whole or as a product of a secretion, but not as inert distance or as an inert vehicle whose speed is a function of some exterior operation. Within the organism, distance itself is organic; it allows itself to appear in its inorganic reality only through the degradation of the living being + +(slow reflexes in the sick and the old, etc.). + +With groups, however, the inorganic (as worked materiality) is an inert mediation between the functions of the community. This leads initially to the presence of an internal alterity not produced by the group and which, depending on circumstances (but independently of the objective, or, at least, without any practical link to it, established by the agents) appears as practically negligible or threatens to tear the community apart. ('Our supporters are not turning up, or are coming in smaller numbers because we are meeting too far from where they live, because transport is too expensive', etc. A particular revolutionary movement, which needs to manifest itself at several places in the country at the same time, may fail because links cannot be established. 58 A particular fighting group may be wiped out because its links with the army to which it belongs have been broken.) Such internal conditioning causes a reappearance of interiorised multiplicity; and, so to speak, re-exteriorises it in interiority. The group has eliminated facticity by setting itself a transcendent aim and by eliminating the organic hazards of its praxis; but then it encounters it again, within itself, in the form of a dispersive limit to its unification. But it should be noted that this factidty, unlike basic facticity, does not present itself as a special biological determination of unworked materiality, but rather as a contingent determination of the practico-inert field. This + +5 8. This is only an individual event: if fundamental contradictions produce an + +exigency for Revolution, the failure will only be incidental. + +determination is said to be contingent not because it lacks either strictness or intelligibility (given the practico-inert field on the basis of which the group arises, it is inevitable that the problem oflinks should present itself to the common practice in some way or other), but because it is external to the practice in so far as it organises the group in accordance + +with a particular objective. + +The second - + +aspect of this dependence is of even more concern to + +our inquiry than the first: in so far as the group wishes to struggle, with contemporary techniques and tools, against the dispersive force of the practico-inert field, it must produce within itself apparatuses of mediation, supervision, and inspection, whose essential function is to put the sub-groups into relation either with one another (as with a federal structure, for example) or with the central apparatus (with a centralised structure). The active function of such mediators - whether they are missi dominici, timekeepers in a factory or inspectors in secondary education - is to unite two inertias as such. And these inertias were not produced by pledged freedom; they came to the group through dispersal in exteriority and the mediating apparatus constitutes them as inertias which have been transcended and mediated by its mediation: and without this mediation the central administration would have no power over the local executive and vice versa; the mediating apparatus may of course be produced by the administration, but as soon as it has been produced, the administration is dependent on it, as well as the local executive. In such cases, a control body is often created to supervise the mediating organ. Of course, these remarks would be even more appropriate and complete in relation to a hierarchical group subject to controls. But we have not yet examined such a structure. But in any case, the link reveals and develops the inertia of exteriority while struggling against it by rearranging pledged inertias. The peculiarities of organised praxis are that it is constituted by a pyramid ofinertias, both external and internal (through the exteriorisation of the inertia of interiority and through the interiorisation of the inertia of exteriority) and that the object of any apparatus (the subgroups which have to be linked together) appears as an externalinternal inertia and must be treated as such, while in its relations with other co-ordinated organs the same apparatus is treated as inertia by + +subordinate apparatuses. + +But means of communication are only one example of the separation of interiority. Depending on the task and the circumstances, it may also find expression in temporalisation: each particular task in its + +particularity may be completed and be separated by a time-lag from the particular task which it makes possible in the development of the common action. In an industrial complex (either a socialist Kombinat or a capitalist organisation: we are not directly concerned with exploitation here, but rather with technical necessities which are the same everywhere, east and west), the extraction of raw materials or the manufacture of intermediate products (blast furnaces and forges; iron and steel, etc.) is objectified in a certain object (such as crude oil, or steel ingots) which absorbs labour just like 'commodities' and allows it to crystallise in it. The process will be resumed, the oil refined, the steel transformed into a crank-shaft, a drive shaft, etc., somewhere else (possibly nearby) and in a third process it will be enabled to perform its functions directly (the machine will be assembled out of its separate + +parts, etc.). + +But it is clear that the praxis of every sub-group is absorbed as an inert seal of worked materiality and transcended by a new operation. From the point of view of the economy of the firm, it is very importan t that workers, premises, organisers and managers should be integrated into a single complex. But to the sub-group which produces blast furnaces it is of very little importance whether the treated raw material was mined by a sub-group belonging to the complex or whether it was transported by train from some distant region. In the second case, the fact that the so-called 'raw material' is already worked (the fact that men have laboured in common to extract the mineral) is practically irrelevant. Even if the worker in the forge belongs to the same class as the miners, this class solidarity is not a structure of the group as such, at least not directly, and, besides, it affects the members of the class (whether they belong to the group or not) rather than the members of the group. For the worker, in fact, the inert exigency of the object may refer to those who have produced it, but, as we have seen, it may also be perceived as a sort of inhuman function of materiality. At this moment, it separates more than it unites, or rather it unites in seriality. But still we have not relapsed into seriality: the group loses its abstract purity, but it still has its efficacity and its structure of interiority. But the important point here is that in the technological complex under consideration, the task of the preceding agent is perceived - owing to the time-lag (the transportation of the product from one workshop to another, or from the mine to the forge, etc.) - as inverted and turned back into passivity by its basis of inert passivity. It becomes a mortgage of the future of the new worker, a limitation of his possibilities to + +which he must submit, whether it was done outside the group by others as Others or whether it was the result of an undertaking which was common to certain members wlw are invisible in so far as they are the same. There are many ways in which this reorganising correction can occur: the mediating sub-group may improve integration by increasing contacts between workers in different sectors; it may ensure that everyone understands the common praxis by giving theoretical instruction to enable every worker to see the meaning and importance of his own function and also to learn to recognise the meaning of other tasks; or it may institute a system of rotation which puts everyone into each of the different jobs of the ensemble in the course of three or five years, + +etc. + +I am not mentioning these practices because of their social efficacity, but simply to show their common character: they take up organisation at the 'neutral' point at which it was left by temporal dislocation; and they treat the isolation of each sub-group or individual in relation to other individuals and sub-groups as an inert negation which has to be dissolved, and they treat each worker as a massified unit who has to be won back from emerging seriality. 59 By means either of a real rearrangement (rotation of jobs) or of a verbal action (teaching, explanation), they have a material effect on inorganic materiality. It is true that this work is intended to replace a cloud of isolations (such as time-lags) by a functional unity; but in terms of the common praxis of organisation, it shows that concrete organisation is a perpetual negation of the negation, that is to say, a practical, effective negation of the developing disorganisation. From this point of view, the heterogeneity of functions in a totally and abstractly pure group is, as we have seen, a creation of freedom. In a complex group, however (in which spatial distances and time-lags are constant sources of massifying dispersal), and from the point of view of totalisation, it is clear that differentiation, if it is determined both by the organising apparatus and by spatio-temporal 'lag', can collapse, in a moment, into a statute of accidental heterogeneity (of exteriority). In an effective, practical, but real group, there + +is a constant danger that the current will cease to flow. + +And, as we have seen, what is true of the elements which are mediated by the apparatus is true also of the apparatus which mediates. The + +)9. Obviously these mediating activities are inspired by different principles in the East (the humanism of labour, and political propaganda) and in the West + +('Human Engineering'). But this has little importance here. + +group uses up part of its energy (the energy of its members, its numerical strength, credit, money, etc.) in maintaining itself in a state of relative fluidity. Thus by a scissiparity of reflection (which is highly intelligible since it involves mediating sub-groups and mediators between these sub-groups, etc.), the group as interiority, that is to say, as a developing totalisation, is in danger of being resolved (and will in fact be resolved) into a hierarchy and circularity (both of them, for reasons we shall discover later) of unifying actions which take actions and agents of a lower level60 as inert quasi-objects, or, conversely, into a hierarchy of quasi-objects deriving their statute from an Other (a sub-group, or an individual considered as a quasi-subject) as a quasitranscendent determination of their suffered, adopted inertia. At this level, the group tends to have more in common with the kind of complex which is constituted by a machine and by the workers who use it for a particular job than with practical organisms which dialectically transcend every inert moment of the worked object, every inert organisation of the practical field; and this occurs without the moment of passive negation and arrest being directly produced by praxis, but, on the contrary, in so far as it returns from the worked object to the work as a limitation of the developing objectification which is immediately transcended by the inorganic statute of materiality. In fact, even if it is true that the group never relapses to the level of the machine (even that of a 'feedback' machine as has been suggested), and if it is also true that it can never raise itself to an organic status, this is because it is actually a human product, that is to say, an instrument made by men in accordance with laws which make it possible to create automatic devices on the basis of the inorganic, and because it is simultaneously constituted by the free, dialectical praxis of human individuals, in so far as it acts in interiority on every member, and in exteriority on the + +common object. + +There can never be a social machine, because it would resolve into a massified plurality of organisms as soon as every practical organism received a suffered statute of inertia in relation to the group; on the other hand, its operations become more machine-like as integration advances, that is to say, as the group, through the organisation of its structures, increasingly produces itself as a function of the practical organism (as a regulatory schema of the constrU\.:ted relations of + +60. Inferiority, like hierarchy, bei ng determined arbitrarily, that is to say in + +accordance with the conjuncture and the common praxis. + +interiority). This in no way implies that this organisation, as an impossible mediation between the organic and the inorganic, is of itself unintelligible. But it does mean that it is a constituted dialectic; that is to say, there is no dialectical praxis here to realise the unity of individuals but, on the contrary, there are individual, constituent dialectics inventing and producing, through their work, a dialectical apparatus which encloses them and their instruments and which is determined in accordance with the aim. Within the apparatus, everyone is transformed with and through all the others, and the common individual as a structure of the totalisation appears as the highest level of integration which the group is capable of realising in its attempts to produce itself as an organism; but the group can be comprehended only as a particular dissolution of the practico-inert field at a certain degree of depth; and as such, it preserves the dissolved field, at least in the form of a constant danger of the resurrection of seriality and its very complication leads it towards the passive statute of inert things, of worked products. As I have said, even this is provisional : later, we shall examine the avatars of the group and what becomes of them when the group is reconquered by seriality. The important point here is that + +the common praxis is both an action and a process. 61 + +Since every moment of the action, in so far as it is everywhere the same, is produced as a finished action by a practical organism as the mediation between function (common individual, structure) and objectification (inscribing the common work on the object), in common praxis, there is a common aim, objectification, labour, transcendence, reciprocal adaptation, etc., just as there is in individual praxis; and every partial result must be grasped in its constituent intelligibility as a free, practical realisation of one detail of the common aim. But the common aim itself, whether regarded as present in the structure of individuals or as the reflexive rule which governs the reorganisation of the whole by means of a differentiated apparatus, appears as a determination of the future by a project on the basis of concrete circumstances. At this level, the individual dialectic actually transcends itself towards another form of intelligibility, since it can already reproduce and comprehend the specific modalities of the group - which would be unknown to an isolated individual, if there could be such a thing - that is to say, structure, being-in-the-group, function, power and, ultimately, + +61. This is, of course, before any description of alienation an an avatar of the + +�roup-praxis. + +the pledge. The pledge, in fact, as a determination of mediated reciprocity, is incapable of being produced, or, therefore, comprehended, by an isolated freedom. And if everyone understands the group in this way, in so far as it appears to transcend itself towards a new form of integration, this is because membership of the group is given to concrete experience at the same time as practical-individual existence; thus there are not two separate moments of comprehension here, but rather two types of activity (practical and theoretical) which + +are always possible, either separately or together. + +But, as we have seen, at the moment in which the group transcends itself towards the organism through its individuals, it is still inoperative. It can go no further: being-in-common can produce new relations with others (and therefore with oneself) in everyone; but it cannot produce an integrating and integral organism; the totalisation cannot become a totality. And if the group is to remain an effective power to produce particular results, it will clearly be necessary that the number of readjustments and mediations in it should increase; that is to say, it should become within itself a practical multiplicity of points of view perceiving it in all its forms as an inertia which has to be transcended. This second procedure is simply the result of the failure of the first: since, at best, integration leads to the transformation of multiplicity into ubiquity, but never succeeds in replacing it with a new unity, this multiplicity without parts inevitably reproduces itself as a quantitative, discrete multiplicity, within the group itself, under other relations and + +through the mediation of the practico-inert. + +Circular recurrence does not yet establish itself on this basis, but the circularity of passivity always does, for the mediating organ must itself be mediated and it turns out to be split by the separations it mediates. Now, in this circular ensemble - and even when we introduce, as we soon shall, the functions of authority - everything occurs also as an autonomous result, positing itself for itself in the inertia of isolation, while its practical Reason lies in the mediation of a sub-group of reorganisation. At this level, passivity is given first - as an effective but isolated process (as the work of one machine in a group of machines) and teleological activity is simply what comes, from above, to break up isolation and to restructure functions ; totalisation constantly breaks down and is always re-established by others (who are now no longer quite the same); its free, practical reality comes to everyone as a passive recovery of his common individuality. From this point of view, which is also that of the interior practice of the group (and which tends to + +directed process. + +What difference is there, then, between process and praxis? Both are dialectical : they are defined by their movement and their direction; they transcend the obstacles of the common field and transform them into stepping-stones, stages, steps marking and facilitating their develop ment. Both are defined in terms of a particular determination of the field of possibilities, by which the meaning of their different moments can be explained. Both are violence, fatigue, wear and a constant transformation of energy. But praxis is directly revealed by its end: the future determination of the field of possibilities is posited at the outset by a projective transcendence (depassement) of material circumstances, that is to say, by a project; at each moment of the action, the agent produces himself in a particular posture, accompanied by a specific effort in accordance with present givens in the light of the future objective. I have called this praxis free for the simple reason that, in a given set of circumstances, on the basis of a given need or danger, it creates its own law, in the absolute unity of the project (as a mediation between the given, past objectivity and the objectification which is to be produced). The process is comparable neither to an avalanche or flood, nor to an individual action: it actually retains all the characteristics of individual action, since it is constituted by the directed action of a multiplicity of individuals; but at the same time these characteristics receive in it the modification of passivity because, through the resurrection of the multiple, every here presents itself as a passivity (and implies passivity as ubiquity in every here) and activity appears as the evanescent elsewhere, that is to say, as the dissolution here of suffered inertia in so far as this activity of the Other must, in another elsewhere and for Others, be an inertia which has to be dissolved by activity. In the group as common praxis, the pledged inertias are the forever concealed and veiled mediation between organic activities. In the group-process, practical activity, as an ungraspable, fleeting event, serves as an organising mediation between suffered inertias (in so far + +as it dissolves them temporarily). + +There cannot be any question of determinism in either case, since the development is concrete, and directed, and grows richer with each transcendence, and defines itself in terms of a particular future end. In the first case, that is to say when the group is manifested in its abstract purity as a living organisation, comprehension is quite simply the production of the member or of the transcendent (transcendant) + +spectator by himself in his being-in-the-group: this act is always possible because the organic individual is always a common individual. This understanding is richer than inter-individual understanding, because implicitly or explicitly it reproduces new dialectical structures as the pledge. And this pledge is still intelligibility, although it is, in everyone, other-freedom, because in itself it is a free operation performed on the fundamental relation of reciprocity. However, translucidity is effaced as a function of complexity: structures, law, and terror contain no mystery; these new determinations do not contain any opacity, and it is both possible and necessary to produce them dialectically in the explanation. However, in so far as they arise on the basis of a relation to the third party who I am not - and who, of course, appears as the same, here - and in so far as reciprocity bases them on inertia pledged by the other, that is to say, on abstract alterity as an inert pledge never to be other than myself, the certainty of the structures is based on an empty relation, whose other term is active in me in so far as it is not me and in so far as it denies itself the possibility of being totally itself in isolation. The action is intelligible because it is the same as my own; but I consider it in a vacuum because, in the ubiquity of the pledge, the same, everywhere, is not myself. We are therefore confronted with a negative limit of transparency rather than with a positive limitation (as by some irrational effusing of common manifestations). Apart from these two differences (comprehension is richer from one point of view, and poorer from another) , a common action is intelligible to me as organic action, that is to say, through some graspable end which totalises us (or the group, in am situated outside it) negatively. The totalisation of a multiplicity, whether this multiplicity is inert, living or practical, is effectively a fundamental operation of praxis as dialectic. And common praxis in its purity is understood on the model of organic praxis, that is to say, as the individual action of a community in the light of a common aim. For understanding, common praxis appears precisely as a mediation between the practical community and the common aim by the singular, just as the action of the individual organism is the constant mediation between the common individual and the common objectification. There should be nothing surprising in this comparison: the common praxis actually reveals itself through an organised multiplicity of free, individual undertakings (within the limits of functions and powers) and each of these presents itself as exemplary, that is to say, as the same as all. Thus the schema of intelligibility is not provided by some super-individual undertaking, + +but, on the contrary, by the dialectical (and perfectly comprehensible) relation between pure, simple, individual action (modified by the relations mentioned above) and a common aim. Individual praxis is the + +synthetic mould into which common action must be poured. + +In the second case, the process manifests itself as an object. This does not mean that we perceive it as a totality; on the contrary. But, whether I am in the community or outside it, the movement which animates it is not of the kind that I can produce, as a practical organism; it belongs to the category of those which I suffer in so far as I have my beingoutside-myself-in-the-world. In other words, it reveals itself as a reality in relation to which I shall always be outside, even if it envelops me and leads me on; and which will always be outside me, even if, with everyone, I help to produce it. This reality is structured in interiority (for, in spite of everything, whether they are inert or isolated, functions subsist and function together), and yet it does not have interiority. It does not produce in immanence its own determinations : on the contrary, it receives them as a perpetual transformation of its inertia. But as these received determinations are themselves synthetic and 'internal', since they are always directed to a future end, and they represent a constant enrichment and an irreversibility of time, they proceed .not from analytical Reason or the laws of exteriority but, if one is not to prejudge them, from an external law of interiority. This law might of course be referred to as destiny, since an irresistible movement draws or impels the ensemble towards a prefigured future which realises itself through it. But it i� more interesting to see it as the celebrated external dialectic which was criticised and rejected at the beginning of this essay. Indeed, it is precisely this which appears as a transcendent law of interiority, and which is given as the movement of constituent reason and as destiny or fatality. And if one becomes its dupe, it makes 'processes' appear not as temporalisations, but as temporalised realities. And it is because of it that all projective and teleological structures are reabsorbed by necessity. The process develops in accordance with a law from outside which controls it in accordance with earlier conditions; but this necessity is still directed, the future is still prefigured, and the process retains its finality, though + +it is reversed, passivised and masked by necessity. + +But this conception of human activity as process takes rather different forms - especially non-dialectical or aberrant ones - in the work of many American sociologists. Lewin's Gestalt is based on a vision of praxis as process; there is destiny, totality (as an external law of + +interiority), and the synthetic passive organisation of results. The works of Kardiner and Moreno, and the studies of the culturalists are always based on the directed, irreversible, and overblown passivity of an inert fatality which we have just seen; and the group-process is, from one point of view, a constant reality of our own investigation. Its characteristics are not their invention; they have not chosen to see only + +it and to study it at the level of its complete unintelligibility. + +This unintelligibility is simply a moment of intelligibility: it is the first appearance which certain groups display. Moreover, it becomes intelligibility at a level of greater complexity, which we shall soon reach, at the level at which the group interferes with the series. For the moment, it is better to present process as the permanent obverse of common praxis. Its intelligibility, taken on its own, comes from the fact that it can be dissolved and reversed; in fact, it simply represents the moment where the interior action of the group intensifies so as to counteract the multiplicity which begins to erode it. Everywhere reabsorbed by the inert, at every level, it tries to dissolve it everywhere; and if it escapes or flees, it is through its own negative character. It appears parasitical though it is in reality practical reality itself. And as long as the group, with its control mechanisms, remains effective and active, its fundamental truth is still praxis. However, we must retain this first aspect of process if we simply wish to mark the concrete limits of praxis. As long as one isolates it from the world in order to study it in its abstract purity, it will yield its intelligibility without transparency as an individual and common practice. When it is considered in the world without relation to anything except time and place, it will display new aspects : separations, scleroses, useless survivals, local wear, stratifications, the inertial force of apparatuses, fragmentation of the group, tendencies, antagonisms of function (carefully defined competences cease to be so as praxis develops, because of the need to adapt to new circumstances). And the negative praxis of mediating apparatuses which attempt to dissolve these callosities and knots is essentially in danger of being simply an ever anterior liquidation, a preparation for common action, a restoration of instrumental functions without any other positive connection with the praxis of the group in the common + +field. + +Thus, while continuing its real development, the group also appears as an object which is constantly being repaired and the teleological aspect of the repairing is lost through its very negativity: it appears to be subordinated to the inert structures which have to be maintained. + +The possibility of the group being seen inside out as an enormous, passive object, being dragged towards its destiny, and expending its energy in internal reactions, absorbing the human conduct of its members and subsisting by a sort of inert perseverance is still no more than an abstract limit of dialectical intelligibility. It simply shows that the group is constructed. on the model of free individual action and that it produces an organic action without itself being an organism; that it is a machine for producing non-mechanical reactions and that inertia like every human product - constitutes both its being and its raison d' etre. And when we say that, considered as a process, it represents the limit of intelligibility, we do not mean that it is unintelligible in the depths of its inertia, but, on the contrary, that this fundamental inertia must be inserted into its very intelligibility; in other words, that the praxis-subject of a pledged community maintains itself in being as a process-object, and that this is its own materiality. The materiality of the group is suffered in so far as it is forged, and forged in so far as it is suffered: the pledge is a function of distance (becoming correspondingly more weak or inflexible); distance (as a reciprocal path which cannot be entered without difficulty, and an expenditure of strength and wear) is created by the pledge; and in the form of this double conditioning of inertias, it makes it possible to indicate the state of the + +group. + +By this, I do not mean either its being, which we shall come to shortly, or its constitution (as a structured ensemble: an exogamous system, or an administrative apparatus), but simply the relation between constituted inertia (suffered and pledged) and praxis, at any given moment. It is at this level that explanations will be found of such matters as the ageing of one part (that is to say, both the decline in recruitment and the stratification of the controlling organs) and the effect of scarcity on the possibilities open to a group (scarcity of men empty classes, etc. - being either a national circumstance in the light of which the group determines itself, and which determines its density, or an event proper to the group itself and to its modalities of recruitment, renewal, etc., Or an objective relation - both internal and external between the objective of the group and the objectives of other groups or serial individuals in the society under consideration).62 At this + +62. Scarcity of money is crucial and bound up in many ways with scarcity of men. (A shortage of money may be due to a shortage of men , and equally, a shortage of men may be due to a shortage of money. And this second meaning is + +level, too, one can speak of softness, or, on the other hand, of hardening, of routine or of a frenzy of innovation; at this level it is possible to explain the difficul ties of a given group in new circumstances, by showing, for example, that whereas all its structures were organised with a view to a defensive praxis, the conditions of struggle are forcing it to go on the offensive, etc. Examples could be multiplied indefinitely; it will be sufficient to remark that the state is not inertia as an inert foundation, as a sclerosis of structures, etc., but inertia as a condition of praxis, to the extent, that is, that it acts as an un transcend able limit (in which the suffered and the pledged are mingled and bound together in an indissoluble reciprocity) of any action which tries to negate it. It is at the level of the state - and we shall return to this - that the group is totally conditioned, in a form for which it was not prepared, by the practico-inert field which it attempts to modify: a particular action, in + +duplicated: (I) the men do not come because we do not have the means to pay them, (2) they come in large numbers but we turn them away because we cannot give them work - we are short of weapons or machines.) My reason for not discussing this here is that my purpose is not to study the concrete conditions of the 'functioning' of a group, which would involve taking a real group at a given real time and tracing its historical evolution from beginning to end. But this work, however important and desirable it may be, goes well beyond the limits of the present problem. Money necessarily depends on the system of production, and on the relations which arise on the basis of it. The statement 'there is no historical group without money' (such as Labiche's La Cognoue) means: there is no group which does not reflect the true condition of man in that moment of History; there is no group of exploiters, for example, which did not arise in a milieu of exploitation and signify it in its very organisation, whether the aim of the organisation is to set up an amateur orchestra or a circulating library. I also admit that the investigation of a group in which there is no scarcity of money is in danger of being completely abstract. Nevertheless, a group of exploiters (as long as no crisis threatens their property) may be assured as a group that its expenses will be automatically covered by fees as long as they stay within reasonable limits: this applies to clubs (whether English or American). This amounts to saying that for certain groups in the exploiting class - and when the means of the members are far in excess of the needs of the group - money is no problem; it does not represent suffered inertia or restriction, but, on the contrary, power. It is for this main reason that I have not taken scarcity of money into account - that is to say, because, at least in theory and in certain special conditions, it may not be an essential and negative factor. There is another reason: this is that a group cannot exist in a pure state and that we shall shortly arrive at the concrete, that is to say, at the line of intersection of the group and seriality; and that, at this level, we shall once again encounter the real problems of a society, that is to say, precisely its + +system of production. + +a particular locality, may be aimed at intimidating, at improving wages; but it may appear inopportune, instructions may be ignored because the dangers which have to be avoided are not yet sufficiently clear and above all because the workers in the biggest firms are about to begin + +their paid holidays. + +We seem to be on the point of encountering seriality again. And in fact we shall encounter it. But, for the moment, it is sufficient to comprehend the group as constituted praxis. In it, through the determination of its members, the contradictory tension which opposes totalising praxis to the multiplicity of the agents can be seen arising as a dialectical conflict. However, it must be recognised that both the dialectical structures and the synthetic movement which produces the opposition proceed from organic praxis and that multiplicity is a factor of dialectical intelligibility only in so far as it manifests itself as untranscend able inertia, that is to say, as the explosive exteriority of the interiorisation of number. The group at work is individual praxis, initially exceeded and reified by the seriality of actions, and everywhere turning back on the amorphous multiplicity which conditions it in order to extract from it the serial, numerical statute, so as to negate it as discrete quantity and, in the same movement, to make it, in practical unity, a means of achieving the totalising objective. Praxis remains fundamentally individual because it is constituted as tlte same, that is to say, as the directed exploitation of multiplicity without parts. In this first moment,praxls does not treat this multiplicity differently from the inorganic gatherings of the practical field (when it combines them to make an instrument), but the crucial difference is that, after the pledged agreement, every detailed action (in so far as it is both the same and differentiated) turns out to make use of its own multiplicity, which becomes an interior feature (power, structure) of the individual unit. When, for the second time, this interiorised multiplicity is placed in exteriority, this does not mean that it has escaped common control, or removed itself from the multiple unity in everyone, so as to reconquer its quantity: this would be inconceivable except on the assumption that it had a dialectical power of its own. But the suppression of multiple inertia and of relations of exteriority has, quite simply, occurred practically, that is to say, in and through practical objectification, and yet the ontological statute of multiplicity (the plurality of organisms) is not affected by this. Under fire, the unit replaces dispersal with practical organisation; it encloses its multiplicity in itself. But first the unit is counted; and before long, it will count its wounded and its dead; + +and the enemy, if they have observation posts, can always count the able-bodied soldiers it still has at its disposal. And this inertia as the ontological limit of integration (we shall see that there are other limits) is not a theoretical given of some passive knowledge : it is, in fact, the objective field of the unforeseen; through it, indeed, the passive action of the practico-inert is reintroduced into the free group which is organised to combat it; and this passive action reappears not as the action of an interior force but as an interior danger of dispersal; this pure exteriority is, so to speak, lived in interiority as a permanent threat and a permanent possibility of betrayal. Thus multiplicity is reactualised in its untranscendable objectivity by the practico-inert and the practico-inert is simply the activity of others in so far as it is sustained and diverted by inorganic inertia. Thus a passivised form of activity reactualises discrete multiplicity, and the group, as dialectical praxis, perceives it in its very dispersal as an internal danger, that is to say, as a dispersal produced by the unity of an action. (This action is passive activity, seen, through the unity of the praxis which it contradicts, as an active negation of this praxis by a directed counter-praxis. It is at this level that Manichaean explanations, in terms of English gold, the plot of the aristocrats, counter-revolutionary activity, etc., appear.) And it is in opposition to this action - which reactualises in itself discrete multiplicity as the ubiquity of the possibility of betrayal - that is to say against itself, that the organisation reorganises itself, breaking up old frameworks and, through mediating organs, etc., trying to reduce the passive act of multiplication to a simple, multiple, discrete inertia, ineradicable, but negligible from the point of view of action. Thus we rediscover organic praxis everywhere, in so far as it acts on its inert multiplicity; and this multiplicity manifests itself initially at every level of reflection as sustained by passive activity, in so far as it is the point + +at which practico-inert forces act. + +But we have seen that the practico-inert field is in itself a caricature of the dialectic and its alienating objectification. Thus, common praxis is organised at every level against the anti-dialectic, first by jointly settling the objective and the means of attaining it (dissolution of seriality), and then by perpetual rearrangements of its structures. And the internal life of the group manifests itself through the positive and negative consequences of these rearrangements, that is to say, through new determinations of the practico-inert in the interiority of the organisation and through the practical (and dialectical) reaction of the organising praxis to the common consequences of these determina- + +tions; but, at the same time, every partial reinteriorisation of the multiple is a way of introducing it at another level as inert quantity and separating force. In this sense, the hostile group, if there is one, determines the enemy both as praxis and as process. It cannot actually be unaware of the enemy praxis as such; it must comprehend and anticipate it on the basis of its aim; but at the same time, if it wishes to prevent it from being achieved, it must strike the enemy at the level at which praxis is also the development of a process (destroying its supply-bases, cutting its lines of communication, etc.). And the group which is under attack, in so far as it anticipates the enemy, must appear to itself, in + +action, in the form of a process : this is the basis of reflection. + +The complex intelligibility of the constituted dialectic therefore arises from the fact that organic praxis, in everyone, works, with all, on multiplicity as a practico-inert determination so as to make it an instrument allowing action to become common while remaining individual. And, as work is the paradigm of dialectical activity, the group in action has to be understood in terms of two kinds of simultaneous activities, each of which is a function of the other : dialectical activity in immanence (reorganisation of the organisation) and dialectical activity as the practical transcendence (depassement) of the common statute towards the objectification of the group (production, struggle, etc.). The object which is realised is (if we temporarily ignore the dangers of alienation) the expression in transcendence (transcendance) of the organisation as a structure of immanence, and conversely. There is, therefore, no ontologically common praxis: there are practical individuals constructing their multiplicity as an object on the basis of which everyone can perform his task in the free, agreed (and pledged) heterogeneity of common function, that is to say, by objectifying themselves in the common product as necessary details of the develop- + +ing totalisation. + +But this does not mean that constituted intelligibility demands the dissolution of every common praxis into individual actions : such a dissolution would imply, in effect, that there was no intelligibility apart from constituent intelligibility; moreover, it would blind us to the real metamorphosis which the pledge causes in everyone and to the 'fraternity-terror' relation as the foundation of all subsequent differentiations. On the contrary, there is such a thing as comprehending common praxis as such, that is to say, in so far as it is related to the group as a practical subject (in the sense in which one speaks of a 'subject of History') rather than to the individuals who are integrated + +into it. It is simply a matter of regarding the group as a product of human labour - that is to say, as an articulated system - and of seeing the common action as a determination in passivity (through the constructed instrument) of individual praxis. These precautions will make it possible to comprehend group praxis in terms of this reciprocity of inertia: the instrument as a positive and negative image of activity, and the final product as a definition-exigency of this same activity + +by the future. + +On this basis it will be possible to grasp the synthetic connection between the two permanent actions - reorganisation and production in so far as each is the condition of the other; but the limit and specification of the constituted dialectic and of its intelligibility is that in it action is defined and carried by passivity and that the modifications of the common action occur in everyone. Originally, therefore, we can understand any common praxis because we are always an organic individuality which realises a common individual : to exist, to act and to comprehend are one and the same. This reveals a schema of universality which we can call constituted dialectical Reason, because it governs the practical comprehension of a specific reality which I shall call praxis-process, in so far as it is the rule both of its construction and of my comprehension (that is to say, of my production of myself, on the basis of the common, as a developing praxis-process.) Both as object and as subject of the constituted dialectic, the group produces itself in complete intelligibility, since it is possible to see how every determination in inertia transforms itself, in it and through it, into a counter-finality or a counter-structure (and, also, in the best cases, into structure and finality) ; this intelligibility is dialectical because it shows us the free, creative development of a practice. But its specificity as a constituted dialectic means that freedom is not the free activity of an autonomous organism but, from its origins, a conquest of alienation; moreover, the specificity of the object demands that freedom be sustained, channelled, and limited, both in interiority and in exteriority, by a pledged and suffered inertia which is simply the free determination + +- direct and indirect - of the field of passivity. + +The whole of this practical development produces undeniable results ; in other words, it constitutes the first abstract determination of History as such - in relation either to the taking of the Bastille or to the silk-weavers' revolt; and these results - though directly susceptible to alienation, as we shall see - represent in reality the objectification of a community as such. In other words, the constituted dialectic, as the + +ubiquity of the same praxis penetrated with inertia, transcends itself in the case of a practical success - in its result: the objectification really is common, to the extent that the objective was common. But as an organising, effective praxis, the untranscendable limit which it encounters is that of organic, practical individuality, precisely because this constitutes it and because, as a constituent dialectic, it is the regulatory schema and untranscendable limit of the constituted + +dialectic. + +It is at this level, I think, that it is possible to grasp the strange circular conflict, where all synthesis is impossible, which is the untranscendable contradiction of History: the opposition and identity of the individual and the common. I would like to illustrate this conflict and this lack of distinction by means of an example. The one I have chosen is certainly neither pure nor abstract and it scarcely concerns the group (at least as homogeneity), because it was conditioned by the capitalist mode of production and the class struggle, and it occurred towards the end of the nineteenth century, on the eve of the second industrial revolution. But this has very little bearing on the formal researches which we are conducting. What I wish to show, in effect, is the identity of individual action and group action, of group action and mechanical action, in short, the organic praxis as the regulatory praxis of the group and of machinery, and at the same time the irreducible + +opposition between the individual and the machine. + +5 Taylorism + +Taylor was without any doubt the first of what we now call organisationmen.63 His aim was to increase output by eliminating wasted time. If a worker's task comprised five successive operations, then five operators, each performing one of these operations five times, would take up less time than five workers each performing one complete action. The ingenuity of the organiser here consists in replacing temporalisation by passive temporality. An action is a temporalisingpraxis. Ancl, in a way, every elementary operation is also temporalised (in fact, it too is an + +63 . In English in original. [Ed.] + +action, complete in its realisation, and incomplete in the common signification of its result). But what makes the living totality of the action disappear is that the five operations are separated both spatially and (at least) by a time-lag which is the time of waiting. (For operation 2 to begin, it is necessary and sufficient that operation I should once have taken place.) Thus every operation is passive in relation to the succeeding one, because it does not form part of the same temporal development, but each is separated from the other by a determination of time (and, incidentally, of space) through the negative exteriority of inertia. Moreover, every operation, in itself, in so far as it has been timed and in so far as its 'normal' duration has been established by means of a determination of exterior time (that is to say, of the nondialectical time of inorganic materiality, in so far as it is defined by specific practices of measurement) , reintegrates a passivity into its free, practical realisation. Instead of being conditioned by the result which had to be achieved, and by the free organism in action, it temporalises itself dialectically by preserving, as its internal ossature, the passive + +temporality defined by the workshop clock. + +Thus the action is now constituted by five practices which are determined by the interiorisation of a passivity and separated by the passive flow of time (that is to say, by the abstract ossature of the time of Others: employers, other workers, customers, etc.). It disappears as an organic action; and, in isolated - and differentiated - work everyone is thereby disqualified as an individual practical agent: his operation is no longer an action. But at the same time he still becomes a common individual (but in alienation - this goes beyond the cases considered above) in so far as his operation depends on the first two, for example, and conditions the other two at a distance. In so far as he lives his labour and his solidarity as a member, with his comrades, of an exploited class, this interdependence may become power and function (but this is not very relevant here) . In any case, clipped and mutilated and torn from his hands and muscles by an exterior rhythm, the operation is still his practical operation and, despite its determination in inertia, it realises itself dialectically through him, if only at the most elementary level. The important point is that the skilled job, destroyed by Taylor, expropriated from skilled workers and distributed to the four corners of the factory, regains objectivity in its totality as a manufactured product of five separate workers. The only difference is quantitative, so it must be taken as a simple determination of exteriority: five specialised workers, each performing a single unchanging + +operation, produce n objects in a given period of time, while five skilled workers each performing the whole task from beginning to end will produce n-x. The reification of work is undeniable; it is simply a consequence of exploitation. What is striking is that this reified labour, in so far as it is the praxis of everyone, regains its synthetic character as afree determination of the practical field in inorganic matter. If we know that a particular product can, a priori (and given a certain level of technique), be made either by a single skilled worker, with years of apprenticeship, or by five unskilled workers, who have had apprenticeships of only a few months, there is no way of telling, without some other source of information, whether a given sample of the product was constituted by a multiplicity of actions, external to one another and + +determined in passivity, or by a single totalising process. + +This first moment of the example shows the absolute homogeneity between a dialectical action which composes itself, and an alienated, decomposed operation, between free temporalisation and expropriated temporality. This homogeneity does not manifest itself in the concrete moment of labour - which is very different in the two cases - but in the synthesis of objectification which is effected in the inertia of the product. The inorganic product, in effect, has this double character: by its passivity, it sustains but inverts the synthetic action which is inscribed in it; and endows it with a hidden exteriority; by its false unity, it holds together, and integrates into a single seal, various different operations, coming from different points in time and space; in it, the unity of a praxis becomes a false unity, and this false unity becomes a false integration, outside themselves, of an objective diver- + +sity of operations. + +This observation suggests another: no action is a priori incapable of being decomposed into several operations ; these operations are passivised and can be grasped by analytical Reason. And some of them, such as the ossified structures of the group, can become the object of an ordinal mathematics. No analytical treatment of these operations is even conceivable if the synthetic point of view of the objective totality is not retained, that is to say, if they are not integrated in advance in the produced object as their totalisation: in the same way, analytical Reason can conceive a universal combinatory of functions in a given group; it will have the concrete ability to construct it only in so far as it is a special case of dialectical Reason, that is to say, a function produced, directed and controlled by it. There is no action so complex that it cannot be decomposed, dismembered, transformed, and infinitely + +varied by an 'electronic brain' ; it would be impossible to construct or use an 'electronic brain' except within the perspective of a dialectical praxis of which the operations under consideration were merely a + +moment. + +But it should be remembered that the deskilling brought about by T aylorism is soon followed by a second moment: that of specialised machines. For in so far as each operation becomes mechanical, each machine can perform an operation. And of course if this operation is performed by a man, it will be praxis; but this is because the practical organism has no reality apart from organic praxis and because it realises everything it does in praxis. By itself the operation already has no specific character. Piling bricks into a truck is a human action if it is done by a man and a mechanical action if entrusted to a machine. Specialisation passes from man to machine, and a worker who is tied to his machine after an apprenticeship of a few weeks, sometimes a few days, is aware of his interchangeability. Finally, through automation, the individual operation, combined with all the others, becomes the task of the machine or of the complex of machines ; in the end, human action is completely absorbed and re-exteriorised by the passive instrument. However, the product does not change, or at least not much: it presents itself in the synthetic unity of an instrument which is constructed by men, and appropriated by them for the needs and ends of other men. Its inert unity reflects to the consumer the creative power of human labour. And rightly so: for automation itself presupposes an analytical Reason which is sustained and guided, both in the inventor and in the producer, by a dialectical Reason; and also because the new machines, far from eliminating human tasks, merely dis tribute them differently. But there is still the objective interchangeability, as it can be observed in the product, of individual praxis, of the passive addition of common operations, of production by specialised machines and of automatic machines as a substitute for practical autonomy. From our point of view, this at least means that the original praxis of the organism serves as a model equally for machines and for groups. Constantly decomposable, and constantly deskilled, it remains untranscendable, and there is no other constituent schema, whatever the type of efficiency being sought. In automation, however, praxis becomes pure process, and, with Taylorism, it becomes semi-passivity. These transformations are crucial, but they always occur below the level of the final objectification; they must be regarded as infra-transformations which leave the goal and the distant ends unchanged as determinations + +of the field of possibilities. The individual schema contains within itself everything that comes to man through man (with the exception of seriality) ; it is the practical category par excellence. And it is in it, and through its mediation, that the equivalence between the specialised + +group and the automatic machine can be affirmed. + +But, in addition, this example also shows that this practical category guides the analysis of tasks and the construction of instruments, but that it is necessarily negated by this analysis or by this construction and also by the work of the pledged group on itself - in so far as neither the group, nor the addition of tasks, nor automation can of themselves realise the immediate integration of an action which gives itself its own rules by revealing them as exigencies in the object. Thus, in the case which concerns us here - and the only one which is relevant to the dialectic - the group both seeks and negates in its heing the only translucid unity of active integration, that is to say, the unity of which the only example is the organism. It both seeks this unity and negates it, by the very means which ought to establish it, and at the same time it realises it by this very means in its objectification (construction, discovery, victory). Now this practical, dialectical, unity which was the group and which causes it to negate it in its very effort at integration, is simply what we have elsewhere called existence. The final problem Qf intelligibility arises on this basis: what must a group be in its being in order to negate existence in and of itself and in order to realise its own common ends in the object as the amplification of ends which have been freely posited by practical organisms as free dialectical existences? + +5 + +The U ni ty of the Group as + +Other: the Militant + +The group derives its unity from outside through others, + +and in this initial form its unity exists as other + +A group, as the erosion of a seriality, the practical unity of a developing objectification, and the manifestation, immediately suffered by the other, of a specific (positive or negative) efficacy, determines a negative, practical totality in external seriality: the totality of the non-grouped. And the not-being-grouped of every Other is the common relation of serial individuals to the grouping totalisation and to every non-grouped Other (as such) within the series. In other words, the Other is also determined, as Other, as a common individual. Obviously only the particular circumstances can determine, for a given historical group, whether the totality induced in seriality is just an abstract signification or whether the relation between the serial non-grouped and the grouped is a practical, concrete relation. The practical constitution of pigeonfancying or numismatics clubs, if it occasions any negative unity among the non-grouped, does so in a very abstract way. This is a case of a logical determination. On the other hand, the organised constitution of a fascist militia which specialises in surprise attacks may, according to circumstances, be the occasion of the negative unity of the unarmed population (fear), or even of positive anti-fascist regroup- + +ments. + +But, above all, when an institutionalised or quasi-institutionalised ensemble (in a few pages we shall see how the group leads to the institution) appears to have some public utility (given a more or less developed division of labour, where it takes on a given task, so relieving Others of it in so far as they are serial), it will produce a totality of dependence in the serial flight of the Other; in other words, it will + +determine its consumers. These consumers may remain in a state of recurrence (the customers of the post office, for example) or else in circumstances which we have already described - the inducing group may occasion an induced group (the state's quasi-monopoly of education induces a Parents' Association corresponding to the + +practical community of secondary education). + +In considering this new practical category, that of the non-grouped practically engendered by the group, we must recognise that it can take various concrete forms : the volunteers who march past with their arms, after the first victories of an insurrection, and who display themselves to the people who have not been fighting (but who, for the most part, support them) as 'those who defend, or liberate them', produce a lateral totalisation whose structure actually involves other groups : 'the king's army', or 'the bandits', are in fact the true inducing groups, having already totalised the population of a district or town (by attempting extermination). On the basis of this inducement, a group constitutes itself on seriality. But the passive ensemble (women, children, etc.) turns out to be designated by a double contradictory praxis: the enemy (at least this is the aim which is interiorised by the concrete certainty of the people, which, indeed, is always true - in a sense that will become clear later) totalises through a vacuum: the whole town will be razed to the ground; the group which resists the enemy totalises hy the negation of a negation. But at the same time, as a totalising negation occasioned by and resisting the external negation, it reconstitutes the negative totality of the non-combatants into a seriality of impotence, in opposition to the exterminators; they will be those who are defended, but their relation within the town will still be either an inert gathering or molecular isolation (both these statutes exist, one when the housewife - whose husband is on the ramparts or the fortifications is queueing for food, and the other when she tries, in her home, to preserve her family in conditions which become more difficult day by day) . However, this seriality, haunted by a passive, induced unity, is thereby subject to a certain modification: the proof of this is that, if circumstances deteriorate, a new section of the population may be incorporated into the defence group and other sections may be organised to back up the first (a health committee, a supply committee, etc.). The initial unity of the non-combatants is the unity of those who suffer their seriality; and this seriality, conceived as suffered, as socialised impotence, amounts to the beginnings of a recognition of + +recurrence and of alterity. + +The post office, on the other hand, as a public service which functions smoothly and permanently, initially constitutes its customers as a serial exigency, although its complex, totalising work becomes, for the 'public', a common interest, that is to say, the basic possibility of totalising itself so as to protect or control the functioning of this organised group. In any case, whatever the induced relation, as a tension between seriality and unification, may be, the totalisation of the group is an inducer for the social ensemble (which, for the moment, we are treating as a set of groups and serialities) . It is so as a purely formal determination, in so far as the group leaves the unity of the nongrouped outside itself by a negative totalisation; and it is so above all as a practical determination in so far as this same group has practical relations with the non-group; and lastly it is so - as we shall see later in so far as the group - on the basis of a certain social volume, which varies according to circumstances - expresses in itself the society as a whole, in the form of a totalisation. Through this totalising relation of transcendent (transcendante) multiplicity, the group realises itself as the first historical mediation between the practico-inert and practical freedom as sociality. But it is not from this point of view that it concerns us at present. We are describing its effect on seriality only in order to explain how modified seriality reacts on the community which + +modifies it. + +Indeed, from the moment in which the group becomes a mediation between the non-grouped, they become - either in the individuality of each, or in the alterity of the collective, or in an initial developing totalisation - a mediation between the members or the sub-groups of the community. If I am a postal clerk, with the task of registering postal orders or parcels, my relation to my bosses passes through the mediation of others, of those who queue in front of my counter (seriality). And each of these individuals perceives the totalisation of the group as a completed, fully functioning totality; this totality is constituted, of course, as a totalisation of functions and instruments; and the serial individual's serial thought expires in the practico-inert field and implicitly conceives common individuals as instruments, and inorganic instruments as living functions, as absolutely equivalent. When a customer hands a registered parcel to a post-office clerk, or puts an express letter in the special box for such letters, he sets in motion an operation which begins, in the one case, with a relation between men (though not necessarily with a human relation) and, in the other case, with a relation to inorganic instruments. But in both cases + +the entire operation presupposes both instruments and men to use them in a particular perspective. And for the customer the practical character of the juridical exigency is that the user makes no distinction between the instruments and the men. Ought we to say that in this respect he is conditioned by his practico-inert field? The answer is both yes and no: his practico-inert thought, as an interiorisation of his impotence, certainly encourages him to perceive the group as a unity which seals an inorganic passivity. But, on the other hand, his relation as a user to the common instrument and to the common individual is a free juridical relation/4 and, from this point of view, his individual operation is narrowly confined within the operation of the clerk as a common individual: the clerk reads, corrects, or recopies the forms which the customer fills in in order to send his parcel, etc. ; a reciprocity is established which qualifies him from a certain point of 'View as common (a common beneficiary and a common starting-point, that is to say, communi sed by the common aspect of the operation, its pledged inertia becoming its own past guaranteed by the pledge of the others + +and by a form or receipt which is handed to him). + +There is, therefore, a certain practical homogeneity between the customer and the clerk, to precisely the extent that the initial operation creates a practical reciprocity across the real limits of the group (and material ones, in the inorganic sense: for instance, the counter) and by connecting the exteriority of the customer to the interiority of the clerk. Now, from the point of view of this practical homogeneity (that is to say, from the free point of view of pledged faith), the customer will discover, as such, the active unity of men and instruments in the 'service'. On this occasion unity is created in another sense, as the dissolution of instrumentality and multiplicity in the act. This is what one feels whenever one performs one of those everyday actions which involve a public service: posting a letter, in one sense, for a particular Parisian, is to put it in his uncle's letter-box in Marseilles, or, in other words, to put it into a hollow pipe which sucks it up like a vacuum cleaner and finally deposits it on the table of the addressee; and it is also - since circumstances vary, for example one may learn 'that a + +64, Right and power grow from the pledge and from function, and consequently inside the group. But on the basis of free, pledged inertia and in the context of a common praxis, the group acquires the ability to give a power over itself to non-grouped individuals or to external groups, either in the form of contractual reciprocity (through inertia pledged in the Other from outside), or + +in any other form. + +particular letter-box was closed in a particular part of Paris without the users being told and that hundreds of letters therefore went astray to entrust an important message to the many hands of a free, pledged, but fallible organisation. The post office is my instrument, it is an extension of my arm, like a cane, a spade or a broom, or it is a free, pledged action which gives me a power but which may also fail me. What is involved here is not the two opposed terms of a dilemma, but rather two limits between which there are many possible intermediaries. And, in a sense we encounter once again process and praxis as we defined + +them above. + +However, precisely to the extent that the original relation is a power (of the customer over the group, or of the organised group over the inorganic gathering), those who are not grouped still recognise both aspects (or the synthesis of them) on the basis of a pledged inertia which constitutes for their practice the interior of the group. Whether instrument or organisation, the group must be responsive to the exigency of the customer (or the massified individual to the exigency of the group) : if the instrument alone is visible (the plane for its passengers), it must function as a free common function; and if men appear in their mediated inertia, they must respond to the exigency. This second freedom is not transparent, individual praxis; it is common freedom, determined by its limits, grasped by a freedom which is common to every user (despite its preserved seriality). And this common freedom defines the character of the common praxis for the customer in so far as it is expressed by a tension which affects the whole group (the whole postal system and the whole of France is penetrated by the pledged praxis which carries a letter from Lille to Nice). Thus the Other (the customer) posits the grouped totality as a practical ohject whose exis is pledged freedom; he posits this totality as producing totalising actions and as manifesting itself as a whole in these practical expressions of itself. At the same time, the customer posits the individuals who compose it (and the instruments which are in them) as inessential particularities. Or rather: as he proceeds from need to the practical power which the group confers on him, and from this power to the apparatuses which the group produces to give him satisfaction, he sees each person (as a common individual) as an a posteriori specification produced by the group in the course of its development. And this is not untrue, for the common individual is a product of the pledge; but at the same time the organic individual remains indeterminate for him: he sees the clerk as a human generality specified and signified by + +the total group and does not (or not necessarily: in fact, very rarely) know the details of the individual and his free praxis. He does not see this praxis as an individual mediation between function and concrete result, but as the free production of a preliminary operation by the group through an individual organ: the phrases and letters which correspond to the recording of a number of parcels, and which are specified in contact with the individual parcel which is to be recorded, are traced as the group-praxis through the otherwise indistinguishable hands of these particular clerks. Generally speaking, individuality will be grasped as pure negativity (clumsiness, slowness, lack of intelligence or courtesy), in short as the brute resistance of matter to freedom. Furthermore, this is another case of a reciprocity (usually based on scarcity, and particularly on the scarcity of time), for in the moment at which the operation-exigency of the customer constitutes me as an inessential product of the community and treats function, in me, as an essential line of force of the totality as such, I, as the clerk, treat him as an interchangeable member of a series, who exists for me only as a support of a precise, general exigency (or as an inessential member produced by a grouped totality: for example, for me, as a teacher, or a representative of the Parents' Association). Of course the relations between the administrator and the customer can become individualised: this happens, for example, if the reciprocal operations take place frequently. But this individualisation reveals a free reciprocity with no + +practical relation to their practical, functional bonds. + +Thus by the mere juridical exigency of the customer, the user, etc., the Other dissolves me into my group as a part into the totality and dissolves my free practice into the juridical freedom of common praxis. He then constitutes this totality, which digests and transforms external solicitations, and responds to it with a totalising and totalised operation as a being in interiority. In effect, the structure of the group, which must correspond to the power of the user, cannot be anything but pledged inertia, and consequently Being - but Being conceived as a norm (as the counterpart to a power). Thus, from the outset, we see the identification by the Other of Being and of having- to-be and this radical identity will constitute for the Other the ontological statute of the organised group. But this required-being is constituted through certain relations of interiority, since the customer understands the group, through his own action, as a synthetic operation defined by its aim and by the unity of its means. In this way, the 'being/norm' contradiction is resolved : for the Other, Being as pledged inertia arises in the form of totality (or, so + +to speak, the totality-object can exist only if inorganic inertia, seen as an invariable being, sustains it), but this inert totality is structured in interiority. So its inert being is produced in interiority as a norm of common freedom. On the basis of this norm, the totality produces its differentiations not as totalising efforts, but as diverse expressions of the totalised whole. The being of the whole, lived in interiority, becomes a normative scheme which occasions the production of total operations, and these operations, as interiorised practices, produce their own men and instruments. For the user, the public service is an object with an interior, that is to say, an internal milieu with its own tension, its index of refraction, its web, its spatio-temporal directions, its structures and its reflexivity. What is involved is, therefore, what might be called practical intersubjectivity as a milieu of the totalised totality. And this intersubjectivity does not relate to any abstract or 'collective' consciousness: it is quite simply + +the reflexive structure of the group as seen by the user. + +Now the member of the group, that is to say, the common individual, the clerk, realises himself practically in the reciprocal operation which unites him to the customer or user as an inessential product of reflexive intersubjectivity: this means quite simply that the determination of inessentiality comes upon him on the basis of the Other and that he has to assume it through his operation itself. In short, I produce myself through the Other and for myself as an inessential, passing mode of the intersubjectivity of my group in so far as I operate with and on the Other on behalf of this group. And in the practice itself I perceive myself as an objective expression for the other of a totality, whereas the internal movement of the community which is not mediated by strangers is given reflexively as a simple developing totalisation. + +This will appear still more clearly when the other mediators between the members of the group become for each member, not only through their actions but also through their material density, the real factor of his separation, of his isolation; when their resistance (either inert and serial or organised) conditions the possibilities of his communicating with his comrades in the group. This happens very often: however close the internal bonds may be, it is rare for a group to be constantly actualised, that is to say, gathered together in its entirety in a particular place. Besides, in many cases, these plenary meetings are a priori impossible : for example, the sheer size of the group may preclude any real gathering; political parties hold conferences in which each individual is the representative of several others. Thus each member of the group is temporarily or permanently set apart from the other members by the + +forest of humanity. For example, a militant in a non-underground party is constituted - as a common individual - by his fidelities (the pledge) and by his practical functions (which assign him a given ·place of residence in a particular town). But at the same time the forest of humanity which surrounds him is, like Macbeth's, active and alive. Its density is material and practical: the human environment treats him (whether with favour, contempt, hostility, trust or mistrust, etc.) as a party militant. That is to say, the serial or common practice of the Others constitutes him on the basis of the political and social programme, of the present action and of the past history of his party. His individual practice - with its style and colour, its skill or incompetence, etc. - intervenes only a posteriori and lacks efficacity and therefore reality except within a very narrow framework (for example, in relationships with other militants or sympathisers or with a layer of sympathisers who hesitate to join) . But in the first instance the overt militant is constituted in his being as a normative inertia in so far as, in a period of political tension, for example, the positions of Others are + +adopted, harden, and become unshakeable. + +However, it would be a mistake to think that these attitudes of trus t or hostility are directed towards him as a particular Communist, for example, or a particular Socialist. The force or violence of these practices of themselves signify that they are directed at the Party through any inessential individual. When fascist terrorism or lynchings are directed against one Communist, in sole charge of some office, it is to the Communist that they are directed: that is to say, they are directed at the Party as a present and essential totality through an inessential individual whom they never consider in his individuality. But, to take a simpler and more everyday case, the political discussions between a given opponent or enemy and a particular militant are not aimed at convincing him, but at refuting the Party in his person; and the interlocutor systematically ignores the personal limitations of the individual (slowness, lack of education, lack of aggression, or poor projection: someone else might have given a better answer, or routed the enemy) : in any case, his reactions are those of the group as a totality which is embodied in each of its temporary modalities. Conversely, the militant finds himself constrained by this practical separation, to which he is subjected by the human environment, to interiorise this relation between the inessential and the essential and between the part and the whole. He constitutes himself as a signifier to precisely the extent that he appears to all as signified. In effect, it becomes extremely + +important for the common practice that it is impossible either to confound his free individual practice with the praxis of the Party as such, or to judge the latter in terms of the former. And since the ordinary manoeuvres of the entourage consist either in penetrating the acquired characteristics of the individual without seeing them in order to go straight to the Party as his sole profound reality or, on the other hand, in taking individual characteristics, and isolated weaknesses, and making them into the common reaction of the political group as a totality, the isolated militant tries to dissolve personal characteristics in himself so as to make himself merely the local presence of the Party in totality. It is irrelevant that the militant is fair-haired, and has a stammer, or that he is intelligent or stupid: he makes himself for all what all make him, namely, the non-specified embodiment of a centralised mass revolutionary Party, etc., which gets six million votes at each election and which takes up and elaborates the exigencies of its electors and members. He becomes exigency-being, accusation-being; and he learns the common thought both as a determination of memory and as a pledge, in such a way as to make certain that this normative inertia will be reproduced in him as the same as in all the other mouths + +of the Party.6 + +5 + +But this transformation, which happens concretely under the pressure of the Others, is not an individual initiative: it expresses what the group - through its organs of mediation, liaison and direction, and through each particular sub-group (cells, committees, or sections, whatever they may be called) - requires of each of its members in so far as they are all isolated and besieged. However, the formal rigidity of the identification with the whole is accompanied by complete confusion as to its material content. In so far as he has imprinted certain functional relations on himself, the militant has at his disposal an ideology which enables him always to take stock of the situation and which, through his mouth, gives the common interpretation of the historical situation + +by the militant totality as a determination of discourse. 66 + +65. This is not a stratification of discourse in memory, but a stratification of + +the relations which determine discourse. + +66. This interpretation will have been devised by leaders in a specific subgroup, taking account of all the circumstances and, amongst other things, of the implicit exigencies of the practical community. These leaders may be perfectly competent; they may have public confidence and they may deserve it. But nothing can prevent a radical transformation when a militant who is isolated (or in an embattled minority) takes up - as a thought produced by the totality of 'the + +But, at the same time, individual s - through the indefinite recurrence of the serial - or enemy groups - by systematically appropriating his action - divert or dissolve the significations which he gives to his practice and to the course of things, both here and for every same in every other here. Refracted by a dark density, bristling with projects and actions which elude him, these significations become indeterminate objects or - and this comes to the same thing - objects with thousands, or hundreds of thousands, of facets. When the militant publicly reaffirms the abstract, schematic determination of discourse, he immediately reveals, to everyone, the Party as a group-totality. But it remains schematic, and the more it identifies him with the group, the more it cuts him off from reality. It should be clear that what we are discussing here is not the political difficulties of any particular situation: I am simply trying to show that the forest of humanity - as materiality and as the praxis of isolation - must, for the militant, be interiorised as the ubiquity of the group. But we have seen that this ubiquity - which, despite the pledge and the heterogeneity produced, remains fluid as long as the relations of common individuals are direct - freezes and ossifies as soon as it is affirmed in opposition to the practice of the nongrouped. At the moment in which the group as a totality-object becomes an abstract schematisation for the militant, he becomes unable to comprehend either his own organic praxis, or that of the others, or the concrete course of events. But, at the same time, he refers to what he realises as his common reality constantly and for his every decision, that is to say, to the Party as a normative inertia and a completed totality, as pure objectivity and inter-subjectivity (that is to say, possessing an interiority), in short, as a substance which is total everywhere and which recreates its own instructions everywhere. + +But it should not be forgotten that this new constitution comes to the member of the group through Others. This means that it arises in the milieu of alterity and that he adopts it in accordance with his functional relations to the non-grouped. Thus this structure, as the practical instrument of his operations, represents in everyone his Being in the milieu of the Other and the practical reinteriorisation of the Other- + +Party', that is to say, as a totally expressive exis of this totality - a practical decision, taken by a few common individuals (in the name of all in virtue of their powers, of course) and reinteriorised ill a practical movement of reorganisation by every common individual, that is to say, by each inessential embodiment of + +the group as an essential substance. + +Being of the group. For it is in its objectivity for the Other that the group can superficially appear as a totality. 67 And it is clear that in itself, as an internal relation, it becomes a totalisation. On the other hand, the structure of embodiment (the inessentiality of the individual, and the present essentiality o f the whole) is not lived by the organised member for and in itself; he does not grasp it in the reflexive unity of an organising action which has the totalisation of the group as its direct objective: he produces it through the mediation of the Other as the controlling schema of his relations to the Other. Thus it is important to recognise that the practical and theoretical object, for the person in the group, is the Other and that he does not grasp his own reality as an inessential embodiment except as an implicit rule of action and as a signification which is discovered and projected onto the Other in the course of the antagonistic reciprocity of combat or of argument. This univocal relation to the Party or to the Group (his being-in-the-group being lived as the dissolution of the part in favour of the whole) can never be either the aim of his action or the ohject of any intuitive, practical certainty. Nor is it ever explicitly formulated, unless it is first formulated by others. It is an empty knowledge, and also an inertia which is received and suffered, but interiorised into an abstract pledge and reexteriorised into stereotyped actions (or rather actions whose relational structures tend to be stereotyped) and a sort of regressive intentionality aimed at relating every particular circumstance, as a pure accident, to the totality as a substance which digests and dissolves all concrete reality (as inessential) . And, in a way, if one is careful to avoid equivocations, one can say that the praxis of the militant - when he is connected to other third parties by the mediation of the forest of humanity - brings a certain alienation to the group; this is because he experiences, as a bond of interiority to the totalising organisation, a relation of exteriority to the group-object (as an exterior object) which is + +67. It is worth recalling what was said above: that any grasp of a group in the practical field is a totalisation by the individual who is not grouped, and that this totalisation formally engenders a totality-object. But if the group is given in its actual operation, then, as we have seen, this totality proclaims itself as an appearance in so far as it makes it possible to perceive the object as a totalisation independent of the individual synthesis. The totality remains as what calls a halt both to investigation and to praxis when the group gets too large, too ramified, or too complex to offer itself in its entirety. Thus the sub-groups which are present, though they are totalisations, appear as inert embodiments of a totality which is + +referred to in a vacuum. + +reinteriorised as a defence. + +Nevertheless, he is constituted by a complex relation, composed of two opposite mediations: the Other's mediation between the common individual and the group-object; and the group-object's mediation between the common individual as an agent and the Other as the object of his action. And the abstract meaning of this relation - as an empty, inert, and formal intention - is still fundamental: going back through the everyday practices of the agent in relation to pledged inertia, this relation indicates the immanence of the individual in the intersubjective totality, that is to say, the dissolution of the mode into the substance or, in other words, the fusion of individual organisms into a hyperorganism, as the future which has to he realised once the group as such + +is fully assembled. + +6 + +The Institution + +In the interiority of the group, the movement of mediated reciprocity constitutes the unity of the practical community as a perpetual detotalisation engendered by the totalising movement + +lMediated Reciprocity in the Group + +When, at a Party conference or demonstration, the militant is put back into the midst of the group, or when the clerk, ceasing to communicate with his colleagues through the medium of the customers, turns back to them and rediscovers the direct bonds of the organisation, their expectations are disappointed and their relation to all is metamorphosed : for they rediscover the real milieu of immanence, to precisely the extent that it is impossible for them to dissolve into it; and, to precisely the extent that alienation to the group-object disappears with the Other, they rediscover a community which could never become a totality-subject. At this level, in effect, where the organisation takes itself as an immediate objective in the light of a transcendent aim, being-in-the-group is no longer, for everyone, mediated over there by the Other; instead it is mediated here hy the same (by the negated multiplicity of every same). It would be pointless here to enumerate and describe the intermediate mediations which actually give the being-ofthe-group its inconceivable complexity: for example, I may, through the absent, abstract Other, communicate with the same (avec les memes) in a concrete, reciprocal relation (there have been complaints about a particular clerk and he has to explain his behaviour, etc.). It will be sufficient to contrast :he two extreme, opposed relations : on the one hand, alienation to the totality and the false bond of interiority which constitutes the group through everyone as an inter-subjective substance whose Being is defined both by inertia and by having to be (Ie devoir-erre); and on the other hand, the relation of true interiority + +through mediated reciprocity, the practical recognition of functions, of sub-groups and of individuals through totalising reorganisation. + +But if we examine this being-of-the-group in immanence more closely, we will discover a new statute of intelligibility. We have seen that organisations are based on a pledge. Everyone pledges himself to remain the same. This pledge occasions a first contradiction in that it becomes the basis of the heterogeneity of functions. And this contradiction produces another, since it is free individual praxis which, through individual action, realises the detail of the common objectification. Thus the urgency of danger and of need is reflected not only in 'fraternity-terror', as a relation of indissolubility and violence, but also in more complex structures whose necessary effect is to allay terror and mask fraternity. This would be unimportant; but as we have seen the fundamental integration of the third party into the group is performed through mediated reciprocity. And by fundamental integration, we mean both the individual's coming-to-the-group (as the initial movement of grouping) and the permanent act of totalisation which is carried out by and for evpryone in various forms and through the complex evolution of the group in action. Now, this mediated reciprocity, despite mediation, retains its original structure as a detotalised duality (with a double centre); and this detotalised duality manifests itself here, within the movement of integration, and through a temporal dislocation of the totalisation, as reciprocal praxis. Indeed, when describing the fused group, we noted the main features of the regulatory third party., in particular what we called his relation of immanence-transcendence to the group of which he was a part. Let us return to this point, now that we are more familiar with common structures, and describe it more fully. And, in order to concentrate on one example, let us imagine that two individuals, A and B, in the course of a common action, totalise themselves reciprocally, both with and in the group, + +through mediated reciprocity. + +This totalisation is practical. We are not concerned here with ritual recognitions, which have no objective aim other than to preserve the bonds of interiority; we are concerned with reciprocities which are already organised and functional: the concrete relation between two powers which come together in order to produce a given result in the objective. In this sense, every function integrates the other into the differentiated totalisation through their heterogeneity seen as reciprocal. The regulatory act performed by A - that is to say, his practical behaviour as defined by the common individual A - does not arise in + +B as such (unlike what happens in fused groups). But, through the reciprocal grasp of the common field, the act remains regulatory because it Occurs in a signifying totalisation, the meaning of which is known to both agents, and because the two agents are themselves reciprocal products of the organisation: they have been formed, trained and equipped in such a way that B could see a forecast of his future action in that of A. (Thus in the common field of the football match, on the basis of the common game and the given conditions, each movement of each back is regulatory for the actions of the goalkeeper.) Now, the structure of the regulatory act is complex: it is, in a sense, a limited affirmation of sovereignty. By sovereignty, in effect, I mean the absolute practical power of the dialectical organism, that is to say, purely and simply its praxis as a developing synthesis of any given multiplicity in its practical field, whether inanimate objects, living things or men. This rearrangement - in so far as it is performed by the organic individual - is the starting-point and milieu of all action (whether successful or unsuccessful). I call it sovereignty because it is simply freedom itself as a project which transcends and unifies the material circumstances which gave rise to it and because the only way to deprive anyone of it, is to destroy the organism itself.68 In conditions in which this rearrangement of the diverse into a totalised field is also realised by action as material transformation of this field in its internal configuration and real content, sovereignty is not only ahsolute but also total. Now, at first sight, this regulatory action - whether it occurs in a fused group or in an organised group - resembles the exercise of absolute, total sovereignty. The play of A practically totalises the group: in fact, for its part and in this moment, it defines the orientation of the praxis and the momentary organisation of all; through individual readjustments and owing to the power of each over all, a particular run or breakthrough will arrange the entire team in a certain practical order (the meaning of which, for example, may be both to support the manoeuvre and to anticipate a counter-attack). Through this totalisation of the team and by means of it (for it) B will be inte- + +68. But it is very important not to conclude that one can be free in chains. Freedom is a complete dialectical development, and we have seen how it can become alienated or bogged down or allow itself to be caught by the traps of the Other and how simple physical constraint is enough to mutilate it. But still even the most oppressed slave, simply in order to be obedient to his master, both can + +and must perform a synthesis of the practical field. + +grated into the structured whole: he will realise this practical integration by determining his own position on the basis of the present state of play, of the tactics being used, of the order adopted by all and of his own special function. Thus, A's sovereignty will define the mode of integration of B into the group in his operation; and A will totalise B, + +C, D, E, etc., by means of his regulatory action. + +But if the exercise of sovereignty were complete, the sovereign would have to be external to the group and to totalise it as totalityobject in his practical field. We should then encounter a type of relation which we have already defined: either, in its crude, fundamental form, the univocal synthetic bond between the agent and the (material and human) environment or, in an elaborated form, the relation, both in interiority andin exteriority, of the customer as Other to the clerk. Now, we are aware of the limit of this sovereign synthesis: it is that the bond is not univocal but reciprocal, that the regulatory third party integrates himself into the group in so far as his regulatory action succeeds in integrating me into it. His practical field, and mine, and ours, are one and the same. Thus sovereignty is limited by its very reciprocity; everyone is sovereign: but it should not be inferred that no one is. Or. the contrary: since each is sovereign over the sovereignty of all, at the same time as being the organised object of each practical synthesis in interiority, he ought to be described as quasi-sovereign and quasiobject; and the group itself, in so far as it is totalised by the practice of a given common individual, is an objective quasi-totality and, as a negated multiplicity of quasi-sovereignties, it is in a state of perpetual detotalisation. In fact, the dislocation which, in the practical temporalisation, separates the moment where A becomes the regulatory third party from the moment in which B in turn is a regulator, constitutes B's being-in-the-group, as well as A's, as an ambivalent statute of interiority. In so far as B adapts Ilimse/fto the initiative of A, he defines himself practically as a restructured element of this collective materiality (suffered and pledged inertia) which each third party, as a third party, reunifies in his quasi-sovereignty. His objective, practical truth (that is to say, the action to be performed, as signified in interiority by other third parties) therefore comes to him through A as quasisovereign, through common mediation; he grasps it through his action, which submissively realises the regulatory signification. But, by submitting - and in conformity with intentions which have come from outside, by means of the Other and interiorised by himself - B tries to realise the unity of immanence as the fusion of the mode into + +the substance; but in fact, this unity is destroyed by the simple fact that his action, as a free mediation between the common individual and the common objective, by a practical organism, realises the synthetic objectification of the group in the worked object by negating his interiority of immanence in and by his dialectical development, that is to say, by negating his being as an inessential mode in relation to the essential substance. Wherever the action develops freely, he posits himself as essential (if only as a detail) through its very development. At one and the same moment, therefore, B not only manifests his being-integrated-into-the-group as a practical and objective integration based on his inability to integrate himself ontologically into a substance, but also, at the same time, in the mediated reciprocity which harnesses his actions to the regulatory action of A, he sees himself by and through A as an integrated element of a quasi-objective totalisation performed + +by a quasi-sovereignty. + +But this ambivalence - which is simply a developing contradiction also refers B to his own sovereignty; in becoming the third party through whose mediation B will rediscover himself over there, merged and organised with the others in the inter-subjective substance, A forces B to recognise him, in a new movement of reciprocity, as the third party who has the power to integrate (and not as the abstract sovereignty of the individual organism), and therefore as a member of the group. In other words, B has to see A as a simple modality of intersubjectivity (a definite function as the specification of the substance by itself), and this will force him, in A and in all, to snatch himself away from the common substance - that is, away from the integrating operation - so as to become a mediation between the individual A and his common-being-in-the-group. A therefore becomes not only, for B (and by means of B), an alter ego (the same - positive reciprocity) but also an excluded third party (as a quasi-sovereignty: a quasi-exile, the tension of immanence-transcendence) ; and B, by means of A and in the same conditions, also becomes an excluded third party and an alter ego. Everyone can and must be determined over there in his inessentiality in relation to the group through the integrating sovereignty of the other - who becomes the provisional subject of the group. But in order for this operation to take place outside him by means of the alter-ego, everyone must posit himself in his irreducible essentiality as the one who (with all the others) guarantees the Other's membership of the group by means of his pledge, his powers and his action. + +Thus, in the pledge with which B becomes, through his practical + +subjection to the regulatory action, the object of an integration which is mediated over there in A, he constitutes the group as detotalised (or helps to do so): through his obedience he produces A as a quasisovereign, and therefore as quasi-excluded; and in the moment in which he grounds this quasi-sovereignty by a mediated recognition of A's powers and functions - that is to say, of his concrete membership of the group - he produces himself as regulatory (either for A or for Others; as when he acts as a guarantor for A and declares to the Others, in the name of his own powers: he must be followed, helped, obeyed, etc.), and so realises in his person the quasi-exile of quasi-sovereignty. However, it cannot be denied that the interiority of relations, my common being's intimate membership of the whole, the inessentiality of my own existence (in so far as we are the same) and the essentiality of my function as a structured relation to the totality, are all practical truths: and the proof of them is that, in a living group, they are realised and verified every day by concrete action; discipline, self-sacrifice, etc. , are practical affirmations of all these truths. But in fact, in the living milieu of interiority, these truths, as determinations of my ontological statute, appear only in a perspective of flight and as a quasi-transcendent meaning of immanence. My real membership of this particular group as a transcendent rule of my concrete life is realised in me as a lived impossibility that my group-being should merge with those of other members in an undifferentiated ontological totality. From this point of view, each of my regulatory actions appears as a false totalisation, detotalised, in fact, by the surety which all the Others give me; and my guaranteed sovereignty never becomes transcendent sovereignty; and none of my regulated actions ever succeeds in submerging me in immanence since it is itself a surety for the regulatory action which occasioned it. Being-in-the-group, in interiority, is manifested through a double, agreed failure: it is being unable to leave and also unable to integrate oneself into it; in other words, being unable either to dissolve it in oneself (pledged inertia), or to dissolve oneself in it (practical unity being the absolute contradiction of ontological unity). However, the being-one of the group does exist: it is pledged inertia, the same in everyone, that is to say, one's own freedom become other through the mediation of the Other. But apart from the fact that this inert-being (hre-inerte) resolves itself, on examination, into a tight web of inert, mediated reciprocities (and thus loses its appearance of unity), it cannot be regarded as the real ontological statute of the group, since it is in fact a means of producing practical differentiations. To reduce + +the being of the group to the set of its inertia-means (inerties-moyens) is to transform this basically practical organisation - which exists only through its action - into a skeleton of relations capable of being treated by an ordinal calculus. But the illusion remains as an essential structure + +of any community, for two fundamental reasons. + +First, the violence and coercive force of fraternity-terror as a true relation of interiority between the members of the group are based on the myth of rebirth; they define and produce the traitor as absolute evil to precisely the extent that they define him as the man who destroyed the previous unity. In other words, both terror and the pledge relate to the deep fear of a dissolution of unity. They therefore posit it as the essential security and as the justification of any repressive violence. But the basic contradiction of the group - which is not resolved by the pledge - is that its real unity lies in common praxis or, to be precise, in the common objectification of this praxis. When the community affirms itself as the reign of common freedom, it cannot in fact -whatever it does - either realise the free interpenetration of individual freedoms or find an inert being-one which is common to all freedoms. Secondly, for those who are not grouped and for other groups (rivals, enemies, allies, etc.), the group is an object. It is a living totality. And, as we have seen, it has to interiorise this objectivity. It would be pointless here to examine the dialectical relations between groups and show how they are determined through their oppositions, each in relation to the others, and how they are transformed by interiorising their being-for-the-other and even, in certain circumstances, the being-for-others of the other, as their own immanent being. This has already been done many times - though never very rigorously. The only point that has to be remembered is that, as we have seen, the group is seen in its totalised unity by the ensemble of the others and that this pressure is so strong that even in its relations of pure interiority it interiorises this unity as its being-from-behind (etre-dederriere), that is to say, in the last analysis, as the material but synthetic source which sustains and produces it. Thus, in its developing reorganisation, it perpetually refers to its deepest interiority which is in reality only its most abstract exteriority. There is a being-X of the group - as its transcendental reality - and this is produced at an infinite degree of compression and gathers together the totalised ensemble of its structures, of its past and of its future in so far as they are externally the common object of the ignorance of Others; and this being-X as the pure abstract object of a regressive intention becomes the + +interiorisation of the ignorance of Others, that is, the meaning and historical destiny of the group in so far as they are the object of its + +own ignorance. + +2 Purges and Terror + +This untranscendable conflict between the individual and the common, which oppose and define each other and each of which returns into the other as its profound truth, is naturally manifested in new contradictions within the organised group; and these contradictions are expressed by a new transformation of the group; the organisation is transformed into a hierarchy, and pledges give rise to institutions. This is of course not a historical sequence; and indeed we shall see that - on account of dialectical circularity - any form can emerge either before or after any other and that only the materiality of the historical process can determine the sequence. The only purpose of arranging them in a series is to indicate the complex characteristics which are to be found in most concrete groups; our investigation proceeds from the simple to the complex because it is both formal and dialectical and it does so as it + +proceeds from the abstract to the concrete. + +If we look at it closely, we can see that the basis of terror is the fact that the group has not, and cannot have, the ontological statute which it claims in its praxis; conversely, it is that each and all are produced and defined in terms of this non-existent totality. There is a sort of internal vacuum, an unbridgeable and indeterminate distance, a sort of malaise in every community, large or small; and this uneasiness occasions a strengthening of the practices of integration, and increases with the + +integration of the group. + +It should be realised, in fact, that the conflict between the essential and inessential is not at all theoretical : it is a permanent danger both for the group and for the common individual. In fact the pledge posits the inessentiality of the organic individual by making it impossible for him to dissolve the group in himself; besides it is obvious that, in every structure, the presence of the developing totalisation in the individual part also indicates the importance of every part and their interchangeability; finally, the Other treats the organic individual as a general + +reality which can be ignored, and tries simply to approach the group through the mediation of the common individual; and as we have seen, this inessentiality of exteriority is also interiorised. It is at this level that the group-individual is defined by the practices of all the members, within the community, as a common individual. He is a determinate function, power and competence: the practical relation with this contradictory being (freedom becoming a legal claim through the transcendence of free, pledged inertia) is juridical and ceremonious: even outside action, each relation within the group is a reciprocal recognition + +of attributions and of the system of 'rights and duties'. + +Attempts have sometimes been made to base the transition from the repressive to the restitutive, from violence to contract, from contempt for life to respect for the human person, on the historical differentiation of functions. The individual, as such, is presented as a product of the division of labour. But these arguments are senseless: they only express the common wish to reduce the practical organism to its social function. Now, conflict occurs precisely at this leyel; in relation to the common operation, each function has a relatiye importance and therefore the common individual is inessential or relatively essential; but in relation to carrying out this particular social task, the practical organism is an essential mediation. Of course this does not mean that any particular individual, as a specific product of History, is indispensable for the task which the group has assigned to him. This may happen in makeshift organisations, but in a group which itself produces the workers it requires, this dependence is automatically eliminated. But this means that - irrespective of the individual and even if he could be immediately replaced - the moment of praxis - that is, the essential moment - is always that of the free, individual dialectic and of the sovereign organisation of the practical field. No individual is essential to a group which is coherent, well integrated, and smoothly organised; but when anyone realises the mediation between the common individual (who has no real existence except through the organic life of the agent) and the object, he reaffirms his essentiality in opposition to the group. And this essentiality has nothing to do with the historical individuality of the operation (or not necessarily), but rather with practical freedom as an indispensable moment of any operation, even in the practico-inert field of alienation. The individual agent has not transcended or betrayed his pledge; he has executed his mission, performed his function; and yet, in a way, he has created a new isolation for himself, as beyond the pledge, as a bracketing of inertia + +(whether suffered or pledged). In short, through the powers and responsibilities which have actually transformed him, through the instrumentality which increases his power, he has returned to transparency and can realise his fidelity in the group only through a transcendence which removes him from the common statute and projects him into the object outside. However it is lived, this contradiction will be objectively expressed as a permanent danger of exile, or even as real exile. And the fear of being exiled, in reciprocity, gives rise to the fear that the group may be dissolved, as inessential, in the essentiality of individual actions. This is not the fear which, in the fused group, occasioned the pledge: the fear then was that the group might be dissolved by default (negative behaviour, rout, abandonment of post, etc.). What is feared now is dissolution through excess, and a pledge has no power against this new danger, since it arises precisely from + +pledged fidelity. + +But alchough the structure in reciprocity already extends it to all, even if it is lived in the particularity of individual labour, the contradiction between the inessential and the essential would be no more than a simple cause of disquiet unless it were taken up and amplified by the relation between the regulatory and the regulated action. The counterpart of the integration of each third party into the group is, as we have seen, reciprocal exile; but as each member of the group is the third party through whom integration is effected, it follows from this that the practical realisation of this integration has as a counterpart a shifting exclusion, a circular succession of exiles for each and all. Through the permanent practice of integration and ritual recognition, the group resists the dangers of seriality. But it is precisely these continuous operations which, for everyone, occasion a way of living one's own being-in-the-group as a constant but masked separation, and the beingin-the-group of other third parties as a perpetual danger of secession. Particularly in the case of groups which can meet together or live in a particular place which gives material support to their unity, a contradiction emerges here between geographical position and real relations : if the group is protected by a wall, for example, then I may see myself as being really in it, but this only means that I identify its being with + +that of its container. + +In one sense, such an identification is legitimate, since the container (in so far as it has been chosen, defined, and worked, and in so far as it occasions special conduct, etc.) clearly represents the practical materiality of this interiorised multiplicity. But, at the same time, in my + +relations with the third parties I realise my own tension of immanencetranscendence as the truth of our human relations, and this truth is either that I am not really in the group or that my heing-in-it cannot be taken in a naive way as a relation between content and container. Thus the interior of the place as such acts as a basis for my human relation and it aggravates my exile in interiority in so far as membership of the material whole, as a support and expression of the totalisation, is no longer lived as a security, and becomes secondary and slides towards annihilation, although being-in-the-group, as the practical interiority of relations, does not emerge in intuitive experience and as a new security: what is realised in everyone is interiority as a spatial bond between the container and its contents in its inadequacy and as an anonymous mystification. I am inside but I am still afraid that I may be outside. In other words, everyone grasps his quasi-sovereignty (which is nevertheless an indispensable moment of the reorganising re-totalisation) defiantly, as if it threatened to designate him as essential: in effect, the synthetic operation of regulation indicates him as the final term of the integration, but without integrating him: it therefore isolates him. This did not matter in the moment of the fused group, because differentiated functions had not yet been produced. But when quasi-sovereignty is realised as the exercise of any kind of concrete power over Others and as an individual practice which eludes the pledge (not by transcending it, but through being its basis), the regulatory action is revealed in all + +its contradictoriness: intercession-secession. + +And once freedom - seen as the free, organic negation of common freedom and as the free dissolution of deposits of inertia in everyone becomes afraid of itself, and discovers in anguish its individual dimension, the dangers of impotence and the certainty of alienation which characterise it, and the regulatory third party has become a regulated, integrated, third party, integration by the Other will be revealed to it by dislocated reciprocity both as a danger to sovereignty (through the reification of the group within the practical field of a single individual) and as a danger of exile (which means a danger of being killed - for the third party seen in his implicit secession - as well as a danger of betrayal). What emerges at this level is that mediation by all is itself reciprocity between third parties, each of whom is, in himself, the perpetual explosive contradiction which we have called quasisovereignty. In this sense, mediated reciprocity relates to circularity in so far as the relation of the powers A and B depends not only on their reciprocal recognition but also on a series of sovereign recogni- + +dons each of which may, depending on concrete circumstances, be either essential or inessential to the unity of the group. (The power relations between two organising sub-groups actually depend on how those who are being reorganised acknowledge the powers of the two 'organs'; on their giving one of them precedence over the other - even if the order of precedence has been fixed the other way round; or on + +their rejecting them both). + +Thus the heing-one of the group (both as an abstract, ontological aim and as the concrete reality of the detailed objectification) depends on my individual freedom - that is to say, on the movement which constitutes exclusion, physical liquidation and betrayal as real possibilities for me - in so far as my heing-in-the-group eludes me and constitutes itself in the shifting circularity of regulatory actions (in so far as these can, in themselves, and as far as I can tell, become the liquidation of the group or the petrification of the community into an inorganic object). 69 Separation as suffered inertia which comes to reinforce pledged inertia increases the tension between sovereign exile and impotent dependence: if the group goes beyond the boundaries of the place or of the container (or if, for some reason, relations within the place, the camp, or the city, are penetrated by distance, as happens, for example, with a clandestine action: the work of the enemy police, as the common action of a hostile group, is equivalent to being conditioned by spatiality as practico-inert extension), the quasi-sovereign third party is still my brother, but he is also almost or completely unknown. Yet his action does not cease to be regulatory: through the organs of mediation, I may learn that a particular common initiative has begun elsewhere in the spatio-temporal destiny of the practico-inert field, and with others who are present I will define our action as a sub-group in relation to this initiative. And of course elsewhere is still here; but it is a here whose special characteristics are essential (because I am anxious to know them) and whose universal ubiquity is an inessential abstraction. By this shifting flight of reciprocities, everything is finally put in its place, and thus the organised group can, through its own freedom, develop a circular form of seriality. And, though it may seem surprising, this appearance of the Other does not present itself as an alienation of + +69. This second possibility cannot correspond to any real operation; and it manifests itself to everyone as an expression of the freedom of the third party in so far as, through his own practical affirmation, it is a negation of reciprocitie\$ in + +and by a reciprocal act. + +praxis to the practico-inert (though this alienation must occur elsewhere), but as the rediscovery of free individuality as the sole means and the sole obstacle for the constitution of an organised group . In + +fact, it is the new reaction of negated multiplicity. + +Of course, what we have been describing are dialectical possibilities of a purely formal order. By themselves and in their structural formalism, these implicit contradictions, which relate to structures common to all groups, do not and cannot give rise to a revival of seriality within unity, to betrayal or repression by Terror, or to the liquidation of the group. In fact, whatever happens, they have to be lived and produced, because they define the intimate contexture of the organised group, and because neither actions nor members can be produced in their concrete reality except through the internal curvatures proper to the groups which produce them. But it is the historical process as a whole and, in a totalising context, particular circumstances, the aims of a group, its past history, its relations with other groups, etc. , which will settle how the reciprocal, serial connection of exile-secession will be lived in the concretely differentiated zones of a particular practical community. For example, it is obvious that a relatively small group, which organises the complexity of its apparatuses through a victorious praxis, cannot even live its reflexive contradictions in the form of uneasiness: real unity is transcendent and practical, it imposes itself from the future in real modifications of the common object, in the structures of the future revealed by the object (possibilities reveal themselves, facilities which absorb action like real exigencies, crevices in which praxis becomes lost, short-cuts, etc.). For the easier, the more urgent and the more glorious this objective future, the more it abridges the mediating behaviour of reflection inside the group: if the organisation can be clearly decoded in the object negatively (en creux), if it presents no difficulty in itself, and is indistinguishable from the transcendent operation, then it becomes a lateral interaction of reciprocities in the development of a common action. No doubt it will be necessary to sanction and reorganise it; but, for us, the important point is that, when successful, the object provides the ontological unity of the group, at least as the quasi-certainty of each of its members. And this quasicertainty is not a subjective determination: it is the character and modality which everyone's action has for him, in so far as he sees it produced as common in his hands. Failure or - to take a less extreme case - the difficulties of a slow, disappointing action, obviously give rise to reflexion (by raising the question of reorganisation) and make every + +individual or sub-group live separation as defiance: 'We here are doing what we can .. " etc.'. In the moment of free individual praxis, action displays its contradictions precisely to the extent that its individual success here is no longer immediately absorbed by the common success. In itself, personal, localised success tends to posit itself for itself as an essential moment all the more when common success seems compromised or more distant. And separation occurs in each individual agent to precisely the extent that the local success of his action produces in the object an incomplete determination which signifies nothing (since the true, intelligible meaning of the action, of the complete development of the practical individual, lies only in common realisation) and which demands (objective exigency) that the common object should adopt it and integrate it through broader modifications produced by the labour of all.70 Above all, everything depends on a complex ensemble which connects the members of the group, their multiplicity, their means of communication, their techniques, their instnments, the nature of their object and their aim in a single historical movement. For example, a group whose aim is a synthetic, unifying action (agitation, propaganda) and whose object is serial gatherings which go beyond it in every direction will find it easier to interiorise the objective seriality against which it struggles; thus one can see balances being established (generally damaging to the developing action) between the seriality-object which is in the process of dissolution and the group-subject (in the practical sense) which is in the process of serialisation. But it is sufficient to mention these well known examples. What is important is the relation of the common structures to their historical content (that is to say, to the temporalising temporalisation of the group by its individual praxis in relation to its temporalised temporalisation by the praxis of other groups); and this + +70. It goes without saying (though the example does not concern us here - in relation to the dialectical development, it appears accidental) that separation is seen more violently and in all its irrepressible negativity when a given individual in a group which is succeeding in its undertaking realises his own action as a failure (of detail). But all this has often been described by psychologists and novelists. I refer to it only as a reminder. Suffice it to say that the individual-failure becomes a pure object of common repression. The terror exercised over him is a common action (mediated reciprocity) aimed at destroying in him and with him the possibility, which is proper to everyone, of transforming suffered separation and revealed circularity into secession or exclusion. In a traitor, everyone nnds in reciprocity (for himself and for everyone) - his own permanent possibility of + +betraying and being betrayed, and believes he is destroying it for ever. + +relation can be expressed as follows : circular serialities, as structures of secession-exclusion, cannot be a priori realities or reflexive determinations independent of History; they realise themselves as a temporalisingtemporalised moment of the life of the group, under the pressure of particular circumstances and in particularised forms (factional struggles, terror, internal anarchy, absenteeism, discouragement, etc.). But historialisation, in the form of internal conflicts - whether masked or explicit - of circular seriality as a proper product of the group, only temporalises, through the action of specific factors, the contradiction proper to communities; and this basic contradiction - which is to be found both beneath and beyond the pledge - is that their practical unity not only demands their ontological unity but also makes it impossible. Thus the group creates itself in order to create and destroys + +itself by creating itself. + +And being-in-the-group is a reality which is in itself complex and contradictory, because it is, in the past, the co-emergence in the group of pledged inertias through reciprocity and, in the temporalisation towards the future, the reaffirmation of this common emergence through organic, free, regulatory action which thereby transposes it into transcendence-immanence and negates it by living it as the contradictory and simultaneous impossibility for the individual of being either completely inside the group or completely outside it. Thus being-in-the-group is an inert 'being-in-the-midst-of-the-group' seen as an untranscendable past and realised by a movement of integration neutralised by a movement of secession. And everyone's concrete operation, as a free adoption of pledged untranscendability, manifests itself in its full positivity as having been able to be a refusal to take up the pledge and as having freely reproduced this past inertia. Hence, to the extent that it replaces the pledge as a vivid opacity within the transparent freedom of commitment, it constitutes for it, in the future and simultaneously, both the pledged non-possibility of being transcended and the permanent possibility of dissolution. And, no doubt, it is my freedom as Other which swore in me : but any action, both as a concrete expression of my translucid freedom and as mine, reestablishes the priority of the constituent dialectic over the constituted dialectic and, precisely to the extent that it is subjected to my otherfreedom (liberti-autre), it indicates that behind this, in the past, there lies a moment of free transparency which, in a word, is the basis even of the other freedom (l' autre liberti). In fact, this moment was real because + +we experienced it as the reciprocal decision to pledge. + +The group reacts to this permanent danger, appearing at the level or organisation, with new practices: it produces itself in the form of an institutionalised group; which means that 'organs', functions and powers are transformed into institutions; that, in the framework of institutions, the community tries to acquire a new type of unity by institutionalising sovereignty, and that the common individual transforms himselfinto an institutional individual. But, since the new internal constitution is intended to combat a re-emergence of seriality by strengthening inertia and even, as we shall see, by exploiting recurrence in order to consolidate pledged passivity, the interference between these two inorganic movements tends rather to produce degraded forms of community. 'Degraded', here, does not, of course, have anything to do with a system of values, even the ethical affirmation that freedom is the basis of values: I merely mean that the group - whose origin and end reside in an effort by the individuals who are gathered together to dissolve seriality in themselves - will, in the course of its stru!!gle, actually reproduce alterity in itself and freeze into the inorganic so as to struggle against it within, so that it gradually gets closer to the 'collective' statute. In other words, our dialectical investigation makes a turning here and goes back towards the practico-inert from which Freedom-Terror removed hself a little earlier: it is beginning to appear that the movement of the investigation may possibl y + +be circular. + +There can be no doubt, in fact, that the new recurrence is perceived by the members of the group in and through the struggle which they wage against it. It is sufficient to recall the rising tide of mistrust within the Convention from September 1793 on, that is to say, from its first meeting. We can certainly see increasingly violent conflicts of interest emerging within this regularly constituted group. And these conflicts, which reflected the real conflicts which divided the country, inevitably split the elected Assembly. But still it is worth noting that the parliamentary system is established for the purpose of resolving conflicts within groups of electors or elected: the majority decides. This is a serial organisation, but this determination and the preservation of unity by action on seriality are nonetheless an organisation. Now, on the whole, past and present circumstances as well as the immediate future practically relegate the system of conciliation by vote to the level of pure pretext and replace it by integration-terror. This presents itself in fact as an exigency for unanimity and a rejection of opponents as traitors: the formal system of voting will be retained (and in certain + +moments it may regain decisive power), but the Convention's real action on itself will occur in the heat of the moment, through violence, + +with the strength of the armed people. + +Besides, there can be no doubt that, if the Girondins ended up by representing the interests of the conservative · bourgeoisie or even, unwittingly, of a section of the aristocracy, the differentiation of the groups (in particular of the Girondins and the Montagnards) was a slow process, involving a complex evolution whose moments have been well described by Lefebvre: in the beginning, questions of federalism, of hostility to Paris, and of social and political views did not arise. Everything was constituted in the course of the struggle and through irreversible episodes. The irremediable split in the Convention was a legacy of the Legislative Assembly: in fact everything - their social origins, their milieu, the professions they were engaged in before the elections of 1792, and their education - tended to give real homogeneity to the deputies of hath Assemhlies. So it would be a mistake to regard the Convention (and still less the Legislative Assembly) as primarily and fundamentally divided by social struggles, even class struggles, rather than as a homogeneous Assembly the overwhelming majority in which was constituted by petty-bourgeois intellectuals, and whose irremediable contradictions were the result of a slow past evolution, which gave each of them - in relation to his group, to his electors, to the nation, and to hostile groups - a pledged untranscendahility. Every day, each of them adopted an inert alterity by repeatedly pledging himself to be other than those Others, those enemies who, + +frozen in inertia, regard him as the Other. + +Let there be no mistake : we are not dismissing the Montagnards and the Girondins together: the Girondins were entirely responsible for the violence of the conflict, first for having thrown the revolution into war, that is to say, for having produced Terror as the sole means of government, and secondly for having been the first to take an inflexible line, which inevitably led them to become representatives of particular interests ; and lastly, the Girondins were bad politicians and the Montagnards good ones : they embodied the movement of a revolution which was being radicalised by the pressure of circumstances; the Others embodied the bourgeoisie which was attempting to put an end to the revolution. It was not a matter either of politics or of day-to-day tactics; and in any historical situation violence is a result of pledged inertia. Nevertheless the Montagnards made themselves, and were made, Into pledged enemies of the Girondins through the development + +of the revolutionary process and through the pledges of rhe Girondins themselves. There can be no doubt that the essential aim of the 'May 31st revolution' (of 1793) was to re-establish homogeneity within the Assembly, by eliminating the twenty-nine most prominent Girondins. The new, purged Assembly would be able to set up its own + +apparatuses of control, supervision, administration, etc. + +Now, this situation of false homogeneity is precisely what concerns us here. For the homogeneity of the renewed Convention was false: in the first place, as has been clearly shown by Georges Lefebvre, the majority of the deputies would never forgive the Montagnards for the humiliadon of 2 June; secondly, there were still many Girondins sitting in the Assembly; and lastly, new circumstances were to create deep divisions among the Montagnards. The difference comes to this, and this is what concerns us: before the first purge, the antagonistic groups in the Convention based their irreconcilable heterogeneity on the irreconcilability of their political actions; whereas after it, the ruling apparatuses gradually produced the unity of the common praxis. But this practical unity was scarcely sufficient to conceal an imperceptible, but irreconcilable heterogeneity which, this time, concerned individual people. This heterogeneity was not based either on individual practice or on organic individuals as factors of numerical multiplicity: it originated in the violence of the past (3 I May, 2 June) in so far as this was connected, as suffered inertia, to the pledged inertia of the representative of the nation, that is to say, in so far as power as an untranscendable and pledged statute transmitted a statute of untranscendability to them (violence against power becomes violated power which has to be re-established in its purity by violence). In fact what we learn from historical experience, especially in recent years, is that though purges are intended to re-establish an internal homogeneity, tlley actually replace a quasi-structured heterogeneity (the function and powers of opposition) by a diffuse heterogeneity. Thus Terror begins after the + +purge. + +Once those who are the same again (they vote the same way and are committed to the realisation of the same policies) have become simultaneously and secretly Others, alterity becomes the secret truth of unity for everyone. Whatever the direct relations between each deputy and the Committee of Public Safety, other relations established themselves - if only through the necessity of living in the same district between the deputies themselves. And these relations - which are normal while homogeneity is guaranteed - appear as other relations + +(relations autres) which determine everyone in his alterity: in so far as he is other than his pure integration, that is to say, than his direct relation with the organising axis, he enjoys the relations of a free, practical individual with his neighbour in so far as this neighbour is other; and the reciprocity which is established between them is defined as a reciprocity of alterity in relation to the developing totalisation. And since these reciprocities are, or may be, mediated (since they establish themselves inside the group in activity), this means that everyone, in so far as he has no direct relation with his neighbours (but only relations of function, or of power, passing through the ruling apparatus and defined by it), comes to be determined in his common activity, and in his ability to carry out his task, and finally, in the depths of his being-in-the-group, by the direct or mediated relations between his neighbours. Hence a contradiction arises for everyone, as a member of the Assembly, between the undertaking of practical totalisation, which eliminates particular individuals in favour of an individualisation of functions, and circular seriality, which, in the form of the developing totalisation, constantly anticipates the same group relapsing into a collective. Unification as an organising praxis continues to elude everyone - in so far as he is a unifying agent - because of the other relations which the Others have with this unifying synthesis (are they not using them to lay a trap for him or for some + +Other? etc.). + +Far from realising its unity through its committees' efforts to unify it, the Convention became an object at precisely the point when totalisation broke against recurrence.71 In fact there was one Convention because, in this practical group, the absence of an ontological statute for common individuals allowed the ontological statute of circular seriality to establish itself, as an indestructible foundation of impotence. There was one Convention in so far as the foundation of its unity was always based on the Other, that is to say, in so far as this + +71. The unspoken antagonism between its two ruling apparatuses - the Committee of Public Safety and the Committee of General Security - was necessarily a mediated, though negative, reciprocity. This relation actually presupposed that each sub-group opposed the other in so far as the deputies as a whole recognised its powers. But each apparatus therefore produced the entire Assembly as other for the other 'organ', and, for the entire Assembly, everyone was both positive and negative, at once the same and other. Thus the other-heing of each of the Committees lay in the reciprocity of the deputies, when this reciprocity was mediated by the other Committee, as an other determination of unity. + +unity fell outside the practical and was, in fact, simply the impossibility, endured by everyone, of either pursuing integration or escaping it. At this level, everyone was inside, to precisely the extent that all the Others were outside : the tension of immanence-transcendence was again degraded and passivised in the collectivised group; the collectiye object is me-in-the-group-without-me. In it, I feature as Other, and become the object of actions and determinations of which I am unaware; I either become the passive victim of projects which are concealed from me or, without being aware of it, I become involved with conspirators or with suspects through an interdependence which they frame without telling me, and perhaps without knowing it themselves; and it may be that within it I become an object of fear too; certainly as a means and + +possibly as a (relative or immediate) end. + +But it is impossible for me even to determine this imposed alterity in the abstract without effecting a synthesis in mediated reciprocity of the social field which passes through the mediation of the organising axes and which, at the same time, proclaims me in my own eyes as suspect: this practical synthesis is in fact a regulatory action. Hence, in the tension of immanence-transcendence, I find, in indissoluble connection, not only my being-outside-myself-in-the-group as an alterity of impotence, but also my impossible integration as a danger of exilesecession. In the purged Convention, the 'collective' manifested from below the impossibility of the group being a subject (contrary to what Durkheim believed) and its degree of reality was directly proportional to this very impossibility. It is on this account that it had its own structures, laws and rigidity; it was on this account that it acted on its members - not as a consciousness, nor as a Gestalt, but as a real object, that is to say, as a structure of exteriority limiting our attempt at interiorisation, as an indirect counter-unity which is merely the negation of subjective unification and its inverted image; and lastly as the mark of the impossible integration. (If this was not even attempted, we would be back with the pure collective of dispersal - prices, the market, etc. ; and if it were completely carried out - which is impos- + +sible - the group could no longer be an object for itself). + +However, in so far as everyone attempts to realise the group as a unified praxis, and in so far as he reveals the other-reality of the community as an unpredictable serial deviation to which his own regulatory action will be subjected in this milieu of alterity, he must strive to liquidate the Other as a factor of dispersive inertia and circular deviations; and as the Other is everyone as Other, fraternity has to be imposed by violence. This means that everyone must risk being radically destroyed in so far as he supports any particular embodiment of the Other. The contradiction is blatant: integration-terror is supposed to eliminate the other; but the Other is indestructible. The Other is simply a particular relation which manifests itself in precisely those circumstances which also engender the attempt to destroy it; besides, everyone is Other in the Other. Thus terror would be a pointless circular course unless it did, in fact, suppress individuals in so far as they are themselves, that is to say, in so far as their free practical undertakings designate them as excluded regulatory third parties, always + +capable of lending themselves to the Other. + +Of the two negations of the group - individual praxis and seriality the first, as we have seen, is accompanied by the realisation of the common undertaking; it is both an ontological negation and a practical realisation. The second is definitive and it was in opposition to it that the group originally constituted itself. Yet it is individual praxis which appears suspect to the apparatuses of terror. But this is because terror itself is suspect in its own eyes: in so far as it actually becomes the function and power of certain sub-groups and common individuals (public prosecutors, juries, judges in the revolutionary tribunal, the Committee of Public Safety, etc.), it is produced not only through deliberations and decisions which themselves create recurrence but also through processes which are realised in the tension of transcendenceimmanence. Through a purge - of whatever sort, whether exclusion or execution - the purger constitutes himself as suspect and as always liable to be purged; he produces himself as such in his own eyes and it is therefore the freedom of the regulatory third party which he everywhere pursues, confusing it with elusive alterity. And this free practice is undoubtedly capable of regrouping the opposition, of constituting a conspiracy, etc. : as such, in the moment of Terror, it appears to the apparatus as intolerable. And if it is at this moment - rather than earlier or later, when the regime is more relaxed - that it seems intolerable, this is because, on the basis of well defined exterior circumstances (invasion, disturbances in the provinces, the revolt in the Vendee, social unrest and the danger of famine), 72 terror established itself as the only means of governing. And, whatever the historical context in which we consider it, it always arises in opposition to seriality, rather than to + +72. I am not putting these factors in any particular order but simply enumer- + +ating them. + +freedom. In fact, both in its origins and in its manifestation, it is freedom liquidating the indefinite flight of the Other, that is to say, impotence, through violence.73 In the Convention, Terror was born of the objective contradiction between the necessity for a common praxis, free and indivisible, and the objective but inconceivable - and, indeed, unformulated - divisions of a governing Assembly which remained chaotic and which was altered by the violence it had suffered. In this fundamental atmosphere free praxis was suspect: seriality mediated by freedom appeared as passive alterity, and practical freedom was + +73. Concerning this event (which, as we know, began on 14 July 1789), I repeat what I have mentioned at various points in this book: there is no Platonic Idea of Terror, but only different Terrors and if the historian wishes to identify characteristics which are common to them, he will have to do it a posteriori, on the basis of careful comparisons. What I am trying to describe here is not the development or the factors of the Terror-process (which does not exist either 'in itself' or 'in the mind'); nor is it some long historical sequence which people have chosen to call Terror (the Terror of 1793, the White Terror, the Red Terror, etc.). The Terror of 1789 to h94 is inseparable from the Revolution itself and has meaning only within a totalising reconstruction effected by historians. All I want to do is to use an abstract example to show the connections between free praxis, the pledge, violence and recurrence inside organised groups. I am not attempting to set out the essential relations, even reduced to the utmost simplicity, which might constitute an essence of Terror: there is no such essence. I only wish to describe certain conditions - the dialectical chain of abstract determinations (infinitely indeterminate except at a particular point) - which is necessarily realised by the being-in-the-group of a common individual when Terror occurs as a historical development in specific circumstances. The plurality of Terrors even during the revolutionary Terror (1789 to 1794) seems to me so obvious that I have chosen for my example a limited and induced terror (the circular Terror 'in a homogeneous group which was being eroded by seriality), whereas the primary phenomenon (Terror as a fundamental relation between the French people and the Assembly as the government) was created in order to combat non-circular, indefinite seriality. In 1793, given that the first invasion had taken place, that several towns had precipitously surrendered to the enemy, and that the enemy occupation of border areas resulted in fraternisations in various places, and given that the idea of a nation was new whereas that of international solidarities between aristocracies was very old, the frontiers did not in any way make Frenchmen into a multiplicity contained in one place. At the frontiers there was the danger of treason as an anticipation of indefinite seriality (with a sudden or imperceptible transition - through treason - from heing-French to heing-German). The refraction of an order - as a synthetic process of organisation - in a case of mortal danger, into indefinite seriality gave rise, hy itself, to the practical necessity (the free necessity) of breaking seriality by violence (like breaking ice) to give a + +synthetic milieu of execution to the synthetic order. + +therefore denounced for generating alterity. All this could be lived as the diffuse reality of the group (integration refused to the newcomer: in the confined milieux of prisons, detention centres, houses of correction, etc., Genet has suffered and defined the permanent experience of terror; fraternity realised itself in only one form: against him) . The experience can also be had if one experiences in oneself the praxis of specialised apparatuses (surveillance, police supervision, threats, arrests, etc.). In any case, everyone is both purger and purged, and Terror is neyer a system based on the will of a minority; it is the reappearance - in specific circumstances - of the fundamental group relation as an interhuman relation; subsequently, differentiation may or may not create a specialised organ whose function is to govern according to terror. In a terror-group, my bond with my brother is terror: the regulatory action by which he unites me to all gives me a respitefor myselfbecause I am constituted in the group and because my exile dissolves; but he thereby determines it as lying at the limit of interiority and thereby shows the infinitesimal gap between the regulatory movement (that is to say, his quasi-sovereignty in the common praxis) and the true sovereignty of the absolute Other (enemy group or individual) whose synthetic activity may gather us together from outside as a herd-object in his practical field. We are united, but we are threatened by him.74 Thus as an arbitrary member of the group, I perceive, in the two forms of my praxis (regulated and regulatory), freedom, the non-being of the future which has to be made, as an indication of group non-being. And my individual terror behaviour consists in consolidating inertia within myself in so far as this reciprocal practice of consolidation is also realised in the other third party through the mediation of all the others. At this level, the pledge appears as a necessary but insufficient basis for common unity; it is the foundation stone on which unity as inert-being- + +eyerywhere has to be based. + +However, this inert unity - at least as everyone can realise it in himself and, through himself, in others - must be very different from serial inertia since it is the struggle of freedom against an internal revival of seriality. This systematic petrification, that is to say, the + +74. These indeterminate possibilities are concretely determined both in trust and in defiance in the totalising situation: but trust - which is immediately connected with defiance against others - is here only a mode of terror. It is a trustmenace and a trust-exigency which controls and controls itself: at the slightes + +divergence, it is replaced by suspicion. + +struggle of inertia against inertia, ought to be described as an inorganic, created, counter-seriality. There would be no point here in describing in detail the well known process by which everyone tries to expel from himself and from others the regulatory moment of immanence-transcendence, in order to be able to identify himself purely with the common producer of regulated action. The fundamental modification consists in transferring the common-being-ofthe-group, regulatory freedom and impossible ontological unity to the praxis of the group as such. Since it is this, and this alone, which creates common unity and since the group requires the ontological statute in proportion as a revival of seriality threatens to dissolve it, everyone's reciprocal work consists in projecting ontological unity into practical unity: praxis becomes the being and the essence of the group; in praxis it will produce its men as inorganic instruments which it requires in order to develop. And freedom resides in the praxis, rather than in each individual action. This new structure of the group is not only the practice of Terror, but also a defensive reaction against Terror. It consists in a double relation of mediated reciprocity: everyone construes himself, through the Other and through all, as an inorganic tool by means of which action is realised. Everyone constitutes action as freedom itself in the form of terror-imperative. This new structure gives a certain amount of vicarious freedom to its tools. But this vicarious freedom is not disturbing; it is the reflection of the common freedom onto a particular inorganic object rather than the practical freedom of an individual agent. It is at this level that the institution is defined; or not to abandon our guiding thread - it is at this level that certain practices which are necessary for the organisation acquire a new + +ontological statute by institutionalising themselves. + +3 Institutionalisation and Inertia + +In the living moment of the group (of fusion in the first stages of organisation), the common individual is not inessential because he is the same in all, that is to say, the ubiquity of the group as multiplicity negated by a praxis; it would be better to say that everyone comes to everyone, through the community, as a bearer of the same essentiality. + +But, at the level of the degraded group, the individual, in his terrorist and terrorised negation of his own freedom, is constituted as inessential in relation to his function. Functions and powers are, of course, nothing but concrete determinations of the common individual. But, in the living group, a temporary balance was established between the common individual as a social product and organic freedom as the adoption of this individual-power and as the free execution of the common task with the common means. Through the undertaking of the pledge and through the concrete determination of the future, through pledged inertia, it actualised the power and sustained it in the milieu of freedom - thereby producing common freedom as constituted freedom - and, through its mediation (between the group and the object) it produced the common, here, as individual. On the other hand, freedom, conceived as a common transcendent subject, denies individual freedom and expels the individual from function; function, positing itself for itself, and producing individuals who will perpetuate + +it, becomes an institution. + +These purely abstract descriptions may give the impression that this is a matter of the idea working upon itself. But the changes we have described are, in fact, a product of real, concomitant transformations, one of which is suff ered as an inorganic force while the other is a real + +act of differentiation. + +(First transformation.) An institution cannot result from a free determination of practice by itself. And if practice readopts the institution as a defence against terror, it does so in so far as its petrification is a metamorphosis which has been induced, and whose origin is elsewhere. And we are familiar with this origin: it is precisely the reemergence of seriality. For the institution has the contradictory characteristic, often remarked on by sociologists, of being both praxis and thing. As praxis, its teleological meaning can become obscured; but this is either because the institution is a mere carcass or because those who are institutionalised have a real comprehension of its aim but cannot or will not communicate it: in fact, whenever we acquire the means to decode it (for example, whenever we examine the institutions of a contemporary industrialised society), we discover its teleological characteristics, that is to say, a frozen dialectic of alienated ends, liberating ends and of the alienation of these new ends. On the other hand, however, the institution, as such, has a considerable force of inertia, not only because it is part of an institutional whole and is incapable of being modified unless all the others are modified too, but + +also, above all, in itself, because it posits itself, in and through its inert-being, as essentiality and defines men as the inessential means of + +its perpetuation. + +But this inessentiality does not come either from the institution to the individual or from the individual to the institution: it is actually practice isolating itself in so far as it is produced in a common milieu defined by new human relationships. These relationships are based quite simply on serial impotence: if ! regard the institution as basically unalterable, this is because my praxis in the institutionalised group determines itself as incapable of changing the institution; and this impotence originates in my relation of circular alterity to the other members of the group. Terror is practised against sub-groups - chiefly against those which might form spontaneously under pressure of circumstances; and even, to a certain extent, against sub-groups which are organised and specialised by a common and reciprocal differentiation of the entire group (or against people who, as we shall see, are constituted by the authorities as the legitimate 'organs' of the entire community). And this, as we have seen, is simply because pledged heterogeneity, when merged with suffered separations, in the irreversibility of temporalisation, produces alterity as a revival of the practicoinert in interiority. When a group is inyaded in this way, everyone lives mistrust as a reciprocity of impotence: I become suspect if! ask another third party to modify some structure, power, or practice, by joining with me and with others: what separates is not in fact the object to be changed so much as the possibility of founding a faction in the group as a negative determination, negated by the developing totalisation. Thus I do not dare make a proposal (take the initiative of the regulatory action) or, if I do make one, my proposition will elicit no response. Besides, I myself know that the other third parties are genuinely others and, with the possible exception of those who are closest to me, it is impossible for me to estimate how my regulatory action will appear to them, that is to say, I do not know with what alterity it will be affected : it will be deformed and diverted, and there is a danger that it will bring about results quite contrary to those I intended; it may damage the common object of the common practice (at least, as I discover it in my experience); or it may be turned against me to destroy me. And this very concrete reason always tends (according to the concrete conditions of this particular terror) to plunge me even deeper into silence. But still this is unimportant since it is only a matter of individual actions. But let us recall that separation, in whatever form, does a lot to raise + +the threshold of communication between third parties; and consequently, it is objectively more difficult - if not impossible - to make contact with them; and those who can be contacted might be unable to reach others. In a degraded group, to sum up, every proposal is 'divisive', and its proposer is suspect - because he offers a glimpse of his freedom - and a divider; and any local regroupment, provided it is determined in interiority by the individuals present rather than by the others, elsewhere, who hold power, is a faction, because the inertia of the Others will make it into a separate group inside the group rather than a sub-group; any concrete proposal from individuals will be lost because - even if some Others are prepared to adopt it - the only possible means of communication with the Others, in so far as they have already been serialised, is the serial unity of the mass media: 75 separation + +definitively eliminates 'orders passed on by word of mouth'. + +This impossibility of changing the practice in a given domain and adapting it to particular circumstances need not be directly perceived by the individual as a thwarted or failed attempt to bring about some particular change. His attitude to any given common activity, with its powers and functions, may well be positive. If I have stressed the impotence of the third party and treated it as the determining factor in the transition to the institution, this is only because this impotence, as a basic reciprocal relation between third parties in relation to a given practice, necessarily results in a modification of the attitude of each and all toward their operation; and this modification has as much to do with adhesion as with refusal. Both attitudes are, in effect, lived in the concrete mode of impotence. It is too bad in do not agree: I shall have to come to terms with it. And if! agree, so much the better : it is a fluke, an accident, crucial for me but indifferent for the practice itself, and might be expressed in these words: since it cannot be changed, it is just as well that I am willing to go along with it. Whether it is an internal practice of organisation, co-ordination, supervision, a struggle waged within the group against scarcity (of men, of money, or of communications), in short, a factor of integration, or whether it is a detail of the common, transcendent action on the object or the enemy, the practice becomes an institution as soon as the group, as a unity which has been eroded by alterity, becomes powerless to change it without completely disrupting itself, that is to say, as soon as everyone comes to be conditioned by the shifting flight of the others. And this + +75. In English in original. [Ed.] + +metamorphosis does not in any way imply that it has become useless. Of course, it may be sustained either on the real basis of conflicts of interest between members of the group or, quite simply, as an integrating part of a practical group practice which gets older without being able to change (because of balances of opposing forces which reduce the ensemble to impotence in the midst of a society in the process of being transformed, etc.). But these different possibilities (which themselves refer from antagonism to alterity) should not be allowed to conceal the fact that the institution, as a detail of common action, can, at the level of the institutional group, retain its usefulness (either for the individuals as a whole - an exogamous system - or for a dominant fraction within the group). Similarly, as a detailed practice, it can and must realise itself through individuals who have been selected or produced by the group; it therefore presupposes powers, tasks, a system of rights and duties, a material localisation and an instrumentality. Thus it is characterised by the same features that enabled us to define organised practice: but, in so far as it is an institution, its real being and its strength come to it from emptiness, from separation, from inertia and from serial alterity; it is therefore the praxis as other. + +We have considered active passivity both as the regulated production of pledged inertia and as a condition for common activity; and, in the practico-inert field, we have also investigated passive activity as a result of alienation. We must now consider the institution in a declining group as the transition from one to the other. There can be numerous intermediaries between active passivity and passive activity, and it is impossible to know the statute of a given institution a priori: this can only be determined by its entire concrete history. The important point is that - at least as long as it still has its finality - it can never be entirely assimilated to the practico-inert: its meaning is still that of an action undertaken in the light of a certain objective (regardless of what counter-finalities may have developed) ; but on the other hand, the presence of alterity in it as suffered separation makes it impossible for it to become identical with the inert (if slight) forms of active passivity which are based simply on the pledged untranscendability of certain possibilities. At this level, the group is still entirely practical, despite the seriality which eats away at it, and the institution (or rather the institutional ensemble as systems of solidified relations) is simply the modality of its praxis. And the institutional character which is concealed by the common action is the strongest bond between the third parties, because its being is based on everyone's impotence, in other + +the community's not-heing-substance (non-etre-substance). + +The being of the institution, as the geometrical locus of intersections of the collective and the common, is the non-being of the group, produced as a bond between its members.76 The unity of the institution is the unity of alterity in so far as it is introduced into the group and used by the group to replace its own absent unity. But its relation to everyone is one of interiority, though it may define itself as praxis in exteriority: in fact, it determines everyone both in inertia and in practical obligation. Indeed, it transcends everyone in so far as it resides in all the Others, and is unpredictable and other in them, and dependent on this unpredictability. On the other hand, as an institutionalised praxis, it remains either a power over everyone (in the name of pledged faith) or, if everyone represents and maintains it, his own free power over the Others. This free power is now being challenged: for everyone, along with his power, will appear to everyone in the contradictory unity of the same and the Other. Thus recognition is challenge, and challenge is recognition. Permanent trade-union officials will appear worthy of trust If they are put to the test (thus the Other relates to the same and, ultimately, to freedom; but if the freedom appears too manifest, defiance will immediately be rekindled : it is necessary to identify a man who is at the service of his function, but the function must always have precedence over the man). But supposing they had deserved and won such trust, they would lose everything and be in danger of possibly serious violence if they were so inept as to oppose some wild-cat strike (or to try to impose some unpopular course of action) ; but by their violent reaction the workers would be acknow� ledging the power that they were challenging: they would react less + +strongly to the protests of a non-unionised worker. + +Thus the new statute of power emerges everywhere, even in the army, the archetypal institutional group. In the context of the organised group, we defined it as the right to do one's duty; but here it must be defined as the duty to do one's best in order to get one's right to do + +76. Here too it is necessary to rebut an idealist interpretation: institutions are generally sustained by the 'forces of order', that is to say, armed sub-groups enforce order by violence. But since not only these sub-groups, but also - as we shall see - sub-groups of authority, are institutions, it is still the case that the institutional system, including the coercion which maintains it, depends on the original reciprocal impotence of every third party in relation to every Other and + +through his relations to all. + +one's duty recognised. Institutional man has to get this recognition by means of two opposed and simultaneous practices: on the one hand, when his institutional power is not directly threatened, his general tactic will be to liquidate the Other in himself so as to liquidate it in the Others (the officer who lives with his men and models his whole life on theirs) ; on the other hand, in the moment of exercising his power, institutional man will immediately constitute himself as the absolute Other, by adopting certain behaviour and dress ; and he will base the firmness of the power exercised and of the decisions made, on his institution-heing (etre-institution), that is to say, on inertia and the total opacity of the alterity which has become the particular institution's presence in him, and, hence, the group's presence as common praxis. At this level, in fact, mystification is very probable: with the institution remaining a practice and [he group not being dissolved, the institution, in its negative being (which is really only the ubiquity of non-being) appears, in appropriate circumstances, as the ontological statute of the community. This means that it refers to the whole of the institutional system as a relational totality of the synthetic determinations of the grouped multiplicity. Through the power-man (t' hommepouyoir) who reveals himself - through familiar rituals and dances - as institution-being, the organised individual believes he can see himself as integrated into the group through the institutional ensemble (and in fact this is what every citizen says and believes), whereas the institution can actually appear only at a particular moment in the involution of the group, and as an exact index of its disintegration. And, if the dance has been well done, if the power-�an has, as he should, referred to the inorganic as the fundamental human reality, the order or decision will themselves appear as inorganic (unshakeable), and at the same time they will be obeyed in the name of pledged loyalty, that is to say, of pledged inertia. The freedom of the power-man, for the individual who acknowledges this power, is a pure mediation between the inertia of the institution and the inertia of the particular order. This is certainly a case of the abstract being transcended towards the concrete, but although this transcendence is acknowledged, it does not posit itself for itself, as in free practical labour: the mediation exhausts itself and disappears, remaining, for example, an inert determination of discourse, in that it is based on an inert, synthetic determination of human multiplicity and is addressed to the double inertia of organised individuals + +(pledged inertia based on serial impotence). + +In this moment, freedom is completely hidden or else appears as the + +inessential and ephemeral slave of necessity. Necessity, on the other hand, is absolute in the sense that its free, practical form (necessity produced by freedom) merges with its form as serial alienation. The imperative and impotence, terror and inertia are based on each other. The institutional moment, in the group, corresponds to what might be called the systematic self-domestication of man by man. The aim is, in effect, to create men who (as common individuals) will define themselves, in their own eyes and amongst themselves, by their fundamental relation (mediated reciprocity) with institutions. More than half of this task is carried out by circular seriality: everyone systematically acting on himself and on everyone else through all, resulting in the creation of the strict correlate of the man-institution, that is to say, the institutionalised man. In so far as the ossification of the ossified praxis which is the institution is due to our own impotence, it constitutes for each and for all a precise index of reification. This does not necessarily mean that we suffer it as a constraint, but rather that it is our own inorganic inertia in the social milieu. But the moment of common degradation in which the institution emerges is precisely that in which everyone aims to expel freedom from himself in order to realise the endangered unity of the declining group as a thing. So at this level of involution (under the pressure of exterior circumstances), the common individual tries to become a thing which is held against other things by the unity of a seal; the model for the institutional group is the forged too!' And everyone is implicated as such in institutionality. But on the other hand this is also because they are its victims even before they are born. The previous generation already defines their institutional future, as their external, mechanical destiny, that is to say, as determinations of untranscendability (or as determinations of their being), even before they are born. 'Obligations' - military, civic, professional, etc. - constitute in advance an untranscendability deep inside everyone who is born into the group; and of course, it is necessary to fulfil these obligations (not 'play these roles' or 'adopt these attitudes' as the 'culturalists' would put it, indiscriminately mixing up material conditions with possibilities defined by the historical ensemble on the basis of these conditions and with institutional obligations). Being born into the group is a pledge (reiterated by rites of passage), and to make such a pledge is to take on the institutional inertia with which the others affect the child, in the form of a free commitment to realising the institution. From this point of view, institutional being is, in everyone, a prefabricated inertia of inorganic + +being, and will be transcended by a practical freedom whose pledged function will be to objectify itself in this same being as an inert determination of the future. The institution will produce its agents (organisers and organised) by giving them institutional determinations in advance, and institutionalised agents will then reciprocally identify themselves, in their relations of directed alterity, with the practical system of institutional relations, in so far as it is necessarily inscribed in a complex of worked objects of inorganic origins . Thus the institution as a stereotyped praxis (though, under the pressure of certain circumstances, its efficacity may reside in being stereotyped) adumbrates the future in its rigidity; and as the inert persistence of a reified organisation within a grouping which might well reorganise itself in any case, it constitutes itself as the elementary and abstract permanence of the social past as heing, even, and above all, if the developing rearrangements reveal the perpetual changes of this past as signification. 77 + +4 Institutionalisation and Sovereignty + +(Second transformation.) The institutional system as an exteriority of inertia necessarily refers to authority as its reinteriorisation; and authority, as a power over all powers and over all third parties through these powers, is itself established by the system as an institutional + +guarantee of institutions. + +The foundation of authority is in fact sovereignty, in so far as, after the stage of the fused group, it is the quasi-sovereignty of the regulatory third party. Thus the leader emerges at the same time as the group itself and produces the group which produces him, except that at this elementary moment of the investigation, the leader might be anyone. In other words, everyone ' s quasi-sovereignty is one of the constitutive bonds of the group. We then pointed out that if certain individuals became regulatory third parties more often or for longer periods of time than others this was on the basis of particular historical circumstances, and, as such, initially of accidental ones. Lastly we pointed out + +77. Which occurs whenever the institution is preserved while the common transformations around it give it another relation to all in the developing totalisa + +(ion, in interiority and without even touching it. + +that, in revolutionary periods, groups which appear and disappear within a day are organised and reorganised around quite specific individuals who may be trusted for long periods. Such 'agitators' are regulatory third parties, but they should not strictly be called leaders : they mimic or express for all the praxis which is implicitly defined everywhere, in the ubiquity of mediated reciprocity. At the level of the pledge and of the organisation, we have observed the emergence of powers. At that point we did not describe authority since powers (as reciprocal quasi-sovereignty) do not directly involve the specific power which is called authority. However, we did observe the emergence of a truly common relation of everyone to each and a11 - which is the diffuse power of life and death over the traitor, or, in other words, + +fraternity-terror as a basic determination of sociality. + +This permanent living structure of coercion is a necessary determination of sovereignty as authority. From the moment in which a regulatory third party (or a sub-group acting as a regulatory third party) becomes a pledged holder of the power of regulation as organised function, and when this third party receives and concentrates the internal violence of the group as a power to impose his regulation, everyone's shifting quasi-sovereignty is immobilised and becomes authority as a specific relation of one individual to all. This relation may appear at the level of organised groups; but, in so far as the group is alive, and therefore constantly being rearranged, the relation itself moves and passes from one to the other, according to the requirements of the situation. Authority does not emerge in its full development except at the level of institutions : institutions, that is to say, a rebirth of seriality and impotence, are necessary for the consecration of Power and for ensuring its de jure permanence; in other words, authority necessarily depends on inertia and seriality, in so far as it is constituted Power; but, on the other hand, its real efficacity must, through its coercive strength, tend to increase the power and number of institutions, as products of recurrence and massification and as the only effective common weapon in the struggle against factors of dispersal. Or, to look at it from the other point of view, the institutional system presents itself, by a permanent mystification, in its inorganic-being as the real unity of the declining group. But if the system is simply revealed in itself, it will unfold as a multiplicity of diverse, non-totalised relations. We have seen in effect that the institutionalisation of functions occurs through the medium of a history, in otherwise disparate places, and that the diversity of circumstances and problems necessarily + +causes a local diversity of temporalisations. There are dislocations, delays, asymmetries: in one place the apparatuses of co-ordination will be directly established in an institutional form, while in another, mediating 'organs' will never reach the stage of institutionality (some disappear, and others survive). This kind of social solidification, therefore, does not present itself as a praxis, or even as a unifying process. Thus authority fulfils a definite function: as the synthetic power of a single individual (possibly, though not necessarily, as an expression of a united sub-group), it gathers up the multiplicity of institutional relations and gives them the synthetic unity of a real praxis. Institutions claim to be the inorganic being-one of the serialised community; the leader claims to be the dissolution and synthetic reunification of this external passivity in the organic unity of the regulatory praxis, that is to say, of the praxis of the group in so far as + +it is reflected to him as the common praxis of a person. + +But this is the essential contradiction of authority: the individual reincarnation of the fused group and of Freedom-Terror- the leader - himself as such enters the institutional multiplicity, since he is a real product of an institution. Thus the leader preserves institutions to precisely the extent that he apparently produces them as an internal exteriorisation of his interiority, and he dissolves their inert-being in his historical praxis. But this historical praxis - as the reciprocity of the sovereign and of common individuals - is itself produced by the inert eternity of institutional relations. This dialectical movement must be examined more closely: through it and on the basis of it, the search for the intelligibility proper to the institutional group will be + +completed. + +Now, the first point to notice is that, contrary to what is so often maintained, sovereignty in itself does not constitute any problem or require any foundation. The illusion that it does is due to the fact that the state of massification is normally regarded as logically and historically basic, and that the reified relationships which occur in societies based on exploitation are treated as the prototype of human relations. From the moment in which ahsence of relationship becomes the fundamental relation, one can ask how the type of synthetic relation known as Power can set itself up as the bond between the separate molecules. And all means of interpretation except two have been foresworn a priori. These two are, that Power emanates from God, and that Power emanates from certain intermittent metamorphoses which transform society into a totalised-totality, and that it + +expresses the constraints of collective representation, etc. Unfortunately, neither God nor the totalised group actually exist. If it were really necessary to find a foundation for sovereignty, we would be + +searching for a long time: for there is no such thing. + +There is none hecause there is no need for one : sovereignty is simply the univocal relation of interiority between the individual as praxis and the objective field which he organises and transcends towards his own end. There is no place for a foundation for the right of praxis by which man reproduces his life by freely rearranging the matter around him: on the contrary, this dialectical transcendence, which shows the becoming-praxis (Ie deyenir-praxis) of need is itself the foundation of all rights. In other words, sovereignty is man himself as action, as unifying labour, in so far as he has a purchase on the world and is able to change it. Man is sovereign. And, in so far as the material field is also a social field, the sovereignty of the individual extends without limit over all individuals : these material organisms have to be unified as his means in the total field of his sovereign action. The only limitation on man's sovereignty over all Others is simple reciprocity, that is to say, the total sovereignty of each and all over him. When this original relation is lived outside any institution, it just reconstitutes every person as an absolute for any other person, that is to say, as the untranscendable means of which everyone is both the means and the end to precisely the extent that every individual is the means to his own end and the end for every means. In this way, sovereignty is both the univocal bond already described and the basic relation of reciprocity + +( co-sovereignty) . + +Sovereignty within the group, therefore, does not have to explain its positive power, but rather the negative and limiting determinations to which it is subjected. In fact, we have seen how it became quasisovereignty in the tension of 'trClnscendence-immanence'. And from our point of view, this limitation is still the foundation of Power: the sovereignty of the leader can only be a quasi-sovereignty, since otherwise he would not be a regulatory third party and the bond of interiority would break. An Assyrian King who had his prisoners of war (members of the other army) executed was exercising total sovereignty over them, but, at the same time, it was impossible for him to treat them as men; his sovereignty could express itself only as a univocal relation of violence with a given multiplicity, invading his practical field from outside, which he had the material means to annihilate. On the other hand, his relation to his own soldiers is one of quasi-sovereignty + +precisely hecause the relation of authority is no 10llger hased on physical strength. Let there be no misunderstanding: discipline could not be more strict, supervision more vigilant, the organs of coercion more numerous, or the 'forces of order' more powerful. But the 'forces of order' present themselves to the mutineers, or rebels, as the same to the same; the soldiers who shoot them are the same as those who are shot and there is no a priori way of assigning a given military subgroup to either of the two categories (marksmen, victims). Alterity makes them into forces of order, and this means that the primary relation of authority is a quasi-sovereignty of interiority, as violence creating its means, with sub-groups which - either through their interests or through the common interests of the group or through the specific connection between their interests and those of the group define their coercive action as a function of its regulatory action. In the same way, the technical and instrumental superiority of the repressive group (in the service of authority) over the group as a whole is not always either obvious or necessary, especially to the army since the forces of order and the rebels have arms which are a priori similar. Of course, the 'forces of order' will always, as long as order reigns, have heavy, common weapons (whether horses, artillery, or planes), but this is precisely because their relation of violence to the rebels is a power over the majority of third parties, lived and acknowledged by the non- + +rebels as a whole as right-duty. + +A 'public force' as the support of authority expresses itself as just violence only in the milieu of 'F reed om-Terror' and through the 'F reedom-Terror' which is in any case going to destroy itself. 'F reedom-Terror' becoming specialised function - this (and, as we shall see, the seriality of impotence) is the relation of interiority for repressive groups. And interiorised withdrawal is precisely the common milieu of the group which, as long as it remains the same, gives repression a regular victory. The defeat of a rebellion is settled in the precise moment where it discovers its own limits in extension: this unity, and no more. It is these limits which pass sentence: and the sentence comes from the group. By remaining entirely what it is - an institutionalised group - regardless of its sympathies and of the individual sympathies of other soldiers for the rebels, within itself it constitutes the group of insurgents as its radical negation. In fact, and precisely to the extent that the 'loyalists' resist any reorganisation of the group as a new totalisation proposed by the rebel group, that is to say, in sa far as they see the group not as producing a new possibility for the future, but as + +negating their own future, purely and simply (that is to say, the rigid future of institutionality), these 'loyalists' constitute the group as a pure internal weakening of unity, as a negative, corrosive power, as a threat of seriality and an inert force of negation. So, as the 'majority', they are the party which is linked to the public forces of destruction: they legitimate this annihilation by means of their fidelity and, furthermore, they make it materially possible either by abstaining or lending their support. 78 Thus the bond between Power and the regulated third parties, in spite of and above all because of the failure to challenge the sovereignty of the leader, is based chiefly on the transformation of total sovereignty into quasi-sovereignty. This simply means that the leader, as a unifying, reshaping and repressive function, is inside the group itself. At the moment in which the group constitutes itself, under the pressure of circumstances, from the first stirrings of the crowd which liquidates its own seriality? to the last avatars of a group in the final stages of petrification, everyone makes himself quasi-sovereign and this determination in interiority of the regulatory third party, as a transition from the Other to the Same, is a fundamental structure of + +praxis as community. ,... . + +No, it is not sovereignty which has to be explaim:d, or even the initial limitation which gives it its efficacity. It is the second constitutive negation: why, on what basis, in what external and internal circumstances, to what end, etc. , is the circular reciprocity of quasi-sovereignties suddenly halted, and why is the common individual (or the subgroup), which is the material place at which the blockage occurs, + +defined as sovereign? + +The problem is often obscured by ascribing the sovereign's enormous actual power to him from the outset and by seeing it as a manifestation of some positive force (as if he were the incarnation or reflection of 'collective sovereignty'). To do this is to forget that quasi-sovereignty, like the mediated reciprocity of each to all, is characterised by its ubiquity rather than by some synthetic virtue + +78. This does not in any way mean that the common individuals of the group support the policies of the leaders, the conduct of the war, etc. But it does at least mean that they regard the dissolution of institutional unity as a much more serious danger than any which might be incurred through the incompetence of the leaders. And in so far as this appraisal expresses the aberrant synthesis of the seriality of impotence and practical unity, it necessarily characterises the individuals who are institutionalised: once again, the meanings which are produced are + +basically structured by the relational statute of the group. + +which combines all the 'powers' of the group. In fact, it is the same everywhere because it is always, for everyone, the possibility of defining a here and defining oneself as a regulatory third party. Quasisovereignty is not, and never can be, a totalised power of the · group over its members, nor can it be the successive power of each over all. Power enters with the first limitation, that is to say, with the pledge. Quasi-sovereignty was originally the following simple contradiction: in every third party the synthetic power of reorganising the practical field manifests itself as his membership of the rearranged group, and, therefore, as the same in everyone, now; thus the common praxis is realised everywhere at the same time and it is both means and end. Thus every quasi-sovereign, as a regulatory third party, transcends the grouped ensemble by a head, without ceasing to be integrated into it, and, as a regulated third party, he allows himself to be transcended by + +a himself who has emerged in some arbitrary here. + +The sovereign, by contrast, can be defined within the group by a statute peculiar to him, the basic reality of which is negation: no one can claim that he is outside the group, or that he has ceased to be a third party. Sovereignty-institution designates the common individual who exercises it as a non-transcendable third party, at least in the performance of his functions. Ifhe is not transcendable, and ifhe still does not leave the group, his regulatory action (either actually performed or defined as an organised operation) is always determined as common praxis laying down its own laws before all. But untranscendability produces the untranscendable third party as the member of the group through whom this regulation always has to be carried out. Thus the existence of a sovereign is based negatively on the impossiblity (suffered or agreed or both: this has still to be determined) of every third party becoming directly regulatory again. This does not mean that every practical initiative, every attempt at reorganisation, every invention and discovery has to originate in the sovereign: it means that they must pass through him, be reinteriorised by him, and, through him, appear to the group as a new practical orientation. The sovereign can make use of the means of communication (whether roads or canals or the 'mass media') because he has sole responsibility for communication. We have seen how the group, in the process of organising itself, produces apparatuses of control and mediation. But whatever their importance, these apparatuses are always specialised : the function of the sovereign is to ensure the mediation of all the mediations and to constitute himself as such as a permanent mediation between the + +common individuals. But this mediation is aimed at more than the preservation of the unity of the group: it attempts to preserve it in the + +light of practical realisation of the common aim. + +Now, the fixity of the mediation arises as both a result and a condition of certain expropriations which are suffered and accepted by common individuals: in fact it constitutes the negation of direct reciprocity and the alienation of indirect reciprocity.79 The negation of direct reciprocity is centralisation, as the necessity that two given sub-groups whose practices are complementary should go through 'the departments' or 'the Council' in order to adapt their actions reciprocally. The alienation of indirect reciprocity is that mediation is itself a modifying action on this reciprocity. Mediated reciprocity, which is the constitutive structure of the group, is direct and free as long as the mediati,on is done through all, that is to say, quite simply, within common praxis. It becomes an uncertain, other object when the common praxis, embodied in a single, untranscendable mediator, works as an individual activity on the reciprocal relation: in fact, communication may always be broken (by a break of any origin) or altered; reciprocity may return to everyone in the form of a task laid down by the central power on the basis of reciprocal relations, that is to say, in so far as they are revised and corrected by a third party. Thus the relation of the same to the same returns to everyone as Other. + +And this alterity is expressed in its new structure: it is either an order or a defence. The structure of 'Fraternity-Terror' and pledged inertia will no doubt already have determined a structure of alterity in each practical freedom, and this will have produced the imperative and power as structuring, structured relations of the statutory group and the organised group. But these free imperatives defined themselves through initiatives which were both assumed and controlled, and which were a direct function of the task to be done. But the stratified action of the sub-groups on the group as a quasi-object will already be marked by a certain passivity, through the multiplicity of rearrangements: it is this that transformed what was originally a pure common praxis into a praxis-process. But, in any case, the new mediation emphasises this movement. Thus the sovereign, being untranscendable, is other than everyone. It is no longer possible to say that all members + +79. I am referring to the relations between representatives of powers as such rather than to free relations of reciprocity (although, in special conditions, the + +latter may be seriously altered thereby). + +are the same or that every elsewhere is Itere. In effect, there is a common individual who, as a member of the group, is other than all because he cannot become a regulated third party. And this third party will of course be an institution, in that, like all the Others, he will be the inert, imperative, unity of all the institutionalised members. But, on the other hand, the paradox of this institution is that it has to realise itself through a free, organising praxis to which all are subjected by an Other. The praxis of the group becomes other in so far as it is manifested in a particular temporalisation and as an individual action: or rather, it becomes other in so far as the common project presents itself as + +individual will. + +And so, for every third party, the imperative which defines his power returns to him as the will of an Other, which he obeys because of his pledge. It is a new structure (the individualisation in a sovereign Other of the common imperative) which constitutes the command as such. In obeying the Other as Other in the name of the common praxis, everyone becomes other in so far as he is the same. This is the basic structure of obedience: it is realised in the milieu of 'F raternity-Terror' and against a background of violence: in everyone, inert pledged being is an untranscendable negation of the possibility of not carrying out the imposed action; refusal would effectively mean the dissolution of the group (both as an organised group and as a pledged group); but, in so far as action is, in this case, an interiorisation of an other will (volante autre), it introduces an induced passivity into it, and comes to be occasioned by an untranscendable sovereignty with no reciprocity; and the refusal to dissolve the group in oneself, that is to say, the legitimation of common violence (as repressive terror) by readopting the pledge becomes no more than submitting to the individual decisions of the untranscendable third party and to his quasi-sovereignty as + +violence without reciprocity. + +It is at this level that freedom in itself (and not only in its objectification) becomes alienated and hidden from its own eyes. Task and function, as imperatives, referred only to all and to the urgency of the job to be done: pledged inertia referred to everyone's free praxis (as other, admittedly, but formally, and not as the concrete freedom of one Other). Thus the imperative as such arose in the milieu of dialectical freedom and, in the completion of the task, revealed free organic action (as a mediation between the common individual and the object of the common praxis). Obedience to orders cuts out these references. But in spite of all the masks, organic praxis is still the only modality of + +action; the most disciplined soldier, when he shoots on command, has to take aim, estimate distances, pull the trigger at the right time (that is to say, as soon as possible after the order, making allowance for special circumstances). But the sovereignty of the untranscendable third party expresses itself as an order through the will of an Other; and the pledged (and suffered) impossibility of not adopting the order becomes an interiorisation of the other will as the real unity of the practical temporalisation. In the moment of organic mediation, the free project of the transcended third party arises, with its own comprehension as an other project (projet autre) (or project of an Other) referring every ensemble not only to the community, to reciprocal powers, and to the remade pledge but also to a free praxis which is not mine, and which imposes itself on mine as regulatory, that is to say - because of its own untranscendability - as an individualisation of the common aim. In developing the Other's project in terror (that is to say, both under the constraint of the sovereign's coercive forces and in the climate of fraternity-violence, the two being ultimately identical), I deny myself + +in my organic individuality, so that + +. + +,the Other can accomplish his + +project in me. + +At this level, a double transformation takes place. (1) At the level of the common individual, my powers are conferred on me by allbut only through the mediation of the 0 ther; there is still reciprocal organisation, but it takes the form of a univocal rearrangement, without reciprocity; and common praxis manifests itself in the form of an untranscendable praxis of an individual in freedom. (2) At the level of my own individual activity, my freedom is stolen from me and I become the actualisation of the Other's freedom. This does not mean that I feel as though I were being subjected to some external or internal constraint; or that the Other manipulates me from a distance like a hypnotist; the specific structure is that my freedom is freely lost and divests itself of its translucidity so as to actualise, here, in my muscles, in my body at work, the Other's freedom in so far as it is elsewhere, in the Other, and in so far as it is lived, here, by me, as an alienating signification, as a rigid absence and as the absolute priority, everywhere, of interiorised alterity - everywhere, that is, except, in the untranscendable Other, who is other than all precisely in being alone in being able to be him- + +self. 80 + +80. Whatever the historical situation, there is a serious error which must be avoided. It would be absurd to define an order as an exigency in exteriority (the + +master commanding the slave) based on force, and then to go on to derive institutional powers of authority from these initial relations. To do so would be completely to mistake the true structure of an order and of obedience, that complex: dialectic in interiority, of the same and the other, of constraint and legitimacy. When a slave obeys his masters' orders, this does not in any way mean that he regards them as legitimate. Neither, of course, does it mean, a priori, that he denies their legitimacy: the relation is in fact quite indeterminate. A given slave may be reconciled to his fate; he may be privileged in relation to the other slaves, born in the domus, etc., and, especially if he has personal relations with the master, he may regard the master's authority as legitimate, that is to say, he may almost unconsciously betray his fellow-slaves. But another, who is deeply rebellious, and conscious of the injustice of his condition, may obey either cynically and out of mere prudence or, possibly, in the expectation of a revolt which he will join. If one sets out from this absolute indeterminacy it will be impossible to comprehend why obedience, as a simple fact (a surrender to constraint) may sometimes appear as pledged faith, as a permanent legitimation of authority, etc. The rational order is in fact quite strict: authority, as a complex relation between an untranscendable third party and the common individuals who legitimate his powers by obeying him - this is what is given in the first instance. And the violent integration of new individuals into the group (for example, the slaves in familial exploitation) takes place in the name of this legitimate authority. Obviously the mystification is complete. But it results precisely from the juridical structure of the community: newcomers are introduced into it with a certain statute, certain functions, etc., and the sovereign (for example, the pater familias) demands their obedience in the name of a pledge which they never made but which they accept in spite of themselves, for the other members of the group, because it is the synthetic basis of all common relations and because they are in fact (through either capture or birth) integrated into the community. On the other hand, when the historical development of the oppressed class is just beginning, while it is paralysed by impotence and seriality, while individual antagonisms make any common action impossible, and, above all, when individuals are placed (by birth, for example) into a juridical group which exercises 'fraternity-terror' on itself through the mediation of a leader, obedience legitimates the sovereignty of the exploiters in the eyes of the exploited. As the case of the Lyon silk-weavers proves, revolt is not born of systematic questioning of the system but rather, amongst men who still respect and acknowledge the employers' right to own machines and to govern, of the sheer impossibility of survival. It is revolt - as permanent praxis, initially blind, imposed by need, and by the danger of death which gradually creates the illegitimacy of public powers and in the end reduces class relations to a new and basic truth: that of power relations. Except in a case of suddenly instituted tyranny, of military occupation, etc., it is not and never can be the illegitimacy of the powers which occasions revolt. In other words, cynical obedience to orders which are regarded as illegitimate is a historical moment in the evolution of authority: that in which conflicts which are initially spasmodic and disordered, in the process of becoming more ordered, create an objective situation in which it is possible to reduce the relations of exploiters to exploited + +or of oppressors to oppressed to mere power relations. + +In the light of these considerations, it is possible to establish the original finality of sovereignty as an institution as well as the formal conditions of its possibility. The problem of its historical emergence in + +each case is not our concern. + +We have seen how the group's common praxis can, through the institutional system, be conceived as its transcendent freedom and at the same time as its fundamental being. But we have also learnt that the institution is a practical relation (to the common object), based on impotence and separation, as the reified relationships between members of the group. Furthermore, we have observed that as soon as one tries to explain an institutional system, it tends to appear as an ensemble of relations in exteriority. Lastly, praxis as common freedom is no more than an index of the alienation of our individual freedom. However, the group remains effective and practical : the army may make use of the institutional relations which characterise it in order to define a local tactic or a strategy. Wherever common praxis retains its vitality and reality, the constituent dialectic - that is to say, organised practices sustains the constituted dialectic, even beneath the thick stratifications + +of serial and institutionalised ensembles. + +Now, the contradiction which is proper to institutional systems (and which derives both from the fact that they are prod,UFed as the only practical instruments in the circumstances and from the fact they are produced through the resurrection of serialities) is that, in themselves, they represent both the irresistible force of transcendent praxis and the permanent possibility that it will break up into serial relations of seriality. This danger is increased by the fact that a group's tendency to define itself in terms of its institutions is proportional to the importance of the serialities which penetrate it. In practice, this means that the group is constantly threatened by the danger that an increase in its level of seriality may lead each institution to function for itself, as a pure practico-inert exis, and that their practical unity may explode into a mere exterior dispersal. In this light, it is possible to discern the true function of sovereignty: it is the institutional reinteriorisation of the exteriority of institutions or, in so far as the latter are reifying mediations between passivised men, it is the institution of one man as a mediation between institutions. And this institution has no need for any group consensus; on the contrary, it is based on the impotence of its members. Thus the sovereign is a reflexive synthesis of dead-practices which were tending to be separated in a centifugal movement. Through his personal unity, he unifies them into a totalising project which + +individualises them; and this no longer has anything to do with relations tending towards the universal (like the taxation system, the military law, etc.), but instead with an individual historical ensemble of which every institution forms a part as an instrument of all, and whose totalisation is its practical employment for attaining the common objective. Of course, the sovereign and his praxis are products of the institutional system: in this sense, they participate in the exteriority of all the relations, in their analytical universality and in their inertia: not only is there an ensemble of laws specifying the mode of recruitment and professional training for the untranscendable third party, but also since in himself he is no more than the institutional system lived in a reflexive synthesis of interiority - the limited field of his practical possibilities is simply a determination of his future by the unifying + +ensemble of institutional instruments. + +But we have already seen that these institutions are themselves the practical relations between the institutionalised third parties and that they define them in reciprocity in the endlessly repeated movement of a single process-practice. At this level military service is an objective process which can be studied in exteriority: each year, at a given time, X young men of such and such an age are called up for X months or X years. It is also a finality in the process of being passivised: the national group must be able to defend itself by arms. Lastly and, from our point of view, most important, it is a determination in inertia of the reciprocity between the people in the group (conscripts, those refused admission, or called up, or recalled, or granted deferment, or released, etc.), and this reciprocity is naturally practical because it creates diversities both of passive functions (postings, technical abilities) and + +of interest. + +Now, the institutional production of the sovereign represents the practical reinteriorisation of these determinations of exteriority. First, the passivised end of the military institution becomes a common objective and means of achieving some specific exterior end. The problem is really to keep the institution inside the framework of a concrete policy and as an indispensable means of maintaining it; if he is not prevented from doing so by his statute, the sovereign must be able (directly or indirectly) to modify the institution (increase the length of service, for example) in accordance with political needs, or to give an appearance of practical reorganisation to processes which are conditioned by external changes (the development of industry and of weapons, the reorganisation of the army around new weapons). But + +above all, the revival of free praxis, as un transcend able interiori�ation, has the effect of referring this unified activity to the institutionalised third parties as the truth of their institutional being. Without the sovereign, it is impossible to dissolve their passivity: military service, in fact, becomes no more than a process. But free sovereign praxis presents itself as the meaning and the embodiment in freedom of the inert-being of the third parties. The institutional group, constituted reason, the dialectic imitated and already distorted by seriality, appears in the practical unity of the sovereign as constituent reason. Separation at the base remains necessarily what it is, but it transcends itself (elle se transcende) through everyone and returns to the apex, as a consequence of sovereign unity; impotence, as a relation of exteriority at the base, is conceived by everyone at the apex as a systematic and ordered deployment of the original synthesis. This is because, as we have seen, the institutional group alienates the practical freedoms of its members to the free praxis of the community. But this praxis exists only as the abstract, negative object of an empty intention. The institution of the untranscendable regulator has the effect of reinteriorising this common freedom and of giving it an ambivalent statute of both individuality + +and generality. . + +In so far as the sovereign is one person in pursuit; of the common objective and realising quite specific activities, this untranscendable third party refers this common action to the institutionalised third parties - who perform it without recognising it in themselves - in the strict form of an indiyidual activity. Such is the first relation between the third party and the sovereign: in one way, it is a relation between two individuals (the first, inert and impotent, finds individual action in the second and finds his own justification in him, in the Other). On the other hand, the sovereign is signified by sovereignty-institution as a general and indeterminate individual who simply has to respond to certain conditions (relating to his mode of recruitment). And his power, born of the institution itself, as a common product of the group as serial impotence, is in itself common; in other words, the sovereign is, so to speak, a common individual through himself, like any third party. From this double point of view, he tends in exteriority to flee historical, individual determinations and his authority will always appear to be the temporalisation of the eternal ('The king is dead, long live the king'). Lastly, as he is the product and temporary embodiment of an institution, his institutional-being is inorganic inertia - that is to say, the impotence of the Others. Thus he can reflect to each and to all the + +common, institutionalised individual as any arbitrary member of the group: his common reality is institutional-being (suffered impotence, pledged inertia), as producing its own power in inertia and freedom; and from this point of view, his actions always have a structure of generality: they apply to everyone, as an individual defined by his function, because they emanate from an individual who is himself defined by his function. The group rediscovers itself through everyone in the universalising power of their individual actions. Thus the sovereign-individual and the sovereign-institution are both present in + +every decision of sovereignty. + +But the institution of authority cannot prevent the dispersal of institutions as such: in itself, it is strictly homogeneous with all the others. In fact, only the realisation of the universal through an individual, historical action can reinteriorise the centrifugal exteriority of inertia. Every action practically reinteriorises the institutional system by em; ploying it in its entirety for a synthetic complex of historical operations; every individual practice realises itself as a temporalisation. This merely means that the group cannot perceive itself as praxis in the sovereign, except in that highly suspect moment of the undertaking, in which free praxis acts as a mediation between the common individual and the object. Only the sovereign can and must be free; he alone has to produce his actions as moments of a free dialectical development. There is only one freedom for all the members of the group: that of the sovereign. And this ambiguous freedom is both the common freedom (in its institutional origins) and his individual freedom in the service of the community. But it is an organisational freedom: it rearranges the group by issuing orders; and these orders, as we have seen, have the effect of detaching everyone's free praxis - buried beneath institutionality - and at the same time of alienating it, by realising themselves as other through it. Now, at the level of this alienation, the presence of the Other is produced as a substitute for the ubiquity of the same: the sovereign is present in everyone as Other in the moment when he is obeyed. And everyone thereby distances himself slightly from the statute of alterity in relation to the Others, because he hecomes the same as a bearer of the universal Other and as mediated by him in his + +relations with everyone. + +But the ambiguity of the obedient third party, in his relation to the Other will which he actualises, indicates sufficiently the function and, as it were, the failure of sovereignty as the practical reunification of an institutionalised group. The question whether the members of the + +group will be reunited in a common praxis rediscovered through particular orders and sovereign operations or whether they find their unity as organic individuality in the person of their sovereign, and then accept his own wishes as a common aim, cannot be settled a priori. Here again we encounter the absolute limits of the constituted dialectic: if the group seeks its common-being in the institution of sovereignty, its being wi1l be dissipated in abstract exteriority; if it wishes to grasp its own ontological unity (which, as we have seen, does not exist) in the concrete, it will run up against an organic and untranscendable individuality; and this untranscendable individuality presents itself as a transcendence (depassement) of every multiplicity of individuals + +(because it really emerges as the group, inside the group). + +Emhodiment, as a fact of sovereignty, the production of the group by the group in the form of this particular person, with these individual characteristics, these ailments, this irreducible physiognomy, and of this particular age, is the manifestation of a constitutional impossibility which we observed long ago: it is impossible for a multiplicity, even if it is interiorised in each of its members and negated, to produce itself for itself, in itself, under any ontological statute other than those of dispersal through inertia and organic individuality. The latter form of being, maintained by the institution as a common re�lity but utterly inadequate to the group, presents itself to every member of the group not only as generality (institutionality), but also as a practical individuality, homogeneous with every separate individuality (though superior in power, dignity, etc.), and as a condensation of the common by means of an immense pressure which is liable to transform it into idiosyncracy. The future leader, son of the present one, has just been born: the third parties worship the group which they and their sons will compose in the future, in the form of a child. In fact, when the mode of recruitment is defined as the inheritance of functions, the group is reborn, materialised, concretised, and produced as the eldest son by the leader; it is reborn by the flesh, recreated through the virility of one individual, and, within the reflexive structure, his inert-being comes back to him as transcended, and transformed into a living, physical unity. At the same time, he is the father, as an organic praxis with a common structure. The formal untranscendability of biological integration is concretely realised inside institutional groups by the + +untranscendability of the third party. + +Thus, in a group which is eroded by serialities, the sovereign (in his quasi-sovereignty) emerges initially as an organ of integration. He is + +untranscendable, and his quasi-sovereignty places him above recurrence; living and one, he reveals common unity to the half-dead group as a symmetrical synthesis of the human body. He is a universal mediation, and he destroys reciprocity wherever it exists, and relations between transcended third parties cannot establish themselves except through his mediation. But in fact he emerges in the moment where these relations are on the decline. His instituted presence undoubtedly contributes to their decline: at least, he re-establishes them as his own products (in other words, he creates a concrete, practical reciprocity between given sub-groups or individuals, sovereignly and by order). This relation solidifies in so far as its reason lies outside itself in the praxis of the Other, and in so far as this is its only reason for preserving itself. But the institutional individual mistrusts the free relations which reveal the threat of everyone's freedom everywhere as a dissolution of the institutional monolith: he sees integration as a petrification by which alterity will be merged into an inertia of homogeneity (which he takes to be the rediscovered Being of the group). At times of mistrust, the untranscendable third party in the mediated relation is a surety for every third party for the other; and everyone appears to the other as a common project in so far as its details are defined by an individual will. And when the sovereign organises new sub-groups - either directly or through official mediation - he is the body of the constituted body, his decree is the practical, imperative milieu in which every member of the sub-groups was reborn, from a point of view which is defined elsewhere, by the Other, and with powers which he derives from the group in so far as they are defined by the wishes of a particular individual. These reciprocities (and limits of competence, etc.), as others, are for everyone the concrete, or life itself, in so far as their still synthetic character and their alterity represent in and for everyone a protection against seriality (the victory of the inorganic over the practical organism), by the total and reciprocal alienation of all practical organisms to a single one. The last word is no longer dust (dust thou art and unto dust thou shalt return), but the living totality. And, in serial isolation itself, obedience to or reverence for the sovereign saves everyone from his sclerosis of inertia: unable to sustain relations with all or to realise the inessentiality of his person and the essentiality of the common being, everyone emerges - in respect, fear, unconditional fidelity, and sometimes in worship - as an inessential embodiment of the whole, that is to say, of the sovereign. Here the relation is inverted : the sovereign once embodied an impossible ontological unity as the + +organic, individual unity of all in one; and conversely, everyone can relate concretely to the all-sovereign of whom he becomes both a constituted part and an inessential embodiment - and these amount to the same thing though their logical orientations may be different. The alienation of an individual to the individual-totality represents a further decline of the group as common praxis; but, at the same time, it revives the structural bond in a bastardised form. This bond defined itself, in practical unity and in it alone, as a synthetic relation of the part to the totalisation; and it seems to reproduce itself here as an ontological relation between an element in the process of massification + +and the totality which reaffirms itself as already created. + +But the practical perception of inessentiality comes to people when quasi-sovereignty, as untranscendability, constitutes them from outside as quasi-objects - not theoretically or through speeches or ceremonies (though there may well be some of these), but practically, through the perpetual rearrangements which the apparatuses of sovereignty make by order and which are carried out at all levels by the manipulation of each and all. Such a rearrangement should, in principle, advance the integration of the group in accordan�e with imposed transcendent objectives. It realises itself as a means within the closed world which is determined by the pencil of rays which unite the sovereign and the object (the exterior object which has to be produced, destroyed, etc.). Thus he encounters common praxis in both manipulation and command, but in the form of individualised will. But this does not matter: this will radiates from a single source, it is transmitted by specific apparatuses, and it determines a field of pure will in which every quasiobject recognises itself in its quasi-objectiyity as a product, a point of application and transmitter of this other will. The important point for him is that this will should be one, that its practical development should simply be a temporalisation of the organic unity of the sovereign and, most important of all, that its immediate objective should be to impose (by his command, by constraint, and if need be by terror) biological unity at every level of dispersal, in opposition to the multiplicity of + +alterity and as the ontological statute of the totality. + +The sovereign is produced by terror,81 and he has to become the + +8 I. It may be said that power is often far from bringing about a reign of terror. This is true and we shall see the reason for it. But what we are studying here is not sovereignty as it occurs in a historical society; we are considering it as an apparatus which constitutes itself inside groups which are institutionalising themselves. + +agent responsible for it: everyone abandons mistrust in favour of the untranscendable third party, on the understanding that he will express everyone's mistrust of everyone. In fact, there is still recurrence, and the shifting mistrust grows deeper because it has become power (the duty to betray one's neighbour to the apparatuses of sovereignty, the soverign power to liquidate anyone in particular); and, most important of all, serial circularity as a unity of flight becomes the object of a permanent, sovereign operation aimed at destroying it. The apparent progress of reflexivity here is due to the fact that the untranscendable third party, from his eleyated position, believes that he has a synthetic view of the common field whereas, in fact, the means of transmission necessarily serialise his information (he thinks he can see but really sees nothing, apart from other, ready-solidified views, provided by others and originating at the common level). The politics of integration corresponds to these synthetic views: through his apparatuses, the sovereign tries to constitute the group not only as a practical object, but also as a living object. For him, as a product of mistrust and separation, who regards all plurality and alterity as suspect, and therefore as having to be liquidated immediately, the only non-suspect unity is his own practical unity and the ontological structures which develop in it: in short, the unity of the organism - his right hand trusts his left and + +no other. + +Through an intelligible inversion of the contradiction, this power, which is institutionally defined as a permanent reinteriorisation of the group in exteriorisation, already represents, both in itself and ontologically, the impossibility of common-being; but in the name of its practical function, integration, it makes an authoritarian attempt (using violence if necessary) to realise the organic-heing which actually indicates the impossibility that the common praxis should be based on a common-being, as the common-being of the group. In the practices of authority, the impossibility of giving oneself an ontological statute becomes, within the group, a violent and vain reduction of third parties by the regulatory third party to an other ontological statute, by definition unrealisable. This at least is what the sovereign 'believes' he is doing, and what he is 'believed to do'. But here we confront once again the contradiction between the two ontological statutes: the mixing and manipulation of third parties with the object of constituting organic unities, actually produce inorganic quasi-objects whose inertia receives sovereign orders just as the inertia of wax receives the seal. And the conduct of every third party, as a molecule of the quasi-object, moves + +from enthusiastic realisation of an other will to passive, resigned acceptance of this will. Thus the sovereign's praxis on the group, being both transcendent and immanent, is expressed, successively, or even, sometimes, simultaneously, in two kinds of determination of discourse. The goal may be expressed in terms of mechanical unity: the group is a machine which the sovereign sets in motion (perinde ac cadaver). Or the group may define itself as an extension of the sovereign, that is to say, as the arms, legs and eyes which he produces in order to realise the common objective. But, in fact, the second formulation relates to sovereignty-mystification, whereas the first necessarily reveals the function of the sovereign as dispossession, alienation and massification. The false unity of common quasi-objects (instrumentality) can in fact arise only on the basis of an accelerated process of passivisation; so that when constraint is relaxed, individuals revert to a molecular dispersal which separates them even more than their + +previous alterity. + +Could it be said that the sovereign is the group's chosen means of maintaining its unity in specific circu�stances? The answer is both yes and no. The emergence of a sovereign is in fact the J:"esult of a process. In circular recurrence, the slightest short circuit will create sovereignty: and such short circuits occur, in given conditions, as reinforcements of the differential by recurrence. In universal impotence; this recurrence will run up against a sub-group or individual with differential characteristics which make reciprocity less obvious, and which are produced as univocal bonds of interiority. In fact, regardless of what these characteristics are, they cannot extract a future sovereign from the reciprocal relation until the group is eroded by alterity. On the other hand, in a group which is in the process of being institutionalised, impotence, as a shifting separation of peers, makes the actual power of certain individuals appear as untranscendability - not only because serial paralysis prevents everyone from acquiring these characteristics for themselves, but also, and most importantly, because - whatever the characteristics may be - the group (still effective in its transcendent objective, though affected with inertia in its internal relations) does not in fact have any common power with which to oppose the strength of a particular individual. This is the process : the possible sovereigns are installed and there is nothing for the third parties either to accept or to support, since they are incapable of refusing anything. When the sovereign takes power, he establishes himself as the free, directed transcendence of common passivity: and this will mean the re-emer- + +group. + +De facto power - in so far as it is consolidated by recurrence - is prior to de jure power. But in order that untranscendability should move from fact to right, power must become institutionalised. Here, through institutions, a kind of passive finality re-emerges : the need which everyone feels either to allow the institutional system to lose itself in exteriority, without surety or internal unity, or to reinteriorise it as an instrumental system employed in a unique, individual temporalisation. This is the exigency of institutional practices as practiceprocesses maintained in their being by everyone's impotence and freedom. This means, then, that the movement of institutionalisation involves the institutionalisation of the practical individual as such as its only chance of completion; or, in other words, the institutionalisation of the freedom of a single individual as an institution. With the emergence of free praxis, in fact, the whole movement of institutionality turns in on itself and reverts to being a practical field and an instrument. Thus authority, as the internal unity of institutions, is required by their very being (by the contradiction between their practical efficacity and the inertia of their dispersal). The expulsion of individual freedom by inertia would become the occasion for a relapse into the practico-inert, unless common, transcendent freedom were embodied in the free praxis of an institutionalised organism; through the institution everyone sacrifices his freedom for the sake of inert efficiency, but he gets it back at the apex in the double, undifferentiated form of common and individual freedom; the order reincarnates it in + +him as the freedom of an Other actualising itself through him. + +The purpose of these last remarks is to show that the sovereignty of the untranscendable third party arises, in groups which are in the process of being institutionalised, when the empty, inert exigency of an institutional system in search of its unity coincides with an interruption of recurrence by some material, accidental superiority. There is an integration of de facto power with the generality of power and, therefore of a process of impotence which constitutes a given man or ensemble from outside as the strongest, or the richest, of the Others (or as happened in the early stages of feudal authority - as the-man-witha-horse) with a passive finality born in the institutional system of the still practical character of the institutionalised men. De facto power gives a practical content to the institution: for the institution of sovereignty does not designate the sovereign as the passive unity of + +the system, but as the unifying force which condenses, integrates, and changes it by making use of it. The institution, on the other hand, in so far as it preserves the exigencies of Terror and of violence, demands force and legitimates it. In the other functions, the power of each specialised individual may involve the right to call on force for support, though force itself is not the content of their power. On the contrary, the reunification of the institutional skeleton requires that the work done by the ins titutions (and if necessary against them) should be directly produced by sovereign force; unifying force is the immediate content of sovereign power. In this way, force is both the right and the duty of authority: it is the concentration in a single individual of Terror as the struggle against seriality. But this concentration would be no more than an idea or a material exigency of the system unless the regulatory third party already had the necessary strength. In short sovereignty does not create sovereign strength, but rather makes the sovereign's pre-existing strength sovereign.82 However, this positive strength is tiny compared with the real strength which the group would have if it were to dissolve its emergiqg seriality. Thus the relation of untranscendability is originally that of a relatively small strength to + +generalised impotence. + +At this level it is possible to discern one of the contradictions of sovereignty: the sovereign reigns through and over the impotence of all; their living practical union would make his function useless, and indeed impossible to perform. However, his proper activity is to struggle against the invasion of the group by seriality, that is to say, against the very conditions which make his office legitimate and possible. We have seen how the contradiction is resolved, in practice, by a new form of alienation: that of each and all to one person. In order to avoid relapsing into the practico-inert field, everyone becomes a passive object or an inessential actualisation for the freedom of the Other. By means of sovereignty, the group alienates itself to a single man so as to avoid alienating itself to the material and human ensemble; in fact everyone experiences his alienation as life (as the life of an Other, through his own life) , instead of experiencing it as death (as a reification of all his + +relations). + +82. Of course, this applies only to the original moment in which sovereignty constitutes itself in opposition to recurrence. Once the powers of sovereignty have been strictly defined by tradition, executive powers will be transmitted from + +one sovereign to the other. + +However, the synthetic relation of the sovereign to all through institutions presents a new contradiction, due both to the 'immanencetranscendence' tension which produces a mere quasi-sovereignty in him and to his untranscendability which, though it does not remove him from the group, separates him from all the third parties. As it realises the integration, this quasi-sovereignty, being untranscendable, treats the group as a whole as a field of inorganic materiality or as an organised extension of his organs. The object of the exercise is to realise a praxis, to attain a transcendent objective; and the essential relation posits itself as that between the sovereign and the object. There is therefore no a priori answer to the question whether the practical objectification will be that of the sovereign by means of his group or that of the group through the mediation of the sovereign - whether, in other words, the aim is the object of the sovereign individual as such (in his practical individuality) achieved by common means (by setting to work a multiplicity of common individuals), or whether it i + +s a + +common aim achieved by common action which has been planned, thought out, and organised by means of an untranscendable regulator. Is the object the objectification of a reign, or is it that of the men who have lived under it, maintained it, and created it? This indeterminacy is expressed in the phrase ' my people', which means both the people who belong to me and the people to whom I belong. It would not help to claim that the sovereign is a specific product of given institutions and that he sets himself constant aims (defined by circumstances and by the constant possibilities of geopolitics: to defeat the house of Austria, etc.), which he can achieve only by using specific instruments, namely institutions. We have already made this point, but it is not relevant to the present problem. Nor is it sufficient simply to claim that the sovereign, as a product of the group (considered as a practical multiplicity of individuals), expresses the deep relations, the conflicts, and the tensions within the group, in spite of himself, and that his praxis can be no more + +than the practical reinteriorisation of these human relations. + +But the problem is not so simple. To judge by the claims of those who wish to dispose of him, the sovereign apparently establishes his authority either over a fused group or over an organised group, that is to say, over free practical men, whose only inertia is pledged faith. If this were so, then the sovereign would effectively be no more than the medium of his group. But the sovereign does not exist at this stage of integration. Since his authority is based on serial impotence, and given that he exploits the inertia of internal relations in order tQ give the + +group the greatest possible external efficiency, it must be acknowledged that his power is not based on consent (as a positive act of adhesion), but rather that consent to his power is an interiorisation of the impossibility of resisting it. In other words, he imposes himself through the impotence of all, and everyone accepts him as a way of bartering inertia for obedience. This element of nothingness, this 'Devil's Share', is the true support of sovereignty. Everyone obeys in seriality : not because he directly adopts an attitude of obedience, but because he is not sure whether his neighbour has undertaken to obey. This is far from preventing orders from being seen as legitimate: in fact it prevents the question of legitimacy from being raised. So if the sovereign works on the inorganic, it is not that 'his' group is using him as a reflexive medium, but rather it is himself using 'his' group in order to + +achieve certain ends. + +And of course the limits of his options and choices are indicated by institutions themselves, which are his instruments; that is to say, they are indicated by the petrified ensemble of institutionalised men. But, in the first place, within these limits, his power can vary according to institutions and circumstances; and this power may become quite large. But the most important point to grasp is that, in the course of the repressive Terror which he has to practise in the name of integration, certain stratifications, blockages, and regroupments constitute themselves, each of them calling a temporary halt at this level of Terror, that is to say, in more or less stable equilibrium, and which, as a whole, constitute a passive structuring of the group on the fringe of institutions - a sort of geological section which is nothing other than sovereign praxis maintained in its unity by the inertia of separation. And this structured ensemble which is dependent on the practice of the untranscendahle individual is not only a material formation which he maintains and constantly engenders, and which will collapse when he dies, but also the ensemble of avenues and paths of his power: as he reigns the sovereign increases his power, because he produces the group in his own image. Naturally, the converse is also true: the group condenses into the indissoluble unity of an organism, and the sovereign dilates through the multiplicities of the group. Nevertheless, the group, through these acquired structures, performs an extra-institutional �ask on itself, and this is simply an inert extension of sovereign praxis. And these very conditions of sovereignty suffice to show that there is no a priori answer to the question. From the point of view of the group, the institutions, the circumstances, the common objective, etc., the + +sovereign posits himself either as the medium of the group or as its end. And, on the second hypothesis, and depending on the situation, he may either posit himself in his practical, free individuality as a goal of the community, or regard the institutional system as essential in so far as he himself has the institutional power to reinteriorise it (while the multiplicity of institutionalised members is inessential). Whether it is the man or the apparatus which posit themselves, a new alienation results for the third parties : provided that the goal of the sovereign really is the common object of the group, no one will have any aim other than serving the sovereign himself, and everyone will pursue the common aim, not because it is common, but because it is the object of + +free sovereign praxis. + +This is the particular embodiment of sovereignty which is normally encountered in History. Its dialectical reason is simple, and we summarise it here only so as to reveal a few of the formal structures of sovereignty. And in fact our inquiry is leading to a new moment of our investigation: the institutional group coming into contact with the various serialities of the non-grouped. Several different objectives, in fact, are possible and logically definable; the aim of the group may be the production and reproduction of the life of its members, struggle against some other group, or direct action on collectives. This last category includes agitational and propaganda groups as well as publicity associations or groups of cadres, etc. Now, if a group which is still effective (though possibly eroded by seriality) really acts on serial individuals, its action on the series is due to its unity. At this level, we are now in a position to complete a description which we gave at an earlier and more abstract level of our investigation, where we spoke of newspapers and the radio as collectiyes. And this was not a mistake, since everyone reads or listens to the opinions of the Others. But our description missed another aspect of its reality: the fact that what is lived and used as collective by the serial flight of alterity is also an organised group (the newspaper) or an institutional group (the state radio) which, in a common undertaking transcends itself (se transcende) towards collectives and inert gatherings as their own objectives. + +At this level, the group is capable of adapting to the collective: it has been through it; and each of its members is himself - in other moments, and in relation to other individuals - a serial being; besides, each of them, even inside the group, is already more than half serialised; and finally, experience in his job may have taught him the effect of a given item of news or of a given statement when it is reproduced in the + +privacy of a couple or of a family and appears as a collective opinion. At this level, group praxis (unless it is aimed at the dissolution of inertias of seriality in a given place) is, in itself and for all its members, a rational employment of recurrence. It is by starting from impotence and separation, in the knowledge that every thought in every individual is a thought of the Other, that they manipulate the inert material of their work. The group, as a practical totalisation, which organises itself in the unity of its directives through the practical thought which reveals and combines the elements of alterity outside it, becomes the free, synthetic unity of alterity as such, that is to say, it relies for the effectiveness of its action on the impotence and dispersal of its objects. An advertising project, or a film which has to be seen, or a view which has to be expressed, establishes itself in every Other with its own coefficient of alterity which, as we have seen, shows that the otherthought (fa pensee-autre), in seriality, has to reinteriorise and reactualise the thought of the Other. Thus a group which works on an inert gathering produces itself both in relation to this gathering and in itself as a sovereign in an institutionalised group, except that, in our examples, its action is not institutional in character. This does not mean that collectives can simply be manipulated according to one's wishes. On the contrary, as we have seen, these serial flights have· �nflexible laws. But regardless of his range of choice, even the sovereign cannot manipulate the group just as he wishes, any more than workers or technicians can do what they like with their tools and materials. This is not the issue: the important point is that the group is active and that the practico-inert man is its passive ohject - not as a practical organism, but as an Other. It is also important that the action which rearranges the practical field has both the result and the aim of working inert gatherings so that the force of the inertia should itself produce the intended result. In this way, an organised group can exercise sovereignty over collectives, since it treats them as an individual treats the objects of his practical field and because it acts on them in accordance with their laws, + +that is to say, by exploiting their relations of exteriority. + +In this sense, in the case of an institutionalised group which has a sovereign in some form or other, he becomes the sovereign of the collective in so far as he is the sovereign of the group. But there is one all-important reservation: this sovereignty is not itself institutionalised. But this is not important. Hearst, the magnate of the conservative press in America, with his newspaper chains, over which he exerted authoritarian control, was sovereign and reigned over public opinion. Besides, + +an inert gathering is more likely to accept the institutionality of the sovereign when it thinks of him in serial impotence and through indefinite alterity - which means that he appears to every member of the series as a benefactor of the indefinite recurrence which is known as public opinion. The sovereign is both man and infinite; he is outside the practico-inert, and his freedom opposes the suffered alienation of alterity. The action of the group on the gathering has to be conceived synthetically on the basis of knowledge of the serial and it is realised serially through the directed and controlled serialisation of agents. But when, in a gathering, separate individuals rise from produced seriality (press, radio, etc.) to an individual who directs the operation, this Other, who is other than all of them because of his organic and practical unity and his power, seems to them to determine - and actually does determine - their indefinite flight, so as to occasion an abstract, totalising unity in it: the whole indefinite series of the newspapers and the other readers is condensed in him; and, in him, recurrence is free temporalisation; in him, public opinion is one individual, historical thought, a free determination of discourse, though without ceasing to + +be multiplied to infinity in the practico-inert. + +All I have wanted to show by these formal remarks is that the unity of the sovereign, as the sole practical freedom of the group, occasions an abstract phantom of unity within the series, and that this relation is really no more than a degradation of his relation to the third parties of the community. For this reason, when an emergency threatens a concrete ensemble composed of a group and a gathering (the raw material of the group being the gathering), or when the division of functions makes some regulation necessary, the group may claim the power to distribute tasks to the members of the series, and the members can accept them, without escaping from seriality. In fact, it is worth remarking that the presence of constituted groups - except ones which are explicitly aimed at the dissolution of seriality - prevents the formation of fused groups out of the collective (or at least it makes it more difficult). Induced unity is sufficient; alterity is liquidated when there is no other means of struggle, and no other hope. When there is a group, orders are accepted partly from a simple inability to refuse and partly because the transcendent unity of the group creates an economy of dangerous unification for every other. The mobilising group may impose its institutions on the series because they are homogeneous with it in so far as they are still practices of impotence. But when they become serial, institutions decline a little further and they become + +suffered processes whose concrete meaning is dissipated in the milieu of exteriority. For every Other in the gathering, it will suffice to know that the institutional ensemble takes on a meaning for the sovereign. In this sense, collectives and inert gatherings never legitimate either sovereignty or institutions : they accept them out of impotence and because they have already been legitimated hy the Others (in the group). In one way, in the milieu of alterity, the mere fact that a group exists outside them and in its synthetic unity constitutes a basis for legitimacy. Not for them, however: for it. The group is legitimate because it has produced itself by a pledge in the synthetic milieu of practical freedom, that is to say, in the milieu which rejects the gathering on principle. In fact, through the other of alterity, the group as such (as its own production from the clay of seriality) is legitimate, because it both realises for itself and manifests for all (by determining impotence in depth) the action of freedom in opposition to necessity. This means that, through the group, the sovereignty of praxis over the practicoinert manifests itself to seriality as a basis for, and an impotent rejection of, passive activity. Free activity is manifested elsewhere to passive activity as the absolute reign of law" And this absolute reign, as a negation of the practico-inert, involves, at least as an abstract connection, the univocal power bursting open the chains of seriality in every Other. In this sense, although the collective has no ahility to confer sovereignty, and no structure to enable it to do so, it can grasp it as a mode of existence proper to certain practical forms of sociality, and may even, with an institutional group, go back to the origin of totalisation, to individual freedom conceived as the will of all. And its relation to the group (unless the group has produced hostile groups, rivalries or competition, etc.) may be a capitulation to inertia, not only because the Other is manipulated in everyone and because every Other sees the group in and through the Other as freedom creating itself, its legitimacy, and all legitimacy, and, in the same movement, the gathering as in principle foreign to every statute of legitimacy (neither justified nor unjustified: the question of justification does not arise, a priori, as far as it is concerned). Besides, though manipulated both as an inert object and as an Other, manipulation does not change every Other; but the intention of producing an effect by transforming the whole series may occasion, in the very locus of alterity, a kind of transcendent unity as Other; the relation of exteriority, worked on in the collective by the group, takes on a synthetic, impracticable meaning for every other: in so far as the group deigns to use it for its unitary undertaking, this + +unity of alterity. + +5 States and Societies + +These remarks have nothing to do with the historical orIgms of sovereignty, but only with entirely abstract logical and dialectical relations, which must, however, be present as the intelligibility of any historical interpretation. Within groups, sovereignty is in fact at least relatively simple. But the ensembles in which sovereignty, in some form or other, manifests itself in its full development and power are societies. And we have already established that a society is not a group, nor a grouping of groups, nor even struggling groupings of groups. Collectives are both the matrix of groups and their grave; they remain as the indefinite sociality of the practico-inert, nourishing groups, maintaining them and transcending them everywhere by their indefinite multiplicity. Where there are several groups, the collective is + +either a mediation or battlefield. + +Society, which our dialectical investigation has, up to this moment of its development, approached only very abstractly, thus yields up its highly formal and indeterminate structure: in the material context of needs, dangers, instruments and techniques, there can be no such thing as society unless there are, in some way or other, human multiplicities united hy a container or hy a soil, unless these multiplicities are divided, by Historical development, into groups and series, and unless the basic internal relation of the society - whether production (division of labour), consumption (type of distribution) or defence against the enemy (division of tasks) - is ultimately that of groups to series. And among the many differentiations of this internal bond, one of the easiest to grasp is the institutional ensemble, cloaked and reunited by the sovereign institution, by the State, in so far as a small group of organisers, administrators and propagandists take on the task of imposing modified institutions within collectives, as serial bonds which unite serialities. In short, what is known as the State can never be regarded as the product or expression ofthe totality of social individuals or even of the majority of them, since this majority is serial + +anyway, and could not express its needs and demands without liquidating itself as a series, so as to become a large group (which either immediately opposes authority or else renders it completely inoperative). It is at this level of the large group that dissolving alterity permits concrete needs and objectives to constitute themselves as common realities. And the idea of a diffuse popular sovereignty becoming embodied in a sovereign is a mystification. There is no such thing as diffuse sovereignty: the organic individual is sovereign in the abstract isolation of his work; and in fact, he immediately becomes alienated in the practico-inert, where he learns of the necessity of impotence (or of impotence as a necessity at the basis of his practical freedom). At the level of the series, juridical and institutional power is completely denied to human multiplicities by the very structure of their relations of exteriority. Thus, inert gatherings do not have the power or nature either to consent to or to resist the State. Sovereignty does not rise from the collective to the sovereign; on the contrary, sovereignty (as command, as a phantom of unity, or as the legitimacy of freedom), descends through the sovereign to modify collectives, without changing their structure of passivity. As for the institution as such, and the concrete power which fills it, it is clear that they arise in the group when it is institutionalised and that what er,isures its efficacy is a process-praxis which also preserves a certain unity in the com- + +munity which is being serialised. + +Thus, within a given society, the State cannot be said to be either legitimate or illegitimate; it is legitimate within a group, because it is produced in a milieu of pledged faith. But it does not really have tllis legitimacy when it acts on collectives, since the Others have not sworn anything either to groups or to one another. However, as we have just seen, the Others do not claim that it is illegitimate, at least as long as they still do not themselves constitute a group. If they do not make such a demand, this is, in the first place, out of impotence: as a series, they have no means of either contesting or establishing legitimacy. Secondly, it is because the group, whatever it may be, appears to establish its own legitimacy in that it freely brings itself into being, when it is seen by the Other in alterity as the synthetic signification elsewhere of his bonds of exteriority and as the abstract and permanent + +possibility that the collective too should become a grouping. + +Something like acceptance may therefore occur; but in itself this is ineffectual since it exists in every other only as an awareness of impotent recurrence. I obey because I cannot do otherwise; and in itself + +this confers serial pseudo-legitimacy on the sovereign: his power to command proves that he has a different nature from mine, or, in other words, that he is freedom. But if I were a member of the group I would somehow find my freedom in that of the sovereign and even, as we have seen, in the alienation of the third party to the living organism of the untranscendable third party. Thus I am in league with the sovereign, and I can pursue his ends as though they were common ends, and therefore as my own, even if, for me, he is already, as the pure unity of integrating violence, my untranscendable end. But, given that the institution maintains itself in the series as pure inertia, and given that - once a skilful practice has imposed it - it belongs to the world of practico-inert constraints ; given that it presents itself as an exigency rather than as a synthetic signification within a totalisation, it produces itself within the collective (as inert repetition) purely and simply as a reality (a de [acto constraint), while retaining a character of sacred exteriority in so far as it relates, through empty intentions, to the free fulguration which created it. It is the realist element which predominates: resistance is futile and there is no point in trying to comprehend : 'That's how things are. ' From this point of view all negations which reduce to impotence are assimilated to one another whether alienations originating in seriality itself, impossibilities resulting from the economic and social system in the conjuncture, or 'enforceable' or sovereign orders. Reality, as Mascolo rightly observed though he did not understand why it was so - is, for the exploited, the unity of all the impossibilities which negatively define them. The State is therefore primarily a group which is constantly reorganising itself and altering its composition by means of a partial, discontinuous or continuous, renewal of its members. Within the group, the authority of the sovereign is based on institutions and their exigencies, on the need to ensure the strict unity of the apparatus in the face of the dispersal of series. In other words, this integrated group sets itself the aim of manipulating the collectives without extricating them from seriality and of establishing its power over the heterogeneity of its being and of serial being. The impotence of the series as alterity in flight is both the origin and the limit of state power: always living, always commanding obedience here, authority is always threatened elsewhere, and in the very + +moment when the Other who is here obeys it. + +This radical heterogeneity of the State and of inert gatherings provides the real intelligibility of the historical development of sovereignty. If classes exist (that is to say, if practical, historical investigation reveals + +them), then, in effect, the State institutes itself in their struggle as the organ of the exploiting class (or classes) and sustains, by constraint, the statute of the oppressed classes. In fact, as we shall soon see when we finally reach the concrete, classes are a shifting ensemble of groups and series ; within each class, circumstances occasion practical communities which attempt regroupment, under pressure from certain specific emergencies, and which finish by relapsing, to some extent, into seriality. But if, as we have been assuming, such regroupments occur inside societies in which dominant and dominated classes confront one another, they differ radically according to which class they are in; if they occur within the dominant classes, then, whatever their aim, they necessarily participate in the process-practices of domination; and if they occur in the dominated classes, they will (even if, to Others, or in the light of subsequent developments, they may appear as complete betrayals) contain an initial, abstract negation of class domination as + +one of their basic determinations. + +Of course, this does not mean that the problem of sovereignty cannot arise within exploited classes (at least when they reorganise in order to intensify the class struggle) ; but it dQes imply that the formation of a State, as a permanent institution and as a constraint imposed by a group on all serialities, can occur only through a complex dialectic of groups and series within the dominant class. A revolutionary organisation may be sovereign. But the State constitutes itself as a mediation between conflicts within the dominant class, in so far as these conflicts run the risk of weakening it in the face of the dominated classes. It embodies and realises the general interest of the dominant class over and above the antagonisms and conflicts of particular interests. This amounts to saying that the ruling class produces its State (that its internal struggles produce the possibility and the exigency for a group to arise to defend the general interest) and that its institutional structures will define themselves in terms of concrete reality (that is to say, in the last analysis, in terms of the mode and relations of production) . In this sense, for example, the nineteenth-century bourgeois state reflected the unity of bourgeois society: its molecular liberalism and its programme of non-intervention were not based on the fact that the molecular statute of the bourgeoisie was really given, but rather on the exigencies of a complex process which developed industrialisation through the contradictions and antagonisms of competition. Order negative here - is identical with the general interest of the capitalists as a negation of the powers of association and organisation of the exploited + +classes; they are realised in the relation of the dominant classes by means of a strenuous effort to subordinate the strength of the landed aristocracy to that of industrial and financial capital; lastly, within the most favoured class, they consolidate a hierarchy which has already been proclaimed - at least, it was in France before r848 - and ensure the bankers' control of the country as a whole. This means that they absorb their de facto power as untranscendable third parties and transform it, through new institutions, into de jure power. Thus Marx was right when he wrote 'Only political superstition still imagines today that civil life must be held together by the state, whereas in reality, on + +the contrary, the state is held together by civil life'. 83 + +Marx was right, suhject to the qualification that there is a circular process at work here and that the State, being produced and sustained by the dominant, rising class, constitutes itself as the organ of the contraction and integration of the class. And of course this integration takes place through circumstances, and as a historical totalisation; but still, it takes place through the State, at least in part. Thus it would be wrong to see the State either as the concrete reality of society (as Hegel apparently wished to believe), or as a pure, epiphenomenal abstraction which merely gives passive expression to changes effected by the + +concrete development of its real society. + +This is particularly important in so far as the State cannot take on its functions without positing itself as a mediator between the exploiting and the exploited classes. The State is a determination of the dominant class, and this determination is conditioned by class struggle. But it affirms itself as a deep negation of the class struggle. Of course, it derives its legitimacy from itself, and series have no alternative but to accept it. Moreover, they ought to accept it: it must appear to the dominated classes as their guarantee. It is absolutely wrong to ignore the fact that the government of Louis XIV, or of Hitler or of the Convention, claimed that it was the embodiment of the legitimate interests of the people ( or the nation) as a whole. The State therefore exists for the sake of the dominant class, but as a practical suppression of class conflicts within the national totalisation. The term mystification is not appropriate to this new contradiction: in a sense, of course, it is a mystification, and the State maintains the estahlished order; in class conflicts it intervenes to tilt the balance in favour of the exploiting + +83. The Holy Family in Marx and Engels, Collected Works, Vol. 4, Lawrence + +& Wishart, 1975, p. 121. + +classes. But, in another sense, the State really does produce itself as a national institution; in the interest of the privileged, it takes a totalising view of the social ensemble; it sees beyond antagonistic individuals, and may devise a paternalistic social policy which it will subsequently impose on the dominant classes, even though it is created in their interest. Lenin noticed this when he said that the State arbitrates whenever power relations tend to a state of equilibrium. But this means that it already posits itself for itself in relation to the class from which it emanates: this united, institutionalised and effective group, deriving its internal sovereignty from itself and imposing it as accepted legitimacy, tries to produce itself and to preserve itself in and through itself as an essential national praxis, by acting in the interests of the class from which it emanates and, if necessary, against them. One need only look at the policies of the French monarchy between the fourteenth and the eighteenth centuries. to see that it did not confine itself to providing mediation when forces were evenly balanced, but rather created this balance by perpetual changes of alliance, so that the bourgeoisie and the aristocracy would control each other, so as to produce itself, on the basis of this deadlock (which was due partly to social evolution and + +partly to the economic policies of the governmeni + +as an absolute + +monarchy. + +, + +Thus, from our formal point of view, and regardless of the historical reasons for its development in any particular society, the State belongs to the category of institutionalised groups with a specified sovereignty; and if, amongst these groups, we make a distinction between those which work directly on an inorganic common object, those which are constituted to struggle against other groups, and those whose objectification demands the manipulation of inert serialities, etc., it is obvious that the State belongs to the second c1ass.84 Having emerged from a certain kind of seriality (the dominant class), the State remains heterogeneous with it, as with the dominated class, because its strength is based on its impotence and it appropriates the power of others (the dominant classes) over others (the dominated classes) by interiorising it and transforming it into right. It sets the unity of its own + +84. In fact, the categories are always more complex: seriality, the inorganic, the enemy group, etc., are always present in some degree at the same time, as the example of supplying an army in enemy territory shows. But what is important to us here is the abstract and formal clarity of the schemata. One can encounter + +the complexity of the real for oneself and at leisure. + +praXls m oppositIOn to all classes, especially, perhaps (at least in capitalist societies), in opposition to employers who have long been paralysed by their mutual antagonisms, rather than to the proletariat, which is very ready to attempt to replace seriality by unity, that is to say, by its autonomy. And there can be no doubt that the most powerful private interests can always influence its decisions (as can the totalising evolution of circumstances). Coalitions of the privileged may destroy it or put it out of action, but on the whole its autonomy is preserved because, for the oppressed classes, it is the organ of legitimacy and because, in so far as they agree that it should be its own legitimation, the privileges and inequalities are also given a juridical statute. Whenever a ruling class has wished to attack the State, the ruled classes have quickly formed groups and carried forward the liquidating action against the classes which began it (the best known example being the aristocratic revolution which, in 1787, paved the way to the bourgeois + +revolution, which in turn led to the popular revolution). + +In fact, the overthrow of a State normally takes place within the State apparatus, as a crisis of sovereignty. The rich bourgeoisie was able to halt the Revolution when the final consequences of the Terror had lost the Committee of Public Safety the support of the sans culottes. But 9th Thermidor was neither a surprise attack, nor a 'day' (journee) (unlike the 'days' of 31 May, 2 June, etc., which were popular and as such revolutionary): it was a legally and institutionally resolved crisis of authority within the government apparatus. Thus, there are many transformations of the possessing class, including ones which occur in the concrete domain of real society rather than in the abstract domain of civil society, which have to be publicly realised by the State acting on the citizens. And, until the exploited classes reach full revolutionary consciousness of themselves, this is because the passive legitimation of sovereignty by the popular classes becomes the State's guarantee against those who hold power. Though it is imposed by the exploiters as a cloak for exploitation, it is also guaranteed by the exploited. This position of autonomy, and heterogeneity of structure, and these possibilities of manoeuvre, lead it to posit itseljJor itself as the nation itself; it tries, as a sovereign institutional group, to become the creator of the objective which is common to all, the designer of the plans through which it will be achieved and the manipulator of all the series (each as a function of the others and simultaneously). This does not alter the fact that the supposed mediator favours one or more of the dominant classes (at the expense of the Others and of the dominated classes). And + +we are now in a position to add the crucial point that the institutional group, in so far as it aims to preserve its being (in the organic being-one of the sovereign), wishes to carry out its policy as a means of developing the milieu of sovereignty, rather than to put its sovereignty at the service of a policy. The real contradiction of the State is that it is a class apparatus pursuing class objectives and, at the same time, positing itself for itself as the sovereign unity of all, that is, in the absolute Other- + +Being which is the nation. + +6 Other-direction: the Top Ten, Racism and + +Anti-Semitism + +Having now reached the complex level where the group becomes a mediation between collectives and where collectives serve as intermediaries for groups, and where the immediate (or even absolute) goal of certain communities is the manipulation of series and of the masses as such (that is to say, of the practico-inert field in so far as men within it mediate between worked objects), we must nov) define, in their abstract intelligibility, the resulting new model of common praxis and the new long-term effects of this praxis on the sovereign group. + +The principle of the new praxis (propaganda, agitation, publicity, the diffusion of information which is more or less misleading - or at least selected with a view to action rather than truth - campaigns, slogans, the muted orchestration of terror as an accompaniment to orders, 'stuffing people's heads' with propaganda, etc.) is to exploit seriality by pushing it to an extreme so that recurrence itself will produce synthetic results (or results capable of being synthesised). The sovereign will rethink seriality in practice as a conditioning of indefinite flight, in the context of a total undertaking which is controlled dialectically. Alternatively - and by now we should be accustomed to this contradictory tension which constitutes practical thought - he will define the operation on the series as a unity of action which is serialised in the synthetic context of a broader totalisation. Thus serial Reason becomes a special case of dialectical Reason. But this practical view of a transcendent series cannot arise in a dialectical context unless the nonsynthetic unity of alterity is reproduced in the practical scheme with at + +least a formal appearance of synthetic unity. It must be possible to embrace this flight in the unity of a circular act. Now, this act is given in the group itself as a developing serialisation of the still efficacious praxis; effectively, the sovereign is born of circular recurrence and arises as an obstacle within it; and the relational system which constitutes the skeleton of his practical devices implies a constant incurvation of recurrence: it is by passing through blocked, circular recurrence towards indefinite seriality that he becomes able to see this seriality as the ubiquity of a circular, infinite recurrence whose centre is every- + +where but whose circumference is nowhere. + +In fact, however, this seriality is not really of this kind. Nevertheless, this is how institutional agents working under the orders of the sovereign will constitute it: on a basic foundation of alterity, they will give it an artificial statute. This statute will consist in the fact that through the mediation of a directed operation, everyone's alterity by and for everyone will present itself as the index of refraction of a united social milieu whose law is that each of its practical features is produced through the determination of every Other (in alterity and through all the Others) and conversely. To allow this unitary milieu to exist fully through recurrent dispersal, it is necessary and sufficient that every Other should make himself completely other, that is to say, that he should direct his free praxis onto himself so as to be like the Others. This is what various American sociologists have aptly called 'otherdirection'.85 The third party, in each of the groups under consideration, effectively presents himself as inner-directed, by which I mean that his powers and actions are determined for him on the basis of an interior limitation of his freedom. And, through reciprocity, the other (as the formal alterity of my freedom) certainly figures in my pledge as pledged inertia. But it is still true that my own praxis, in so far as it is strictly subordinated to the interests of the group, is produced from within, on the basis of my own limitations and powers. It is not necessary either to do or to be like the Others, but simply to remain the Same here, through differentiations imposed by action and interiorised. Manipulated seriality, on the other hand, has no common aim - which is appropriate since its metamorphosis into a group is necessarily and fundamentally the beginning of a revolution; it derives its inertia from its impotence rather than from a pledge, and people are involved in it only in so far as their actions and thoughts come from Others. The + +85. See David Riesman, The Lonely Crowd, Yale University Press, ]950. [Ed.] + +praxis of the sovereign group therefore consists in conditioning everyone by acting on the Others. But this is not sufficient to create the passive quasi-unity of other-direction. In order to realise it, it is necessary to fixate every Other on an illusion: the totalisation of alterities (that is to say, the totalisation of the series). This is the trap of other-direction: the sovereign intends to act on the series so as to extract a total action from it in alterity itself; but he produces this idea of practical totality as a possibility of the series totalising itself while remaining the fleeting unity of alterity, whereas in fact the only possibility of totalisation for the inert gathering consists in dissolving + +seriality in itself. + +These considerations may seem very formal. I shall now give a simple example, which will illustrate two characteristics of otherdirection: the mediating action of the group which conditions every other through all the Others, and everyone's practical fixation on the + +illusion of totalised seriality. + +In 1946, when I was in the United States, several radio stations broadcast a list of the ten best selling records of the week every Saturday and, after each title, they played a few bars of the record they had just mentioned (usually the tune). A series of tests and comparisons revealed that this programme increased the sales of t!I� ten records in the following week by between thirty and fifty per cent. In other words, without the programme at the weekend, the number of buyers for the ten records would have been between thirty and fifty per cent less. Thus the programme tended to preserve and perpetuate the previous week's result. But this result was itself statistical and serial. No doubt it was partly due to advertising campaigns: but these campaigns were in competition with one another, or at least - as when several bands belong to the same company - they served several records at once. Above all, they were attempts to determine a future action in everyone, that is to say, to define a possibility of his practical field. They did not give anything (everything was in the future: the record which you will like, etc.); or else they related to the action of some small group - the Top Record Prize, for example - and tried to persuade serials that the specialised group which awarded the prize was simply a channel for the expression of the opinion of all. In this case, there was already an attempt to establish an equivalence between a synthetic unity and alterity (the jury is the public). But the public does not really co-operate, except for a few prizes or choices whose legitimacy it accepts and ,is subjected to. In any case, its relation to the small + +group is complex and ambivalent: the decision of the group must signify both the judgement of the nation (as a seriality of serialities) and the decision of those competent to judge. In one way, the jury represents the great dispersals of alterity in the astringent milieu of the group; it establishes how one should behave. Thousands of people are prepared in advance to behave in this way: it involves buying, or giving, and it remains abstract in everyone (as a fleeting relation of reciprocity) in so far as it lacks an ohject (a means and end). The jury therefore appears to live in symbiosis with serial alteri�'Y, and, indeed, it does have the power to choose which record will be bought. It should be observed that this power - like all powers which relate to seriality - is conferred on it by a small group, namely the group which organised it; the public merely accepts it. No doubt the public could have remained in a state of negative inertia (neither challenging nor accepting this legitimacy, which was none of its concern). If it chooses serial docility as Other, this is on account of concrete historical circumstances which we need not go into here. Formally, this very symbiosis is the beginning of fixation and this is what gives it its hold over the Other in inert gatherings. It apparently gives two different statutes to the same act: buying the record, because one always buys the 'Prize Record', and giving it (because it is the New Year present for music fans). Here we have a set of alienated actions based on alterity (the 'Prize Record' is acknowledged by the Other - by later generations; and then someone will hear the record at a later date, as belonging to this year, and when we meet he will expect me to have heard it). This behaviour not only constitutes the prize as an Eternal Return (and a socio-natural one: it corresponds to the beginning of winter as a social season) by making it return every year in a new form, but also leaves open the purchaser ' s value judgement (a different act) concerning the object he buys. As an act, the Prize is other and indeterminate; it is the annual (and only) relationship between IOO,OOO persons and music, mediated by a small group. + +And here we encounter the second characteristic of the group as seen by the series: it is a group of experts. This means that the evaluation of music is their profession. No one actually believes that the record is really the best of the year, but at least it must be 'worth listening to'. The quality of being an expert is sovereignty in the milieu of alterity (that is to say, it is transcendent of seriality): and this sovereignty, which is expressed in one specific act, flows into one object and becomes a definite power in it, a right over a certain category of serial individuals. Here we can see precisely the mirage in its elementary form: the record, + +in a shop window, fresh and new, unique amongst the other records, is the individual unity of interiority-objectification of the individual who produced it and of the small group which chose it. If I go into the shop, buy it and take it away, it is a record-seriality, a record which I must have because the Other has it, a record which I listen to as an Other, adapting my reactions to those which I anticipate in Others.s6 Mirage and metamorphosis: synthetic unity can manifest itself as an abstract determination, in a transcendent milieu, for individuals in an inert gathering; but once an object which has been produced in this way is introduced into the gathering, it acquires structures of aiterity, and + +becomes, in itself, a factor of alterity. + +But although this initial behaviour towards the object which is prized or acclaimed is totally alienated, it does not determine the actions of small groups or of practical individuals, in so far as these elementary units lie helow the level of seriality. There is a kind of pleasure or displeasure in the listener which, apart from his alienated evaluations, expresses either his personal valuation (that is to say, his power: in so far as it relates to some group to which he belongs elsewhere, or in so far as his free practical activity turns to evaluation through the very alienation which takes it away from him) or, perhaps, that of his family group. At this level, the group's choice is never in dispute: in order to be able actually to prefer another record, one would have to have heard it; and the opportunity to read two or three potential prizewinning books, of trying to anticipate the decision of the academicians or to prepare oneself in advance to criticise it, is obviously confined to a very small social category (the liberal professions, certain housewives, etc.). But their pleasure or disappointment are expressed in their assessments in rather the same way as by lovers of Burgundy; there are good years and bad years; the Prix Goncourt, for example, is an annual product which exists in its raw state hefore December and which is worked as a result of December's activities; and the deep identity of this annual product (a product of vegetable spontaneity and human labour) is subject to the same yearly variations as Beaujolais. 'The + +Goncourt's pretty boring this year.' 'Oh, I quite liked it.' + +86. If a book has not been socially acclaimed, it may unite a few isolated readers - but only spontaneously, by itself, by being interpreted by everyone and by referring, through this very interpretation, to the same who composed it, samely (mememem), as a common object. But if a book is acclaimed, then, when I open it, it is produced by the other and as a serial formula of alterity. + +This last observation brings us back to the example of records. The Prix Goncourt, the Prix du Disque, the Prix de la Chanson: these initial operations extend the group's action at a distance on series through the sovereign unity which it gives itself and which is not challenged (it could be challenged, in fact, only by other, more powerful, more numerous groups, etc.); and the fact that it goes unchallenged appears to serial impotence simply as a security: and the Other, as an alienated individual, is in any case incapable of making a challenge in practice. But if real practical groups are either neutral or in favour, sovereignty as a causa sui will radiate from itself, up above, at the level of the jury. But this initial transcendent unification is not a case of other-direction: it conditions the series by producing its possible unity in transcendence (transcendance), but it does not yet employ intraserial behaviour as a unitary and fixating method of conditioning of other-behaviour in everyone. But with the radio programme, everything becomes quite different: the reflexivity whose only truth lies in the group (and then only at a given level of development) enters the series: an action-group (in this case concerned with advertising) shows the series what it is doing (of which it was necessarily unaware since every Other was lost in the milieu of the Others). In other words, the initial reaction of the series (to external and transcendent conditionings) is reflected back to it through the mediation of a group which is itself transcendent in its basic structure, and which is capable of establishing the fleeting series of actions by the means appropriate to seriality (statistics, averages, etc.) and of totalising them into one action, as far as its structure and its totalising function permit. The series becomes aware of what it has done. Thus it is produced as a whole (through the 'mass media') for each of the Others who compose it. Cardinal becomes ordinal; quantity, quality: the quantitative relations between the sales figures of two or more particular records suddenly come to indicate a preference, and the objective ranking of the records sold becomes the objectivity of a system of values proper to the group. The systematic transmutation of quantity into quality is completed by connecting the name of the work (usually a 'catchy' name) with its individual quality (the fragment of a theme) and with the names of the performers (singers, etc.): a given song has a certain indefinable objective quality which puts it at the top of an equally objective hierarchy. And everyone sees the hierarchy as an expression of collective choices and as a unified system of values. The two aspects complement one another; a serial + +action expresses and sustains a hitherto hidden hierarchy. + +In reality, it is clear that the group is lying when it tells the truth. The figures are correct, but they have no validity except in the domain of the Other: of course they may result partly from various unities of preferential choice in the individual cases of particular individuals or small groups. But, apart from the fact that as such this choice is the exception (the other-choice forces itself on one as a choice of the Other, through circumstances and through the concerted action of organised groups, propaganda, etc.), the failure to make any comparison with total record sales for the week (for it is crucial to know whether the record which is placed first represents five or fifty-five per cent of all the records sold) deprives this exception (if indeed it can be considered in isolation) of any real, that is to say differential, significance. In fact, the result that is given has no more than the false appearance of interiority: it is neither the choice of the group nor the choice of the Others; it is the Other as choice. In other words, it is the negation of choice as such (as free choice), or alienation produced as freedom. And its totalisation is the result of the hidden work of an advertising group which gave it its structure of pledged inertia and of practical unity. But, we should remember that this radio programme is addressed to Others in separation (as we noted above) and that it is aimed particularly at two categories of listeners: those who hav� pot bought the 'top ten' records (or not all of them) and those who have bought them (or at least - depending on their resources, who have bought some of them). For the first group, the 'top ten' is an exigency: it indicates to the temporarily isolated individual that a broad social process of unification and agreement has taken place this week and that the listener at whom the broadcast is aimed has not taken part in it. This 'spontaneous' phenomenon is over (wages are received weekly in the U SA, where the week is a unit of consumption: calculations are made by the week and not by the month); the week closes in on itself and displays the unity of the others to the non-buyer in this small individual exile (which becomes the expression of seriality for all exiles). In reality, the factors which prevented the purchase are purely negative: the man was sick, or absent, or busy, he did not notice the advertisements, etc. Or rather, the question has not arisen so far: his circumstances and behaviour presented themselves as a sort of positive process relating only to itself. It is because of the totalisation of serial results by the group that he now feels the need for an explanation: in relation to the number of top records sold, the words, 'I did not notice the advertisements' take on a negative meaning of quasi-interiority, whereas without the 'top ten', they would + +indicate a mere relation of exteriority. But now, hearing the first bars of this guaranteed music, the serial individual experiences the information as an accusation: he was out of touch (if he did not buy any records that week); he had no taste (if he bought others which did not get into the top ten); or he was unlucky (if he did not notice the advertisements). Fortunately, records last more than a week; their owners will not tire of listening to them within a week. The guilty party can still make up for his mistake on Saturday afternoon: he will buy one or more of the records mentioned, depending on his resources. It is true that this serial action is not in time with the 'spontaneous' ceremony of purchase: but the ceremony of listening - that Mass of alterity - is always possible and he can repeat it on subsequent days as often as he + +likes. + +The contradiction here is due to the fact that the totalising power of the ceremonies comes from the mediated and actualised reciprocity of all the members in a group; but the isolated reactualisation of a unity which has never existed except in the concerted efforts of an advertising group, succeeds only in depicting unity and in realising alterity as separation: for the individual listens to the selected record through Others and through himself as Other. The 'Top Record Prize' leaves him a little more independence: of course, he is overwhelmed by the opinion of the experts, but as we have seen, his own reaction takes the form either of mute dissatisfaction or of wholehearted endorsement. The case of the 'top ten' is quite different, since here the mystification consists in offering him, once he has bought the records, the otherchoice as though it were his own. There can be no doubt that the action of the advertising group produces in him the vague project of uniting with the Others by enjoying what they have enjoyed completely spontaneously in the depths of his own spontaneity; but the realisation of the project leads to total alienation, since the isolated ceremony consecrates him as Other even in his own feelings. This operation will trick him even in his social relations, because when he is in the office, or with friends, he will take himself to be communicating in reciprocity with some Other who has also hought the record, whereas - as we have seen - they are really just the instruments of well-organised + +collectives. + +But what is important for us is the praxis of the group. Its goal is synthetic: to sell as many records as circumstances permit. The means is to manipulate the practico-inert field so as to produce serial reactions which will be retotalised at the level of the common undertaking, that + +is to say, reshaped and forged like inorganic matter. And the means to this means is to constitute the serial as a false totality for everyone. Recurrence, controlled from outside as a determination projected from everyone, through Others, into the false totality of a common field and, in reality, into pure reflexive flight, is what we shall call other-direction (l'extiro-conditionnement). This has two complementary aspects: from the point of view of the praxis of the transcendent group, it appears as a labour which transforms seriality into antiphysis; from the point of view of the serial individual, it is an illusory grasp of his Other-being as unifying itself in the totalisation of the common field, and the realisation of radical alterity (directed by the outside group) in him and in all the Others on the basis of this illusion. In short, other-direction takes alterity as far as it can go because it makes the serial individual do the same as the Others in order to become the same as them. But by doing the same as Others, he loses the chance of becoming the same, except in so far as everyone is other than the Others and other than himself. Now in the totalisation of the common field, lines of flight appear (as reflected by the 'mass media') as characteristics, or as habits (in the sense of exis), or as customsp, Thus, by capitalising on their impotence everyone comes to be affected by these characteristics, habits and customs in so for as they are manifested, in the false unity which is given by the external group, as structures of totality. Thus his alterity for the Others is gradually constituted for him, and introduced to him: if he listens to the radio every Saturday and if he can afford to buy every week's No. I record, he will end up with the record collection of the Other, that is to say, the collection of no one. But the reflexive action of the advertising group, as it affects every other, gradually brings together no one's collection and everyone's collection. In the original state of recurrence, in effect, statistical results as such were not worked out systematically and had no tendency to perpetuate (or universalise) themselves; if figures for record sales in the United States were not published, then if one studied the annual figures there would be no a priori reason for supposing that the overall results should correspond to the contents of the majority of record collections: in fact it would be necessary to distinguish categories, levels of education, social contexts, fashions and the sectors where they were promoted, etc. Thus there would be several popular lists, and not just one; or rather, buying one record might appear incompatible with buying another, in a given social milieu. But the fact that a single list is constituted and carefully diffused every week has the effect of breaking down social and cultural barriers, + +of creating homogeneity (by a double movement, both upward and downward), and of gradually assimilating regional lists to a universal list. Ultimately, the record collection which is no one's becomes indistinguishable from everyone's collection - though without ceasing + +to be no one's. + +The interest of this praxis is immediately obvious, at least in contemporary societies: transcendent action on seriality, in advanced capitalist countries, tends to constitute a distribution-pattern for the market (for everyone and no one, and therefore for every individual) and a control of consumption. Rivalries between advertisers then become irrelevant: at a national level the different sectors of industry and commerce reach a more or less tacit agreement to take advantage of rising incomes and to drive the masses (as inert gatherings): (I) to consume more, and (2) to adapt their budgets not only to their own needs or tastes, but also to the imperatives of national production. If a wage-earner, with long habits of prudence and, where possible, ' of saving (inner-direction) retains his thrift when wages rise, the techniques of other-direction will have to replace his inner directions by those of the Other. But this is not really possible unless the serial individual has been produced from childhood as other-directed. It has recently been shown, in fact, that in infant schools in America (and, of course, throughout the child's education), everyone learns to be the expression of all the Others and thereby of his whole social milieu, so that the slightest exterior serial change returns to him and conditions + +him from outside in alterity. + +Everyone has seen the newspaper competitions in which the names of ten buildings, artists, or cars, etc. are listed in a random order, and the object of the competition is to guess the hierarchy-pattern (which really means the average hierarchy) which will be established by collating the replies of all the Others. The competitor whose list is closest to this list is the winner. In fact whoever wins - that is to say, is chosen, selected, publicly named, and rewarded - does so because he has been more perfectly Other than all the Others. His practical individuality, in the milieu of seriality, is his ability (at least in this particular situation) to become the medium of the Other as a unit of the flight of alterities. Should we say that he was already this mediumistic product of recurrence, or is it that he made himselfa pure prediction of seriality? The answer is, both of them inseparably. The ambivalent statute of prophetic being and passive activity is simply that of every otherdirected individual. This never arises at the level of production, even + +alienated production, even within an exploitative system, simply because work defines itself in terms of need as a free practical operation, in spite of, or even because of, the fact that it may confront the worker as a hostile force. But still it would be a mistake to suppose that this is confined to consumers in heavily industrialised societies. In any society which is haunted by the need to predict and mutually adjust production and markets from a particular point of view, other-direction plays an increasingly important part; it represents a real and new statute of the massified individual, namely the direct hold on the + +masses of control, management and distribution groups. + +But to treat this new relation between the group and the mass as created ex nihilo, form and matter, would be a complete misunderstanding of dialectical rationality. What is new is the historical content and the circumstances which determine it; what is actualised, but permanent, is the synthetic form of unity which appears here. This formal link has in fact always been filled by a content; but what is apparent today, at this moment of History, in which the structures of other-direction are more manifest in and around us is, in fact, the crucial importance of these structures for the comprehension of historical events. There has been a regrettable tendency to see certain collective actions as the product of suddenly formed groups ..:: .. of mass 'spontaneity' - or simply as the result of the more or less disguised activities of those in power. In many cases, both approaches are misleading. For example, there is the seriality of racism, which I have explained: it is always the attitude of the Other. But seriality - though it may cause lynchings or pogroms - is not a sufficient explanation of, for example, the active anti-semitism of the German petty bourgeoisie under the Nazi regime. Now some highly ingenious recent studies have shown that anti-semitism as a historical fact has to be interpreted in terms of the systematic other-direction of the racism of the Other, that is to say, in terms of the continuous action of a group on a series. And this action is defined primarily by its reflexiyity: the group demonstrates racism to the series by producing within it practical signs of its hostility to Jews, or by causing them to be produced; these signs - caricatures, definitions endlessly repeated on the radio, in the newspapers and on walls, tendentious information, etc. - ultimately play the same role as the standard list for everyone and no one. In short (ignoring for the moment their deliberately Manichaean, projective and sadistic characteristics, etc.) they are both concrete designations of a particular monster and the created formula of the series as an indication of the + +masses as a totality. The hatred which these dummies excited in everyone belonged to the Other; but totalising propaganda constituted this hatred into other-direction as an exigency of a totalising ceremony. Then it depended on the government (that is to say, on the determination which it brought elsewhere to Others and which it then diffused as a possible unity of all through the 'mass media'), whether the circums tances for this totalising ceremony would be created, that is to say, whether the petty-bourgeois masses would become the practicoinert agents of an induced pogrom. Anyway, the arrest or execution of a Jew on government orders passively realised the same ceremony of alterity in the masses; every act of violence was irreversible, not only because it destroyed human lives, but because it made everyone an other-directed criminal, adopting the leaders' crimes in so far as he had committed them elsewhere and as an other in an other. Conversely, the acceptance of the sovereign's acts of violence, as an exis in the milieu of other-direction, may always, through the transcendent action of the directing group, be reconverted into a pogrom, as the passive activity + +of a directed seriality. + +And this exis, along with the practical process which its reconversion may produce, remains a false unity for two essential reasons, both of which are dialectical in character. First, even the most enthusiastic consent only means the inability to offer resistance, and therefore separation.87 Secondly, and most important, the serial acceptance of this irreversible other-direction itself increases separations, impotence and the real index of alterity. In fact, both with an approved action and with the practical process seriality re-emerges (in a moment of looting or execution for example) as a force for separation, simply because there has been no real resistance from a hostile group, and no practical totalisation through threats of extermination, to occasion, as real negations, the dissolution of the serial in the Others. On the contrary, looting and firing of undefended shops are in themselves dispersive acts of destruction: they have nothing to do with unity of agents (on the contrary, violence is engendered by disorder) and, from outside, + +87. This does not mean that it is impossible for aparticular individual's approval of the acts of violence to arise also on the basis of a possible challenge; but only that the practice of the sovereign group consists in intensifying separations in every domain, so that the illusion of unity (acceptance-pogrom) is manifested on the basis of a serial inability to realise any other unity. The pogrom becomes the only solution in so far as the police regime introduces mistrust as an + +additional factor of separation. + +they make everyone into the other who is responsihle for the maximum violence committed in the gathering by an other. At the level at which 'collective responsibility' is serial responsibility, its acceptance or rejection by a given other are simply two contradictory expressions (in discourse) of one and the same fact. And this serial responsibility - as the projection of a precise, totalising policy in the milieu of alterity increases the power of the sovereign group to precisely the extent that it deepens everyone's impotence while sustaining the misleading + +scheme of the totalising ceremony. + +With this example, I have tried to show what differentiates a racist exis (which is what is usually studied) from an anti-semitic movement; I have tried above all to indicate that the government apparatus and its sub-groups for constraint and propaganda are careful not to occasion what might be called organised action within inert gatherings. Every organisation disturbs them in so far as it dissolves seriality. Thus the real problem, at this level, is to extract organic actions from the masses without disturbing their statute as non-organised. At this point, the problem of 'organised spontaneity' (l'encadrement) is bound to be raised: modern societies, both East ana West, provide the example of organised demonstrations. A procession - on I May, I4 July, I October etc. - gives a serial public the spectacle of strict organisation. An order is given: soldiers, workers, peasants, intellectuals march in Peking according to some pre-existing plan; there are leaders who regulate the march, its speed, the number of stops, etc. But these supposed groups, in which everyone does the same as all the Others, and regulates his action by that of the Others, and whose leading feature is sheer quanti ty, have nothing in common with the structures of communities. It is true that the march is regulated from outside; but the result of this transcendent action of a member of the sovereign group is precisely to keep them under the statute of other-directedness. These few examples, though very superficially studied, enable one to see - though the point cannot be developed or proved here - that the relation of the State to concrete society can never, even in the best of cases, transcend other- + +direction. 88 + +88. Even if its mode of recruitment is 'democratic', it is still a matter of cooption: the sovereign group confronts series of series and it is its organs which determine them by reflecting their seriality to them in the form of standard lists. All kinds of electoral systems constitute the set of electors as a passive material for other-direction; and the election results no more represent the will of the country, than the top ten records represent the taste of the customers. The only + +7 Bureaucracy and the Cult of Personality + +Thus a sovereign group increases the inertia of collectives and governs by means of it. But, as I said above, it will be worth giving a brief account of how seriality reacts on the sovereign. There are already too many commentaries on it, so I shall not dwell on it for long. As we have seen the ensemble of the sovereign (sub-groups and constituted bodies) forms a complex system whose apparatuses, at the b'ase of the hierarchy, are in direct contact with the masses and constitute what are variously called, very misleadingly, cadres, nuclei, liaison organisations, etc. In reality, these are inorganic instruments whose very inertia constitutes the surface which is in contact with serial inertia, and their role, defined by superior groups, is to manipulate the other-directedness of Others. I have already observed that these sub-groups are surrounded by series; and in separation, as I have shown, they in turn become serialised, Everyone becomes sovereign to himself alone; but, in the milieu of the Other, the sovereign elsewhere is other. On the other hand, other-directedness is based on the passivity of the masses; but this passivity conditions their own passivity: first, because for those who are other-directed they themselves become the embodiment of the standard lists, solidified exigencies, etc., and, in the unity of a single petrification, the representatives of the law - that is to say, of sovereignty-as-an-individual in so far as this produces itself as a universal + +power. + +By this double petrification, they mean either to eliminate change or to control it, depending on the case. These sub-groups retain a practical appearance as long as they can really act as a mediation between the central authorities and the series. But such mediation cannot establish itself as a permanent function: a group may become the mediation between two groups, an individual between two communities; but mediation between the series and the sovereign cannot continue if the sovereign praxis is determined to keep the series in impotence and + +possible manifestation of a 'will' amongst the masses is their revolutionary grouping against the inertia of institutions and against the sovereignty which is based on their impotence. As a passive means, elections may bring about changes - though insignificant ones - in the composition of the sovereign body; but they can never claim to modify government policy (unless the circumstam;t:s which + +accompany it are such as to modify it anyway), + +alterity. Needs will be determined and, where possible, satisfied from outside, in so far as they can be measured by biologists, doctors, etc., but not in so far as they are the object of a genuine demand. This is because their serial structure prevents individuals from forming a group on the basis of a demand, and because the task of other-direction is constantly to raise the threshold for effecting regroupment. In the world of the Other (which is the world of government) violence, rejection, exigency and even riots, sometimes occur: but such disturbances, which are quickly repressed, never serve as a lesson, or as an indication of the depth of popular discontent, precisely because it is always the Other who rebels or makes a demand: the Other, the alien, the suspect, the trouble-maker. The notion of a trouhle-maker, in particular, is senseless except for a member of the sovereign group, that is to say, for a functionary convinced that the only ontological statute of human multiplicities is other-directed passivity. He controls this passivity in the light of the general interest; and the trouble-maker is an anti-sovereign who controls the same passivity in the light of his individual interest (or some other sectional interest). At this point the leader who is criticising the trouble-maker makes a self-criticism on the + +back of an Other, that is to say, as Other. + +Thus there can never be any such thing as popular discontent from the point of view of the sub-group which is immediately responsible for arrangements, and this is for the good reason that discontent is the practice and exis of a group and that the serial statute rules out the possibility of regroupment. The relation between sub-groups and series becomes reijied: they no longer do anything but act materially on the series by means of the serial combinatory, that is to say, the schemes which arise from a serial constitution and make it possible to interpret actions of seriality. The difference between the local leader and the led individual is almost imperceptible: they are both serialised, and both of them live, act and think serially; but the leader thinks the seriality of the Other and acts serially on other-directed series. Thus nothing can be transmitted from the local level to the top because there is no longer anything being transmitted from the popular series to the leader whom they have serialised. It is precisely for this reason that, for his superior, the local leader is the object of a sovereign and univocal praxis. He is a tool for stirring the human material, and no more than a piece of inorganic matter. His autonomy and powers could give rise to reciprocity, if, in virtue of his function, he were to express the people's demands to his superior as human exigencies. But these demands and + +exigencies do not exist: which simply means that they are still the product of the living, suffering individual who is paralysed by alterity. If at some time in the future they do manifest themselves, it will be as those of a group which rejects all mediation and constitutes its own sovereignty; demands always become 'known' too late. This is either because they have no being, and emerge as revolutionary or because they remain unexpressed, depending on circumstances. For his superior, the local leader is an inert guarantee of the inertia of the masses and he hecomes such because they do not offer him, nor does he accept, the counter-power of making demands to the sovereign on + +their behalf. + +Thus, the multiplicity of subordinate agents appears, to the next level 'up', as a superior instance of seriality; and their passivity becomes a material to be worked by other-direction. But this by no means prevents everyone from being suspect, in that his operations could be carried out as a free, practical initiative, or, in other words, assert themselves as an individual's individual sovereignty over the serialities which fill his practical field. Both other-direction and terror have the aim, in relation to local leaders, of replacing real activity by the inert practice of worked matter at every level. Thus each level treats the agents of an inferior level as inorganic objects governed by laws, and loses their guarantee and their free support in relation to the superior level; it, too, becomes serial in so far as it is effective. This means that throughout the hierarchy, objects which are governed by laws of exteriority govern other objects which are placed beneath them, according to these laws and other [in-]organic laws; and that the combination of laws which, at each level, makes it possible to move the material on the inferior level is itself produced within the leaders on this level by a combination of their laws which was created above them. The paralysis of the system necessarily rises from the series which are led to the top, the sovereign alone (whether a small group or an individual) remaining unaffected. Or rather he is affected with passivity as a totalising individual; he becomes inorganic from below, from the depths of the hierarchy; but there is no superior who can + +transform him into a thing. + +In this new constitution of the group, we can observe the following characteristics: at every level of the hierarchy, everyone is a possihle sovereign over the agents of an inferior level or a possible regulatory third party (taking the initiative in agitation or in the formation of a group); but everyone denies these possibilities out of mistrust for his + +peers and fear of being suspect in the eyes of his superiors. Towards his peers, indeed, he adopts the attitude of the pledge and binds himself to inertia in order to be able to lay claim to theirs: separation and recurrence both encourage the re-emergence of the discrete multiplicity which he rejects. The shifting alterity of his equals unravels interiorised plurality into relations of exteriority. The exteriorisation of relations which we observed above is realised in the one who is the institution (and through all his peers). But the structure of sovereignty produces itself at every level as an institutional reinteriorisation; and so everyone, looking towards the superior level, demands perpetual integration from the sovereign; he dissolves his organic individuality in himself as an uncontrollable factor of multiplicity, and merges with his peers in the organic unity of the superior, finding no guarantee for his individual + +existence other than the free individuality of an other. + +It is this triple relation - other-direction of the inferior multiplicity; mistrust and serialising (and serialised) terror at the level of the peers; and the annihilation of organisms in obedience to the superior organism - which constitutes what people call bureaucracy. We saw it emerge from sovereignty itself, when sovereignty was no more than an institutional moment of the group; and we now see it asserting itself as a total suppression of the human, except at a minute point at the top of the hierarchy, as a result ofinertia at the bottom. Its form and dialectical meaning are obvious: the impotence of the masses is the support of sovereignty, and sovereignty undertakes to manipulate them by means of mechanical laws - that is to say, of other-direction - but this voluntarism (that is to say, the affirmation of the practical sovereignty of man over man and the concerted maintenance of the practico-inert statute at the bottom) necessarily implies the mineralisation of man at every level, except the highest. It asserts itself everywhere as the opposite of freedom and tries with all its strength to destroy itself. Thus the impotence of the masses becomes the impotence of the sovereign; it becomes impossible for the half-paralysed man or subgroup at the top to maintain the pyramid of mechanisms, each of which is supposed to set the other in motion. The historical conditions for a bureaucratisation of powers are of course defined in the course of the historical process and through temporal totalisation. But this is not our subject. What relates to the dialectic from the point of view of temporalisation, can be expressed in a few words. Where the State is an apparatus of constraint in a society divided by class conflicts, bureaucracy - the const;;ln t thre;;lt to the sovereign - is easier to avoid than in + +the building of a socialist society: tensions between classes, partial and more or less organised struggles, and groupings - as a developing dissolution of serialities - force the 'public powers' into a more complex action, and confront them with communities, however ephemeral, which challenge the sovereign. He has to define a flexible, living praxis towards them through the other-direction of Others : the scintillating life of the fused group will either reject the old worm-eaten sovereignty of the bureaucracy, or, if it has already manifested itself, as a permanent danger, it will prevent the sovereign from being constituted in + +the most bureaucratised form, namely, as police. + +The omnipotence of police, as an absolute petrification of the functions of the sovereign group, is based on the separation of impotence; such separation must exist for the police-state to maintain and use: in a society which is 'hot' - in Levi-Strauss's excellent phrase - that is to say, in a society in which all forms of class struggle are perpetually alive in opposition to the statute of seriality (among the oppressed and the oppressors), the action of the sovereign will be a politics. Repression, though always in the background, will not be used as much as antagonisms (other-direction will partially disappear and re-emerge in the classic form of ' divide and rule'), tactics and strategy will have to be worked out by apparatuses and the circulation of sovereignty will have to be ensured in both directions. The job of the subordinate functionary is not, of course, to express the demands of popular groups, but to inform on these groups and, in particular, on their demands. This will assure him a sort of quasi-mediating function; the permanent danger that seriality will dissolve around him may confront him with a vital hostile praxis whose menace and urgency demand immediate action. Even if no such thing actually happens, the subordinate agent is defined in his possibilities as capahle of taking such an initiative. On the other hand, a particular contradiction sets the sovereign group, as the unity of the individual and the universal positing itself for itself, in opposition to the dominant class which produces it and sustains it (pays it) as its own apparatus. The dependence of the sovereign is, as we have seen, beyond doubt; but so too is the perpetual affirmation of autonomy with respect to every level. This leads to a tension, which varies with circumstances, and which can determine various methods of reconquest, in the power-groups of the dominant class: osmosis (regulated exchanges between government officials and economic groups), infiltration, influence (direct and indirect), etc. The sovereign group defends itself against these methods, which are in general aimed at altering its + +internal composition, by perpetual vigilance. But this vigilance, or white terror, does not have the paralysing effects of real terror, since, in this particular case, the problem is to defend the sovereign against the over-solicitous concern of his original allies. Of course, they dream of denying either his legitimate sovereignty or the correctness of his praxis in the long term; but they do try to set aside (or suggest) shortterm objectives, to propose some operation, etc., or (if a rebellion has been crushed) to push for sharp repression. All this has to be integrated by the sovereign group: it may take over the proposals, dissolve them in its praxis while appearing to accept them, etc., but it can neither reject them a priori nor ignore them. This bond of interiorisation between the wishes and common demands of the dominant class (as expressed by pressure groups) on the one hand, and sovereignty as praxis on the other, represents, so to speak, the class existence of the sovereign. It requires certain subordinate agents to become real mediations between at least one serial ensemble and the top: and this serial ensemble is just the dominant class, in so far as pressure groups form within it in order to create - in opposition to the policy of the + +government - independent sectors of @ther-direction. + +These remarks are not designed to prove the superiority of sovereign groups in bourgeois democracies, but rather to show that they derive their life from the social contradictions they express. When a sovereign group, with its implacable homogeneity, has integrated every practical grouping into itself, in other words when sovereignty has the monopoly of the group, and when this grouping of groupings defines itself in the last instance by its direct hold over passive serialities and its strict practices of other-direction, and when this sovereignty is not a class product (like a monarchical or bourgeois state) and is necessarily recruited by co-option, producing its legitimacy by and for itself, then the sovereign pyramid will turn on itself in the void, regardless of its transcendent tasks. It will elude the control of a dominant class (for example capital) and will have to struggle only against itself, that is to say, against the dangers of separation and institutionalisation; and it is precisely this struggle against itself which will lead to bureaucratisation. No one today could believe that the first stage of a socialist revolution realises the dictatorship of the proletariat. But, in a perpetual state of extreme emergency, and in the light of well known gigantic tasks, a revolutionary group has institutionalised itself and as such has produced its own legitimacy as sovereign and, monopolising the possibilities of grouping, it has set in motion and arranged serialities by practices + +of other-direction. It should be understood, in fact, by means of dialectical Reason itself, that any creation by a sovereign institutional group of a supposed regroupment of serial individuals (whether trade unions or other regimented formations) can only be a new differentiation and extension of the group itself to the extent that its members are all bearers of the sovereign power and that regimentation, even at the lowest level, does not transform the Other-Being of serial individuals into being-in-the-group, but rather, by means of a false, fixating totalisation, defines a new sector of intensive other-direction. The limi t on the real power of the most dictatorial State is that it cannot create a group outside itself: all it can do is, when circumstances permit, grow to some extent and differentiate itself (by producing new sub-groups) . The only effect of the determinations which it directly produces within inert gatherings is that it transfers them - in a given place and situation - from the serial level to that of an 'other-directed zone'. Every group, in fact, in so far as its own totalising movement contains the abstract possibility of establishing its own sovereignty, constitutes itself either outside the State (even if it is more or less directly connected with it, through subventions, official encouragement, etc.), by positing the autonomy of its praxis, or, primarily in opposition to the State, as a denunciation and rejection of its transcendent sovereignty, through a practice of abstention, passive resistance, disobedience or revolt. The internal contradictions of the socialist world bring out, through the immense progress that has been made, the objective exigency for debureaucratisation, decentralisation, and democratisation: and this last term should be taken to mean that the sovereign must gradually abandon its monopoly of the group (the question arises at the level of workers' committees). In fact, in the USSR at least, the destruction of the Soviet bourgeoisie was completed long ago. This means that the 'dictatorship of the proletariat' was an optimistic notion, constructed too hastily through misunderstanding the formal laws of dialectical Reason: there was once a time when it was too soon. for such dictatorship in the USSR: the real dictatorship was that of a self-perpetuating group which, in the name of a delegation which the proletariat had not given it, exercised power over the bourgeois class which was in the process of being destroyed, over the peasant class and over the working class itself. From the point of view of the masses the sovereignty of this group was neither legitimate nor illegitimate : its practical legitimation was due to the fact that the sovereign constructed his own illegitimacy by his mistakes and crimes: this is the judgement of History. Today it + +is too late, and the problem which really arises is that of the gradual withering-away of the State in favour of broader and broader re- + +groupments of other-directed serialities. + +And the reason why the dictatorship of the proletariat (as a real exercise of power through the totalisation of the working class) never occurred is that the very idea is absurd, being a bastard compromise between the active, sovereign group and passive seriality. Historical experience has shown quite undeniably that the first moment in the construction of socialist society - to consider it at the still abstract level of power - could only be the indissoluble aggregation of bureaucracy, of Terror and of the cult of personality. This first stage seems to be approaching its end, despite some terrible setbacks; and, in any case, wherever a new socialist regime is established today, the developing socialisation of half the world will produce this new revolution in a conjuncture and historical totalisation quite different from those which characterised the revolution of 1917. From our point of view, the impossibility of the proletariat exercising a dictatorship is formally proved by the fact that it is impossible for any form of group to constitute itself as a hyper-organism. Bureaucratic terror and the cult of personality are just another expression of the relation between the constituent dialectic and the constituted dialectic, that is to say, of the necessity that a common action as such (through the multiple differentiation of tasks) should practically reflect upon itself so as constantly to control and unify itself in the untranscendable form of an individual unit. It is true that Stalin was the Party and the State; or rather, that the Party and the State were Stalin. But his violence is an expression, in a specific process, of the violent contradiction between the two dialectics, that is to say, of the impossibility that the group as constituted praxis should transcend the statute of this organic individuality which it contains within itself, and transforms and transcends in so far as it is, in common interiority, a function of multiplicity. However, the untranscendability of the ontological and practical statute of the regulatory third party is not a de facto and therefore unintelligible limit assigned to communities: we have seen how it arises, in the translucidity of the critical investigation, in the course of development of the constituent dialectic, as a free, organic praxis and as a human relation of reciprocity. In other words, the constituent dialectic, while producing itself as the Reason of action, and realising its structures in the light of temporalisation, already determines the possibilities and impossibilities of common praxis; it naturalises + +(nature) constituted Reason. Thus constituted Reason derives its very intelligibility - as the structured logic of common action - from constituent Reason: and if our critical investigation enables us to grasp the formal genesis of the second dialectic, in its double character as praxis and process, with its scope and its limits in terms of the practico- + +inert field and of dissolutions of seriality, this is enough. + +Our investigation has now arrived at a shifting flight of elucidations: the practical unity of the group which organises itself lies in its object, in groups external to it; it passes momentarily through every participant in an undertaking as an 'excluded third party' (tiers exclu); and it resurfaces theoretically and practically in the activity of the sovereign. But it is never really given inside the group itself, in the way that the unity of the moments of an individual action lies in the unity of an active development. On the other hand, we can immediately see the true power of the group in the impotence of each of its members : this impotence endows functions with a material force of inertia, and turns them into hard, heavy organs which are capable of striking, crushing, etc. Thus the true efficacity of the group, as a praxis bogged down in matter, lies in its materiality - that is, in its becoming-process. But, in so far as praxis is process, goals lose their teleological character. + +Without ceasing to be genuine goals, they become destinies. + +7 + +The Place of History + +Dialectical investigation as totalisation: the level of the concrete, + +the place of history + +z The Reciprocity of Groups and Collectives + +The group emerges from the more or less complete dissolution of collectives and in the unity of a common praxis. And the object of this praxis can be defined only in relation to other groups, which may or may not be mediated by series, or to an inert gathering, which may or may not be mediated by other groups, or to worked matter, which may + +or may not be mediated by series and groups. + +" + +But if the collective from which the group arises bears at least some superficial mark of its dissolving praxis, then the result of the common action, regardless of its other characteristics, must also be a determination of the collective and of worked matter. Thus, in a sense, the objective reality of the group (its practical objectification) is the collective and the inorganic. In other words, looking at the praxis of the group outside itself in the transcendent milieu of its objectification, + +we can see that it is defined by three principal characteristics. + +(I) It practically realises new and unifying realities in the social and physical material which constitutes its practical field. In the friendly or hostile groups which are adjacent to it it directly produces certain modifications which are both suffered and readopted in the course of internal rearrangements. Indirectly, by its mere presence in the common field (as a practical field for every community at various levels), it produces transformations at a distance, that is to say, induced rearrangements readopted by distant groups through the totalising transformation of the field. Since the field is, effectively, a synthetic unity of practical totalisation, the distant appearance of another group as a non- + +totalisable retotalisation of diversity (and as a totalising mutual reconditioning of elements in a sort of formidable, fleeting autonomy) confronts each group with the permanent threat of a radical alteration of all the internal references of the system and thus of the modification of the group itself through a retotalised totalisation at least as an unrealisable signification. The question whether these practical results represent a partial failure or a success need not concern us at present. What is obvious is that the efficacity of a praxis is directly linked to its concrete objective and that the different actions which it performs here are all unified within the common field at eyery leyel of inyestigation and + +by all groups present. + +(2) These synthetic results are necessarily alienated, although the moment where alienation appears is not necessarily that in which objectification occurs. The alienation of a free, isolated praxis - as it occurs in the practico-inert field - has to be immediate because this pseudo-isolation is already in itself a statute of impotence created through the mediation of the inorganic. But the objectification of common praxis can be an immediate, total success: since the group is the negation of impotence, its success is conditioned by the reigning relations of forces. An army may annihilate an enemy army and entirely occupy the defeated country. But in so far as this objectification is ultimately an inert object and an individual reality within the developing totalisatio'n, it is necessarily appropriated and alienated. Even defeated groups in the practical field can manipulate this field itself, and endow it with a real polyvalence which deprives the object of any univocal, uncontested signification. In other words, the object which is produced is in itself pluri-dimensional and there is no guarantee that its different significations will not be contradictory. It is also clear that they present themselves to the group as unrealisable significations, related to an elsewhere. By means of an indirect, antagonistic reciprocity, the object returns marked by the developing totalisation of the totalising groups : the common field as a pluri-dimensional insecurity becomes the mediation between the object and the group. But since the truth of the group lies in its object, the practical plurality of the objective dimensions of the thing which is realised turns back on the active community and modifies it in turn, to precisely the extent + +that its own victory has modified other communities. + +This does not mean that we have to return to historical scepticism on the contrary; but we must recognise that these multiple significations can be integrated only from a point of view in which it is possible to + +integrate all the groups of the common field and all its practical determinations, that is to say, from a historical point of view. Nevertheless, even if the group survives this practical success, and even if it organises and maintains itself, we must abandon any idea of humanity historialising itself in the development of a single temporalisation which began with 'the first men' and which will finish with 'the last': the dialectical investigation establishes that here too, in the absence of a temporal hyper-organism, we have treated diachronic totalisation as though it were a free, individual temporalisation. Humanity treated as one Man: this is the illusion of the constituted dialectic. There are in fact several temporalisations; what I have in mind are those diachronic multiplicities known as generations. Each generation is a natural and social product of the previous generation; but each generation separates itself from the previous one and, as a material condition of its praxis, transcends the objectification of the previous praxis, that is to say, the being of the previous generation, in so far as this being becomes, through this very transcendence, an inert object which needs to be rearranged. Thus the temporal development of the objective process to which the group gives birth entirely eludes it as one moves further away from the moment in which it was realised by praxis: it becomes the condition for a new praxis within this praxis become object, the condition of a condition, material, etc. Of course this does not mean that new generations can, by their own praxis, arbitrarily assign it any signification and use, but it does mean that however rigorous its objective features, they will acquire their meaning only in the course of a process of dialectical development (of the totalising synthesis of various circumstances) which, being dialectical, must be not only inflexible but also, from the point of view of the first generation, completely unpredictable (at least given a certain time-lag, whose length will vary + +according to circumstances). + +The plurality of temporalisations together with temporal unification (a synthetic unification of the antecedent by the consequent, a present unification of the new multiplicity through old frameworks) actually constitute the evolution of humanity as the praxis of a diachronic group, that is to say, as the temporal aspect of the constituted dialectic. Synchronic groups are a work of unification of simultaneous multiplicities in the light of a common objective. Diachronic groups are the result of the retro-anterogressive unification of temporalisations; thus the temporality of a nation, for example, as a created unity and a constituted dialectic is to the living temporalisation of the members of + +one generation what common praxis is to free organic practice. We shall return to this point. What is certain is that the result achieved by the original group (original in the sense of being first on this occasion, rather than absolutely) is a quasi-object for the young and passes progressively to the total inertia of the inorganic object; similarly, the living temporalisation (or rather the mediated reciprocity of temporalisations) which produced it is transformed by the transcending praxis of the newcomers into an inert and finished determination of temporality (as a created process and a diachronic unity). Produced by the praxis of their parents, children reinteriorise their praxis, divert it, transcend it and make it other through its new results: they appropriate it. And there is no reason to suppose that defeated groups will not produce, through the changes caused by their defeat, sons who will take advantage of it and wipe out their conquerors. Thus objectified praxis must necessarily allow itself to be modified by a double alienation (both synchronic and diachronic). . The costly French victory of 1918 was expressed on every level by a multiplicity of social transformations. Let me describe just two of them - perhaps not the most important - to illustrate these points. On the one hand, the first occurrence of total war (or national war, as it was called at the time) was expressed after the peace by a demographic fact which was (at least originally) of an almost mechanical nature: empty class-rooms. Th� military practice known as the 'strategy of a million' (strategie du million d' hommes) re-emerged, alienated and passivised, as a simple numerical relation characterising the succeeding generations. But this numerical relation was itself preserved by the Malthusian practices of the survivors. These practices existed at the level of pure recurrence, being the object of religious and political prohibitions, but through the alterity of the collective they helped give the result an appearance of analytical necessity. The conditions of the war and of the post-war years - which were very different in Germany - led to an increase in the numerical superiority of the German population. Thus the victory of 1918 created in the common field of Europe the possi- + +bility of the defeat of 1940. + +On the other hand, for the French children born between 1914 and 1920, the war lay behind them as a hideous object, a product of paternal madness. Most of them transcended it towards a militant pacifism or a dream of universal peace, precisely because it had ended in victory. The German defeat, in contrast, was transcended as a revolt against the defeated fathers and as a wish for revenge among young Germans + +through the practice of Natism. This reversal, which is often remarked on, therefore expresses a double alienation (synchronic and diachronic) of the French victory. Thus group action is always doomed to synchronic alienation89 except when the practical community is identical to all the individuals in the common field; then it is doomed without qualification to diachronic alienation. On this basis one can see counter-finalities re-emerging at the level of group praxis, and tearing up the common field (empty classrooms, in so far as they are produced with the mediation of Malthusianism as recurrence, manifest themselves as a counter-finality of total war and of victory, its ob- + +jectification). + +(3) But, apart from these interactions, group action is of itself a radical transformation of the common statute in so far as its results, without losing their synthetic unity, imprint themselves on inorganic matter or become the strict determination of a collective (or of any practico-inert concretion). The practical unity of the group and the free pledged inertia of its members are reflected to it as the inorganic passivity of a pure physical or human materiality which retains, in itself and in the exteriority of its parts, the false unity of a seal. The group was constituted in opposition to recurrence; and it becomes the means of determining a serial process through the knowledge and application of laws of alterity. We have seen how the paralysis of seriality rises from other-directed gatherings towards the sovereign. But the embodiment of powers is a special case. As a general rule, the group develops counter-finalities which elude it in so far as it acts on the inorganic, either directly or through the mediation of collectives, and in so far as it acts indirectly on groups and brings about a serial process in a gathering. Such, ultimately, are the limits of its praxis: born to dissolve series in the living synthesis of a community, it is blocked in its spatiotemporal development by the un transcend able statute of organic individuality and finds its being, outside itself, in the passive determinations of inorganic exteriority which it had wished to repress in itself. It is formed in opposition to alienation, in so far as alienation substitutes the practico-inert field for the free practical field of the individual; but it cannot escape alienation any more than the individual + +can, and it thereby relapses into serial passivity. + +89. By this I do not mean that alienation must follow action immediately, but that it will occur in the historical temporalisation of the group and of its genera- + +tion. + +We have seen institutionalisation as petrified practice. But if we were to make a simple investigation of the social field around us, we would find plenty of examples of even more extreme petrification. In the extreme case, the group (as a praxis of other-direction) merges completely with its object; that is, it is not its praxis, but itself which passes entirely into objectified being. In particular, I would single out the studies of shop workers by American sociologists. Recent studies in the USA have examined the practical behaviour of such workers, as agents integrated into an organised economic group. Today they must undergo a real apprenticeship in order to learn techniques of manipulation: the customer (as a serial object) must be manipulated as a complex apparatus according to certain methods based on certain laws (which are also serial). But in order to manipulate his customers, the employee must first learn to manipulate himself (change his mood, put the customer in the right, etc.). The operation itself turns out to be the same: one manipulates oneself in order to manipulate others, or one manipulates Others in so far as one is manipulated oneself. For, ultimately, to manipulate oneself - as this study clearly demonstrates - is, for the employee himself, and without any possible douht, to have heen manipulated (apprenticeship) in such a way as to adopt practical selfdeterminations in particular circumstances and for a given aim. This manipulation, as a determination in exis of manipulative-being (Ntre manipulateur) relates to two indeterminates of seriality, one vertical (the hierarchical group, manipulations of manipulations, etc.) and the other horizontal (the exterior series of the manipulated). But each of them relates to the Other, and ultimately manipulation, which was originally simply a technique of treating the Other as Other,90 becomes the universal law of alterity. The only difference between the manipulating group and the manipulated series is that in the latter alterity is the constitutive law of the practico-inert field, and therefore a law which is obeyed in exteriority, whereas in the group it is the radical exteriorisation of a praxis which is organised in interiority, but which allows itself + +to be defined entirely by its object. + +Of course, the group's reversion to the collective statute does not + +90. The problem is to persuade the customer to buy what the Other is buying: that ohject which as a private individual he would reject. This 'privacy' has to be masked by treating him as an Other and, for this purpose, it is necessary to approach him as the Other. Manipulation consists in producing oneself as the Other in order to refer the customer to his alterity through the simple reciprocity + +of relations. + +necessarily take any particular period of time. It is determined by the historical process as a whole and by the special features of the undertaking: nevertheless, if the group were not already dissolved, constituted temporality would tend to make the group as an inert instrument of passive action equivalent to an acted-on gathering as the end, reason and means of this practico-inert connection. It would be easy - but outside our subject - to show how the generalised practice of other-direction tends, in economically advanced societies, to constitute a new objectivity of the social object as an object of external, infinitely infinite conditioning, every part of which is itself induced in other objects by other conditioning. The absolute destruction, even in the conditioning groups (power-groups, propaganda-groups, pressure-groups, etc.) of common, totalisingpraxis, and its metamorphosis (through the sclerosis of the group and the multiplication of series) into a fleeting unity of alterity, have the effect of dissolving the unitary praxis of manipulation into the horizontal and vertical multiplicities of infinite seriality. At this level, the image of organic individuality as the untranscendable schema of the constituent and constituted dialectic either dissolves or remains as a crossroads of serialities. But the dialectical structure of action will also have inscribed itself in inertia as its law of exteriority: and the example of Taylor, as we have seen already, shows how a dialectical operation can be divided and redistributed between pure, inorganic inertias (specialised machines) through an analysis by positivist Reason. The total objectivity of man for himself, in so far as he is an Other-Being for and through the other, is not yet reinteriorised as a pure, transcended condition for a dialectical and unified act of integration: on the contrary, any employment of the other field (champ autre) transforms the group into an Other, that is to say, into a practico-inert unit of alterity. The historical and practical problem does not concern us here, though it is of crucial concern from the point of view of our real activity as concrete men. What concerned me was to lead the group through the triple character of realised praxis to the last of its + +incarnations, that is to say, to see it dissolve into seriality. + +2 The Circularity of Dialectical Investigation + +This enables us to reach the concrete at last, that is to say, to complete our dialectical investigation. We now confront not the real concrete, which can only be historical, hut the set of formal contexts, curves, structures and conditionings which constitute the formal milieu in which the historical concrete must necessarily occur. Or rather - since nothing is settled except past being - we are at last encountering the set of structures of transcended-being which historical praxis transcends when it produces itself as a constituted dialectic in accordance with laws imposed by the constituent dialectic on the basis of this transcended-being, so as to constitute themselves as the conditions for a + +new praxis, with the same statute of transcended-being. + +And if it is asked how our basic investigation, as such, can be completed (that is to say, since it is also a praxis, why it can be completed and entirely identified with its results), our reply is that the obvious criterion of its totalising value is its circularity. In fact we have seen how the first and most concrete characteristics of the individual as an abstract reality lie in alienation to the practico-inert; but the practico-inert, as a non-dialectical thickening of Being, enables sociality to b� created as the common work of groups on series, and allows alienated freedom to reappear as a violence exerted upon necessity. And this common praxis gave its practical truth to the field of serialities: it unveiled it and constituted it as what has to be dissolved. But our study of the different structures, in an order of increasing complexity, has shown inertia reappearing inside groups, at first as the free violence of freedoms against freedoms and then becoming a common heing in a reciprocally created inertia. This IS what we have called freedom as necessity. On this basis, and through the force of inertia itself, this necessity, freely accepted under the pressure of increasingly urgent circumstances and in the milieu of scarcity, becomes pledged faith, and an agent of the re-exteriorisation of interiority (organised and institutionalised relations) until the most extreme mode of exteriority (the institution) produces in its own institutional statute the conditions + +and means of re-interiorisation. + +In fact, the sequence of the dialectical investigation has shown sovereignty as an agent of petrification, and as a consequence an essential factor of increasing seriality. And this seriality is not simply + +the formal development of pledged inertia in material conditions which demand it (separation, etc.) : in so far as the group constitutes itself in direct contact with inert gatherings, alterity rises into it from its material. However just as the group as worked reciprocity is a human product rather than a given of nature, so its action on series produces the form of worked seriality which we have called other-direction. Thus the difference between a group whose unity becomes more and more like a seal impressed on a human wax which is solidifying, and a gathering whose very inertia turns into a source of energy, in so far as it is exploited for serial actions by a false unity which is induced within seriality, tends to disappear. So it appears that we left collectives in the moment where the group was extricating itself from them and where the common initiative (through its half-failure: practical success, or at least possibility of practical success, but ontological failure) forced us back to them, to the extent that the necessity of freedom implied the progressive alienation of freedom to necessity. But when we reach the eng of our investigation, we do not find collectives as we left them: the mere constitution of a group at the epidermic surface of a series constitutes for other layers of seriality a kind of abstract, negative unity (that of the non-grouped) ; at every moment of the investigation, a group's practices and manipulations differentiate certain sectors of series by employing recurrence as a mystifying synthesis in the form of other-direction; and in the end petrified groups collapse into the series, their practical unity having become an inert seal of pure exteriority. In this way series preserve and serialise significations (totalisations which are either dead or else have become false totalities) just as worked matter preserves determinations produced by work Of, in other words, series, in certain sectors, become inorganic, worked + +materiality. + +To go back to the deepest origin of the group, there can be no doubt that, whatever its manifest aim may be, it produces itself through the project of taking the inhuman power of mediation between men away from worked matter and giving it, in the community, to each and to all and constituting itself, as structured, as a resumption of control over the materiality of the practical field (things and collectives) by free communised praxis (the pledge, etc.). From its first appearance as the erosion of the collective, it is possible to see in it - to use Marxist terminology - the project of removing man from the statute of alterity which makes him a product of his product, in order to transform him, hot (d chaud), by appropriate practices, into a product of the group, that + +is to say - as long as the group is freedom - into his own product. This double concrete undertaking is realised, of course, in concrete circumstances and in the basic context of need and scarcity. But this is a dialectical development; it asserts itself and gets lost in the antidialectical being of the practico-inert and produces itself anew as the very negation of this being; and consequently, although this conditioning by need is both indispensable and strict (directly or indirectly), it does not explain, in the sense of positivistic reason, the constitution of the particular reality which is the group. And, indeed, we have seen how threats and needs can give rise to a negative unity in those layers of the gathering which are inert in so far as they are already unified (by the enemy, by a natural but totalising threat, etc.): and it is on the basis of these abstract significations of synthetic unity that every Other acquires the ability to liquidate the Other in himself. Thus, in serial impotence, the negative possibility of the group produces itself everywhere as that which denies this impotence, or as that which is made temporarily impossible by this impotence. The group defines and produces itself not only as an instrument, but also as a mode of existence; it posits itself for itself - in the strict determination of its transcendent task - as the free milieu of free human relations; and on the basis of the pledge, it produces man as a free common individual, and confers new birth on the Other: thus the group is both the most effective means of controlling the surrounding materiality in the context of scarcity and the absolute end as pure freedom liberating men from + +alterity. + +These observations are intended to demonstrate the basic reciprocity between groups and the collectives. Since, in effect, the group constitutes itself with the Others of the collective, all the imposed external characteristics of the collective are transferred to the group itself, are interiorised and, having been adopted through the pledge, determine it in interiority. A revolutionary party, intent on liquidating certain prejudices and ideological tendencies (imposed on the exploited class by the exploiting class by means of propaganda), will be formed through the union of the exploited who are determined by such an ideology and such prejudices. In the concrete domain of the group, this passivity presents itself as Other-Being which remains an inertia in everyone and which has to be liquidated as such, by everyone and by specialised organisations. A resumption in freedom is therefore characterised - in this negative example - by rearranging the group so as to destroy the inherited characteristic. In this sense, it can be said + +that the tangle of passive determinations which constitutes the collective, is entirely reproduced within the group as a perspective for acting on itself (positively and negatively) in the context of a transcendent objective. The entire temporalisation of a practical community is characterised from within by the evolution of restructured alterities in so far as this evolution is conditioned by practice (that is to say, by acting on the objective and by its reactions). Thus, the First French Republic was proclaimed by royalists. Or rather, at the time of the flight to Varennes, the assemblies, clubs, etc., discovered their royalism as an unnoticed inertia and, in the course of the following year, reclassifications, liquidations, schisms and purges, conditioned by the movement of History, led these power-groups and pressure-groups to + +make themselyes republican hy proclaiming the Republic. + +Conversely, seriality, in so far as the group emerged from it, is profoundly determined by this separation. The unity of the grouping movement is perceived in alterity and negatively: it creates fear, and every Other imagines he will have to pay for the Others; and the action frightens the torpid. But, at the same time, it establishes its own legitimacy by reasserting its freedom and, at the same time, designates the exis of the Other as the inert ensemble which engulfs it in seriality (and which must either be liquidated or readopted in freedom). Now, the alienation of the Other is sustained and lived by everyone through an alienated freedom: alienated in its objectification, in its results, etc., but free and constituent, in so far as it is lost so that the Other can exist. Thus for every practical freedom which exhausts itself in order to produce necessity as alienation, the group is the free possibility of integration (one can join it or sign on). Thus it depends, in alterity, on everyone's choice. And this individual in the series will thereby initiate, by himself and for himself (through the mediation of the group), a liquidation of alterity, according to circumstances and to the particular History; and the Other who strenuously rejects the group will have to adopt alterity as ifit were the result of a free common praxis: he will have to behave as if Other-Being were a system of values and a practical organisation; and he will thereby negatively reflect the action of the + +group and contribute to the dissolution of alterity. + +Dialectical exchanges of an osmotic nature therefore concretely occur between groups and serialities: the series infects the group with its passivity, and either the group interiorises it and transforms it into instrumentality or it is ultimately destroyed by it; the group, in all its forms, forces the statute of alterity to emerge from immediacy, and + +produces a reflexion in the collective as such. But we should not forget that the opposite reciprocal relation is possible: the series may show by still isolated agitations that it is approaching the point at which it will dissolve into a group; thus it may exert real pressure on the active community which 'represents' it, and the group which is in the process of petrification may become an obstacle to the dissolution of seriality in the collective on account of its own inertia. In any case, a directing group, as an epidermic emergence from the collective, produces a double structure of unity in it: one of them is positive but illusory, and is the mirage of totality in the milieu of other-direction; the other is real but negative and ambivalent, and is the totalisation of the nongrouped by their non-membership of the group, which will ultimately be lived by everyone either as an impotence which has to be transcended (a negation of the negative totalisation) or as a practical refusal to join the group (a constitution of alterity into a practical and totalising + +bond of interiority: counter-groups).91 + +Through its decline and relapse into seriality, the group, at a distance, causes pseudo-synthetic or negatively synthetic variations in the collective. The induced, phantasmal unity of the collective from which a fused group has just extricated itself - as the immediate connection of impotence to action, of free praxis to suffered alterity, etc. - is completely different from the unities of other-direction. In so far as a small group knows how to produce them according to rule, it can use these unities to exploit the immense potentialities of an indefinite series (in the strictly physical sense of transformations of energy) so as to bring about specific changes in the social field by means of machines. Thus the group, as praxis, reproduces itself at every level with the + +91. Counter-groups cannot be groups, except when the sovereign integrates them into apparatuses of constraint. In themselves, they constitute by their unity the mirage of a hostile group. They may occasionally present themselves as directed groups (with guides, organisers, etc.). But despite these attributes of practical totalisation their structure is still serial. If they come into contact with an enemy group (but a genuinely practical one) they are immediately dispersed. The difference between them and pure seriality is simply due to the fact that everyone who is marching in step with the Others, and, in the last resort, in ocher-step, is ultimately affected by a practical and adopted alterity. But these two characteristics, being 'practical' and being 'adopted', are induced: it is free praxis which, from outside, forces inertia to become negative action, while the interiorisation of this determination becomes adopted alterity. In fact, nothing is adopted; it is simply that they remain other and try, as Other, to prevent the dissolution of the + +series in the Others. + +statute appropriate to each, in one case other-direction, at a lower level pure seriality, and lower still, the strict, directed equivalence of two + +physico-chemical states. + +The preceding paragraphs can be summed up by saying that the constituted dialectic presents itself as a double circularity. The first circularity is of a static order: we can observe that the group's structures and lines of action are defined by the features of the collective from which it has extricated itself; and at the same time, in its practical relation with the collective, the group reproduces itself as directed alterity and as the-exploitation of passive activity at every level until it becomes purely and simply the movement of the machine and the rhythm of production. 92 . The second circularity is the perpetual movement which will sooner or later degrade actual groups and cause them to collapse back into collectives. I will recall here that this circularity is conditioned only by the movement of History and that, regardless of their statute, groups can either arise from the practico-inert field or be reabsorbed into it; and there is no formal law to compel them to pass through the succession of different statutes described above. A fused group may either dissolve instantaneously or be at the beginning of a long development which will lead to sovereignty; and in the complex world glimpsed here, the sovereign group itself may arise directly from the collective itself (or rather from its sector of other-direction). But it cannot really arise unless all the formal rules of its statute (separation, the institution, the exteriorisation of practices, and reinteriorisation by the untranscendable third party) are given simultaneously in their mutual conditioning. But in itself this should cause no surprise, and only the whole historical complex can determine whether the group will emerge already half-petrified, since in concrete reality, that is to say, in every moment of a temporalisation, all statutes of all groups, whether alive or dead, and all types of seriality (with all their induced unities, whether illusory or real, whether negative or positive) are given together as a tangle of strict relations and as the dispersed raw + +material of the developing totalisation. + +Thus every pledged group, which forms freely at the expense of a series, necessarily relates in itself to some less differentiated structures + +92. In the totalisation of the common field, every group does of course also find its objectivity in every hostile or friendly group. But this horizontal circularity is too obvious to be worth dwelling on. What is important for us is vertical + +circularity. + +and ultimately to the fused group, which is its fundamental form and its surety. Butfusion, as the totalising moment of the regulatory/regulated third party, takes place in the pledge itself, or rather in the moment of the decision to pledge. The first third party to raise his hand immediately gives the series everywhere the opportunity to dissolve, and it dissolves through the pledge as ubiquity. The stage is not missed out; but it is the immediate basis of the second stage (and, if necessary, this of the third, etc.). In the same way, fusion and the pledge, with their masked crude violence, sustain the feeble contractual link of a group in the process of organisation: in fact we shall encounter them again in the intransigence of colleagues and leaders, in a period of rearrangement. It should also be added that, although all forms of group are in themselves created products, produced by human labour, each of them re-produces itself in practico-inert fields and in common fields which are already determined by analogous forms (dead or alive) and under the direct or indirect influence of their presence. And in fact we have just seen that no group of any form can produce itself without influencing all social fields, and that seriality itself is determined, either negatively or positively, by unitary schemata which will be taken up again by the practical movement of regroupment. It is this double circularity, static and dynamic, in so far as it is manifested in shifting relations at every level of every social concretion, which constitutes the final moment of the dialectical investigation and, therefore, the concrete reality of sociality. This concrete moment of the investigation reintegrates all the abstract moments which we have reached and transcended one after the other; it replaces them within the concrete in their concrete function. In the first place, the free praxis of the isolated individual loses its suspicious appearance as a Robinsonade; there is no such thing as an isolated individual (unless isolation is treated as a special structure of sociality). But within the historical totalisation, the real disappearance of the isolated individual and his replacement by the Other or by the common individual is based on organic praxis both as constituent dialectic and as a mediation (at another level) between function and the transcendent object. We will never encounter an isolated individual except implicitly and negatively, as a relativity of the constituted dialectic, that is to say, as a basic absence of a group ontological statute and as the shifting exile of common individuals (Fraternity-Terror) and in the paradox that the group tries to dissolve the multiplicity of persons in the cult of personality. Thus we can now see that the concrete dialectic is that which is revealed through the common praxis of a group; but we also + +know that the impossibility (for a union of individuals) of transcending organic action as a strictly individual model is the basic condition of historical rationality, that is to say, that constituted dialectical Reason (as the living intelligibility of all common praxis) must always be related to its ever present but always veiled foundation, constituent rationality. Without the strict, permanent limitation of relating the group to this foundation, the community is no less abstract than the isolated individual: there are revolutionary pastorals on the group + +which are the exact counterpart of Robinsonades. + +But, in the same way, examining groups independently of series would be just as abstract as examining series independently of groups. In reality, the historical production of one or several groups determines a new kind of practical field, which we call the common field, whereas seriality defines the field which we have called practico-inert. But the circularity which we have just explained makes it possible to see why the dialectic - as a formal law of movement - remains silent on questions of priority. There is actually no a priori ground for supposing that seriality is an earlier statute than the group, although it is true that the group constitutes itself in and against it. Not only do we always find groups and gatherings together, but also, only dialectical investigation and experience will enable us to determine whether the seriality in question is an immediate gathering or whether it is constituted by old groups which have been serialised. Indeed, we have seen that sooner or later they return to the statute of inertia. But are we to regard the stuff of seriality as the inorganic as a foundation of object-sociality (socialite-objet), or should it be reduced to a dust of degenerate dead organisms? And - as we perceive it in everyday experience - is there not a perpetual double movement of regroupment and petrification? We can ignore such questions: our purpose was to explain the intelligibility of these possibilities; and this we have done. + +3 The Working Class as Institution, Fused Group + +and Series + +At this level, it should be observed that the complex forms assumed, in and through circularity, by what are conventionally called social + +realities, need not be confined to any one specific level of intelligibility, and that it may be impossible to confine them to any particular practico-ontological statute. This is not just because groups have a serial destiny even in the moment of their practical totalisation, or because a particular seriality may, in some circumstances, be transformed into a community. The most important reason is that the group is always marked by the series, that it becomes its reality in the milieu of freedom, and that a series is determined, even in its totally inorganic practico-inert layers, by the sovereign self-production of the group. It is therefore necessary to conceive of a specific statute for certain realities whose real unity is manifested as a bond of interiority between common and serial multiplicities. This applies, for example, to social classes (when defined within a system of exploitation).93 We have shown how class-being (for example, in the working class) is defined by the seriality of impotence in so far as it is qualified and determined by practico-inert exigencies : the primary, negative relation of the worker to the machine (non-ownership), the mystification of the free contract, and labour becoming a hostile force for the worker, on the basis of the wage system and the capitalist process. All this takes place in a milieu of serial dispersal and antagonistic reciprocities on the labour market. Alienation as a real and strict process within the system arises in and through alterity as infinite recurrence: it concretises the abstract structure in an entirely concrete historical movement; but the dispersive skeleton, as a relation of fleeting impotence amongst the workers themselves, is a necessary part of this concretisation. Industrialisation produces its proletariat; it drains it from the countryside, and regulates its birthrate. But, here as elsewhere, a statute of impotence is + +produced, through the serialisation of the proletarians. + +But this serial, practico-inert statute would not lead to class struggle if the permanent possibility of dissolving the series were not available to everyone; and we have seen how a first, abstract determination of this possible unity emerges through class interest, as a possible negation of destiny. However, the transformation of a class into an actualised group has never actually occurred, even in revolutionary periods. But we have seen that seriality is always being eroded by action groups constituted at various levels and pursuing variable objectives. Tradeunion organisation, as we saw above, is typical of the organised group + +93 . But it does not apply to classes as defined by sociologists or ethnographers + +investigating 'primitive' societies. + +which becomes institutional and sovereign (and is in constant danger of bureaucratisation). There can be no doubt, however, that in its free production of itself it takes on the inert characteristics which define, in untranscendability, the class-being of workers. I have tried to demonstrate this, in particular, for anarcho-syndicalism. The readoption of a constitution - generally in ignorance - helps to define inert limits to common action: this too we have seen. Thus, the entire class is clearly present in the organised group which constitutes itself within it; and its seriality as a collective, as a limitation, is the inorganic being of its practical community. It is genuinely a case of the class having two forms; the community is not to be regarded as a Spinozan mode of the proletariat-substance, because, on the contrary, it constitutes itself as + +its practical apparatus. + +But the relation between such apparatuses and the series from which they spring is more complex than is often supposed. Clearly it depends on the means of production; and for capitalists there is a necessity to transform these means constantly. Thus the bond changes with the type of machine. In fact, before 1914, with the universal machine, we can observe that trade-union practice was defined by the workers themselves as they practised their trades. Thus the dissolution of series appeared to be an accomplished fact. But really their unity was created at the top: it was that of the working-class elite (skilled workers produced by the universal machine); and each of them, as a member of the sovereign group, gathered around him the unskilled labourers who helped him in his work. But he did not form a true practical community with them (in union struggle), because they did not constitute a group in themselves and because they did not produce it inside the group, as instituted sovereign. In fact, trade unions as a union of the elite constituted their sovereignty in the very act which produced them; and this sovereignty, for unskilled workers, was neither legitimate nor illegitimate; it belonged to another world (that of the group), and in this other world it produced its own legitimation, and could only be accepted in impotence in the serial world. Grouped from outside by their foreman (l' ouvrier su{erain), the labourers remained serial - first among themselves, then in relation to other foremen (who, as the leading group, refused to allow them into the union), and then in relation to other labourers (in other workshops and other factories) linked to them only through the mediation of a group of which none of them were members. Thus they were doubly serial: serial because exploitation was always based on their competitive antagonism and + +impotence, and serial because obedience and trust for other foremen by other labourers conditioned their trust here (participation in the strike, etc.). It would therefore be a mistake to claim that, in the first years of this century, the French working class itself had produced its apparatuses of protection and that a union militant (as a common individual of practical class-uniry) was indistinguishable from the worker (as a member of a passive, exploited seriality). In fact, a particular category of workers - the foremen - had constituted themselves into a sovereign group, the practical embodiment94 of the working class. Through the mediation of its local agents this group imposed a common will on an unintegrated 'sub-proletariat' whose class-being was seriality. And the difference between these two modes was so great that dIe unions never noticed the new workers emerging from and amongst the unskilled labour force - the products of the second industrial revolution, the specialised workers who emerged as a result of the deskilling produced + +by specialised machines. + +In this sense, the development of the working class in the twentieth century, the new characteristics of labour (harassment, etc.), and the disappearance of a sector of skilled workers (in France) gave rise to a new formula for unity which has wrongly been supposed to be radically different from the preceding one. The work of the union militant and that of the specialised worker are practically incompatible. A specialisation is required: the working class produces its own permanent paid officials. The trade union therefore became, for the conservatives, a group which was foreign to the working class. It is true that the permanent official is no longer a worker: this is a truism, since he no longer works as a worker. Besides, he passes into the ranks of the institutionalised third parties (being an integrating part of the sovereign group). But we have just seen that the only way an anarcho-syndicalist skilled worker could turn the class into a group was by deciding that he alone was a worker and by practically excluding 80 per cent of workers from the proletariat. This difference is entirely in the interest of the permanent officials who made the proposals and addressed everyone; whereas the anarcho-syndicalist imposed the decision of the + +94. I say 'embodiment' rather than 'representation', because these workers considered that they were eminently the working class in so far as they still based their condemnation of exploitation on the skill of their work. For them, the skilled worker was a complete worker (and, one might say, a complete man); labourers were unfortunate and their condition was unworthy: but then they were + +not really workers. + +few on the majority. Thus permanent officials avoided the statute of workers precisely to the extent that skill in work was no longer the basis of their demands, to the extent that individuals who are interchangeable in function recognise that they have the same needs. The sovereign's attempts to manifest a kind of authoritarianism reflect the very interchangeability which makes it necessary to tighten discipline and to carry out truly massive actions to prevent the immediate replacement of strikers. And this authoritarianism is simply Fraternity-Terror as it exists in the masses themselves when they dissolve their seriality (by means of a strike or demonstration). The permanent official is therefore precisely the product of the working class in so far as that class is characterised as a mass. Inside the sovereign group he realises a real exigency of the situation which mass movements constitute out of fused groups by liquidating seriality. In himself, apart from a few special characteristics due to the trade-union and professional ensembles which he represents, he is simply the sovereign, abstract invitation to unification. His very universality - he, too, is interchangeable, as a local permanent official - is the transposition of serialising interchangeability into the necessity for practical totalisation + +of the masses. + +Thus one can distinguish two stages, depending whether, in a working-class city at work - when the class is a collective - he represents possible unity in the abstraction of his institutional being (and is characterised by his relations with Paris rather than by his relations with the locality) or whether he becomes, in a tense situation, the practical schema and signification of the unity which is to be realised. However, when this unity is achieved, it excludes him. He will be listened to, provided his views accord with those of the constituted group; but he will be transcended and left behind if he tries to divert the group from its chosen course. It is therefore useful to consider the working class as defined by variable statutes (in space or time). The trade union is the working class objectified, exteriorised, institutionalised, and possibly hureaucratised, but unrecognisable to its own eyes and realising itself as a pure practical schema of unity. 95 It is the sovereignty + +95. And the multiplicity of trade-union apparatuses - in France, for example transposes the real divisions of the working class (divergences of interest, characterising certain partial ensembles 'within' the proletariat) into praxis. This means that these divisions, lived in the seriality of impotence by workers themselves, + +become practical antagonisms when embodied in organised groups. + +of the class, but it is cut off from it, and produces itself elsewhere, in the pure milieu of common praxis. This group - defined by a s tatute of separation (local permanent officials who 'go to Paris' from time to time, controlled on the spot by missi dominici, etc.) - usually has no control over masses in serial flight. In favourable circumstances, every agent attempts to determine local disturbances (improvised meetings, posters, etc.): this is what is called agitation; but in fact, such disturbances are simply circuits of recurrence. In this moment, the working class exists under a double statute since, in its dispersive seriality, the union officials (detegues) are external guarantors of its possible interiorisation. When, in a period of social conflict, the workers of a given city unite in a common decision (taken in an atmosphere of violencefreedom: public voting, and the obligation on the minority to dissolve in unanimity), the working class exists infoct as a practical totalisation. It might be disastrous if the 'movement' were not taken up in other cities: but, from a formal point of view, local unification through the praxis of a strike or insurrection is enough on its own to posit the group as a possible permanent statute for the proletariat, even though, for the actual proletariat and in present circumstances, this group may manifest itself as a fused group (or at most as a pledged group), and maintain its systems of organised, institutional relations outside itself. In fact it will never re-absorb the union or follow the instructions of the unionists; apart from the fact of being institutional, permanent officials seem rather similar to the agitators whom the people required to reflect their practical thought, between 1789 and + +1794· + +This will lead us, as a synchronic determination, to treat the working class - at any given moment of the historical process - not only as an institutionalised organisational group (the 'cadres'), but also as either a fused or a pledged group (the constitution of the soviets, in 190), appears as an intermediary between a pledged group and an organised group), and as a seriality which is still inert (in certain sectors), but which is profoundly affected by the negative unity of the pledged groupings. The institutional group, as an abstract skeleton of the united class, is a permanent invitation to unity; indeed it is the sovereignty of the class if it is entirely serial; and, secondly, it may reflect their absolute sovereignty to the fused groups (and to their concrete developments) and display their decisions to them in the framework of a more distant future, in relation to indirect objectives. But this reflection is not done by a regulatory third party to a group to which he belongs, + +but by a member of a group - in so far as he is the signifier/signified of the group - to another group which produces its own sovereignty. In other words, the appearance of the group as a developing totalisation of the working class - even though it may be the result of the work of the unions, and even though the group may set itself objectives which are laid down by 'central organs' - immediately makes union sovereignty redundant, but without re-absorbing the institutional group (and it will play a part in the material organisation of strikes and in establishing contacts with the employers). It is this concrete group, in fact, which becomes the concrete sovereignty of the working class, and which exercises it; the material conditions of conflict, and power relations with the other class and the apparatuses of constraint which it produces are all strictly determined through it, and they define the situation itself (as a relation of sovereign groups embodying hostile classes and as a relation between these groups and the serialities from + +which they arose). + +In effect, the real efficacity of the common praxis here will depend on the abstract, totalising action of the fused group on the series which surrounds it. In fact, each member of the group is, through innumerable complex relations, also a member of the series at the same time as belonging to the group. One can easily see this when one remembers that the member will belong to a family, to a residential area, to various associations and, through all these more or less inert communities, to series of alterity which extend everywhere. Thus if he is a member of the combat group this will determine these series, practically, though abstractly. Similarly, the mere production of the group, in so far as the organs of diffusion (possibly of the institutional group) spread the news of it, becomes the practical sovereign reunification of the working class in a here for any elsewhere of the series. The process as a whole will then be manifested either through the serial passivity of large working-class concentrations or through a shifting agitation which begins to dissolve collective impotence into a truly revolutionary unification. But the important point here is that the practical constitution of the group (that is to say, the Apocalypse) is - in itself and in its being-outside-itself - the production at a distance, through the series and throughout it, of a schema of totalisation as an abstract ubiquity (and a rigid obligation for everyone to adopt either seriality or unity, even if, in the place and function he occupies, his impotence is insurmountable). And the new groupings which are to be constituted in opposition to seriality (and within it) differ from the first + +at least in that they are induced, and in that the totalising schema was already present in every Other as the possibility of rejecting all alterity. Of course, this does not prevent the groups from producing a new seriality (in separation, and in the variety of situations, of local interests, of circumstances of struggle, and of power relations each group determining the other groups as others by its limited + +praxis), + +As we saw in The Problem of Method, it was this seriality which aborted the peasant movement in Luther's Germany. In the case of the seriality of groups, the trade-union apparatus regained its importance, and its co-ordinating, organisational activities transformed isolated groups into organised sub-groups. But in itself it remained an other-group (groupe-autre) rather than an interior sovereignty. Similarly, the dissolution of series may often be the result of a serially propagated contagion (as with the strikes of I936, when the working class came closest to a total synthetic unification). In this situation reflexivity does not occur till later, in the milieu of the resulting immense group; and the structure of a massive group (that is to say, a group which arises from the masses and is composed of them) has to be studied separately because it is characterised not only by a deep integration, but also, on occasion, by real separation. (Factory occupations in I936 showed this double character: the occupation of a particular factory occurred within the practical awareness of totalisation and ubiquity; it was the same; everywhere the same, here. But they also made communications between sub-groups difficult; many intermediaries were necessary.) But the rebirth of seriality in its very dissolution may in turn occasion liquidating actions. I mention these abstract possibilities only in order to raise the question of the intelligibility of the concrete - in this case, of class. Of course, the terms of the problem are clear : class manifests itself not only96 as an institutionalised apparatus, but also as an ensemble (serial or organised) of direct-action groups, and as a collective which receives its statute from the practico-inert field (through and by productive relations with other classes) and which receives its universal schema of practical unification from the groups which constantly form on its surface.97 And these three simultaneous + +96. On the terrain of the struggle for reforms, of course. + +97. For greater simplicity, I am not taking account of workers' parties or of splits within the working class: these essential characteristics of historical proletariats are themselves material determinations. It does not make any difference + +statutes arise in practical and dialectical connection with one another , through a process which is itself conditioned by the historical conjuncture as a whole. In fact, language always presents class too simply, either as always united and ranged against the exploiters, or as temporarily demobilised (having completely relapsed into seriality). May it not be that these imperfect and incomplete concepts are an accurate reflection of our inability to understand this unique triple reality of a developing historical class? May it not be that in this confrontation between groups as constituted dialectic and as series (as anti-dialectical), + +we run up against the very limits of intelligibility? + +I do not think so; and the incompleteness of these concepts or determinations of language simply expresses political attitudes (that of the militant, that of the oppositionists, etc.) which as such do not concern us here. But this presents no difficulties on either the onto- + +logical or the practical plane. + +On the ontological plane, there are not three beings, or three statutes of being: class-being is practico-inert, and defines itself as a determination of seriality, as we have seen. The two kinds of group (fused and pledged, organisational and institutional) have no innergroup-being; their statute is that their being-outside-themselves (the only group-being) lies in the series from which they have emerged and which sustains them (and which affects them even in their freedom). Of course, the fused group negates the series within itself since it dissolves it; but it also relates to it ontologically because it is its actions as a series, the activity for the whole series in a particular situation of this moving, changing, violent formation, whose future is still indeterminate, but which is the audacity of the series here, the success or failure of all who reject impotence, massification, and alterity here. In other words, the group's class-being lies outside it in the series, and inside the group the series is both the negation and the affirmation of its being through practical transcendence. We have seen how the practical individual always realises class-being in everyone; a workingclass woman who has an abortion carries out the sentence which the exploiting classes have passed on her. But in a common action (whether reformist or revolutionary), there is both a realisation of class-being and freedom: the working-class woman now recognises her being as a + +whether we are dealing with a trade union or a party; what is important is the relation of the ohjectified class (the trade union or any other institutionality) to + +the fused class. + +worker - defined by her wages and her work - and she recognises it in the demands themselves; but she transcends it through the demand however minimal - which is the common practice for bringing about a general change, and above all by grouping with a view to getting satisfac- + +tion. + +The dissolution of the serial may in certain cases be the act of uniting with others, or a total liquidation (at least a temporary one) of the previous seriality (especially in the case of what contemporary sociologists call 'micro-organisms'), but then it is just a matter of transcending seriality. However, this transcendence may be intended to last longer than a demonstration or even than a strike. It may manifest itself in a rebellious practice, and become a revolutionary action: and on this basis, especially if the Revolution is not a failure, and develops according to its own laws, there will be a radical metamorphosis, and everything will shift into a different social world. But with the struggle of a dominated against a dominant class, seriality will always be the product of exploitation and the statute which maintains it, even more than internal dissension. It is seriality which must be overcome in order to achieve even the smallest common result (such as averting too rapid a fall of purchasing power). But it is seriality too which sustains the group making demands, in its very passivity, as a source of possible energy - the group, in fact, from the practical point of view of its action, can no longer conceive it except in the synthetic form of potentiality. It is seriality which appears to it as producing it - to the extent, as I have shown, that it is still engulfed in it by the other serial relations of its members. It is seriality which the group totalises in exteriority, that is to say, for the group and in its connection with seriality, in so far as it conceives the serial unity (of dispersal) in terms of the dialectical reasons which engender it materially and dialectically (historical conditions of the capitalist process). Lastly, it is seriality which, in the dialectical perspective of union struggles and of everyday labour, defines its future as its death and permanent resurrection (the group will dissolve into seriality when the workers - victorious or defeated - resume work; and it will be reborn from seriality when, having learnt from this experience, the workers become active again).98 + +98. Although the lie is spread for purely propaganda purposes, it is not true today that, in a factory constituted by a majority of skilled workers, it is possible hath to do the work which, in the context of capitalist exploitation, enables the worker to live, and to exert constant common pressure on employers. It is true that social bonds remain (and a past too, as we shall see) and so does a etas. attitude + +This means that class-being, as past, present, and future seriality, is always the ontological statute of the worker and that group praxis, as a surface dissolution of the relation of alterity inside the class (and therefore on the surface in the worker) and as a conservative transcendence t